Math 1st & 2nd

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ম্যাট্রিক্স ও ট্রির্াণ য়ক 7.  m  2 6 3 g¨vwUª·wU e¨wZµgx n‡e hw` m Gi gvb:
2 m

A. 6, –1 B. –4, 6 C. –6, 4 D. 1, –6

hw` A = 10 0 ,  5 0  Soln: [A] Xvwe [05- 06] Gi 4 bs Gi Abiy ƒc |
5 2 1
1. B  nq, ZLb AB nq- 8. hw` A  13 24 nq Z‡e, A–1-

A.  5 05  B. 150 05 C.  6 06  D. 182 15
2 2
1  4 13 1  4 12
 1 05   5 10 = 05100 0  05 A. 2 2 B. 2 3
0 2 0 
Soln: [B] A.B =

= 150 0  C.  1  4 13 D.  1  4 12 
5 2 2 2 3

hw`  2 -3  nq, Z‡e A2 mgvb- Soln: [D] A–1 = 4 1 6  4 12 = 1  4 2 
3 2  3 2 3 1
2. A =

A.  5 152 B.  5 12  9. A = 78 6  n‡j A–1 Gi gvb KZ?
12 12 5 7

C.  5 125 D.  5  12  A.  7 67  B.  7 78
12 12 5 8 6

Soln: [D] A2 = A.A =  2 23  2 23 C.  7 76 D.  7 8 
3 3 8 6 7

 4 9  6  64  5  12  Soln: [C] Xvwe [06- 07] Gi 8 bs Gi Abyiƒc |
6 6  9  12 5
= = 10. A = 1 i , B = i  1 Ges i = –1 n‡j AB Gi gvb n‡e-
 i 1  1  i
 2 -03   3 0 
3. hw` A = 0 , B = 5 1 nq, Z‡e AB mgvb- A. 1 0 B. 0 0 C. i 0 D. i 1
0 1 0 0 0 1
 6 03  3  15 i  i 
 15 2   

A. B. Soln: [B] A I B matrix Gi 1g mvwi I Kjvg ¸Y Ki‡j cvB, 1.i – i.1

= 0, hv AB matrix Gi 1g Dcv`vb, hv †Kej B bs option G-B Av‡Q|

C.  1 105 D.  1 52  mZy ivs mwVK DËi Option B|
2 0
11. A = (− − ) Ges (and) B = ( ), AB = ?
Soln: [A] A.B =  2 03  3 0  =  60 0  0  A. (−−22 22) B. (00 00) C. (30 00) D. (−22 −22)
0 5 1 0 15 0  3 [Ans: D] Soln: Option n‡Z cvB cÖwZwUi AB Matrix Gi Dcv`vb wfbœ|
ZvB †KejgvÎ a12 Gi gvb †ei Ki‡jB Ans. cvIqv hv‡e|
=  6 03 22 – 23 = –2, hv †KejgvÎ D bs option G Av‡Q|
 15

4.  α  2 α 2 4  g¨vwU·ª wU e¨vwZµgx n‡e hw` = ?
8 
12. A, B Ges C g¨vwU·ª ¸‡jvi gvÎv h_vµ‡g 4  5, 5  4 Ges 4  2 n‡j
A. 4, 6 B. 6, 4 C. 4, 6 D. 6, 4
(AT + B) C g¨vwUª‡·i gvÎv n‡eÑ
Soln: [A] ‡Kvb Matrix e¨vwZµgx ev Singular n‡e hw` Zvi det zero
A. 5  4 B. 4  2 C. 5 2 D. 2  5
nq |
Soln: [C],We know that,if the dimension of matrix A is
  2 2 4
8  m×n and the dimension of matrix B is np,then the

 Dimension Of Matrix A B is mp.

 ( + 2) ( – 4) – 16 = 0 AT Gi gvÎv 5  4; (AT + B) Gi gvÎv 5  4

GLb option Øviv wm× Ki‡jB Ans. cvIqv hv‡e|  (AT + B) C Gi gvÎv 5  2

5.  P  4 8 2  g¨vwUª·wU e¨wZµgx n‡e hw` p Gi gvb
2 P
 1 0 2 1  x 1
A. 4, 6 B. 6, 4 13.  1 2 + 0 1 = 1 z x, y Ges z Gi gvb n‡e?
 3  y  3
C. 4, 6 D. 6, 4  2 0 2
B. 3, 4, 3
Soln: [A] Xvwe [05- 06] Gi 4 bs Gi Abiy ƒc | A. 1, 2, 3 D. –1, 2, 3 E. None
C. 3, –3, 4
6.  P  4 8 2  g¨vwUª·wU e¨wZµgx nq hw` p Gi gvbÑ Soln:[B]
2 
P

A. –6, 4 B. –4, 6 C. –4, 2 D. –2, 4

Soln: [A] Xvwe [05- 06] Gi 4 bs Gi Abiy ƒc | 14. hw` A   2 0 , B   3 10 nq Z‡e AB mgvb-
0 3 5

|

A.  6 03 B.  2 83  Mx = ax bx
15 5  cx
 0

C.  6 13 D.  5  62  Note: here, x is a scalar .So we will do just matrix scalar
5 1 
multiplication. If x is a matrix, than it is necessary to define
Soln: [A] Xvwe [05- 06] Gi 3 bs Gi Abiy ƒc |
the order of matrix x]
15. A   5 12 n‡j A–1 Gi gvb-
3 21. hw` a b  1 c  1 2 3 Zv n‡j-

A. 1 13 21 B. 1 13 2  A. a = -1, b=-3, c=3 B. d = -1, b =3, c = 3
5 11 5
C. a = -1, b = -3, c = -3 D. a = 1, b = 3, c = 3
 1  1 23 1 13 2  Soln: [D] [a b–1 c] = [1 2 3]
11 5 3 1
C. D. This is a column matrix. So the corresponding elements are
equal that’s why
 5 12
Soln: [B] A = 3 a = 1, b – 1 = 2  b = 3, c = 3

 A–1 = 1 13 52 = 11113 52 22. hw` x  a b Ges y  b Zv n‡j xy n‡e-
 a,
5 6

16. α  3 6 g¨vwUª·wU e¨wZµgx n‡e hw`  Gi gvb- A. 2ab ab
 5 α  4 C. ab ab B. ab
D. m¤¢e bq
A. 6, 7 B. 1, –3 C. 3, –1 D. 7,–6

Soln: [D] Xvwe [05- 06] Gi 4 bs Gi Abyiƒc |

 3 0 ,  2 03 nq, Z‡e AB mgvb- Soln: [A] xy = [a b] b
5 1 0 a = [ab + ab] = [2ab]
17. hw` A  B 

A. 165 013 B.  3 1  23. g¨vwU·ª X GKwU singular g¨vwU·ª n‡e hw` X GKwU-
2 5 A. eM©vKvi g¨vwUª·
B. AvqZvKvi g¨vwUª·
C. 160 03 D. 160 03 C. eM©vKvi g¨vwU·ª hvi wbY©vq‡Ki gvb kb~ ¨
D. eM©vKvi g¨vwUª· hvi wbY©vq‡Ki gvb kb~ ¨ bq
Soln: [C] Soln: [C]

AB = 53 0   02 03 = 16000 0  03 24. hw` X  2 3 Ges Y  1 0 Zv n‡j XY=?
1 0   4  5 0 1

= 160 03 Ans. A. -X B. X C. Y D. -Y

Soln: [B] †h †Kvb g¨vwU· †K Identity matrix Øviv ¸Y Ki‡j GKB

 0 01  x  matrix _v‡K|
1 y
18. hw` A  Ges X  nq Zvn‡j AX mgvb- 25. M  10 11 n‡j M 2 n‡e-

A. X   x  B. X   y  A. 2 B. 4
y x

C. X   x  D. X   y  C.  1 2  D. 10 12
y x 0 1

Soln: [D]  0 01  x   0  y   xy  Soln: [C]
1 y x  0
AX = = =  M2 = M.M = 10 11 10 11 = 1000 1011  1 2 
0 1
=

19. †Kvb g¨vwU·ª wUi wecixZ g¨vwU·ª †bB?

A.  2 1  B.  2 1  C.  3 2  D.  2 2  26. g¨vwU·ª  2 2 4  n‡j A2 Gi gvb n‡e-
1 2 4 2 1 4 4 4 A  1 3 4 

Soln: [B] †h g¨vwU·ª Gi Determinate zero Zvi †Kvb wecixZ g¨vwUª·  1  2  3

_v‡K bv| A. –A B. 0

C. 2A D. A E. I

20. M  a b n‡j Mx = †KvbwU? Soln: [D] By using calculator Ans. D
0 c
27.  a b  GKwU wm½jy vi (Singular) g¨vwUª·. myZivs
c d
ax b  a bx ax b ax bx
A.  cx B. o  C.  c D. A. a = 0 B. b = 0
 o c   o  o cx
 C. c = 0 D. d= 0 E. ad-bc = 0

Soln: [D] M  a b Soln: [E] Avgiv Rvwb, Singular matrix Gi Determinate Zero,
0 c
ZvB, ad – bc = 0

|

28. hw` X = [a b] Ges Y = [b a], Zv n‡j XY n‡e 1 1 1  1
2
A. [2ab] B. [ab ab] A. 2 1 B.  
1 2   
C. ab D. [0] E. m¤¢e bq  2 1 1
ab
1 1 1 1
Soln: [E] X = [a, b], Y = [b, a] 1 1 2 2 2  2
C.  1 1 1  1
Avgiv Rvwb, 1g matrix Gi Kjvg I 2q matrix Gi mvwi mgvb n‡jB D.  1 2  E. 1 2 
2 2
†Kej matrix ¸Yb m¤¢e| GLv‡b X Gi Kjvg I Y Gi mvwi equal bv|

So ¸Y Kiv m¤¢e bq| Soln: [D] Det (A) = 1 + 1 = 2

29. M g¨vwUª· Gi transpose M' Øviv wb‡`©wkZ n‡j det (M') = KZ? 1 1

A. det (M) B. 1/2 det (M) 1 1 1  2 2 
2  1 1 =  1 1 
C. 2 det (M) D. det (M') E. †Kvb ï× DËi †bB  A–1 =  

Soln: [A] Let M =  a b  . Then M =  a c  2 2
c d b d

Now, Det (M) = ad – bc and Det (M) = ad – bc. So we can 34. A  2  1 , B  3 2 n‡j AB n‡e:
 3 5   1 5
conclude, Det (M) = Det (M)

Note: The det of any matrix and its transpose are equal. A. 5  3 B. 7  1
 4 31  4 31
30. 3 0 0 x 9 g¨vwUª·wU mgvavb Ki‡j = KZ?
0 2 0  y  4
 

0 0 5 z   15  C. 4  3 D. 5 9 E. 7  1
 31 5  4 31  5 31
A. (0, 0, 0) B. (3, -2, 3)

C. (3, -2, -3) D. (0, -2, 0) E. (0, 0, 3) Soln: [B]

3 0 0 x  9  2 1  3 2 6 1 45 = 7  1
AB = 3  1 5 = 9  5 6  25  4 31
Soln: [B] 0 2 0  y =  4 5 

0 0 5  z  15 
3 2 x 5
3x = 9 x=3 35. 1  2 y  7 n‡j x Ges y Gi gvb KZ?

2y = –4  y = –2

5z = 15 z=3 A. –3, 2 B. 3, –2

31. hw` `ywU g¨vwUª· A I B h_vµ‡g mn Ges np µgh³y nq Ges A I C. 3, 2 D. 2, 3 E. ï× DËi †bB

B Gi ¸Ydj‡K AB g¨vwUª· Øviv mw~ PZ Kiv nq Z‡e AB g¨vwUª‡·i µghy³ Soln: [B]

n‡e- 3 2 x 5
1  2 y 7
A. nm B. mn =

C. np D. pn E. mp

Soln: [E] A matrix Gi order mn I B matrix Gi order np n‡j  3xx22yy75
Solving x = 3, y = –2
AB Gi order mp.

32. g‡b Ki A  1 0 3 Ges B  2 1 1 36.  1 2 , B  3 4 n‡j A –B = KZ?
3 1 1 0 1 3 AB = KZ? 4  3 6 7
1 0 4 A

5 1 13 5 3 A. 2 2 B.  2 2
A.  3 1 1    2 10  2 10
B.  1 1 

13 1 C.  2 2 D. 2  2 E. 2 2
 2 10  2 10   2 10
5 13 5 1 3 3 1 2
D. 3 2 1  
C.  3 1  E.  2 3 1  Soln: [C] A = 1 2  3 4
  2 1 5 4  3 , B = 6 7
5 5 12

Soln: [A] GLv‡b, A matrix Gi order 23 Ges B matrix Gi order A–B = 13 2  4   2  2 
4  6  3  7 =  2 
33 | Avgiv Rvwb, A matrix Gi order mn I B matrix Gi order np  10 

n‡j AB Gi order mp. So GLv‡b AB Gi order n‡e 23 hv †Kej 0 1 1
1 2 2
Ackb A †ZB Av‡Q| So Ans. A. 37. hw` A  Ges B  Z‡e AB Gi gvb KZ?

33. A= 1  1 n‡j A–1 = KZ? 1
  B. 2
 1 1  A. 2
5

|

C. 0 D. 1 E. 5  2 6 8
1 3 2  
C.  2 4 0  D. †KvbwUB bq

0  2 2  8 78 16
5
Soln: [A] AB = 1 4  = Soln: [A] Use calculator

1  2 3 2 3 5
38. 3 2  x  5 n‡j x Ges y Gi gvb KZ? 44. A  5 1  4 Ges B  1 4  6 n‡j A + B =
1  2 y 7
2 2 5
A. x = –2, y = 3 B. x = 2, y = –3 A. 1 2 4 B. 3 1 8
6 5  10
C. x = 2, y = 3 D. ï× DËi †bB E. mgvavb m¤¢e bq

Soln: [D] 3 2  x 5 C. 1 3 4 D. †KvbwUB bq
1  2  y = 7 5 6 7


 3x + 2y = 5 ---- (i) Soln: [B] A+B = 1 2 23 35 
x – 2y = 7 ---- (ii) 5 1 1 4  4  6

(i) + (ii)  4x = 12

x=3 3 1 8 
= 6 5 10
(ii)  3 – 2y = 7

 2y = – 4 y = –2

39. X  1 2 , Y  3 4 n‡j XY = KZ? 45. A  0 1 Ges B 1 n‡j AB = KZ?
4  3 6 7 1 2 2

2 2  B.  2 2 1 B. 2 C. 2 D. 0
A. 2 10  10 A. 5 5 3 5
 2

C.  2 2 D. 2  2 2 2  Soln: [B] AB = 0  2 2
 2 10  2  E. 2 10 1 4 = 5 Ans.
10 

Soln: [C] use calculator. 46. A  1 Ges B  2 3 n‡j †hvMdj KZ?
6
40. hw` A  1 0 nq Z‡e A2 g¨vwU·ª wU †ei Ki|
3 4
A. 3 B. [3 9]
1 0 1 15 9 D. †hvM Kiv hv‡e bv
A. 15 16 B. 0 16
C. [8 4]

15 16 0 1 1 0 Soln: [D]
16 12 E. 13 12
C.  1 0  D. 47. hw` A  1 2 I  1 0 nq Z‡e A2+2A11l n‡e-
  4  3, 0 1

Soln: [A] use calculator. 0 0
0 0
1 0 2  1  2 A. 1 0 B. 0 0 C. 1 1 D.
0 1 3   0 1 0 1 0 1
41. hw` A  Ges  2 3  Z‡e AB-Gi gvb KZ?

 3 1  Soln: [D] Use calculator

A. 48 B. 36 48. A  0 1 Ges B 1 n‡j AB Gi gvb KZ?
1 2 2
C. 30 D.12 E. 24

Soln: [C] use calculator. A. 0 B. 2 C. 5 D. 3
5 5 2 5
42. A Ges B g¨vwU·ª `ywUi gvÎv (order) h_vµ‡g 23 Ges 35 n‡j

wb‡Pi †KvbwU mZ¨? Soln: [B] Use calculator

A. BA msÁvwqZ n‡e B. AB msÁvwqZ n‡e 49. A  2 1 3 Ges B  6 0  3 n‡j (A+B) Gi gvb-
3 6  4 3 3  1
C. AB Gi gvÎv n‡e 52 D. AB Gi gvÎv n‡e 33

Soln: [B] 3 4 1 4 5 6
2 3 6 7 9 10
 5 7 1  3 2 1 A. B. 1 0 
9  5
43. hw` A   1 2  3  , B  2 3 2 nq, Z‡e AB =

 4  2  16 1 5 1 8 1 0 8
C. 6 9  5 D. 6

 2 6 8 2 6 8  Soln: [C] Use calculator
B. 2 11 
A.  2 11 0  0 

 8  78 16 8 78 16 0 1 n‡j Gi gvb KZ?
50. A  1 0 A2

|

A. 1 B. +1 C. 0 1 10  (P – 4) (P – 5) – 56 = 0
1 0 By using calculator P = –3, 12
D.
11 1
01 60. 1 2 3 wbYv©qKwUi gvb 2 ; k Gi gvb KZ? (00-01)

Soln: [D] †Kvb Identity matrix †K square Ki‡j Zvi gvb GKB _v‡K|

51. A  1 B  3 2 g¨vwU·ª `ywUi ¸Ydj n‡e- 14 k
6,

A. 18 12 B. 3 2 A. 9 B. 8 C. 7 D. 6
18 12
 3 2  11 1
  Soln: [A] given, 1 2 3 = 2

C. 3 6 D. 9 6 14 k
9 12 3 6

Soln: [B] Use calculator c11  c2  c1 0 0 1
c12  c3  c2 1 1 3 =2
52. A = [2 1] Ges B  1 2 0 3 k 4 k
4 5  3 n‡j AB= ?

A. [6 1 3] B. [2 1 3]  1 1 = 2  K – 4 – 3 = 2;  K = 9
3 k4
C. [6 4 3] D. [1 1 2]

Soln: [A] AB = [2 + 4 – 4 + 5 0 – 3] = [6 1 –3] β2 1

53. hw` A GKwU mn AvKv‡ii g¨vwU· Ges B GKwU n p AvKv‡ii g¨vwU·ª nq 61. 5 β4 wbY©vqKwUi gvb 0 n‡j  Gi gvb KZ? (01-02)
Zvn‡j Zv‡`i ¸Ydj AB Gi AvKvi n‡e
A. 5 or 0 B. 6 or 2 C. 5 or –3 D. 1 or –3

A. n  n B. n  p C. m  p D. m  m Soln: [D]   2 1
=0
Soln: [C] Matrix A Gi gvÎv m n I B Gi gvÎv n  p n‡j AB Gi 5  2

gvÎv n‡e m  p  ( – 2) ( + 4) + 5 = 0
GLb option Øviv cheek K‡i †`L‡Z n‡e †Kvb gv‡bi Rb¨ mgxKiYwU
a11 a12 ..... ..... a1n 
54. a21  wm× nq|
a22 ..... ..... a 2n  GB g¨vwUª·wU †Kvb cÖKw… Zi?

..... ..... ..... ..... .....  8 3 3
an1 an2 ..... ..... ann  62. 3  8 5 wbY©vqKwUi gvb- (02-03)

A. KY© g¨vwU·ª B. eM© g¨vwUª· 5 5 8

C. †¯‹jvi g¨vwU·ª D. A‡f`K g¨vwUª· A. 1 B. 1 C. 0 D. 2

Soln: [B] ‡h g¨vwU‡ª ·i mvwi, Kjvg mgvb Zv‡K eM© g¨vwU·ª e‡j| Soln: [C] wbY©vqKwUi gvb = – 8 (64 – 25) + 3 (25+ 24) + 3 (15+

55. 3 1 = ? 40) = 312 – 312 = 0
[1 2]1 2
we:`ª: Calculator e¨envi K‡iI D³ mgm¨vwU mgvavb Kiv hvq|

3 2 B. [5 4] C. [5 5] D. [3 2] 111
A. 1 4
63. hw` x a b = 0 n‡j x Gi gvb KZ ?

Soln: [C] 1 2 3 1  3  2 1 4  5,5 x2 a2 b2
1 2
A. a ev b B. a ev b C. a ev b D. a ev b
56. hw` g¨vwU·ª A = [2 1 3] nq Ges I GKwU 3  3 BDwbU g¨vwU· nq Soln: [D] wbY©vq‡Ki `ywU Kjvg ev mvwii Dcv`vb¸‡jv Awfbœ n‡j Zvi gvb zero
nq | ZvB x Gi gvb a ev b n‡j wbY©vq‡Ki `wy U Kjvg GK nq | So x = a ev b
Zvn‡j AI=
.
A. 0 B. [0 0 0] C. [2 1 3] D. AmsÁvwqZ
Soln: [C] †h †Kvb g¨vwÆ· †K BDwbU g¨vwÆ· Øviv ¸Y Ki‡j GKB _v‡K| xy x y

57. g¨vwU·ª A Gi gvÎv 24 Ges g¨vwU· B Gi gvÎv 43 n‡j, AB-Gi gvÎv 64. x x  z z wbYv©qKwUi gvb-

A. 2  3 B. 4  2 C. 3  2 D. 3  4 y z yz

Soln: [A] Matrix A Gi gvÎv m n I B Gi gvÎv n  p n‡j AB Gi A. 4xyz B. x2yz C. xy2z D. xyz2

gvÎv n‡e m  p Soln: [A] GB ai‡bi mgm¨v mgvavb Kivi Rb¨ Avgiv 1†g x, y, z Gi

58. hw` A, B I C wZbwU g¨vwUª· Ges AB = AC nq Z‡e gvb a‡i wbY©vqK Kie| c‡i option G x, y, z Gi gvb ewm‡q Ans.

A. B = C n‡eB B. B = C bvI n‡Z cv‡i wgjv‡Z n‡e|

C. C, B Gi we¤^ (Transpose) g¨vwU·ª n‡e 312

D. †KvbwU bq  let, x =1, y = 2, z = 3 1 4 3

Soln: [B] 235

59. p  4 7  g¨vwU·wU singular n‡e hw` P Gi gvb nq-  wbY©vqK D = 3(20 – 9) + 1(6 –5) + 2(3 – 8)
8  = 33 + 1 – 10 = 24
p 5 option n‡Z cvB, 4xyz = 4  1  2 3 = 24

A. 3, 12 B. 3, 12 C. 4, 5 D. 4, 5

Soln: [A] Matrix wU singular n‡e hw` Gi Determinate zero nq|

|

65. a  3 1 wbY©vqKwUi gvb kY~ ¨ n‡j a Gi gvb- log  x  log y  log z
8 a4 y z log 2z
log 3z
A. 4 or 5 B. 5 or 4 C. 3 D. 10 log  x  log y 
y z
Soln: [A] Xvwe [01- 02] Gi 2 bs Gi Abiy ƒc | =
log y 
x y x y log  x  z
66. wbY©vqK x xz z Gi gvb- y

y z yz

A. 4 xyz B. 3 xyz C. 2 xyz D. xyz [C1' = C1 – C2, C2' = C2 – C3]
Soln: [A] Xvwe [05- 06] Gi 5 bs Gi Abiy ƒc |
1 1 log z
a 1 bc
= log yx log yz 1 1 log 2z = 0
67. b 1 c  a Gi gvb n‡e-
1 1 log 3z

c 1 ab 71.  hw` 1 Gi GKwU RwUj Nbgj~ nq, Z‡e wb‡giœ wbY©vqKwUi gvb KZ?

A. 0 B. abc(a + b) (b + c) (c + a) 1  ω ω2
C. abc D. (a + b) (b + c) (c + a)  ω ω2 1
ω2 1  ω
a 1 bc abc 1 abc
Soln: [A] b 1 c  a = a  b  c 1 a  b  c

c 1 ab abc 1 abc

cc13  c1  c3  A. 4 B. 2 C. 3 D. †KvbwUB bq

 c1  c3  = 0 [c1 I c3 Awfbœ] 1   2
Soln:[D],   2 1
ααx
68. |β β β| =0, x=? 2 1  
θxθ
= 1(–3 – 1) +  (2 – 2) + 2(– – 4)
A. , ,  B. ,  C. ,  D. ,  = –1 –1 + 0 – 3 – 6
= –1 – 1 –1 –1 = – 4
[Ans: B] Soln: Avgiv Rvwb, wbY©vq‡Ki `wy U Kjvg ev mvwii Abyiƒc

Dcv`vbm¸‡jv GK n‡j Zvi gvb k~b¨|

option n‡Z cvB x =  ev  n‡j, h_vµ‡g 1g I 2q ev 2q I 3q mvwii 20 0

Abiy ƒc Dcv`vb GK nq| ZvB Ans. B| 72. 4 6 12 = 0 n‡j x-Gi gvb KZ n‡e-

69. x-Gi †Kvb †Kvb gv‡bi Rb¨ wbgœwjwLZ wbY©vq‡Ki gvb kb~ ¨ n‡e? x  8  x  3  x 10
x2 x 2
B. –16/3 C. 17
21 1 A. 4 D. None of these
0 0 5
20 0

A. x = 0, –2 B. x = 1, 2 C. x = 0, 1 D. x = 0, 2 Soln:[A], 4 6 12 = 0

x2 x 2 x2 x x  8  x  3  x 10
Soln:[D], 2 1 1=
0 0 5 2 1  2(–6x – 60 + 12x + 36) = 0
 2(6x – 24) = 0
 x2 – 2x = 0; x = 0, 2
x=4
logx logy logz
73. 2 α2 Gi gvb k~b¨ n‡j  Gi gvb-
α4 8
70. The value of log2x log2y log2z is:
log3x log3y log3z A. 6, –4 B. –6, 4 C. 6, 4 D. –6, –4

Soln: [A] Xvwe [01- 02] Gi 2 bs Gi Abyiƒc |

2 B. 0 3 D. 1 xy x y
A. log 3 C. log 2
74. wbY©vqK x x  z z Gi gvb-
log x log y log z y z yz

Soln:[B], log 2x log 2y log 2z A. 4xyz B. 1+x+y+z C. 0 D. 2xyz
log 3x log 3y log 3z D. 0
Soln: [A] Xvwe [05- 06] Gi 5 bs Gi Abiy ƒc |

10 20 30

75. 40 50 60 wbY©vqKwUi gvb-
20 40 60

A. 5 B. –5 C. 20

|

10 20 30 10 10 30 c'1 =c2 – c1 103 1 1
Soln: [D] 40 50 60 = 10 10 60 c'2=c3 – c2 83. 104 2 10 Gi gvb‡K  ai‡j,

20 40 60 10 10 60 105 3 102

wbY©vq‡Ki `ywU Kjvg ev mvwii Abyiƒc Dcv`vb¸‡jv Awfbœ n‡j Zvi gvb zero A.  > 0 B.  < 0
nq | GLv‡b cÖ_g I Z…Zxq Kjvg Awfbœ | ZvB gvb zero. C.  Gi gvb bvB D.  = 0

50 60 70 103 1 1 111
76. 10 20 30 wbY©vqKwUi gvb- Soln: [D] 104 2 10 = 103 10 2 10
3 102 102 3 102
30 60 90 105

A. 1 B. 2 C. 3 D. 0 wbY©vq‡Ki `ywU Kjvg ev mvwii Abyiƒc Dcv`vb¸‡jv Awfbœ n‡j Zvi gvb zero
Soln: [D] Rwe [07- 08] Gi 3 bs Gi Abiy ƒc | nq | GLv‡b cÖ_g I Z…Zxq Kjvg Awfbœ | ZvB gvb zero.

13 16 19 bc  a
77. 14 17 20 wbY©vq‡Ki gvb-

15 18 21

A. 1 B. 10r C. 20 D. 0 84. wbY©vqK D  c  a  b Gi gvb n‡e-

Soln: [D] Rwe [07- 08] Gi 3 bs Gi Abyiƒc | ab  c

10 13 16 A. abc+ B. 0

78. 11 14 17 wbY©vq‡Ki gvb- C.  (b-c)(c-a)(a-b) D.  E. abc
12 15 18 abc

A. 0 B. 1 C. 10 D. 5 bc  a abc  a
Soln: [A] Rwe [07- 08] Gi 3 bs Gi Abyiƒc | Soln: [B] D  c  a  b = a  b  c  b c'1=c1+c3

a 1 bc ab  c abc  c

79. b 1 c  a Gi gvb KZ?

c 1 ab wbY©vq‡Ki `wy U Kjvg ev mvwii Abiy ƒc Dcv`vb¸‡jv Awfbœ n‡j Zvi gvb
zero nq | GLv‡b cÖ_g I wØZxq Kjv‡gi Dcv`vb¸‡jv Awfbœ | ZvB gvb
A. abc B. 0
C. abc(a + b) (b + c) (c + a) D. (a + b) (b + c) (c + a) zero.

a 1 bc a 1 abc 1 x yz
Soln: [B] b 1 c  a = b 1 a  b  c c'3 = c1+c3
85. 1 y z  x  ?

c 1 ab c 1 abc 1 z xy

†Kvb GKwU wbYv©q‡K `ywU Kjvg ev mvwii Abyiƒc Dcv`vb¸‡jv GK n‡j Gi A. 1 B. 3 E. ï× DËi †bB
gvb k~Y¨| C. x+y+z D. 3(x+y+z)

111 1 x yz 1 x xyz
Soln: [E] 1 y z  x  1 y x  y  z c'3 = c2 + c3
80. wbY©vqK 2 1 2 Gi gvb KZ?
1 z xy 1 z xyz
313
wbY©vq‡Ki `ywU Kjvg ev mvwii Abyiƒc Dcv`vb¸‡jv Awfbœ n‡j Zvi gvb
A.10 B. 9 C. 0 D. -8 zero nq | GLv‡b cÖ_g I ZZ… xq Kjv‡gi Dcv`vb¸‡jv Awfbœ | ZvB gvb

Soln: [C] wbY©vq‡Ki `wy U Kjvg ev mvwii Abiy ƒc Dcv`vb¸‡jv Awfbœ n‡j zero.

Zvi gvb zero nq | GLv‡b cÖ_g I Z…Zxq Kjvg Awfbœ | ZvB gvb zero. 86. hw` wbY©vqK 3 4 Gi gvb kb~ ¨ nq, Zv n‡j a Gi gvb n‡e-
5 2a
a1 a2 a3
A. -10/3 B. 6/5 C. 15/8 D. 10/3 E. 5/6
81. wbY©vqK b1 b2 b3 †Z b2 Gi mn-¸b‡Ki gvb
Soln: [D] 3 4  0
c1 c2 c3 5 2a
A. a1c2-a2c1 B. –a1c3+a3c1 C. a1c3 – a3c1 D. a1b3-a3b1
Soln: [C] mn-¸YK = (–1)n  hvi mn¸YK Zvi Kjvg I mvwi ev‡` evwK  6a – 20 = 0
Dcv`vb¸‡jvi Determinate
GLv‡b, n = (Row + Column) number.  a = 20 = 10
63
 b2 Gi mn¸YK = (–1)2+2 a1 a3 = a1c3 – a3c1
c1 c3 123

82. †Kvb wbY©vqK X Gi cÖ_g mvwi Ges cÖ_g ¯Í¤¢‡K ci¯ú‡ii wewbgq Kiv 87. wbY©vqK 4 5 6 Gi gvb n‡jv-
nj; bZ~ b wbY©vq‡Ki gvb n‡e
A. X Gi gv‡bi wecixZ B. 0 789 B. 87 E. ‡KvbwUB bq
C. X Gi gv‡bi wØ-¸b D. X Gi gv‡bi mgvb D. 0
Soln: [D] †Kvb wbY©vq‡K mvwi I Kjvg change Kiv‡K Transpose e‡j| A. 25
Transpose I g~j wbY©vq‡K gvb equal _v‡K| So Ans. D C. 179

|

1 2 3 112 c'2 = c2 – c1 A. 1 B.  C.  2 D. 0
Soln: [D] 4 5 6 = 4 1 2 c'3 = c3 – c1
ω ω ω2   2
7 8 9 712
Soln: [D] ω2 ω2 1 = 2 2 1

wbY©vq‡Ki `wy U Kjvg ev mvwii Abyiƒc Dcv`vb¸‡jv Awfbœ n‡j Zvi gvb ω3 1 ω 11

zero nq | GLv‡b wØZxq I Z…Zxq Kjv‡gi Dcv`vb¸‡jv Awfbœ | ZvB gvb wbY©vq‡Ki `ywU Kjvg ev mvwii Abiy ƒc Dcv`vb¸‡jv Awfbœ n‡j Zvi gvb zero
nq | GLv‡b cÖ_g I wØZxq Kjv‡gi Dcv`vb¸‡jv Awfbœ | ZvB gvb zero.
zero.

88. 1 x yz = KZ? 94. 1 1 1  wbY©vqKwUi gvb 2 n‡j k Gi gvb-
1 y zx 1 2 3

1 z x y 1 4 k 

A. 0 B. 1 E. (x+y+z)2 A. 9 B. 8 C. 7 D. 6
C. xyz D. x+y+z Soln: [A] Xvwe [01- 02] Gi 1 bs Gi Abiy ƒc |

1 x y  z 1 x x  y  z c'3 = c2 + c3 aax
Soln: [A] 1 y z  x  1 y x  y  z
95. hw`   m m n nq, Z‡e Δ = 0 mgxKi‡Yi g~j n‡”Q:

1 z xy 1 z xyz b xb

wbY©vq‡Ki `wy U Kjvg ev mvwii Abyiƒc Dcv`vb¸‡jv Awfbœ n‡j Zvi gvb A. x = a, x = m B. x = b, x = m
zero nq | GLv‡b cÖ_g I ZZ… xq Kjv‡gi Dcv`vb¸‡jv Awfbœ | ZvB gvb
zero. C. x = a, x = b D. †KvbwUB bq

11 x Soln: [B] Avgiv Rvwb, wbY©vq‡Ki `wy U Kjvg ev mvwii Abiy ƒc Dcv`vb¸‡jv
89. x- Gi gvb KZ n‡j 2 2 2  0 n‡e?
Awfbœ n‡j Zvi gvb zero nq | GLv‡b x = b or x = m n‡j 1g I 2q

mvwii Abyiƒc Dcv`vb¸‡jv same nq | ZvB x = b or m n‡e |

345 28 29 30
96. 31 33 35  ?
A. 2 B. 5 E. 1
C. -2 D. 3 34 37 40
11 x
Soln: [E] A. 0 B. 1 C. 5 D. 9
2 2 2 0 Soln: [A]Same as CU no 8
97. wbY©vq‡Ki 2wU Kjvg ev mvwi Awfbœ n‡j †KvbwU mZ¨?
345 A. wbY©vq‡Ki gv‡bi wP‡ýi cwieZ©b nq
B. wbY©vq‡Ki gvb k~b¨ nq
Avgiv Rvwb, wbY©vq‡Ki `ywU Kjvg ev mvwii Abyiƒc Dcv`vb¸‡jv Awfbœ n‡j Zvi C. wbY©vq‡Ki gvb abvZ¥K nq
gvb zero nq | GLv‡b x = 1 n‡j 1g I 2q mvwii Abiy ƒc Dcv`vb¸‡jv same nq D. wbY©vq‡Ki gvb mgvb nq
| ZvB x = 1 . Soln: [B]

12 5 98. GKwU wbY©vq‡Ki `By wU Kjvg mgvb n‡j Gi gvb KZ?
90. 1 3 4 wbY©vqKwUi gvb KZ?

161 A. 1 B. –1 C. 0 D. 2

A. 7 B. 12 Soln: [C] wbY©q‡Ki `ywUi Kjvg mgvb n‡j gvb 0 nq|

C. 16 D. 8 E. 0 1  2
99.   2 1 = KZ ?
Soln: [E] Use calculator
2 1 
b2  c2 ab ca
91. ab c2  a2 A. –2 B. –4 C. –3 D. †KvbwUB bq
bc ?
ca bc a2  b2

A. 0 B. 1 1  2

C. 4abc D. 4(a2+b2+c2) E. 4a2b2c2 Soln: [B]   2 1

Soln: [E] Xvwwe [05- 06] Gi 5 bs Gi Abiy ƒc| 2 1 

12a = 1 (–  3–1)–  (  2 –  2) +  2(–  –  4)
92. 4 5 6 a Gi gvb KZ n‡j wbY©qKwU singular n‡e? = – 2 – 0 +  2 (–  –  )
= – 2 – 2 3 = –2 –2 = – 4
789

A. 1 B. 2 87 42 3
100. 45 18 7 
C. 3 D. 4 E. 5
Soln: [C] Pwe [07- 08] Gi 10 bs Gi Abyiƒc|

59 28 3

ω ω ω2 A. 14 B. 60 C. 84 D. †KvbwUB bq
93. GK‡Ki GKwU RwUj Nbg~j  n‡j ω2 ω2 1 wbY©vq‡Ki gvb KZ?
Soln: [D] Use calculator
ω3 1 ω

|

ভেক্টর 10. m Gi †Kvb gv‡bi Rb¨ 2ˆi  3ˆj  6kˆ Ges mˆi  32  4kˆ †f±i

`wy U j¤^ n‡e?

A. – 18 B. 18

1. A  ˆi  2ˆj  3kˆ Ges B  2ˆi  ˆj  kˆ n‡j A.B =? C. 9 D. –9

Soln:[C],

A. –3 B. –2 11. hw` AB  2ˆi  ˆj Ges AC  2ˆi  ˆj  5kˆ nq, Z‡e AB Ges AC

C. 2 D. 3 †K mwbwœ nZ evû a‡i AswKZ mgvšÍwi‡Ki †¶Îdj n‡e-

Soln: [A]

2.  Gi †Kvb gv‡bi Rb¨ 4i  2j 3k Ges λi  3j  2k †f±iØq A. 8 5 B. 5 6

ci¯ci j¤^ n‡e- C. 3 6 D. 6 5

A. –3 B. 3 Soln:[B], 2ˆi ˆj 3kˆ,  3ˆi 4ˆj 5kˆ 
hw` A  B B
C. –12 D. 12 12.       nq, Zvn‡j †f±‡ii

Soln: [B]   Dci A †f±‡ii Awf‡¶c n‡”Q-
F1 Ges F2 ej `By wUi jwä F3 ; †hLv‡b F1  2i  3j,
3.  –13 2 13 –13 7
A. 10 B. 7 C. D.
F3  5i  4j n‡j F2 = ?
10 7 52

A. 3i  7j B. 7i  j Soln:[A] 
 ab
C. 7i  7j D. 3i  7 j 13. hw` a  ˆi  2ˆj  3kˆ Ges bˆ  3ˆi  ˆj  2kˆ nq, Z‡e Ges

4. SBoln:6[ˆiD]3ˆj  2kˆ †f±‡ii Dci A  2ˆi  2ˆj  kˆ †f±‡ii   b Gi ga¨eZx© †Kv‡Yi gvb n‡e-
Awf‡¶cÑ a

A. 45 B. 90 C. 30 D. 120
Soln:[B]

A. 8 B. 7 14. 2ˆi  ˆj  kˆ Ges ˆi  2ˆj  3kˆ †f±i `By wU ci¯úi j¤^ n‡j  Gi
7 8
gvb †KvbwU?
C. 8 D. 5
58 A. 3/2 B. 2/3

Soln: [A] C. 5/2 D. 2/5 E. 5/3

5. 'a' Gi †Kvb gv‡bi Rb¨      Ges    Soln:[C]

2i + j– k, 3i –2j + 4k i– 3j + ak 15. 2ˆi  aˆj  kˆ Ges aˆi  ˆj  9kˆ †f±iØq ci¯úi j¤^ n‡j 'a' Gi

†f±iÎq mgZjxq? gvb-

A. 5 B. 4 A. 3 B. –3
C. 9 D. None
C. 3 D. 2 Soln:[A]
Soln: [A]

6. ABC wÎf‡z Ri BC, CA I AB evûi ga¨we›`¸y ‡iv h_vµ‡g D, E I F

n‡j-

A. ⃗A⃗⃗⃗D⃗ = A⃗⃗⃗⃗B⃗ + ⃗B⃗⃗⃗⃗C B. A⃗⃗⃗⃗D⃗ = ⃗A⃗⃗⃗⃗F + ⃗A⃗⃗⃗E⃗ 16. 4ˆi  2ˆj  3kˆ Ges i  3j  2k †f±iØq ci¯úi j¤^ n‡j  Gi
C. A⃗⃗⃗⃗D⃗ = A⃗⃗⃗⃗B⃗ + A⃗⃗⃗⃗⃗C D. A⃗⃗⃗⃗D⃗ = ⃗B⃗⃗⃗E⃗ + ⃗C⃗⃗⃗F

7. a Gi gvb KZ n‡j 21i + 31j + ak †f±iwU GKwU GKK †f±i n‡e? gvb-

 2 B.  15  7 D.  23 A. –3 1 C.  1 D. 3
3 6 6 6 B. 3 D. –4
A. C.
3

Soln: [D] Soln: [D]

8. ABC wÎfz‡Ri BC, CA, Ges AB evûi ga¨we›`y¸‡jv h_vµ‡g D, 17. a  3ˆi  ˆj  2kˆ , b  ˆi  3kˆ n‡j a.b  ?

E, Ges F n‡j- A. 3 B. 4 C. –3

A. ⃗ = + ⃗ B. ⃗ = ⃗ + ⃗ Soln: [C]

C. ⃗ = + D. ⃗ = ⃗ + ⃗ 18. iˆ  ˆj  kˆ Ges  ˆi  ˆj  2kˆ †f±iØ‡qi ga¨eZx© †Kv‡Yi

Soln: [B] cwigvY wK?

9. 2i  3k, i  j  k †f±i `wy Ui ga¨eZx© †KvY n‡e- A. 0˚ B. 45˚ C. 90˚ D. 180˚
Soln: [C]

A. sin–1 1 B. cos–1 1  3ˆi 4ˆj 11kˆ Gi gvb (magnitude) KZ?
39 12 r

C. cos–1 –1 D. sin–1 1 19. †f±i   
39 39
A. 10 B. 18
Soln:[C], C. 12 D. 6 E. 8

|

Soln: [D] 28. a Gi gvb KZ n‡j aˆi  2ˆj  kˆ Ges 2aˆi  aˆj  4kˆ ci¯úi

20. A  B  0 n‡j †Kvb&wU mZ¨? (06-07) j¤^ n‡e?

A. A I B ci¯úi j¤^ B. A  nB A. 2, 1 B. 2, 1

C. ci¯úi 450 †Kv‡Y †Q` K‡i D. ci¯úi 600 †Kv‡Y †Q` K‡i C. 2, 2 D. 1, 1 E. 2, 3

E. †KvbwUB bq Soln: [A]

Soln: [B] 29. Vector A  3ˆi  7ˆj  3kˆ Ges B  5ˆi  3ˆj  2kˆ n‡j A Ges B

 2ˆi 3ˆj 4kˆ  ˆi 2ˆj 3kˆ Gi ga¨eZx© †Kv‡Yi gvb n‡e-
p Q
21.    Ges   - n‡j PQ Gi gvb n‡e- A. 60 B. 45
D. 150
C. 90 E. 30
Soln:[C]
A. 12 B. 406
D. 1 E. 0 30. †f±iØq A  2i  aj  k Ges B  4i  2j  2k ci¯úi j¤^ n‡j 'a'
C. 3
Gi gvb KZ?
Soln: [C]

22.  Gi gvb KZ n‡j αˆi  2ˆj  3kˆ I 2ˆi  4ˆj  6kˆ ci¯úi A. 2 B. 1

mgvšÍivj n‡e- C. 4 D. 2 E. 3

A. 2 B. –1 Soln: [E]

1    31. a  3, b  5 Ges a  b  7 nq Z‡e a I b †f±i `wy Ui
C.
D. 1 E. –2 ga¨eZx© †KvY KZ n‡e?
2
Soln: [D] A. 180 B. 120

C. 30 D. 220 E. 1350

23. A  ˆi  2ˆj  2kˆ Ges B  6ˆi  3ˆj  2kˆ †f±i `yÕwUi ga¨eZx© Soln: [B] B  3ˆi  2ˆj  3kˆ nq,
†KvY n‡”Q- 
32. hw` A  2ˆi  3ˆj  kˆ Ges Zvn‡j
   
A. cos1 4 B. cos1 2
25 25 A  B .B -Gi gvb-

C. cos1  4  D. cos1 3 E. cos1 4 A. 2 B. 3 C. 4 D. 1
 21  25 25 Soln: [D]

24. SBoln:6[ˆiC] 3ˆj  2kˆ  33. hw` A  3i  k Ges B  i  2j GKwU mvgšÍwi‡Ki `yÕwU mwbœwnZ
A
†f±‡ii Dci  2ˆi  2ˆj  kˆ †f±‡ii evû nq, Z‡e mvgšÍwiKwUi †¶Îdj KZ?

Awf‡¶c n‡e- A. 1 7 B. 1 17 C. 1 41 D. 41
2 22
A. 7 B. 1
8 8 Soln: [D]

8 1 E. †KvbwUB bq 34. a-Gi gvb KZ n‡j wb‡Pi †f±i A I B ci¯úi mgvšÍivj n‡e,
C. D.   5ˆi  2ˆj  3kˆ Ges   15ˆi  aˆj  9kˆ ? (06-07)
7 B
7 †hLv‡b A
Soln: [C]

25. hw` `wy U mgvb ej †Kvb GK we›`y‡Z wµqv K‡i. hw` ejØ‡qi jwäi A. 6 B. 4 C. 3 D. 5
eM© ej¸wji wZb¸Y nq, Z‡e ej `By wUi AšÍf©z³ †KvY KZ? Soln: [A]

35. P  2ˆi  2ˆj  3kˆ Ges Q  4ˆi  ˆj  kˆ n‡j G‡`i jwä wbY©q Ki|

A. 30 B. 45 E. †KvbwUB bq A. 6ˆi  3ˆj  2kˆ B. ˆi  2ˆj  3kˆ
C. 60 D. 90
C. 2ˆi  ˆj  kˆ D. 2ˆi  3ˆj  2kˆ
Soln: [E]
Soln: [A]   
26. A  i  j  k Ges B  i  j  k †f±iØ‡qi ga¨eZ©x †KvY
36. i  j  k,  i  j  2k †f±i ivwk `yBwU ci¯úi-
E. 180
KZ? A. j¤^ B. mgvšÍivj C. mgvb D. GKK gv‡bi

A. 0 B. 90 Soln: [A]
D. 60
C. 45       
Soln: [E]  
37. i k  k  i -Gi gvb- C. o D. i
A. j B. k
27. A  4ˆi  2aˆj  2kˆ Ges B  2ˆi  ˆj  2kˆ †f±i `wy U j¤^fv‡e
Soln: [C]

Aew¯’Z n‡j 'a' Gi gvb KZ? 38. A = 3i + 2j -6k †f±iwUi gvb KZ?

A. 2 B. 4 A. 49 B. 7 C. -7 D. 0
Soln: [B]
C. 3 D. 1 E. 5
Soln:[A]

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39. A Ges B ci¯úi mgvšÍivj n‡j- C. 2ˆi  4ˆj  5kˆ D. ˆi  3ˆj  2kˆ

A. A  B  0 B. A.B  0 Soln: [B] Use calculator.

C. A  B  0 D. A  B  0 49. i  j Ges i  j  pk †f±i `‡y Uvi ga¨eZ©x †KvY π n‡j p-Gi

40. Soln: [A]   2ˆi  aˆj  kˆ Ges   4ˆi  2ˆj  2kˆ 4
A B gvb KZ?
 Gi †Kvb gv‡bi Rb¨
B.  2
ci¯úi j¤^ n‡e? A. 12

A. 2 B. 3 C. 2 D. 1
D. 6
C. 4 Soln: [B]
Soln: [B] OB  4ˆi  3ˆj  2kˆ n‡j
50. i  j I j  k Gi ga¨eZx© †KvY †KvbwU?
41. OA  2ˆi  3ˆj  4kˆ Ges
AB = A. 90 B. 180
C. 120 D. 60
Soln: [B]
KZ?

A. 2 19 B. 37

C. 3 13 D. 26 সরলররখা

Soln: [A] B. j.2i  3j  k  3 1. hw` (–5,1), (4,5), (7,–4) GKwU wÎf‚‡Ri kxl©we›`y nq Zvn‡j
wÎf‡‚ Ri †¶Îdj KZ? (01-02)
42. †KvbwU mwVK bq?  D. 3ˆi   2ˆi  6ˆj
1 1
A. i.k  0 A. 48 B. 46
 
2 2
C. A  B  B A

43. Shwo`ln:A[D]6ˆi  3ˆj  2kˆ Ges   2ˆi  2ˆj  kˆ nq Z‡e  Gi C. 50 1 [B]
B A.B D. 71

gvb KZ? 2

A. 4 B. 6 2. (1, 4) I (9, 12) we›`Øy ‡qi ms‡hvMKvix mij‡iLv †h we›`‡y Z 5:3

C. 8 D. 10 Abycv‡Z AšÍwe©f³ nq Zvi ¯’vbvsK –

44. SAoln:3[ˆiA] ˆj  2kˆ ,   2ˆi  ˆj  kˆ ,C  ˆi  3ˆj  2kˆ n‡j A. (3, 2) B. (5, 5) [C]
B C. (6, 9) D. (1, 1)

  3. (1, 4) Ges (9, –12) we›`yØ‡qi ms‡hvMKvix †iLvsk AšÍt¯’fv‡e †h
B.(C  A) Gi gvb KZ?
we›`y‡Z 5:3 Abcy v‡Z wef³ nq Zvi ¯’vbv¼-
A. 5 B. 3
C. 1 D. 0 A. (6, –6) B. (3, 5)
Soln: [D]
C. (2, 1) D. (–6, 5) [A]
45. i  j  k †f±iwU x-A¶‡iLvi mwnZ †h †KvY Drcbœ K‡i Zvi gvb
4. (x, y), (2, 3) Ges (5, 1) GKB mij‡iLvq Aew¯’Z n‡j-
KZ?
A. 4x  3y  17 = 0 B. 2x + 3y  13 = 0

C. 3x + 4y + 17 = 0 D. 3x + 4y  17 = 0 [B]

 A. cos1 3 B. cos1  1  5. (2, 2 – 2x), (1, 2) Ges (2, b – 2x) we›`y¸‡jv mg‡iL n‡j, b-Gi gvb-
3
A. –1 B. 1

C. 2 D. –2 [C]

C. cos1(1) D. †KvbwUB bq 6. (2, –1), (a + 1, a – 3) I (a + 2, a) we›`y wZbwU mg‡iL n‡j a Gi

Soln:[B]   gvb-

46. i  j  2k Ges 2i  2j  4k †f±iØ‡qi AšÍM©Z †Kv‡Yi †KvmvBb A. 4 B. 2

gvb †Kvb&wU? 11
C. D. [D]
A. 2/5 B. 3/4
42

C. 2/3 D. 1/3 7. wÎfz‡Ri wZbwU kxl© we›`yi ¯’vbvsK (3, 5), (–3, 3) Ges (–1, –1)

Soln: [C] n‡j wÎfRz wUi †¶Îdj KZ? (13-14)

47. 2ˆi  3ˆj  6kˆ †f±‡ii Dci 2ˆi  6ˆj  kˆ ‡f±‡ii Awf‡¶c KZ? A. 20 B. 18

A. 5 B. 2 C. 16 D. 14 E. 12 [D]
C. 4 D. –4
8. (1, 4) Ges (9, 12) we›`Øy ‡qi ms‡hvRK †iLv †h we›`‡y Z 3:5
Soln: [C]
Abycv‡Z AšÍwe©f³ nq, Zvi ¯’vbv¼-
48. A  2ˆi  ˆj, B  ˆi  ˆj  kˆ Ges C  2ˆi  kˆ n‡j
A. (7, 4) B. (4, 7)

C. (5, 8) D. (8, 5) [B]

(A  B) C  ? 9. P(6, 8), Q(4, 0) Ges R(0, 0) kxl©we›`ywewkó wÎf‡z Ri †ÿÎdj-

A.  2ˆi  5ˆj  4kˆ B.  2ˆi  4ˆj  5kˆ A. 32 Sq. units B. 16 Sq. units

C. 12 Sq. units D. 24 Sq. units [B]

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10. (1, 2) (4, 4) I (2, 8) h_vµ‡g wÎfR~ ABC Gi evûÎ‡qi ga¨we›`y  22.  1, 3 we›`ywUi †cvjvi ¯’vbv¼ n‡e-

ABC wÎfR~ wUi †¶Îdj wbY©q Ki| [01-02] A. (1,60) B. (2,60) C.(2,120)
D. (2,120) E. (2,90) [D]
A. 32 eM© GKK B. 64 eM© GKK

C. 16 eM© GKK D. 8 eM© GKK [A]

11. GKRb †jvK Zvi Kv‡ai Dci GKwU jvwVi cÖv‡šÍ †e‡a †evSv enb 23. x2 + y2-2ax = 0 mgxKiYwUi †cvjvi mgxKiY n‡e-

Ki‡e| Zvi nvZ I Kv‡ai Pvc wKfv‡e cwiewZ©Z n‡e?

A. R  x2 B. R  1 A. r = 2cos B. r = acos C. r = 2acos
x2
D. r = 2asin E. r = asin [C]
1
C. R  x D. R  x [C]

12. a Gi †Kvb gv‡bi Rb¨ (a2, 2), (a, 1) Ges (0, 0) we›`yÎq mg‡iL 24. h Gi gvb KZ n‡j (2,3), (-4,-6) Ges (h, 12) we›`y¸wj mg‡iL

n‡e? [BUET 06-07] n‡e?

A. 0, –1 B. 2, 2 A. 8 B. 4 C. 2

C. –2 D. 0, 2 [D]

13. (– 3 , – 3 ) Gi †cvjvi ¯’vbv¼ KZ? D. 1 E. 0 [A]

A. 66.4 B.  3.4 25. ABC wÎf‚‡Ri kxl©we›`my g~‡ni ¯’vbvsK h_vµ‡g (10, 20), (20, 30)

C.  6.54 D. 6.–4 [C] Ges (30, 10). G H wÎf‡y Ri fi‡K›`ª n‡j GBC wÎfy‡Ri GD

14. (x - 3y – 2) = 0 †iLvi Dci P GKwU we›`y Ges Zv (2, 3) I (6, – ga¨gvi ˆ`N©¨ KZ?

5) we›`y `wy U n‡Z mg`~ieZx©| P we›`wy Ui ¯’vbv¼ nj-

A. (12, 4) B. (14, 2) A. 10 GKK B. 5 GKK
C. (14, 4) D. (16, 4)
[C]

15. (1, 0) we›`y Ges x + 1 = 0 mij‡iLv †_‡K mg`i~ eZx© we›`my g~‡ni †mU C. 65 GKK D. 4 GKK E. 5 GKK [E]

†h mÂvic_ MVb K‡i Zvi mgxKiY n‡e- 26. †Kvb wÎf‡y Ri fi‡K‡›`ªi ¯’vbvsK (7, 2) Ges `ywU kxl© we›`yi ¯’vbvsK

A. x2 = 2y B. y2 = 4x [B] h_vµ‡g (3, 5) Ges (7, -1) n‡j Aci kxl© we›`yi ¯’vbvsK KZ?
C. x2 = 4y D. y2 = 2x

16. (1,4) Ges (9,–12) we›`Øy ‡qi ms‡hvMKvix †iLvsk AšÍt¯’fv‡e 5:3 A. (11, 11) B. (2, 2) C. (2, 11)

Abcy v‡Z wef³ n‡j Zvi ¯’vbv¼- D. (11, 2) E.  11, 11 [D]

A. (6,–6) B. (–6, 6) 2 2

C. (4, 3) D. (–4, –3) [A] 27. GKwU wÎf~‡Ri †KŠwYK we›`my gn~ h_vµ‡g A(x,y), B (-6, -3) Ges C

17. †Kvb wÎfy‡Ri kxl©we›`ymgn~ (–4, 3), (–1, –2) Ges (3, –2) n‡j Zvi (6, 3). A we›`y n‡Z BC evûi Dci AswKZ ga¨gvi ˆ`N©¨ hw` aªæeK
†¶Îdj-

A. 15 sq. units B. 10 sq. units Ges 5 GKK nq Z‡e A we›`iy mÂvic‡_i mgxKiY n‡e-

C. 7 sq. units D. 30 sq. units [B] A. x2+y2 = 0 B. x2+y2+25=0

18. A (1, 1) Ges B (4, 5) we›`y `By wUi `i~ Z¡-

A. 4 units B. 6 units C. x2+y2+5 = 0 D. x 2  y2  5
C. 5 units D. 8 units E. x2+y2 – 25 = 0
[C]

19. ( 3,1) we›`yi †cvjvi ¯’vbvsK- [E]

A. (2, /4) B. (2, /6) 28. wÎf‡z Ri kxl©we›`y¸‡jvi ¯’vbvsK (0, 0), (0, 3) Ges (4, 0) wÎfzRwUi

C. (1, /4) D. (0, /4) [B]

20. (1, 0) (2,1) Ges (4, 5) we›`¸y ‡jv Øviv MwVZ wÎf‚‡Ri †¶Îdj KZ? AšÍ:†K›`ª KZ?

A. 1 eM© GKK B. 2 eM© GKK C. 4 eM© GKK A. (0, 0) B. (1, 1)

D. 10 eM© GKK E. 6 eM© GKK [A] C. (2, 2) D. (3, 3) E. (4, 4) [B]

21. `ywU c`Ö Ë we›`y (b, 0) Ges (-b, 0) †_‡K mg`~ieZ©x mÂvic‡_i 29. (3, 0) Ges (-4, 0) we›`y †_‡K mg`~ieZ©x we›`ymg‡~ ni †mU †h

mgxKiY n‡jv- mÂvic_ MVb K‡i Zvi mgxKiY:

A. Y = b B. Y = -b A. 3x –4y = 0 B. 3x + 4y = 0 C. 3x + 1 = 0
D. 2x +1 = 0 E. 1–4x = 0 [D]
C. X = -b D. X = b E. Y A¶ [E]

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30. X- A¶ Ges (–5, –7) †_‡K (4, k) we›`wy Ui `~iZ¡ mgvb n‡j k Gi C. 2 5 D. 4 5 [C]
gvb KZ?  40. †Kvb we›`iy Kv‡Z©mxq ¯’vbvsK 3, 3 n‡j H we›`yi †cvjvi

7 65 65 ¯’vbvsK-  B. 2 3, 30
A. B. C.  D. 2, 30
 A. 3, 60
65 70 7  C. 3, 90

65 50 [B]
D. E.
[D] 41. GKwU wÎf‡z Ri kxl©we›`¸y ‡jv n‡jv P(1, 2), Q(3, 0)
7 7 Ges R(3,2); wÎfz‡Ri fi‡K›`ª KZ?

31. Y- A¶ Ges (7, 2) †_‡K (a, 5) we›`wy Ui `~iZ¡ mgvb n‡j a Gi gvb A. (1/3,0) B. (0.4/3)

KZ? C. (0, 0) D. (1/3, 4/3) E. (1,0) [A]

42. 4 GKK evûwewkó GKwU eM©‡¶‡Îi PviwU kxl©we›`y w`‡q †h eË„ AuvKv

A. 29 B. 7 C. 27 hvq Zvi †¶Îdj KZ?
7 29 9
A. 4 B. 8

9 29 C. 12 D. 16 E. 42 [D]
D. E.
[A]
27 5
43. (1, 0), (2, 1) I (4, 5) we›`y Øviv MwVZ wÎfz‡Ri †¶Îdj KZ?
32. GKwU we›`y Ggbfv‡e Pwj‡Z‡Q †h, X-A¶ nB‡Z Dnvi `~iZ¡ Y-A¶
nB‡Z Dnvi `~i‡Z¡i Pvi¸Y| we›`wy Ui mÂvi c‡_i mgxKiY n‡e- A. 9 eM© GKK B. 5 eM© GKK

C. 1 eM© GKK D. †KvbwUB bq [C]
 44. †Kvb we›`iy †cvjvi ¯’vbvsK  10,90 n‡j Kv‡Z©mxq ¯’vbvsK
A. x = 4 B. x = 4y C. x = 4

D. y = 4x E. †KvbwUB b‡n [B] KZ?

33. wÎfz‡Ri wZbwU kxl© we›`yi ¯’vbv¼ (3, 5), (3, 3) Ges (1, 1) n‡j  A.  10,0  B. 0, 10

wÎfRz wUi †¶‡Îdj KZ?

A. 12 B. 14 C. (0, 010) D. (10, 0) [B]

C. 16 D. 18 E. 20 [B] 45. (3, 4 ), (a, b) Ges (x, y) we›`y wZbwU mg‡iL n‡j G‡`i Øviv MwVZ

34. †Kvb we›`iy Kv‡Z©mxq ¯’vbv¼ (x, y) Ges †cvjvi ¯’vbv¼ (r, ) n‡j, wÎfz‡Ri †¶Îdj KZ?

bx‡Pi †Kvb& m¤úK©wU mwVK bq? A. 1 B. a + 3

A. x = rcos B. y = x tan C. 0 D. b + 4 [C]

C. r  x2  y2 D. r = y sin 46. †Kvb we›`iy †cvjvi ¯’vbvsK  2, π  , H we›`iy Kv‡Z©mxq ¯’vbvsK-

E. y = rsin [D]  2  B. 2, 3

35. (p + q, p  q) Ges (p  q, p + q) we›`Øy ‡qi ga¨eZx© `~iZ¡ KZ? A. (0, 2)

A. 8q2 B. 2q  C. 1, 3  D. 3,2 [A]

C. 2q D. 2q 2 E. 4q [D] 47. (0, 0), (a, 0) I (0, b) we›`y wZbwU Øviv MwVZ wÎfz‡Ri †¶Îdj KZ
eM© GKK n‡e?

36. (0, 0), (a, 0) (0, a) kxl© we›`y wewkó wÎfz‡Ri †¶Îdj- A. 1 ab B. ab C. a2b2 D. 0 [A]
2
A. a2 B. a
48. t Gi mKj ev¯Íe gv‡bi Rb¨ GKwU we›`iy ¯’vbvsK (at2, 2at) n‡j

C. 1 a 2 D. 1 a [C] we›`wy Ui mÂvic‡_i mgxKiY n‡e-
2 2
A. x2 + y2 = a2 B. y2 = 4ax

37. (3 – 3i) Gi †cvjvi ¯’vbvsK- C. x2 = 4ay D. x2 – y2 = a2 [B]

49. (x, 5) I (8, 3) we›`Øy ‡qi `~iZ¡ 2 GKK n‡j x -Gi gvb KZ?

A. (43, /6) B. (33, /6) A. 6 B. 8 C. 10 D. 12 [B]

C. (23, /6) D. (3, /6) 50. GKwU wegvb AeZiYKv‡j †Kvb GK mg‡q (400, 800) we›`y‡Z

[C] Ae¯’vb K‡i Ges wKQy¶‡Yi g‡a¨ wegvbwU (400, 0) we›`‡y Z Ae¯’vb

38. hw` (–3, 0) we›`y n‡Z P(x,y) we›`iy `i~ Z¡ 2 GKK nq Z‡e P (x, y) K‡i| Zvn‡j wegvbwU wK n‡e?

we›`iy mÂvi c_ †KvbwU? A. wea¶¯Í n‡e bv B. wea¶¯Í n‡e

C. AviI Da¶©gLy x n‡e D. †KvbwU n‡e bv [B]

A. x2 + y2 + 6x + 5 = 0 B. x2 - y2 - 2x + 8 = 0 51. GKwU we›`iy †cvjvi ¯’vbv¼  2,   n‡j, Kv‡Z©mxq ¯’vbv¼ KZ?

C. x 2  y2  1  3
 A. 1,  3  B. 1, 3
4 D. y = 2x [A]

39. (0, 0), (0, 8) Ges (4, 0) GKwU wÎf‡z Ri wZbwU kxl© we›`y. wÎfzRwUi  C. 1, 3  D. 1, 3 [A]
cwie‡„ Ëi e¨vmva© KZ GKK?
52. (1,2) (3,-4) Ges (5,-6) GKwU wÎfz‡Ri kxl©we›`yÎq| GB wÎfz‡Ri
A. 8 B. 4 cwi‡K‡›`ªi ¯’vbvsK-

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A.(11, 2) B. (1, 2)

C. (11, 22) D. †KvbwUB bq [A] DC

53. hw` A(2, 5), B(5, 9) Ges D(6, 8), we›`y wZbwU ABCD i¤^‡mi kxl©

we›`y nq Zvn‡j C Gi ¯’vbv¼ KZ? A (2,1) B

A. (8, 11) B. (9, 11)

C. (9, 12) D. (8, 13) [C] A. (7/2, 2) B. (5/2, 3)

54. A(0, 0), B(0, 8) Ges C(4, 0) GKwU wÎf‡z Ri wZbwU kxl© we›`y n‡j C. (3, 2) D. (6, 3) [A]

ABC wÎfz‡Ri cwie„‡Ëi †K‡›`ªi ¯’vbv¼ KZ? 67. (3, 0) µg‡RvowU Ae¯’vb Ki‡e? (2009-10)

A. (4, 2) B. (2, 4) A. y - A‡¶i Dc‡i B. c_Ö g PZyf©v‡M

C. (4, 2) D. (2, 4) [D] C. PZ_y © fv‡M D. x-A‡¶i Dc‡i [D]

55. (1, 2), (3, 1), (2, 3), (2, 2) we›`y¸‡jv ms‡hvM Ki‡j wK ˆZix 68. †Kvb we›`y †cvjvi ¯’vbvsK (2, 150) n‡j, we›`ywUi Kv‡Z©mxq ¯’vbvsK-

nq?  A. 3,1  B.  3,1

A. eM©‡¶Î B. i¤^m [A]  C. 3,1 D. †KvbwUB bv [B]
C. AvqZ‡¶Î D. mvgšÍwiK

56.  2, 5  -Gi Kv‡Z©mxq gvb KZ n‡e? 69. (2, 1) we›`y †_‡K †h †m‡Ui we›`y mg~‡ni `~iZ¦ 4 GKK †mB †mU
 4 wb‡`©wkZ mÂvic‡_i mgxKiYÑ

A. (2, 1) B. (2, 1) A. x  22  y 12  4 B. x  22  y 12  42

C. (1, 1) D. (1, 3) [C] C. x  22  y 12  4

57. wÎfz‡Ri kxl© we›`¸y wj h_vµ‡g (2, 5), (3, 6), (7, 4) n‡j,

†¶Îdj- D. x  22  y 12  42 [D]

A. 6 eM© GKK B. 7 eM© GKK 70. (2, 0), (0, 0) Ges (3, 5) we›`Îy q Øviv MwVZ wÎf‡z Ri †¶Îdj

C. 5 eM© GKK D. 5 eM© GKK [B] A. 3 eM© GKK B. 2 eM© GKK
2
C. 5 eM© GKK D. †KvbwUB bv [C]
 71. †Kvb we›`yi Kv‡Z©mxq ¯’vbvsK 3,3 3 n‡j, we›`ywUi †cvjvi
58. x-A¶¯’ p we›`y †_‡K (0, 2) Ges (6, 4) we›`y `wy U mg`~ieZx© n‡j p

we›`iy ¯’vbv¼ KZ? ¯’vbvsK (2009-10)

A. (2, 0) B. (4, 0)  
A. 6, B. 3,
C. (5, 0) D. (6, 8) [B]
6 6
59. (x, y) Ges (r, ) Gi mwVK m¤úK© †KvbwU?

A. x = r sin, y = rcos B. x = cos, y = r sin C. 6, D. †KvbwUB bv [C]

C. x = r cos, y = sin 3

D. x = r cos, y = r sin [D] 72. †Kvb we›`iy †cvjvi ¯’vbvsK 6, π  n‡j, we›`wy Ui Kv‡Z©mxq

60. x + 4 = 0, y  3 = 0 Ges 3x  4y + 12 = 0 †iLvÎq Øviv MwVZ  3

wÎfz‡Ri AšÍ‡K›`ª wbbq© Ki| ¯’vbvsK- (20-10)

A. (5, 3) B. (2, 5)  A. 3 3,3  B. 3, 3

C. (8, 11) D. (3, 2) [D]  C. 3,3 3

61. †Kvb wÎf‡‚ Ri kxl©we›`ymgn~ (-1, -2), (2, 5) Ges (3, 10) n‡j Zvi D. †KvbwUB bv [C]

†¶Îdj- 73. ABCD PZyfy©‡Ri kxl©we›`y¸‡jv h_vµ‡g (a,0), (b,0), (0, a), (0,

A. 10 sq. units B. 15 sq. units b); ACB Gi †¶Îdj

C. 4 sq. units D. 18 sq. units [C] A. 0.5(a b)a B. 0.5(b  a)b

62. ABC Gi fi‡K›`ª gj~ we›`‡y Z Ges A I B Gi ¯’vbv¼ h_vµ‡g C. (a +b)a, D. †KvbwUB bq [D]

(4,7) I (2, 5) n‡j C Gi ¯’vbv¼ †ei Ki| 74. (x, y) we›`wy U (a,0) we›`y I x + a = 0 †iLv n‡Z mg`i~ eZx© ; we›`ywUi

A. (1, 1) B. (2, 2) mÂvic_ (2010-11)

C. (3, 4) D. (1, 3) [B] A. GKwU civeË„ B. GKwU DceË„

63. (1, 2) I (6,3) we›`yMvgx mij‡iLv (4, 1) we›`y‡Z †h Abycv‡Z C. GKwU eË„ D. †KvbwUB bq [B]

wef³ nq Zv wbY©q Ki| 75. †Kvb we›`iy †cvjvi ¯’vbv¼ (2, 3/2) n‡j we›`ywUi Kv‡Z©mxq ¯’vbv¼-

A. 2:1 B. 2:3 A. (2, 1) B. (0, 2)
C. (2, 0) D. (0, 2)
C. 3:2 D. 5:3 [A]

64. †Kvb we›`iy †cvjvi ¯’vbvsK (3,90˚) n‡j we›`wy Ui Kv‡Z©mxq ¯’vbvsK? [B]

A. (0,3) B. (3,0) 76. †Kvb we›`yi Kv‡Z©mxq ¯’vbv¼ (1, 3) n‡j we›`ywUi †cvjvi ¯’vbv¼ KZ?

C. (1,2) D. (0,0) [A] A. (3, 120˚) B. (2, 120˚)
C. (3, 110˚) D. 2, 110˚)
65. A = (a, b) we›`y n‡Z x I y A‡¶i `i~ Z¡ 3 I 4 n‡j A we›`y n‡Z g~j 77. wÎfz‡Ri ga¨gv wZbwUÑ [B]

we›`iy `~iZ¡ KZ?

A. 7 B. 5 C. 4 D. 3 [B] A. kxl©we›`y B. mgvšÍivj

66. wP‡Îi AvqZ‡¶‡Îi AB evûi ˆ`N©¨ 3 GKK Ges AD evûi ˆ`N©¨ 2 C. mgwe›`y D. †KvbwU bq

GK n‡j KYØ© ‡qi †Q` we›`iy ¯’vbvsK KZ? [C]

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78. (x1, y1), (x2, y2) Ges (0, 0) we›`y wZbwU Øviv MwVZ wÎfz‡Ri †¶Îdj 90. 5x  2y + 7 = 0 mij‡iLvi Dci j¤^ Ges (3, 1) we›`y w`‡q
KZ? AwZµg K‡i Ggb GKwU mij‡iLvi mgxKiY-

A. x1y1  x2y2 B. 1/2(x1y2  x2y1) A. 2x + 5y + 1 = 0 B. 2x5y+1=0

C. x1y1 + x2y2 D. 1/2 (x1y2 + x2y1) [B] C. 2x + 5y  1 = 0 D. 2x  5y  1 = 0 [A]

79. GK ev GKvwaK kZ©vbhy vqx †Kvb mgZ‡j we›`iy †mU‡K wK e‡j? 91. (4, 2) we›`y †_‡K 5x + 12y = 3 †iLvi Dci Aw¼Z j‡¤^i ˆ`N©¨-

A. mÂvic_ B. Awac_ 83 7
A. 8 B. C. D. [D]
9 7 13
C. mijc_ D. Pjb c_
[A] 92. mij‡iLv 3x + 4y  12 = 0 Øviv A¶Ø‡qi ga¨eZ©x LwÛZ As‡ki

80. ÔKÕ Gi gvb KZ n‡j (2, 3), (4, 6), Ges (5, K) we›`y wZbwU ˆ`N©¨-

mg‡iL n‡e? A. 7 B. 5

A.7 B. 7.25 [C] C. 9 D. 8 [B]
C. 7.5 D. 7.75
93. GKwU mij †iLvi A¶Ø‡qi ga¨eZ©x Ask (2, 3) we›`‡y Z mgwØLwÛZ nq|
81. (1, 1), (1, 1) ( 3, 3 ) we›`yÎq Øviv MwVZ wÎf‡z Ri fvi †K‡›`ªi mij †iLvwUi mgxKiY-

A. 2x + 3y  12 = 0 B. 3x + 2y  12 = 0

¯’vbv¼- C. 2x + 3y  6 = 0 D. 3x + 2y  6 = 0 [B]

A. (1/ 3,1/ 3) B. ( 3, 3) 94. a Gi †h gv‡bi Rb¨ y = ax (1  x) eµ‡iLvi gj~ we›`y‡Z ¯úk©KwU x-

A‡¶i mv‡_ 600 †KvY Drcbœ K‡i-

C. (1/ 3,1/ 3) D. (1/ 3, 1/ 3) [A] A. 3 1
B.
82. †Kvb wÎfz‡Ri fi †K›`ª (6, 4) Ges `yBwU kxl© we›`y (6, 1) Ges (2, 7)|
ZZ… xq kxl©we›`iy ¯’vbv¼ n‡e- 3

A. (0, 0) B. (10, 4) 3 D. 1 [A]
C.

2

C. (5, 2) D. (2, 6) [B] 95. 3x  7y + 2 = 0 mij‡iLvi Dci j¤^ Ges (1, 2 ) we›`y w`‡q AwZµg

83. (b, 0) Ges (–b, 0) we›`yØq n‡Z mg`~ieZx© we›`iy mÂvic‡_i K‡i Ggb GKwU mij‡iLvi mgxKiY-

mgxKiY wK? A. 3x + 7y  13 = 0 B. 7x + 3y  13 = 0

A. x2  2bx = 0 B. x2 + 2bx = 0 C. 7x + 3y + 13 = 0 D. 7x  3y  13 = 0 [B]

C. y-A¶ D. x-A¶ [C] 96. 5x  2y + 4 = 0 Ges 4x  3y + 5 = 0 mij‡iLvØ‡qi †Q`we›`y Ges

84. (–5, 7) I (3, – 1) we›`yØ‡qi ms‡hvMKvix †iLvs‡ki j¤^mgwØLÛK g~jwe›`y w`‡q MgbKvix mij‡iLvi mgxKiY-

†iLvi mgxKiY wK? (00-01) A. 2x  3y = 0 B. 3x  2y = 0

C. 2x  7y = 0 D. 9x + 2y = 0 [D]

A. y – 3 = x + 1 B. y + 1 = x – 3 97.  m~¶‡KvY n‡j, xcos + ysin = 4 Ges 4x + 3y = 5 mgvšÍivj

C. y + 3 = x – 1 D. y – 1 = x + 3 [A] †iLvØ‡qi `i~ Z¡-

85. y = 2x3 + 3x2 – 12x + 7 GKwU eµ‡iLvi mgxKiY| gj~ we›`y‡Z A. –1 unit B. 3 units

eµ‡iLvwUi bwZi cwigvb KZ? (00-01) B. 1 unit D. 9 units [B]

A. 8 B. 12 98. gj~ we›`y n‡Z 3x + 4y = 10 †eLvwUi j¤^ `~iZ¡-

C. 6 D. –12 [D] A. 2 B. 3

86.  Gi †Kvb gv‡bi Rb¨ ( 1) x + ( + 1)y – 7 = 0 †iLvwU C. 4 D. 5 [A]

3x + 5y + 7 = 0 †iLvi mgvšÍivj n‡e? (01-02) 99. 3x + 7y  2 = 0 mij‡iLvi Dci j¤^ Ges (2, 1) we›`My vgx mij‡iLvi
mgxKiY-
A.  = 4 B.  = 10
A. 3x + 7y  13 = 0 B. 7x  3y  11 = 0
C.  = 1 D.  = 6 [A]
C. 7x + 3y  17 = 0 D. 7x  3y  2 = 0 [B]
87. 3x2 – 7y2 + 4xy – 8x = 0 eµ‡iLvwUi ( –1, 1) we›`y‡Z Aw¼Z
100.mij‡iLv y = kx  1 eµ‡iLv y = x2 + 3 Gi ¯úk©K n‡e hw` k Gi
¯ck©‡Ki Xvj- (02-03)
GKwU gvb-
A.  5 5
9 B. A. 1 B. 22
C. 3 D. 4 [D]
9

C.  9 9 [A] 101. y  1  1 eµ‡iLv x-A¶‡K A we›`y‡Z Ges y-A¶‡K B
5 D. 2x

5 we›`‡y Z †Q` Ki‡j AB mij‡iLvi mgxKiY n‡e-

88. (1, –1) we›`My vgx Ges 2x – 3y + 6 = 0 †iLvi Dci j¤^ mij‡iLvi

mgxKiY- (02-03) A. x  2y + 3 = 0 B. x + 2y + 3 = 0

A. 3y – 2x = –5 B. 2x + 3y = –1 C. 2x  y + 3 = 0 D. x  6y  3 = 0 [A]

C. 2y – 3x = 1 D. 3x + 2y = 1 [D] 102. y = x3 – 12x + 16 eµ‡iLvi †h mg¯Í we›`‡y Z ¯úk©K x A‡¶i

89. 3x + 4y = 10 †iLvwUi Dci g~jwe›`y n‡Z AswKZ j‡¤^i ˆ`N©¨- (02-03) mgvšÍivj Zv‡`i ¯’vbvsK-

A. 2 B. 2 A. (2, 0) and (–2, 24) B. (2, 0) and (–2, 0)
C. (4, 12) and (–4, 12) D. (2, 0) and (–2, 32) [D]

C. 5 D. 5 [A] 103. y = 3x + 7 Ges 3y – x = 8 mij‡iLvØ‡qi AšÍf©~Z m²~ ‡KvY-

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A. tan–1(1) B. tan–1  1  E. 3x + y = 2 [D]
2
115. (1, 2) we›`y nB‡Z x – 3y + 4 = 0 †iLvi Dci j¤^ AswKZ Kiv

C. tan–1 4 D. tan–1  3  nBj: gj~ we›`y nB‡Z GB j‡¤^i `i~ Z¡ KZ?
3 4
[C] 1+ 3 2+ 3 2+ 3
A. 3 B. 2 C. 3
104. 2x – 3y + 6 = 0 †iLvi Dci j¤^ Ges (1, –1) we›`My vgx mij †iLvi
1+ 3 3+ 2
mgxKiY- D. 5 E. 7 [B]

A. 3x + 2y = 1 B. 3x – 2y = 5 116. y-A‡¶i Dcwiw¯’Z †h we›`y¸‡jv n‡Z 3y = 4x – 10 †iLvi Dci AswKZ j¤^

C. 3x + 2y = 5 D. 2x + 3y = 1 [A] `iy Z¡ 4 GKK nq, Z‡e Zv‡`i ¯’vbvsK KZ?

105.3x + 7y – 2 = 0 mij‡iLvi Dci j¤^ Ges (2,1) we›`My vgx mij‡iLvi A. (0, 10) and (a – 10/3) B. (0, 10) and (0, 10/3)

mgxKiY: C. (0, –10) and (0, 10/3) D. None of these [C]

A. 3x + 7y – 13 = 0 B. 3x – 7y – 11 = 0 117. GKwU mvgvšÍwi‡Ki †KŠwYK we›`¸y wj (1, 1), (4, 4), (4, 8) Ges (1, 5)
C. 7x + 3y – 17 = 0 D. 7x – 3y – 11 = 0 [D]
n‡j Gi †h †Kvb GKwU K‡Yi© ˆ`N©¨ n‡e-
106. y = mx, y = m1x Ges y = b mij‡iLvÎ‡qi Øviv MwVZ wÎf‡y Ri

eM©GK‡K †¶Îdj n‡e- A. 3 2 B. 4

A. b2(m1 – m) B. b2(m – m1) C. 10 D. None of these [C]
2mm1 2mm1
118. y (x – 2) (x – 3) – x + 7 = 0 eµ‡iLvwU †h we›`‡y Z x-A¶‡K †Q`
b2|m – m1| b2|m – m1|
C. mm1 D. 2mm1 [D] K‡i, H we›`y‡Z eµ †iLvwUi Awfj‡¤^i mgxKiY nj-

107.x + y = 3 Ges y – x = 1 mij‡iLvØ‡qi †Q`we›`yMvgx x-A‡¶i mgvšÍivj A. x + 20y – 7 = 0 B. 20x + y – 140 = 0
C. 20x + y + 140 = 0 D. x – 20y – 7 = 0 [B]
mij‡iLvi mgxKiY- (13-14)

A. y = 2 B. 2y = 3

C. x = 1 D. x + 3 = 0 [A] 119.3x – 7y + 2 = 0 mij‡iLvi Dci j¤^ Ges (1, 2) we›`y w`‡q AwZµg

108.y = –5x + 9 †iLvi mv‡_ j¤^ †iLvi bwZ- K‡i Ggb GKwU mij‡iLvi mgxiKY-

A. 5 B. –5 1 D. – 1 [C] A. 3x + 7y – 13=0 B. 7x + 3y – 13 = 0
C. 5 5 C. 7x + 3y + 13 = 0 D. 7x – 3y – 13 = 0 [B]

109.3x + 5y = 2, 2x + 3y = 0, ax + by + 1 = 0 mgwe›`yMvgx n‡j a 120.hw` x2 – y2 – 4x – 6y + c = 0 eË„ wU x-A¶‡K m¤úk© K‡i Z‡e C

Ges b Gi m¤úK©- Gi mgvb n‡e-

A. 4a–6b = 1 B. 4a–6b = 2

C. 6a–4b = 1 D. 6a–4b = 2 [C] A. 34 B. 31

110. (2, 3) we›`y n‡Z 4x + 3y – 7 = 0 †iLvi mv‡c‡¶ cÖwZwe¤^ we›`iy `i~ Z¡ C. 6 D. 4 [D]

KZ? 121.k-Gi gvb KZ n‡j 2x – y + 8 = 0 Ges 3x + ky –9 = 0 mij‡iLvØq

A. 2 unit B. 4 unit ci¯úi j¤^ n‡e?

C. 3 unit D. 6 unit [A] A. 3 B. 6

111. 4x + 5y –7 = 0 mij‡iLvi Dci j¤^ Ges (1, 2) we›`yMvgx mij‡iLvi C. 5 D. 8 [B]

mgxKiY nj: 122. Gi †Kvb gv‡bi Rb¨ (a – 1)x + (a + 1)y – 5 = 0 †iLvwU 7x +

A. 4x + 5y – 7 = 0 B. 5x – 4y – 1 = 0 9y + 5 = 0 †iLvi mgvšÍivj-

C. 5x – 4y + 3 = 0 D. 4x + 5y – 10 = 0 [C] A. –2

112. 2x + 3y = 7 Ges 3ax – 5by + 15 = 0 mgxKiY `wy U GKB mij‡iLv B. 3

cKÖ vk Ki‡j a I b aªæe‡Ki gvb KZ n‡e? C. 8 D. 5 [C]

A.   5 , 3  B.   5 , 9  123.5x – 2y + 4 = 0 Ges 4x – 3y + 5 = 0 †iLvØ‡qi †Q`we›`y Ges
 7 7  7 7
gj~ we›`y w`‡q MgbKvix mij‡iLvi mgxKiY-

C.  10 , 9  D.  10 , 3  A. 7x – 2y + 1 = 0 B. 3x – 2y = 0
 7 7  7 7
[C] C. 9x + 2y = 0 D. 2x – 3y = 0 [C]

113. 4 y = 3(x – 4) Ges 4y = 3(x –1) †iLv `yBwUi ga¨eZx© j¤^ `~iZ¡ 124.3x + 7y – 2 = 0 mij‡iLvi Dci j¤^ Ges (2, 1) we›`yMvgx

KZ? mij‡iLvi mgxKiY-

9 15 A. 3x + 7y – 13 = 0 B. 7x – 3y – 11 = 0
4 9
A. B. C. 7x + 3y – 17 = 0 D. 7x – 3y – 2 = 0 [B]

9 125.mij‡iLv y = mx –1 eµ‡iLv y = x2 + 3 Gi ¯úk©K n‡e hw` m

C. 5 D. None [C] Gi gvb nq-

114. x – 3y + 4 = 0, x – 6y + 5 = 0 Ges x + ay + 2 = 0 †iLvÎq A. 1 B. 2 2
C. –4 D. 4
mgwe›`yMvgx nB‡j Z…Zxq †iLvi mv‡_ j¤^ Ges g~jwe›`yMvgx †iLvi [D]

mgxKiY †KvbwU?

A. 5x – y + 2 = 0 B. 4x – 3y = 0
C. 4x – y = 0 D. 3x – y = 0

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126.hw` y  1  1 eµ‡iLv x-A¶‡K A we›`y‡Z Ges y A¶‡K B A. 110 B. 120
2x
C. 45 D. 115 [C]
we›`‡y Z †Q` K‡i Z‡e AB mij‡iLvi mgxKiY-
139. x-A‡¶i mgvšÍivj GKwU mij‡iLvi mgxKiY n‡”Q-

A. x – 2y + 3 = 0 B. x + 2y + 3 = 0 A. 3x + 4 = 0 B. 3y + 5 = 0

C. 2x – y + 3 = 0 D. x – 6y – 3 = 0 [A] C. 2x + 3y = 0 D. 2x + 3y + 1 = 0 [B]

127.3x + 7y – 2 = 0 mij †iLvi Dci j¤^ Ges (2, –1) we›`My vgx 149. a, b Ges c ev¯Íe aªæe n‡j a2x + b2y + c2 = 0 mgxKiYUv hv wb‡`©k

K‡i Zv n‡jv-

mij‡iLvi mgxKiY- A. eµ‡iLv B. mij †iLv

A. 7x + 3y + 7 = 0 B. 7x – 3y – 11 = 0 C. AÁvZ R¨vwgwZK e¯‘ D. GKUv A‡f` [B]
C. 7x + 3y + 17 = 0 D. 7x – 3y – 17 = 0 [D]
141. mij‡iLv –3x + 2y – 5 = 0 Gi j¤^‡iLvi

128. x Gi †Kvb gv‡bi Rb¨ y  x  1 eµ‡iLvwUi Xvj kb~ ¨ n‡e? Xvj n‡e-
x
A. 2 B. 3
A. x =  2 B. x =  1 3 2

C. x = 1 D. x =  3 [C] C.  2 D.  3 E. 5 [C]
3
129.(1, –3) †K›`ª wewkó Ges x A¶‡K ¯úk©Kvix e„‡Ëi mgxKiY Kx? 32

A. x2+ y2 – 2x + 6y + 9 = 0 142. x = 2y mij‡iLvi Xvj n‡”Q-

B. x2 + y2 – 2x + 6y + 10 = 0 A. 1 B. 2
2
C. x2+ y2+ 2x – 6y + 10 = 0

D. x2 + y2 – 2x + 6y + 1 = 0 [D] C. 1 D.  E. 1 [A]

130. 2x  5y + 10 = 0 Øviv wb‡`©wkZ mij‡iLv Ges A¶Øq Øviv †ewóZ 63

wÎfz‡Ri †¶Îdj KZ (eM© GK‡K)? 143. Y + X = 1 Ges Y – X = 1 †iLv `ywUi †Q`we›`y n‡jv-

A. 10 B. 20 A. (1,1) B. (1,0) C. (0,1)

C. 50 D. 5 [D] D. (0, 0) E. †Q`we›`y bvB [C]

144. X-A‡¶i mv‡_ 135 †KvY Drcbœ K‡i gj~ we›`yMvgx mij‡iLvi

131. `yBwU mij‡iLv a1x + b1+y c1 = 0 I a2x +b2y+c2 = 0 ci¯•i j¤^ nIqvi mgxKiY †KvbwU?

kZ© †KvbwU? A. x + y = 1 B. x + y = 0 C. x – y = 0

A. a1a2 + b1b2 = 0 B. a1  b1 D. x – y = 0 E. ï× DËi †bB [B]

a2 b2 145. f‚wg A‡¶i mv‡_ 45 †KvY m„wóKvix gj~ we›`My vgx †iLvi mgxKiY

C. a1a2b1b2 =0 D. a1a2 = b1b2 [A] n‡jv-

132. ax + y + c = 0 Ges x + by –8 = 0 mij‡iLvØq ci¯úi j¤^ n‡j A. Y = X + 1 B. Y = 1 – X C. Y = –1 – X

wb‡gœi †KvbwU mwVK? D. Y = X E. Y = 2X [D]

A. c = 8 B. b = –a 146. m Ges c Gi gvb KZ n‡j, y = mx + c †iLvwU (2, 3) Ges (3, 4)
C. b = a D. b = –c
[B] we›`y w`‡q hv‡e?

133. (2, 5) Ges (5, 6) we›`My vgx mij‡iLv †KvbwU? A. m =1, c = 1 B. m = 2, c = 2

A. x  3y 13  0 B. 3x  y 13  0 C. m = 2, c = 1 D. m = 1, c = 2

C. 3x  y 13  0 D. x  3y 13  0 [A] E. m = 2, c = 3 [A]

134. y- A‡¶i mgvšÍivj GKwU mij‡iLvi mgxKiY n‡”Q- 147. 3x – 4y – 12 = 0 mij †iLvi Xvj-

A. 3y  2  0 B. 3x  2  0 A. 4/3 B. –4/3 C. 3/4
D. –3/4
E. †KvbwUB bq [C]

C. 3y  2x  0 D. 3y  2x 1  0 [B] 148.4x + 4y + 3 = 0 Ges x + ay = 0 mij‡iLvØq ci¯úi j¤^ n‡j a Gi

135. a1x  b1y  c1  0 Ges a2x + b2y + c2= 0 mij‡iLv Øq ci¯úi j¤^ gvb n‡e-
n‡e hw`-
A. –2 B. 4/5

A. a1a2  b1b2  0 B. a1a2  b1b2  0 C. –1 D. 1 E. 5/3 [C]

C. a1b1  a2b2  0 D. a1b1  a2b2  0 [A] 149. y + x = 0 mij‡iLvwU x-A‡¶i abvZKœ w`‡Ki mwnZ †h †Kv‡b

136. 2x – 3y + 5 = 0 Ges x + ay – 1 = 0 j¤^vjw¤^ nIqvi Rb¨ a Gi Ae¯’vb K‡i Zv nj-

gvb n‡”Q- A. 75 B. 60

A.  2 B.  3 C.  2 2 C. 45 D. 135 E. 120 [D]
D. [D]
3 2 33 150. †h mij‡iLvwU y-A‡¶i Dci j¤^, Zvi mgxKiYwU n‡e-

137. 2x + y = 8 Ges x + 2y = 10 mij‡iLv Ø‡qi †Q`we›`-y A. 2y + 3 = 0 B. 2x = 3 C. 2x + 2y = 3

A. (4,3) B. (3,3) D. 2x – 2y = 3 E. x + 1 = 0 [A]

C. (3,4) D. (2,4) [D] 151. 4x  5y + 9 = 0 mij †iLvwU A¶ `Õy wU †_‡K wK cwigvY Ask †Q`

138. x – y = 0 mij‡iLvwU x-A‡¶i abvZ¥K w`‡Ki m‡½ KZ wWMÖx †Kv‡Y K‡i?

Ae¯’vb K‡i? A. (4/9, 5/9) B. (9/4, 9/5) C. (9/4, 9/5)

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D. (4/9, 5/9) E. (9/4, 5/9) [B] A. a1  b1  c1 B. a1  c1
a2 b2 c2 a2 c2
152.y = mx + c mij‡iLvwU x2 + y2 = a2 eË„ ‡K ¯úk© Kivi kZ© n‡”Q-

A. c  a 1  m B. c  a 1  m 2 C. b1 D. b1  c1 E. a1
b2 b2 c2 a2
C. c  a 1  m 2 D. c  a 1  m 2 [A]

E. c  a 1  m 2 [B] 164. 3x + 5y – 15 = 0 Øviv wb‡`©wkZ †iLvwUi x-A‡¶i LwÐZ Ask Ges

153.a2x + b2y + c = 0 (a,b,c aªæeK) mgxKiYwUi R¨vwgwZK cwiPq n‡jv- y-A‡¶i LwÐZ Ask h_vµ‡g-

A. e„Ë B. civeË„ C. mij‡iLv A. (15, 0) B. (0, 15)

D. Dce„Ë E. †KvbwU bq [C] C. (3, 5) D. (5, 3) E. (–5, –3) [D]

154.GKwU mij †iLvi Xvj LwÐZvsk h_vµ‡g 0.5 I –5; mij †iLvwUi 165. GKwU mij †iLv x-A‡¶i mv‡_ 30 †KvY K‡i y-A¶‡K –5 GKK we›`y

mgxKiY †KvbwU? w`‡q †Q` K‡i †M‡j mij‡iLvwUi mgxKiY †KvbwU?

A. y = 5x + 0.5 B. y = 0.5x – 5 C. y – 5x + 0.5 = 0 A. x – 3y + 5 = 0 B. 3x – y – 5 = 0
C. x + 3y – 53 = 0 D. 3x + y – 53 = 0
D. y + 5x + 0.5 = 0 E. †KvbwUB bq [B] E. x – 3y – 53 = 0 [E]

155.5x + 8y – 40 = 0 mgxKiY Øviv wb‡`©wkZ mij †iLvi mgvšÍivj 166. x = – 2 n‡j y = x †iLvwUi Xvj n‡e-
3x  2
†iLvi D`vniY-

A. 5x + 8y – 30 = 0 B. x + 8y – 40 = 0 A. 1/2 B. 1/8

C. 2x + 8y – 40 = 0 D. 8x– 5y– 40 = 0 C. 1/6 D. 1/4 E. 1/9 [A]

E. †KvbwUB mwVK bq [A] 167. hw` x0 Ges x1 h_vµ‡g PjK x Gi cÖv_wgK I P‚ovšÍ gvb nq, Z‡e

156.2x + 3y – 6 = 0 Øviv wb‡`©wkZ †iLvwUi x-A‡¶i LwÐZ Ask I y x Gi Av‡cw¶K cwieZ©b n‡e-

A‡¶i LwÐZ Ask h_vµ‡g: A. x1 – x0 B. x0 – x1 C. x1  x0
x0
A. (3, 2) B. (2, 3)

C. (6, 0) D. 0, 6 E. (–3, 2) [A] D. x0 E. x1  x0 .100 [C]
x1  x0 x0
157.GKwU mij †iLv (5, 7) Ges (2, 4) `ywU wbw`©ó we›`y w`‡q AwZµg K‡i Ges

Dnv x-A‡¶i mv‡_ †h abvZ¥K †KvY Drcbœ K‡i Zvnv- 168. y = 3x + 3 †iLvwU x A¶‡K †Q` K‡i †Kvb we›`‡y Z?

A. 30 B. 45 A. (3, 0) B. (1, 0)

C. 60 D. 90 E. 120 [B] C. (–1, 0) D. (–3, 0) E. (1/2, 0) [C]

158.y = kx (1 + x) eµ‡iLvwUi (3, 0) we›`y‡Z ¯úk©K x-A‡¶i mv‡_ 30 169. x A‡¶i Dci Aew¯’Z P we›`y †_‡K (0, 2) I (6, 4) we›`y `By wU

†KvY Drcbœ Ki‡j k Gi gvb KZ? mg`~ieZ©x n‡j P we›`yi ¯’vbv¼ KZ?

A. 1 B. 7 A. (2, 3) B. (3, 0)

73 3 C. (5, 0) D. (4, 0) E. (5, 3) [D]

170. 3x + 2y + c = 0, 2x – ay + 7 = 0 mij †iLvØq ci¯úi j¤^ n‡e

C. 7 3 D. 1 E. 3 7 [A] hw`-

3 A. a = 3 B. a = – 3 C. a = 2

159.(–2, 3) we›`yMvgx Ges x-A‡¶i mv‡_ 135 †KvY DrcbœKvix D. a = – 2 E. †KvbwUB bq [A]

mij‡iLvi mgxKiY †KvbwU? 171.4x  2y  15 = 0 mij †iLvi Xvj KZ?

A. y = –x + c B. x + y + 1 = 0 C. x + y – 1 = 0 A. 1/2 B. 2

D. y = x E. x – y + 1 = 0 [C] C. 3/4 D. 4/3 E. 0 [B]

160. x  5 mij‡iLvwU x-A¶‡K KZ wWMÖx †Kv‡Y †Q` K‡i? 172.GKwU mij‡iLvi A¶`By wUi ga¨eZ©x LwÐZ Ask (3, 3) we›`y‡Z
2
mgwØwef³ n‡j Zvi mgxKiY-
A. 0 B. 30
A. 3x + 2y = 12 B. 2x + 3y = 12
C. 45 D. 60 E. 90 [E]
C. 2x + 2y = 12 D. 3x + 2y = 8
161.`yBwU mij †iLvi Xvj h_vµ‡g 3 Ges 1 n‡j Dnv‡`i g‡a¨
3 E. 2x + 3y = 8 [C]

AšÍfz©³ †KvY n‡e- 173.(5, 7) I (2, 4) we›`My vgx †iLvi Xvj Ges Dnv x-A‡¶i mwnZ †h

A. 0 B. 30 abvZ¥K †KvY Drcbœ K‡i nv n‡e-

C. 45 D. 60 E. 90 [B] A.  1 , 30o  B. (1, 90) C. (0, 45)
2 
162. M (4, 11) Ges N(–2, 2) `By wU we›`y. (MN) mij‡iLvi j¤^

mgwØLÛ‡Ki mgxKiY n‡e- D. (1, 45) E. †KvbwUB b‡n [D]

A. 9x – 6y + 30 = 0 B. 6x + 9y + 30 = 0 174.GKwU mij‡iLv gj~ we›`y w`‡q hvq Ges x-A‡¶i mv‡_ 135 †KvY
C. 6x + 3y – 65 = 0 D. 12x + 18y – 129 = 0
E. 12x – 18y + 129 = 0 [D] Drcbœ K‡i. Zvi mgxKiY n‡e

163. a1x + b1y + c1 = 0 Ges a2x + b2y + c2 = 0 GKB mij‡iLv wb‡`©k A. x = 0 B. x 3y = 0

K‡i hLb- C. x + 3y = 0 D. x + y = 0

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E. †KvbwUB b‡n [D]  A. 2 2,0  B. 2,0
 C. 0,2 2
175.x-Gi †Kvb abvZ¥K gv‡bi Rb¨ y  x  1 ‡iLvwUi Xvj k~b¨ n‡e- D. (0, 2) [A]
x
186. GKwU mij †iLv hv (2,0) we›`y w`‡q hvq Ges A¶Ø‡qi mv‡_ c_Ö g
A. 1 B. 2 C. 2
PZ_z ©vs‡k 8 eM© GKK †¶Îdj wewkó GKwU wÎfRz MVb K‡i. D³

1 E. †KvbwUB bq [A] mij‡iLvi mgxKiY n‡e-

D. A. 4x + y = 8 B. 4x – y = 8
2
D. 6x – y = 8
176.y = x3 3x2 1 eµ‡iLvq (1, 3) we›`‡y Z Aw¼Z ¯úk©‡Ki Xvj wbY©q C. 2x + y = 4 [A]

Ki| 187. x  y †_‡K wb‡Pi †KvbwU wb‡`©wkZ nq?

A. 6 B. 3 A. x = y B. x = –y

C. 2 D. 4 E. 0 [B] C. x  1 D. †KvbwUB bq [C]

177. y  2x = 5 Ges 3y  x = 6 †iLv`ywUi ga¨eZx© †KvY KZ? y

A. 30 B. 90 188. (0,0) I (4,6) we›`yØq 2x + py +4 = 0 †iLvi wecixZ cv‡k¦© Aew¯’Z
n‡j p Gi gvb KZ?
C. 45 D. 90 E. 0 [C]

178. `yÕwU mij‡iLv ci¯úi mgvšÍivj Ae¯’v‡bi kZ© †KvbwU? A. p > 6 B. p > 4

A. m1 + m2 = 0 B. m1m2 = 1 C. 4 < P < 6 D. p < -2 [D]

C. m1 = m2 D. m1m2 = 1 189.A (1, 1), B(3, 4) Ges C(5, -2) ABC wÎf‡z Ri kxl©Îq. AB I AC

E. m1 + m2 = 1 [C] Gi ga¨we›`Øy ‡qi ms‡hvRK mij‡iLvi Xvj KZ?

179. mij‡iLvi mgxKiY¸‡jv i) 2x + 3y = 2, ii) y=2 n‡j, Xvj KZ? A. 3 B. –3 [B]
C. 3/2 D. –3/4

190.a Gi gvb KZ n‡j 2x - 3y + 5 = 0 Ges ax + 4y +11 = 0 †iLvØq

A. 2 / 3,0 B. 1/ 3,0 ci¯úi j¤^ n‡e?

C. 3 / 2,0 D. 3 / 4,0 A. 3 B. –3

E. 3/ 2,  3/ 4 C. 6 D. 8 [C]

[A] 191. 4y = 3x †iLvi mv‡_ mgvšÍivj Ges (1, 2) we›`y †_‡K 2 GKK `~‡i

180. 'm' Gi gvb KZ n‡j mgxKiY [mx  8  6  7(x  3)] Gi †iLvØ‡qi mxgKiY nÕj-

mgvavb m¤¢e bq? A. 3x + 4y +6 = 0 Ges 3x + 4y – 4 = 0

A. 3 B.7 B. 3x – 4y – 15 = 0 Ges 3x – 4y +5 = 0

C. 7 D. 0 E. 1 [C] C. 3x – 4y – 15 = 0 Ges 3x – 4y – 5 = 0

181. mij‡iLvi mgxKiY †KvbwU hv y A¶‡K 8 †Q‡` K‡i Ges x-A‡¶i D. 3x – 4y + 15 = 0 Ges 3x – 4y – 5 = 0 [D]

mv‡_ 45 †njv‡bv Ae¯’vq Av‡Q? 192.mij‡iLv 4x + 5y – 20 = 0 Øviv A¶Ø‡qi ga¨eZ©x LwÛZ As‡ki ˆ`N©¨-

A. x + y + 8 = 0 B. 3x + 8y = 1 A. 41 B. 21
C. x  y = 8 D. y = 8
E. x = 8 [C] C. 15 D. 23 [A]
 193. 3,1 we›`y n‡Z x 3  y  8  0 mij‡iLvi Dci AswKZ

182. 3x – 2y = 1 Ges 6x – 4y + 9 †iLvØ‡qi ga¨eZ©x j¤^`i~ Z-¡ j‡¤^i ˆ`N©¨-

11 11 A. 3 B. 4
A. B.
C. 5 D. 6 [C]
13 2 13
194.5x – 12y – 9 = 0 mij‡iLvi mgvšÍivj, x2 + y2 – 8x – 10y – 8 = 0 e„‡Ëi

22 11 [B] ¯úk©‡Ki mgxKiY-
C. D.
A. 5x – 12y + 131 = 0, 5x – 12y – 51 = 0
13 4 13
B. 5x – 12y = 0, 5x – 12y – 1 = 0
183. y = 3x + 2, y = –3x + 2 Ges y = –2 Øviv MwVZ R¨vwgwZK wPÎ C. 5x – 12y + 31 = 0, 5x – 12y – 5 = 0
D. 5x – 12y + 1 = 0, 5x – 12y = 0
†KvbwU n‡e? [A]

A. mg‡KvYx wÎfzR B. mgevû wÎfzR 195.3x + 4y 12 = 0 †iLvi (0, 3) we›`y w`‡q AvKu v j‡¤^i mgxKiY-

C. mgwØevû wÎfzR D. welgevû wÎfRz [C] A. 4x – 3y + 9 = 0 B. 3 y  4x  9 = 0

184. †h mij‡iLvwU x-A¶ †_‡K 2 GKK cwigvY Ask †Q` K‡i Ges (3, C. 4x + 3y  9 = 0 D. 3y + 4x  9 = 0 [A]
1) we›`y w`‡q hvq, Zvi Xvj-
196.3y + 4x  12 = 0 mij‡iLv w`‡q x Ges y A‡¶i gvSLv‡bi LwÐZ

A. 1 B. -1 As‡ki ˆ`N©¨-

C. 3 1 [A] A. 5 B. 7
D.
C. 12 D. 25 [A]
3
197.KZfv‡e 50 msL¨vwU‡K `yÕwU cvÖ Bg msL¨vi †hvMdj wn‡m‡e cÖKvk
185.GKwU mij‡iLv x A‡¶i mv‡_ 45 †KvY Drcbœ K‡i Ges g~j we›`y
n‡Z D³ mij †iLvi `i~ Z¡ 2 GKK. mij †iLvwU x-A‡¶i †Kvb Kiv hvq?

we›`y‡Z †Q` K‡i? A. 2 B. 3
C. 4 D. 5 [C]

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198.ABCD PZfz y©‡Ri A, B, C, D we›`y PviwUi ¯’vbvsK h_vµ‡g A(6, 211. 5x – 2y + 7 = 0 mij‡iLvi Dci j¤^ Ges (–3, 1) we›`y w`‡q
5), B(1, 1), C(15, 1) Ges D (10, 5), PZzf©Ry wU‡K mgvb †¶Îdj
wewkó `yBfv‡M wef³Kvix y A‡¶i mgvšÍivj mij‡iLv †KvbwU? AwZµg K‡i Ggb GKwU mij‡iLvi mgxKiY-

A. 2x + 5y + 1 = 0 B. 2x – 5y + 1 = 0

A. 2x  3y = 5 B. y  8 = 0 C. 2x + 5y – 1 = 0 D. 2x – 5y – 1 = 0 [A]

C. x  y = 0 D. x  8 = 0 [D] 212. 2y + x – 5 = 0, y + 2x – 7 = 0 Ges x – y + 1 = 0 Øviv MwVZ

199. `Õy wU mij‡iLv 2x + 3y  5 = 0 I 3x + 2y  7 = 0 †iLv `Õy wUi m‡½ wÎfz‡Ri †¶Îdj KZ?

mgvb †KvY K‡i| GB `ywU mij‡iLvi ga¨eZx© †KvY KZ? A. 1/2 B. 3/2 C. 2 D. 5/2 [C]

A. 90 B. 180 213. 2y + 5 = 0 †iLvwU †Kvb A‡¶i mgvšÍivj?

C. 0 D. 45 E. 60 [A] A. xA¶ B. yA¶

200.(0, 2) we›`wy U y = 5x2 + 3x + c eµ‡iLvi Dci Aew¯’Z| H we›`‡y Z C. †Kvb A¶B b‡n D. Dfq A‡¶i [C]

eµ‡iLvi Dci Aw¼Z ¯úl©K ax + cy + 1 = 0 †iLvi mgvšÍivj n‡j 214. GKwU mij †iLvi Xvj 5 Ges y A‡¶i LwÐZ Ask 3 n‡j †iLvwUi

a Gi gvb KZ? 7

A. 10 B. 6 mgxKiY KZ?

C. 3 D. –3 E. –6 [E] A. 7x  5y = 21 B. 5x  7y = 21

201.gj~ we›`yMvgx GKwU mij‡iLvi mgxKiY wb‡Pi †Kvb&wU, hv (-1, -2) I C. 5x + 7y = 21 D. 7x + 5y = 21 [B]
[C]
(1, 2) we›`yMvgx mij‡iLvi Ici j¤^? 215. 2y  x = 6 †iLvwUi Øviv y A‡¶i †Q`vsk KZ?

A. y = – 3x/2 B. y = – x/2 A. 6 B. 7 C. 3 D. 4

C. y = – x D. y = – 2x 216. mij †iLvi Xvj AvKv‡ii mvaviY mgxKiY n‡jv-

E. y = – x/4 [B]

202. 3x + by + 1 = 0 Ges ax + 6y + 1 = 0 mgvšÍivj n‡j- A. y = 3x + 4 B. 3y = 7 + 2 x
3
A. ab = 12 B. 2ab = 1
C. y = mx + c D. y = 4x [C]
C. a + b = 3 D. ab = 18 [D]
217. a Gi gvb KZ n‡j 2x  y + 3 = 0 Ges 3x + ay  2 = 0 †iLvØq
203. (5, 7) Ges (2, 4) `yBwU we›`y w`‡q AwZµgKvix mij‡iLvi Xvj n‡e-
ci¯úi j¤^ n‡e?
A. 1 B. 5

C. 7 D. 11 [A] A. 6 B. 5 C. 10 D. 6 [D]

204. a Gi gvb KZ n‡j 2x – y +3 = 0 Ges 3x + ay – 2 = 0 mij‡iLv `By wU 218. 2x  5y + 1 = 0 Ges x + y + 4 = 0 mij‡iLvØ‡qi †Q`we›`yi ¯’vbv¼

ci¯úi j¤^ n‡e? KZ?

A. 2 B. –3 A. (3, 2) B. (3, 1)

C. 6 D. –6 [C] C. (1, 3) D. (3, 1) [B]

205. wK k‡Z© a1x + b1y + c1 = 0 Ges a2x + b2y + c2 = 0 †iLv `By wU 219. m I c -Gi gvb KZ n‡j y = mx+c †iLvwU (2, 3) I (3, 4) we›`y

mgvšÍivj n‡e? w`‡q hv‡e?

A. a1b2 = a2b1 B. a1a2 = b1b2 [A] A. m = 1, c = 1 B. m = 1, c = 2 [A]
C. a1a2 = -b1b2 C. m = 2, c = 1 D. m = 2, c = 2
D. †KvbwUB bq

206. †Kvb mgxKiYwU y-A¶‡K gj~ we›`yi 5 GKK wb‡P †Q` K‡i Ges x- 220. y = x eµ‡iLvi Dci †Kvb we›`‡y Z ¯úk©K x-A‡¶i mv‡_ 45
†KvY ˆZix K‡i?
A‡¶i mv‡_ 60 †KvY Drcbœ K‡i?

A. y  1 B. y  1 A.  1 ,  1  B.  1 ,  1 
3x  5 3x  5 2 4
4 2

C. y  3x  5 D. y  3x  5 [C] C.  1 ,  1  D.  1 ,  1  [A]
2 3 3 5
207. (0, -a) Ges (b, 0) we›`y w`‡q AwZµg K‡i Ggb mij‡iLvi mgxKiY

n‡e †KvbwU? 221. GKwU mij‡iLv gj~ we›`y w`‡q hvq Ges x- A‡¶i mv‡_ 90 †KvY

A. ax – by = ab B. bx – ay =0 Drcbœ K‡i, Zvi mgxKiY †KvbwU?
C. ax – by = 0 D. bx + ay = 0
[A] A. x = 0 B. y = 0 C. x = 1 D. y = 1 [A]

208. 3x + 4y = 7 mij‡iLvi Dci j¤^ Ges (1, -2) we›`yMvgx mij‡iLvi 222. GKwU mij‡iLvi `ywU A‡¶i †Q`vskØ‡qi mgwó I AšÍi h_vµ‡g 9

mgxKiY n‡e †KvbwU? I 5| H mij‡iLvi mgxKiY †KvbwU?

A. 4x + 3y + 2 = 0 B. 4x – 3y = 10 A. 2x + 7y = 14 B. x + 8y = 8

C. 3x + 4y + 5 = 0 D. 4x – 3y = 5 [B] C. 5x + 4y = 20 D. 3x + 6y = 15 [A]

209. (4, -2) we›`y †_‡K 5x + 12y = 3 †iLvi Dci Aw¼Z j‡¤^i ˆ`N©¨- 223. 2x + y + 7 =0 Ges 3x + ky 5 =0 †iLv `wy U ci¯úi j¤^ n‡j k-

A. 8 B. 8 C. 3 D. 7 [D] Gi gvb KZ?
9 7 13
A. 8 B. 6 C. 5 D. 6 [B]
210. y2 = 4ax Ges y = mx + c mgxKiYØq n‡Z cvÖ ß x Gi mgvb n‡j,
224. †Kvb mij‡iLv (3, 5) we›`y w`qv AwZµg K‡i Ges A¶ `ywU †_‡K
c=
B. a/m wecixZ wPý wewkó mggv‡bi Ask †Q` K‡i| mij‡iLvwUi mgxKiY
A. m/a

C. a2 D. m2 [D] †KvbwU?
m2 a2
A. x + y  3 = 0 B. 2x + y + 2 = 0

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C. x + 3y + 1 = 0 D. x  y + 2 = 0 [D] A. x = 4 B. y = 2

225. 3x  7y + 2 = 0 mij‡iLvi Dci j¤^ Ges (1, 2) we›`y w`‡q AwZµg C. y -7 = 0 D. y = b [A]

K‡i Ggb GKwU mij‡iLvi mgxKiY †KvbwU? 240. x I y A¶Ø‡qi †Q`vsk 7 I 5 n‡j, †iLvwUi mgxKiY KZ?

A. 3x + 7y  13 = 0 B. 7x + 3y  13 = 0 A. 7x – 5y = 35 B. 5x + 7y – 35 = 0
C. 5x – 7y – 15 = 0 D. –7x + 5y = – 35 [B]

C. 7x + 3y + 13 = 0 D. 7x  3y  13 = 0 [B] 241. y = mx + c GB mgxKi‡Y c n‡jv-

226.  m¶~ ¥‡KvY n‡j, xcos  + ysin  = 4 Ges 4x + 3y = 5 A. x A‡¶i LwÐZ Ask B. y A‡¶i LwÐZ Ask

mgvšÍivj †iLvØ‡qi `~iZ¦ KZ? C. Dfq A‡¶i LwÐZ Ask b‡n D. †KvbwUB b‡n [B]

A. 5 GKK B. 5 GKK 242. x  y  1 mgxKi‡Y b n‡jv-

C. 3 GKK D. 9 GKK [A] ba

227. px + qy + 12 = 0 Ges px + qy + 20 = 0 †iLvØ‡qi AšÍf©z³ †KvY? A. y A‡¶i LwÐZ Ask B. x A‡¶i LwÐZ Ask

A.  /3 B. /2 C. †Kvb A‡¶i LwÐZ Ask b‡n D. GKwU aªæeK [B]
C. 
D. †KvbwUB b‡n [D] 243. 3y  x  5  0 mij †iLvwU x A‡¶i ms‡M †h †KvY Drcbœ K‡i
Zvi gvb-
228. x + y = 0 †iLvwUi Xvj KZ?
A. 45 B. 60
A. 0 B. 1
C. 1 [C] C. 30 D. 90 [C]
D. †KvbwUB b‡n
244. y = 1 mij †iLvwUi Xvj-
229. y-A‡¶i Xvj KZ?
A. 30 B. 45

A. 0 B. 1 C. 0 D. 60 [C]
C. 1
D. AmsÁvwqZ [D] 245. x A‡¶i mgxKiY-

230. 2x + 3y 1 = 0 Ges x 2y +3 = 0 †iLvØ‡qi AšÍfz©³ m¶~ ¥‡KvY A. x = 0 B. x = – y

wbY©q Ki| C. y = 0 D. y = b [C]

246. (4, 7) we›`yMvgx Ges y A‡¶i mgvšÍivj mij †iLvwUi mgxKiY-

A. tan 1 3 B. tan 1 7 A. y = 7 B. y = 3
4 4
C. x = 11 D. x = 4 [D]

C. tan 1 4 D. tan 1 4 247. x cos + y sin = k n‡j k
7 3
[B] A. gj~ we›`y †_‡K mij †iLvwUi j¤^`i~ Z¡

231. 3x – 4y – 12 = 0 †iLvi Xvj KZ n‡e? B. ci¯ú‡ii Dci j¤^

C. ci¯úi  †Kv‡Y †Q` K‡i D. j¤^‡iLvwUi Xvj [A]

A. 3/4 B. -3/4 C. 4/3 D. -4/3 [A] 248. 7x + 5y + 8 = 0 mij‡iLvwU A¶Øq †_‡K †Qw`Z As‡ki cwigvY-

232. y – 3x – 5 = 0 I 3y – x + 6 = 0 †iLvØ‡qi ga¨eZ©x m¶~ ¥ †KvY B.   7 , 5 
 8 8
KZ? A. (7, 5)

A. 90 B. 60 C. 45 D. 30 [D] C.  1 , 1  D.   8  8 
9 5  7 5
233. (–2, –5) we›`y w`qv AwZµgKvix †iLv A¶Øq‡K h_vµ‡g A I B [D]

we›`‡y Z †Q` K‡i| hw` OA + 2OB = 0 nq Z‡e Dnvi mgxKiY- 249. gj~ we›`y †_‡K †Kvb mij‡iLvi Dci AswKZ j‡¤^i ˆ`N©¨ 3 GKK mij

A. x + y = 2 B. x – 2y = 4 [C] †iLvwUi mgxKiY-
C. x – 2y = 8 D. x – 2y + 5 = 0
B. x cos + ysin = 3
234. 5x + 4y = 20 †iLv, x A¶ I y A¶ Øviv Ave× †¶‡Îi †¶Îdj- A. y = 3x

A. 10 eM© GKK B. 12 eM© GKK C. 3x + y = 6 D. x + 3y = 6 [B]

C. 9 eM© GKK D. 8 eM© GKK 250. 2x – y + 7 = 0 Ges 3x + ky – 5 = 0 ci¯úi j¤^ n‡j k = ?

[A] A. 5 B. 6 C. 7 D. 4 [B]

235. (2, 2) we›`y †_‡K 4y + 3x + 1 = 0 †iLvi j¤^ `~iZ¡ KZ? 251. 4x  3y + 2 = 0 Ges 8x  6y  9 = 0 mgvšÍivj †iLvØ‡qi ga¨eZx©

A. 5 GKK B. 4 GKK `~iZ¦ n‡e-

C. 2 GKK D. 3 GKK [D] A. 31/13 B. 10

236. a1x + b1y +c1 = 0 I a2x + b2y +c2 = 0 †iLvØq ci¯úi mgvšÍivj C. 7/13 D. 13/10 [D]

252.2x + 3y + 5 = 0 Ges 3x + ky + 6 = 0 †iLvØq j¤^ n‡j k Gi gvb

n‡j- KZ?

A. a1b2 = a2b1 B. a1b1 = a2b2 A. 2 B. 3 C. 2 D. 3 [C]
D. a1c1 = a2c2
C. b1c1 = b2c2 [A] 253.(4,–2) we›`y †_‡K 5x +12y = 3 †iLvi Dci j‡¤^i ˆ`N¨ KZ?

237. y A‡¶i mgxKiY †KvbwU? 83 7
A. 8 B. 49 C. 7 D. 13 [D]
A. y = a B. x = b C. x = 0 D. y = 0 [C]

238. x A‡¶i mgvšÍivj †iLvi mgxKiY †KvbwU? 254.(4, 7) we›`My vgx j¤^‡iLvi mgxKiY †KvbwU?

A. x = 4 B. x = 0 A. y = x + 3 B. x = 4
C. y = 7
C. y – 2 = 0 D. y = x [C] D. †KvbwUB bq [A]

239. y A‡¶i mgvšÍivj †iLvi mgxKiY †KvbwU?

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255.y = x + c †iLvwU x2 + y2 = 42 e„‡Ëi ¯úk©K nIqvi kZ© n‡e- 265.(1, –1) we›`yMvgx Ges 2x – 3y + 6 = 0 †iLvi Dci j¤^ mij‡iLvi

A. c =  2 B. c =  8 mgxKiY-

C. c = 4 2 D. c =0 [C] A. 2y – 3x = 1 B. 3y – 2x = –5

256.x cos  + xy sin  = 5 mgxKiYwU GKwU mij‡iLv wb‡`©k K‡i- C. 2y – 3x = 1 D. 3x + 2y –1 = 0 [D]

A. mZ¨ B. wg_¨v 266 (2, 7) we›`yMvgx GKwU mij‡iLvi Xvj 2, mij‡iLvwUi mgxKiY wbY©q
Ki|
C. AvswkK mZ¨ D. †KvbwUB bq [B]

257.x – y 3 = 7 Ges x 3 –y = 5 †iLvØ‡qi AšÍM©Z †KvY KZ? A. y = 2x + 3 B. x=2y+4
C. 2y = 7x + 9
A. 30˚ B. 45˚ C. 60˚ D. 120˚ [A] D. †KvbwUB bq [A]

258.`yBwU †iLv ci¯úi j¤^ n‡j wb‡gœi †Kvb kZ©wU mwVK?

A. m1 = m2 B. m1m2 + 1 = 0 267. (2, 4) we›`My vgx I x-A‡¶i Dci j¤^ mij‡iLvi mgxKiY-
C. 1  1  1
D. 1  m1  m2 A. x = 2 B. y = 4
m1 m2 m1m2
C. x = 4 D. y = 2 [A]

[B] 268.y A‡¶i mv‡c‡¶ (–3, –2) Gi cÖwZwe‡¤^i ¯’vbvsK KZ?
259.3x – 4y = 12 Ges 3x – 3 = 4y †iLvØ‡qi g‡a¨ `~iZ¡ KZ? (13-14)

59 A. (3, 2) B. (–3, –2)
A. 9 B. 5
C. (2, 3) D. (3, –2) [D]

12 5 [B] 269.g~jwe›`y I (–4, 4) we›`y ms‡hvMKvix mij‡iLvi mgxKiY †KvbwU-
C. 5 D. 12
A. x – y = 0 B. 2x + y = 0
260.y-A‡¶i Dcwiw¯’Z †h we›`y¸‡jv n‡j 4x – 3y = 10 †iLvi j¤^`i~ Z¡ 4
C. x + y = 0 D. x + 2y = 0 [C]

GKK, cÖ_g PZzf©v‡M Zv‡`i ¯’vbvsK KZ? (13-14) 270.x- A‡¶i †Kv_vq y = 3x  2 mgxKiYwU †Q` Ki‡e?

A. (0, 10/3) B. (2, 3/10) A.  2 ,0 B. 0, 3 
3   2
C. (3, 10) D. (2, 3) [A]

261.x – y = 1 mgxKiYwUi †¶‡Î †KvbwU mwVK? (13-14) C. (2, 0 ) D. (3, 0) [A]

A. x A‡¶i FYvÍK w`‡Ki mv‡_ 45 †KvY Drcbœ K‡i 271.(4, 5) we›`y w`‡q hvq Ges x  3y = 7 Gi mgvšÍivj †iLvi mgxKiY

B. x A‡¶i abvÍK w`‡Ki mv‡_ 135 †KvY Drcbœ K‡i KZ?

A. 3x  y  7 = 0 B. x + y 9 = 0

C. x A‡¶i FYvÍK w`‡Ki mv‡_ 135 †KvY Drcbœ K‡i C. x  3y + 11 = 0 D. 2x 3y 7 = 0 [C]

D. gj~ we›`yMvgx mij‡iLv [A] 272.2x  5y = 1 I 5x + 5y = 3 †iLvØq †Kvb PZfy ©v‡M †Q` Ki‡e?

262.x A‡¶i mv‡_ 30 I 60 †Kv‡Y `wy U mij‡iLv Uvbv n‡j Zv‡`i g‡a¨ A. I B. II

AšÍf³‚© †Kvb KZ n‡e? (13-14) C. II D. IV [A]

273.9x  4y = 10 I 6x + 4y = 15 †iLvØ‡qi †Q` we›`yi x ¯’vbvsK I y

A. 30 B. 40 C. 45 D. 50 [A] ¯’vbv‡¼i †hvMdj KZ?

263.gj~ we›`y †_‡K †Kvb mij‡iLvi Dci AswKZ j‡¤^i ˆ`N©¨ 3 GKK Ges Zv x A. 25 B. 23
6 6
A‡¶i mv‡_ 150 †KvY Drcbœ Ki‡j mij‡iLvwUi mgxKiY n‡e- (13-
C. 20 D. 35
14) 7 12 [D]

A. y = 3x + 6 B. x = 3y + 6 274.Ggb GKwU mij‡Lvi mgxKiY wbY©q Ki hv (3, 0) we›`yMvgx I 2x +

C. y = x – 6 5y = 13 †iLvi Dci j¤^|
3
D. 3y = x + 6 [A] A. 5x 2y +3 = 0 B. 5x  y 15 = 0

264.3x – 4y = 2 Ges 4x – 3y + 1 = 0 †iLvØ‡qi ga¨eZx© m~¶¥‡Kv‡Yi C. 5x  2y 15 = 0 D. 5x 2y 3 = 0 [C]

mgwØLÛ‡Ki mgxKiY n‡e- (13-14) 275. 2x  3y +6 = 0 †iLvwU-

A. Ea©Mvgx B. wbgœMvgx

A. 3x – 4y = 2 B. 7x + 7y = 0 C. Abyf‚wgK D. Djø¤^ [A]

C. 7x – 7y – 1 = 0 D. 2x + 4y + 1 = 0 [C] 276. (4, 5) we›`My vgx x-A‡¶i Dci j¤^ mij‡iLvi mgxKiY-

A. y + 5 = 0 B. x  4 = 0

C. y  5 = 0 D. x + 4 = 0 [B]

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277.†Kvb mij‡iLv x-A‡¶i abvZ¥K w`‡Ki mv‡_ 60˚ †KvY ˆZwi Ki‡j C. (0, 7/2) D. (7/2, 0) [C]
Gi Xvj KZ n‡e?
A. 3 B. 2 287 . gj~ we›`y n‡Z †Kvb mij‡iLvi j‡¤^i ˆ`N©¨ 4 GKK Ges A‡¶i mv‡_

H j‡¤^i bwZ 120 n‡j H mij‡iLvi mgxKiY n‡e-

C. 3 D. 2 [C] A. x  3y  8  0 B. x  3y  4  0

278.y-A‡¶i mgvšÍivj †iLvi mgxKiY wK? C. x  3y  5  0 D. x  3xy  8  0 [A]

A. x = 0 B. y = a

C. x = a D. y = 0 [C] 288. a Gi gvb KZ n‡j A(a, 2a) B (2, 3) we›`yØ‡qi ms‡hvM †iLv 4x
+ 3y+5 = 0 †iLvi Dci j¤^ n‡e?
279. gj~ we›`y (0, 0) I (2, 3) we›`yi ms‡hvMKvix †iLvi mgxKiY-

A. y = x B. 3x = 2 A. 5 B. 6
8 10
C. y = 2x + 2 D. y = (3/2)x [D]

280 . wb‡Pi †KvbwU (4, –3) we›`y w`‡q hvq Ges 2x + 11y – 2 = 0 †iLvwUi C. 18 D. 21 [C]
mgvšÍivj? (13-14) 5 5

289. (2, 1) we›`y †_‡K 3x4y+5=0 †iLvi Dci AswKZ j‡¤^i cv`we›`iy

A. 2x + 11y + 25 = 0 B. 2x + 5y + 25 = 0 ¯’vbvsK n‡e-
C. 2x + y + 25 = 0 D. 2x + 11y – 25 = 0
B.  3 ,  4 
E. 2x + 5y + 25 = 0 [A] A.  1 , 7  5 5 
5 5
281.3x – 2y + 5 = Ges x + ay = 0 mij †iLvØq ci¯úi j¤^ n‡j α Gi
C.  1 ,  7  D.   3 , 4 
gvb n‡e- (13-14) 5 5   5 5 [A]

3 B. – 3 C. 2 D. – 2 [C] 290. y = x †iLvwUi Xvj KZ? B. 1
A. 2 3 3 3
A. 1/2
282. 3x – y + 4 = 0 mij †iLvi Xvj- (13-14)

ππ π π C. 3/2 D. 1 [B]
A. 2 B. 2 C. 4 D. 6 [C]
2

283.GKwU mij‡iLv (1, 6) we›`y w`‡q hvq, GwU A¶Øq n‡Z wecixZ wPýwewkó

mggv‡bi Ask †Q` K‡i| †iLvwUi mgxKiY wK n‡e? (13-14)

A. x – y + 2 = 0 B. x + y = 5

C. x – y + 5 = 0 D. x – y – 5 = 0 [C]

284.2x + 3y = 7 Ges 5x – py = 2 mij‡iLv `By wU ci¯úi j¤^ nB‡j p

Gi gvb wbY©q Ki| (13-14)

5
A. 3 B. 17 C. 3

10 E. †KvbwUB bq [D]
D. 3

285. y = 2x †iLvi Xvj-

A. 2 B. 1

C. 2 D. 0 [C]

286. 4x  2y + 7 = 0 mij †iLvi Dci Ggb GKwU we›`y wbY©q Ki hv (2,

3), (2, 4) we›`y `wy U †_‡K mg`~ieZx©-

A. (1, 0) B. (0, 1)

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বৃত্ত Soln: [B]

12. 3x + 2y + k = 0 †iLvwU x2 + y2 – 8x – 2y + 4 = 0 eË„ ‡K ¯úk©

Ki‡j k-Gi GKwU gvb-

1. k-Gi †Kvb gv‡bi Rb¨ (x – y + 3)2 + (kx + 2) (y – 1) = 0 A. 1 B. 27 C. 5 D. –1

Soln: [D]

mgxKiYwU GKwU e„Ë wb‡`©k K‡i? (00-01) 13. (9, 9) I (5, 5) we›`Øy ‡qi ms‡hvRK †iLv‡K e¨vm a‡i Aw¼Z e„‡Ëi

A. 2 B. 1 C. –2 D. –1 mgxKiY-

Soln: [A] A. x2+ y2– 4x + 4y + 90 = 0 B. x2+ y2– 4x + 4y – 90 = 0

2. x2 + y2 – 4x – 6y + c = 0 e„ËwU x A¶‡K ¯ck© K‡i| c-Gi gvb C. x2+ y2+ 4x – 4y – 90 = 0 D. x2+ y2– 4x – 4y + 90 = 0

KZ? (00-01) Soln: [B]

A. 7 B. 4 14. k-Gi †Kvb gv‡bi Rb¨ (x – y + 3)2 + (kx + 2) (y – 1) = 0

C. 5 D. 11 mgxKiYwU GKwU eË„ wb‡`©k K‡i-
Soln: [B]
A. 1 B. –1 C. 2 D. –2
3. x2 + y2 – 6x – 4y + c = 0 eË„ wU y A¶‡K ¯ck© K‡i, c-Gi gvb
Soln: [D]
KZ? (01-02)
15. wb‡gœi †Kvb mgxKiY Øviv wb‡`©wkZ e„‡Ëi ¯úk©K x A¶-

A. 11 B. 7 A. x2 + y2 – 10x – 6y + 9 = 0

C. 5 D. 4 B. x2 + y2 + 10x + 6y + 25 = 0
Soln: [D]
C. x2 + y2 + 6x + 10y + 25 = 0
4. (–9, 9) Ges (5, 5) we›`yØ‡qi ms‡hvRK †iLvsk‡K e¨vm a‡i AswKZ
D. x2 + y2 + 6x + 8y + 25 = 0

e‡„ Ëi mgxKiY- (02-03) Soln: [B]

A. x2+y2– 4x+14y = 0 B. x2+y2– 4x–14y = 0 16. GKwU e„‡Ëi mgxKiY wbY©q Ki hvi †K‡›`ªi ¯’vbv¼ (2, 3) Ges x +
C. x2+y2+4x+14y = 0 D. x2+y2+4x–14y = 0
Soln: [D] y – 2 = 0 †iLvwU eË„ ‡K ¯úk© K‡i|

A. 2(x2+ y2) – 8x – 12y + 17 = 0

5. x2 + y2 24x + 10y = 0 e„‡Ëi e¨vmva©- B. 2(x2 + y2) – 6x – 10y + 15 = 0

A. 7 B. 5 C. 2(x2 + y2) – 4x – 8y + 11 = 0

C. 13 D. 12 D. 2(x2 + y2) – 2x – 6y + 7 = 0

Soln: [C] Soln: [A]

6. (4, 5) †K›`ªwewkó e„Ë hv x2 + y2 + 4x + 6y  12 = 0 e„‡Ëi †K›`ª 17. (2, 4) †K›`ªwewkó I x-A¶‡K ¯úk© K‡i Ggb e‡„ Ëi mgxKiY-

w`‡q Mgb K‡i, Zvi mgxKiY- A. x2 + y2 – 4x – 8y + 16 = 0

B. x2 + y2 – 4x – 8y + 4 = 0

A. x2 + y2  8x + 10y + 59 = 0 C. x2 + y2 – 8x – 4y + 16 = 0

B. x2 + y2  8x  10y + 59 = 0 D. x2 + y2 – 8x – 4y + 4 = 0

C. x2 + y2 + 8x + 10y  59 = 0 Soln: [B]

D. x2 + y2  8x  10y  59 = 0 18. x-A¶‡K (4,0) we›`‡y Z ¯úk© K‡i Ges †K›`ª 5x – 7y + 1 = 0
Soln: [D]
mij‡iLvi Dci Aew¯’Z Ggb e‡„ Ëi mgxKiY n‡e-
7. (5, 0) Ges (0, 5) we›`y‡Z A¶‡iLvØq‡K ¯ck©Kvix e‡„ Ëi mgxKiY-
A. x2 + y2 – 8x – 6y + 9 = 0
A. x2 + y2 – 10x – 10y + 25 = 0 B. x2 + y2 – 8x + 6y + 16 = 0
B. x2 + y2 + 10x + 10y + 25 = 0 C. x2 + y2 – 8x + 6y + 9 = 0
D. x2 + y2 – 8x – 6y + 16 = 0
C. x2 + y2  10x + 10y + 25 = 0
Soln: [D]
D. x2 + y2  10x  10y  25 = 0
Soln: [A] 19. GKK e¨vmv‡a©i e„‡Ë AšÍwj©wLZ GKwU mgevû wÎfz‡Ri evû ˆ`N©¨-

8. (1, 1) Ges (2, 4) we›`Øy ‡qi ms‡hvRK mij †iLvi j¤^ mgwØLÛ‡Ki (13-14)
mgxKiY-
3
A. x + 3y  6 = 0 B. x + y  9 = 0 A. 2 units B. 2 units C. 3 units D. 1 unit

C. x  3y  6 = 0 D. x  5y  6 = 0 Soln: [C]

Soln: [D]

9. x2 + y2  8x  4y + c = 0 e„ËwU x-A¶‡K ¯ck© K‡i c-Gi gvb- 20. wb‡¤œi †Kvb e„ËwU x-Aÿ‡K ¯úk© K‡i?

A. 16 B. 2 C. 4 D. 16 A. x2 + y2 – 2x + 6y + 4 = 0 B. x2 + y2 – 4x + 6y + 5 = 0
C. x2 + y2 – 2x + 6y + 1 = 0 D. 2x2 + 2y2 – 2x + 6y + 3 = 0
Soln: [A]
Soln: [C]
10. x2+ y2 5x = 0 I x2+ y2+ 3x = 0 eË„ Ø‡qi †K‡›`ªi `i~ Z¡–

A. 4 units B. 1 unit

C. 34 units D. 2 units 21. g~jwe›`yMvgx GKwU e‡„ Ëi †K›`ª (4, 3) we›`y‡Z Aew¯’Z| wb‡gœ cÖ`Ë

Soln: [A] we›`¸y ‡jvi g‡a¨ †Kvb we›`ywU e„‡Ëi Dc‡i Aew¯’Z bq?

11. (9, 9 ) I (5, 5) we›`Øy ‡qi ms‡hvRK †iLv‡K e¨vm a‡i AswKZ e„‡Ëi

mgxKiY- A. (–1, 3) B. (9, 3) C. (0, 3) D. (8, 0)

A. x2 + y2 + 4x + 14y = 0 B. x2 + y2 + 4x  14y = 0 Soln:[C]
C. x2 + y2 – 4x + 14y = 0 D. x2 + y2  4x  14y = 0
22. k Gi gvb KZ n‡i 3x + 4y = k mij‡iLv x2 + y2 = 10x eË„ ‡K

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¯úk© Ki‡e? A. x2 + y2  2x + 6y + 9 = 0

A. 40, – 10 B. –40, 10 C. 50, –10 D. –50, 10 B. x2 + y2  2x + 6y + 10 = 0
C. x2 + y2 + 2x  6y + 10 = 0
Soln:[A] D. x2 + y2  2x + 6y + 1 = 0

23. x2 + y2 = b (5x – 12y) e‡„ Ë AswKZ e¨vm g~j we›`y w`‡q hvq| g~j Soln: [D]

we›`‡y Z AswKZ ¯úk©KwUi mgxKiY wbY©q Ki| 34. x2 + y2 –24x + 10y = 0 e„‡Ëi e¨vmva©-
A. 7 B. 5 C. 13
A. 5x + 12y = 0 B. 12x – 5y = 0
Soln: [C]
C. 5x – 12y = 0 D. 6x – 13y = 0 D. 12

Soln:[C]

24. (0, –1) Ges (2, 3) we›`Øy ‡qi ms‡hvM †iLv‡K e¨vm ai AswKZ e„ËwU x 35. x2 + y2 + 4x + 6y – 23 = 0 mgxKiY Øviv m~wPZ e„‡Ëi e¨vm KZ?

A¶ †_‡K †h cwigvY Ask †Q` K‡i Zv n‡”Q- A. 6 GKK B. 8 GKK C. 9 GKK D. 12 GKK

A. 4 B. 2 C. 3 D. 3 2 Soln: [A]

Soln:[A] 36. we›`y e„‡Ëi mgxKiY †KvbwU?

25. g~jwe›`y nB‡Z (h, k) we›`y w`qv MgbKvix †iLv mgy‡ni Dci AswKZ A. x2 + y2 = 0 B. x2 + y2 = 1
C. x2 – y2 = 0 D. x2 – y2 = 1
j‡¤^i cv`we›`iy mÂvi c‡_i mgxKiY †KvbwU?

A. x2 + y2 – hx – ky = 0 B. x2 + y2 – h – 2k = 0 Soln: [A]
D. x2 + y2 - 5h – k = 0
C. x2 + y2 = 2h + k
E. x2 + y2 – 4h - 7k = 0 37. GKwU e„‡Ëi †K‡›`ªi ¯’vbvsK (1,–3) n‡j Ges eË„ wU X- A¶‡K ¯úk©

Soln:[A] Ki‡j, eË„ wUi mgxKiY n‡e:

26. GKwU e„Ë Y A¶‡K gj~ we›`‡y Z ¯úk© K‡i Ges (3, –4) we›`y w`‡q A. x2+ y2+ 2x + 6y + 1 = 0

AwZµg K‡i, eË„ wUi mgxKiY †KvbwU? [KUET 10-10] B. x2+ y2+ 2x – 6y + 1 = 0

A. 3x2 + y2 = 10x B. 4x2 + y2 = x C. x2+ y2– 2x + 6y + 1 = 0

C. x2 + 3y2 = 7x D. 3x2 + y2 = 5x D. x2+ y2– 2x – 6y + 1 = 0

E. 3x2 + 3y2 = 25x E. x2 + y2 + 4x + 8y + 16 = 0 Soln: [C]

Soln:[E] 38. x2 + y2 – 6x – 75 = 0 e„ËwUi †K›`ª n‡”Q-

27. 154 eM© GKK †¶Îdj wewkó e‡„ Ëi e¨vmØq 2x – 3y = 5 Ges 3x – A. (2, 4) B. (3, 0)

C. (4, 3) D. (–3, 4) E. (3,–4)

4y = 7 n‡j e‡„ Ëi mgxKiY n‡e| Soln: [B]

A. x2 + y2 + 2x – 2y = 62 B. x2 + y2 + 2x – y = 47 39. 4x2 + 4y2 = 3 mgxKiYwUi R¨vwgwZK A_©-
C. x2 + y2 – 2x + 2y = 47 D. x2 + y2 – 2x + 2y = 62
A. DceË„ B. cive„Ë

E. None C. Awae„Ë D. e„Ë E. hyMj mij‡iLv

Soln:[C] Soln: [D]

28. k Gi †Kvb gv‡bi Rb¨ x2 + y2 + kx + 2y + 25 = 0, e„ËwU x-A¶‡K 40. z = x + iy n‡j z z = a2 wb‡`©k K‡i-

¯úk© K‡i? A. cive„Ë B. e„Ë

A. 5 B. –5 C. 10 D. None C. AwaeË„ D. DceË„ E. †KvbwU bq

Soln:[C] Soln: [B]

29. †h k‡Z© x + y = 1 †iLvwU x2 + y2 – 2ax = 0 eË„ ‡K ¯úk© Ki‡e Zv 41. x2 – y2 = 0 Gi R¨vwgwZK iƒc n‡jv-

nj- A. cive„Ë B. †Rvov mij‡iLv

A. a2 – 2x = 1 B. a2 + 2a = – 1 C. DceË„ D. Awae„Ë E. †KvbwUB bq
C. a2 + 2a = 1 D. a2 – 2a = –1
Soln: [B]
Soln:[C]
42. a-Gi gvb KZ n‡j (7, a) we›`ywU x2 + y2 – 6x + 4y – 12 = 0 e„‡Ëi

Dci Aew¯’Z n‡e?

30. x2 + y2 – 4x – 6y + 4 = 0 e„ËwU x A‡¶‡K ¯úk© K‡i| ¯úk© we›`iy A. 2 B. 3
¯’vbv¼-
C. 5 D. –5 E. 0

A. (2, 0) B. (3, 0) C. (6.6) D. (4,1) Soln: [D]
Soln: [C]
43. 3x2 + 4y2 = 16 mgxKiY w`‡q Kx †evSvq?

31. (–1, 1) Ges (–7, 3) we›`y w`‡q AwZµgKvix GKwU e„‡Ëi †K‡›`ª 2x A. eË„ B. cive„Ë

+ y = 9 †iLvi Dci Aew¯’Z| e„ËwUi mgxKiY- C. DceË„ D. AwaeË„ E. mij †iLv

Soln: [C]

A. (x + 1)2 + (y–11)2= 100 B. (x – 1)2 + (y–1)2 = 81 44. †h e‡„ Ëi †K›`ª gj~ we›`‡y Z Ges †h eË„ 2x  5y  1  0 †iLv‡K

C. (x + 3)2 + (y–2)2 = 4 D. (x – 5)2 + (y+1)2 = 64 ¯úk© K‡i Zvi mgxKiY n‡e

Soln: [A] A. 9x2 + 9y2 = 1 B. x2 + y2 = 0
C. x2 + y2 = 9 D. x2 + y2 = 1
32. x2 + y2 – 24x + 10y = 0 e‡„ Ëi e¨vmva©- E. 9x2 + 9y2 = 0

A. 7 B. 5 C. 13 D. 12 Soln: [A]

Soln: [C]

33. (1, 3) †K›`ª wewkó Ges x A¶‡K ¯úk©Kvix e„‡Ëi mgxKiY wK? 41. x2 + y2 = 16 n‡j e‡„ Ëi †¶Îdj KZ?

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A.  B. 10  C. 5x 12y+152= 0 D. 2x+2y + 55 = 0
E. 12x 5y + 5 = 0
C. 20 D. 16  E. 15  Soln: [B]

Soln: [D]

42. 2x2 + 3y2 = 18 wK‡mi mgxKiY? 52. (3, 0) Ges (–4, 1) we›`yØq w`qv AwZµgKvix e‡„ Ëi †K›`ª y-A‡¶i

A. e„‡Ëi B. Dce‡„ Ëi Dci Aew¯’Z n‡j e„ËwUi mgxKiY- (13-14)

C. Awae‡„ Ëi D. †Rvov mij‡iLviE. cive‡„ Ëi A. x2 + y2 – 8y – 9 = 0 B. x2 + y2 – 6y – 2 = 0

Soln: [B] C. x2 + y2 – 5y + 9 =0 D. x2 + y2 – 8y – 1 = 0

43. 3x2 + 3y2 – 5x – 6y + 4 = 0 eË„ wUi e¨vmva©- E. x2 + y2 – 5y – 7 = 0

13 15 Soln: [A]
B.
A.
8
6

13 D. 6 6 53. `yBwU eË„ Ggbfv‡e Aew¯’Z †h GKwU AciwUi evwn‡i Aew¯’Z Ges
C. 13 E.
G‡K Aci‡K ¯úk© K‡i Av‡Q | Zv‡`i †KDB hw` we›`y e„Ë bv nq
6 13

Soln: [C] Z‡e Zv‡`i KqwU mvaviY ¯úk©K AvKu v hv‡e?

44. (3, 0) Ges (4, 1) we›`Øy q w`qv AwZµgKvix e‡„ Ëi †K›`ª y-A‡¶i A. 1 B. 2 C. 3 D. 4

Dci Aew¯’Z. eË„ wUi mgxKiY n‡e Soln: [B]

A. x2 + y2  8y 9 = 0 B. x2 + y2  8y  1 = 0 54. GKwU e„‡Ëi mgxKiY nj 2x2 + 2y2 = 25| 5 GKK ˆ`N©¨ wewkó GKwU
C. x2 + y2  6y 2 = 0 D. x2 + y2  5x  7 = 0
E. x2 + y2 + 3y  7 = 0 R¨v e„‡Ëi †K‡›`ª †iwWqvb †KvY ˆZix Ki‡e?
Soln: [ A]
A.  B.  C.  
45. (0, 1) I (2, 3) we›`y `ywUi ms‡hvM †iLv‡K e¨vm a‡i AswKZ e„ËwU
X-A¶ †_‡K †h cwigvY Ask †Q` K‡i Zv n‡e- D.

643 2

Soln: [D]

55. (4, 3) we›`y‡K †K›`ª K‡i KZ e¨vmv‡a©i eË„ A¼b Ki‡j x2 + y 2 = 4 e„Ë‡K

A. 4 B. 5 ¯úk© Ki‡e.

C. 6 D. 7 E. †KvbwUB b‡n. A. 3 B. 2 C. 5 D. 1
Soln: [A
Soln: [A]
56 (x – 3)2 + (y – 4)2 = 25 e‡„ Ëi †K›`ª n‡Z 3 GKK `i~ ‡Z¡ Aew¯’Z
46. 9x2 + 9y2 = 9 mgxKiYwUi R¨vwgwZK A_© wK?
R¨vÕi ˆ`N©¨ KZ GKK?
A. eË„ B. Dce„Ë

C. civeË„ D. AwaeË„ E. mij‡iLv Dce„Ë A. 5 B. 4 C. 3 D. 8
Soln: [D]
Soln: [A]
57. 6 GKK ˆ`N©¨wewkó GKwU R¨v (x – 3)2 + (y – 4)2 = 25 e„‡Ëi †K‡›`ª
47. †h mij‡iLvwU y A‡¶i Dci j¤^ Zvi mgxKiYwU n‡e †KvbwU?
KZ †KvY ˆZix K‡i?
A. 2x + 2 = 0 B. 3y + 3 = 0
A. sin1(6 / 5) B. sin1(3/ 5)
C. 3x  2y = 3 D. 4x = 6 E. 3x + 2y = 3

Soln: [B] C. 2sin1(3/ 5) D. tan1(6 / 5)

48. 2x + 3y + c = 0 ‡iLvi mwnZ 450 ‡Kv‡Y †Q`Kvix †iLvi mgxKiY Soln: [C]

n‡jv- 58. (4, 3) we›`y‡K †K›`ª K‡i KZ e¨vmv‡a©i e„Ë AsKb Ki‡j x2 + y2 = 4

A. x + 5y + 6 = 0 B. x + y + 7 = 0 e„Ë‡K ¯úk© Ki‡e?

C. 5x + y + 7 = 0 D. 2x + 2y + 7 = 0 A. 3 B. 2
Soln: [C]
C. 5 D. 1 E. 7
49. 3x + y = 14, 2x + 5y = 18 †iLv`wy Ui †Q` we›`My vgx e‡„ Ëi †K›`ªwe›`y Soln: [A]
(1, 2) n‡j e„ËwUi e¨vmva© KZ?
59. m Gi gvb KZ n‡j mxy=0 mij‡iLv x2 + y2 = px + qy eË„ ‡K
A. 5 B. 6 ¯úk© K‡i?

C. 14 D. 18 E. 4 A. p + q B. p  q

Soln: [A] C. p/q D. q/p E. pd

50. x2  y2  4x  8y  61  0 mgxKiYwUi e„‡Ëi †K‡›`ªi ¯’vbv¼ KZ? Soln: [D]

A. (2, 4) B. (2, 4) 60. m Gi gvb KZ n‡j (x  y + 3)2 + (mx + 2)(y  1) = 0 mgxKiYwU
C. (4, 2) D. (4, 2)
Soln: [A] E. (2, 4) GKwU e„Ë wb‡`©k K‡i‡e?

51. x2  y2  3x  10y 15  0 e„‡Ëi (4,11) we›`‡y Z A. 1 B. 1
¯úk©‡Ki mgxKiY n‡e-
C. 0 D. 2 E. 3
A. 3x + 4y 22 = 0 B. 5x 12y 152 = 0 Soln: [D]

61. g~jwe›`My vgx GKwU mij‡iLv †Kvb we›`‡y Z y = ex eµ‡iLvi ¯úk©K
n‡e-

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A. 1,1/e B. 1,1 C. 2 D. –1
C. 1/e, 1 D. 1,e Soln: [A]
Soln: [D] E. e, 1

73. x2 + y2 – 24x + 10y = 0 e‡„ Ëi e¨vmva©-

62. 2x + 3y – 5 = 0 †iLvwU (3, 4) †K›`ªwewkó e‡„ Ëi ¯úk©K| eË„ wU y A. 7 B. 5

A‡¶i †h Ask †Q` K‡i Zvi cwigvY KZ? C. 13 D. 12

A.–3 B. 2 C. 4 D.–1 Soln: [C]

Soln: [C] 74. (4, 5) †K›`ªwewkó e„Ë, hv x2 + y2 + 4x + 6y–12 = 0 e‡„ Ëi †K›`ª

w`‡q Mgb K‡i, Zvi mgxKiY-

63. ax2 + 2bxy – 2y2 + 8x + 12y + 6 = 0 GKwU eË„ wb‡`©k Ki‡j Gi A. x2 + y2 – 8x + 10y + 59 = 0
e¨vmva© KZ?
B. x2 + y2 – 8x – 10y + 59 = 0

A. 2 B. 3 GKK C. 4 GKK D. 4 C. x2 + y2 + 8x + 10y – 59 = 0

Soln: [C] D. x2 + y2 – 8x – 10y – 59 = 0

64. (1, 2) †K›`ª wewkó e„Ë x-A¶‡K ¯úk© K‡i| D³ e„ËwU y-A¶‡K wK Soln: [D]
cwigv‡Y †Q` K‡i?
75. (5, 7) (–1, –1) I (–2, 6) we›`y Îq GKwU e‡„ Ëi cwiwai Dci

A. 32 GKK B. 23 GKK C. 52 GKK D. 25 GKK Aew¯’Z| e‡„ Ëi †K‡›`ªi ¯’vbvsK-

Soln: [B] A. (2, 3) B. (1, 2) C. (–2, 3) D. †KvbwUB bq

65. GKwU e„Ë (–6, 5) (–3, –4) Ges (2, 1) we›`yÎq w`‡q AwZµg K‡i| Soln: [A]

eË„ wUi e¨vm KZ? 76. 4x + 4y2 +12x –8y –11 = 0 eË„ wUi †K‡›`ªi ¯’vbvsK †KvbwU?

A. 5 B. 11 C. 12 D. 10 A. (–6, 4) B.  3 ,1
Soln: [D] 2

66. x2 + y2 = 0 wK‡mi mgxKiY? C. (6, –4) D. (–3, 2)
A. mij †iLvi mgxKiY
B. we›`y e‡„ Ëi mgxKiY Soln: [B]
C. Dce„‡Ëi mgxKiY D. †KvbwUB b‡n
77. x2 + y2 – 4x – 6y + c = 0 eË„ wU x-A¶‡K ¯úk© K‡i| c-Gi gvb

Soln: [B] KZ?

67. x2 + y2 + 2gx + 2fy + c = 0 eË„ wUi †K›`ª y-A‡¶i Dci Aew¯’Z A. 6 B. 8 C. 4 D. 5

n‡j g-Gi gvb KZ? Soln: [C]

A. g = f – c B. g = –c C. g = 0 D. g = c 78. x2 + y2 + 2gx + c = 0 e‡„ Ëi †K›`ª †Kv_vq Aew¯’Z?

Soln: [C] A. x-A‡¶i Dci B. y-A‡¶i Dci

68. x2 + y2 + 2gx + 2fy + k = 0 eË„ wU gj~ we›`y w`‡q Mgb Ki‡j k-Gi C. g~j we›`y‡Z D. †KvbwUB b‡n

gvb KZ? Soln: [A]

A. k = g B. k = f C. k = –f D. k = 0 79. †Kvb e‡„ Ëi †K›`ª (3, 5) Ges Zvi GKwU e¨v‡mi GKcÖvšÍ (7, 3) n‡j

Soln: [D] Aci cÖv‡šÍi ¯’vbv¼ KZ?

69. y = 2x + a 5 mij †iLvwU x2 + y2 = a2 e„ËwU‡K- A. (3, 2) B. (4, 1) C. (1, 7) D. (2, 5)
Soln: [C]
A. ¯úk© K‡i B. ¯úk© K‡i bv
80. x2 + y2  a2  2ab + b2 e„ËwUi e¨vmva© KZ?
C. †K›`ªwe›`yMvgx D. R¨v
A. a  b B. b  a
Soln: [A]
C. a  b D.  (a  b)

70. x2 + y2 – 2x – 4y + c = 0 e„ËwU x-A¶‡K ¯úk© Ki‡j c Gi gvb Soln: [C]
KZ ?
81. mvaviY mgxKiY wewkó eË„ Øviv x A‡¶i †Q`vs‡ki cwigvY n‡e-

A. 2 B. 4 A. 2 f 2  c B.  2 g2  c

C. 3 D. 1

Soln: [D] C.  2 f 2  c D. 2 g 2  c

71. (x – 5)2 + (y + 2)2 = 16 e„‡Ëi †K‡›`ªi ¯’vbvsK- Soln: [D]

A. (5, –2) B. (–5, 2) 82. (4, 5) †K›`ª wewkó eË„ wU hw` g~j we›`yMvgx nq Z‡e Zvi x A‡¶i
†Q` Ask KZ?
C. (0, 0) D. (4, 0)

Soln: [A] A. 0 B. 4

72. e„Ë x2 + y2 – 2ky – 4 = 0-Gi GKwU e¨v‡mi mgxKiY 2x – 3y + 1 = 0 n‡j C. 2 D. 8
k-Gi gvb- Soln: [D]

A. 1 B. 1 83. c-Gi gvb KZ n‡j x2 + y2  2x  4y + c = 0 eË„ wU X A¶‡K ¯úk©
3 2 K‡i?

A. 4 B. 3

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C. 2 D. 1 A. 3 B. 3
Soln: [D]
C. 32 D. 32
84. x + 2y = 11 †iLv n‡Z x2 + y2  4x + 6y  7 = 0 e„‡Ëi wbKUZg
we›`iy ¯’vbv¼ KZ? Soln: [A]
A. (4, 1) B. (1, 4) C. (1, 2) D. †KvbwUB bq
94. x2 + y2 – 8x 10y = 0 e„‡Ë AswKZ ¯úk©K 3x 4y + 11 = 0 †iLvi
Soln: [A] mgvšÍivj| m¤úk©‡Ki mgxKiY wK n‡e?

85. 3x2 + 3y2  5x  6y + 4 = 0 eË„ wUi e¨vmva© KZ? A. 3x  4y  27 = 0; 3x  4y + 43 = 0

A. 13 B. 17 B. 4x  3y  27 = 0; 4x  y 18 = 0
5
8 C. 3x  y  10 = 0; 3x  y + 12 = 0

C. 13 D. 19 D. 3x 10y  11 = 0; 3x  10y + 11 = 0
Soln: [A]
66
95. x2 + y2 + 2gx + 2fy + c = 0 eË„ wU x-A¶‡K ¯úk© Ki‡j wbgœwjwLZ
Soln: [A] †Kvb kZ©wU mwVK?

86. x2  2ax + y2 = 0 mgxKiYwU n‡”Q GKwU- A. g2 > c B. f2 = c

A. e„‡Ëi mgxKiY B. mij‡iLvi mgxKiY C. g2 = c D. f2> c
C. Dce„‡Ëi mgxKiY D. cive‡„ Ëi mgxKiY
Soln: [C]
Soln: [A]
96 (3, 5) we›`wy U x2 + y2=9 e„‡Ëi †Kv_vq Aew¯’Z?
87. g~jwe›`y †_‡K (1, 2) †K›`ª wewkó e‡„ Ëi Dci Aw¼Z ¯úk©‡Ki ˆ`N©¨ 2
A. wfZ‡i B. Dc‡i
GKK| e„ËwUi mgxKiY †KvbwU?
C. †K‡›`ª D. evwn‡i

A. x2 + 2y2  2x  4y + 4 = 0 Soln: [D]
B. x2 + y2  3x + 5y  9 = 0
97. x2 + y2 –24x + 10y = 0 e‡„ Ëi e¨vmva©-
C. x2 + y2  2x  4y + 4 = 0
A. 7 B. 5
D. †KvbwUB bq
C. 13 D. 12

Soln: [C] Soln: [C]

88. †K›`ª (2, 3) Ges e¨mva© 5 e‡„ Ëi mgxKiY- 98. x2 + y2 + 4x + 6y – 23 = 0 mgxKiY Øviv mw~ PZ e‡„ Ëi e¨vm KZ?

A. x2  y2 + 4x  6y  12 = 0 A. 6 GKK B. 8 GKK
B. x2 + y2 + 4x  6y  12 = 0
C. x2  y2 + 3x  6y  14 = 0 C. 9 GKK D. 12 GKK
D. x2 + y2  4x + 6y  13 = 0
Soln: [B] Soln: [A]

89. x2 + y2  6x  8y  75 = 0 e‡„ Ëi e¨vmva© KZ? 99. we›`y e‡„ Ëi mgxKiY †KvbwU?

A. x2 + y2 = 0 B. x2 + y2 = 1
C. x2 – y2 = 0 D. x2 – y2 = 1

Soln: [A]

A. 10 B. 15 100.2x – 3y – 9 = 0 †iLvwU x2 + y2 – 2x – 4y – c = 0 e„Ë‡K ¯úk©

C. 5 D. 12 Ki‡j c-Gi gvb KZ? (13-14)
Soln: [A]
A. 8 B. 6 C. 4 D. 2
90. (1, 1) we›`y †_‡K 2x2 + 2y2  x + 3y + 1 = 0 e„‡Ë ¯úk©‡Ki ˆ`N©¨ Soln: [A]

KZ? 102.(1, –1) we›`y n‡Z 2x2 + 2y2 – x + 3y + 1 = 0 e‡„ Ëi ¯úk©‡Ki

A. 1 B. 2 ˆ`N©¨ KZ? (13-14)
2
A. 1 11
B. 2 C. 2 D.
2
C. 1 D. 3
2 2 Soln: [D]

Soln: [C] 103.(1, 1) †K›`ªwewkó GKwU e„Ë g~jwe›`y w`‡q AwZµg K‡i| g~jwe›`‡y Z eË„ wUi

¯úk©‡Ki mgxKiY wK n‡e? (13-14)

91. k-Gi gvb KZ n‡j 3x + 4y = k †iLvwU x2 + y2 = 10x eË„ ‡K ¯úk© A. x + y = 0 B. x – y = 0 C. x + y = 1 D. x – y = 1

Soln: [A]

Ki‡e? 104. (–9, 9) I (5, 5) we›`yØ‡qi ms‡hvRK †iLv‡K e¨vm a‡i AswKZ e„‡Ëi

A. 20 B. 30 mgxKiY n‡eÑ (02-03)

C. 25 D. 40

Soln: [C] A. x2 + y2 – 4x + 14y = 0
B. x2 + y2 – 4x – 14y = 0
92. GKwU eË„ x-A¶‡K (0, 0) we›`‡y Z ¯úk© K‡i Ges (1, 3) we›`y w`‡q

hvq| eË„ wUi mgxKiY KZ? C. x2 + y2 + 4x + 14y = 0
D. x2 + y2 + 4x – 14y = 0
A. x2 + y2  10 = 0 B. x2 + y2 = 10/3
C. x2 + y2 = 10y/3 D. x2 + y2 = 10x /3
Soln: [A]
Soln: [D]
93. e„‡Ëi e¨vmva© 3 n‡j e‡„ Ëi †¶Îdj KZ?
105. (2, 3) †K›`ªwewkó eË„ wU x-A¶‡K ¯úk© Ki‡j e„ËwUi e¨vmva©-

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A. 3 B. 2 Soln: [C],

C. 5 D. 13 117.x2 + y2  3x + 10y  15 = 0 e‡„ Ëi (x, 11) we›`‡y Z ¯úk©‡Ki
Soln: [A]
mgxKiY 5x  12y  152 = 0 n‡j x = KZ ?

A. 2 B. 3 C. 6 D. 4

106.wP‡Îi eË„ wU x I y A¶‡K ¯úk© K‡i| y n‡Z ¯úk© we›`iy `i~ Z¡ 2 Soln: [D]
GKK n‡j †K‡›`ªi ¯’vbvsK KZ?
118.kÑGi gvb KZ n‡j 3x + 4y = k †iLvwU x2 + y2 = 10x eË„ ‡K ¯úk©

Ki‡e?

A. (2, –2) B. (4, 2) 2 A. 40 B. 10
C. (2, 4) D. ( 2, –2)
x C. A, B DfqB D. †KvbwUB bq

Soln: [A] Soln: [C]

119.hw` A Ges B e„‡Ëi cwiwa h_vµ‡g 15.714 GKK Ges 6.28 GKK

107.ax2 + by2 = C mgxKiYwU GKwU e„Ë‡K wb‡`©k Ki‡e hw` nq Zvn‡j Zv‡`i e¨v‡mi cv_©K¨ KZ?

A. C = 0 B. C = r2 A. 5.23 GKK B. 3.0 GKK

C. a/b = 1 D. a  b C. 1.5 GKK D. 0.5 GKK

Soln: [C] Soln: [B]

108.x2 + y2 = 25 e„‡Ëi (5, 0) we›`y‡Z ¯úk©‡Ki Xvj KZ n‡e? 120.GKwU e„‡Ëi †K›`ª (–5, 7) we›`‡y Z Aew¯’Z Ges GwU Y-A¶‡K ¯úk©

A. 0 B. 5 C.  D. 5 K‡i| Gi e¨vmva© KZ? (13-14)

Soln: [C] A. –5 B. 7 C. 5 D. –7

Soln: [C]

109.x2 + y2 –6x – 8y – 75 = 0 eË„ wUi e¨vmva© KZ?

A. 8 B. 10 ট্রবিযাস ও সম্ারবশ

C. 12 D. 15

Soln: [B]

110.2x2 + 2y2 – 4x + 8y + 6 = 0 GB e„‡Ë e¨vm KZ? 01. 1, 3, 5, 7, 9 Aˆ…m¡ ®bL ¢ae¢V wfbœ wfbœ Aˆ ¢eu 200 ®b-L

A. 2 2 B. 2 hªqšl 3 A‡¼i ®k pLm pwMÉ¡ NWe Ll¡ k¡u a¡-cl pwMÉ¡[1996-

C. 3 D. 9 1997]

Soln: [A] (A) 24 (B) 48 (C)

111.(4, 4) I (12, 1) we›`y `By wUi ms‡hvM †iLv‡K e¨vm a‡i Aw¼Z 60 (D) 6
02. SCIENCE në¢Vl ülhZ…Ñ m¡L HLœ ®lM ph Lu¢V hZÑL
e„‡Ëi mgxKiY KZ?

A. x2 + y2 8x  3y  52 = 0 B. 2x2 + y218x  3y  48 = 0 pñ¡hÉ ka Ef¡-u p¡S¡-e¡ k¡u, a¡-cl pwMÉ¡

C. x2 + y2 + 16x  5y+ 52 = 0 D. x2 + 2y2 8x + 3y 11 = 0 [19971998]

Soln: [A]

112.x2 + y2  8x + 6y + 9 = 0 eË„ wUi †K‡›`ªi ¯’vbvsK KZ? (A) 60 (B) 120 (C)

A. (3, 4) B. ( 4, 3) 180 (D) 420
03. 1, 2, 4, 6, 8, 9 A¼¸wj cby ivew„ Ëmn e¨envi K‡i wZb A‡¼i
C. (4,  3) D. (8, 6)
KZ¸‡jv msL¨v ˆZwi Kiv hv‡e ?
Soln: [C]
[1999-2000]
113. (0, 9) we›`wy U, (1, 4) †K›`ª I 6 e¨vmva© wewkó e„‡Ëi-

A. AšÍt¯’ B. ewnt¯’ (A) 20 (B) 60 (C)

C. Dcwit¯’ D. †KvbwUB bq 120 (D) 216
04. 3 Rb evjK I 4 Rb evwjKv‡K GKwU mvwi‡Z KZ cÖKv‡i web¨vm
Soln: [B]

114.†K c_Ö g R¨vwgwZ‡Z exRMwYZxq m‡~ Îi cÖ‡qvM K‡ib? Kiv hv‡e hv‡Z 3 Rb evjK me©`vB GK‡Î _vK‡e|

A. AvwK©wgw`m B. wbDUb [1999-2000]

C. g¨v· cø¨vsK D. †` KvZ© (A) 24 (B) 48 (C)

Soln: [D] 720 (D) 144
05. ‘CALCULUS’ në¢Vl ph…m¡ Arl (¢hcÉj¡e cybl¡hª¢špq) HLœ
115.x2 + y2  6x  8y  75 = 0 e‡„ Ëi †K‡›`ªi ¯’vbvsK KZ?
¢e-u Lai¡-h p¡S¡-e¡ k¡u, ®ke fÊbj J ®no Arl phÑc¡ C qu?
A. (3, 4) B. (3, 0)

C. (2, 4) D. (4, 3)

Soln: [A] [2000-2001]

116. x2 + y2  6x  8y  75 = 0 e‡„ Ëi e¨vmva© KZ? (A) 180 (B) 360 (C)

A. 11 B. 12 720 (D) 5040.

C. 10 D. 13

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06. 3, 5, 7, 8, 9 A¼¸wj GKevi e¨envi K‡i 7000 ‡_‡K eo Pvi (A) 504 (B) 210 (C)

A¼ wewkó KZ¸wj msL¨v MVb Kiv hvq ? 126 (D) 84

[2003-2004] 14. 5 Rb weÁvb I 3 Rb Kjv Abyl‡`i QvÎ †_‡K 4 R‡bi GKwU

(A) 27 (B) 81 (C) KwgwU MVb Ki‡Z n‡e hv‡Z AšÍZ GKRb weÁvb I GKRb Kjvi

72 (D) 56 QvÎ _v‡K| KZ cÖKv‡i GB KwgwU MVb Kiv ‡h‡Z cv‡i ?

07. ENGINEERING k‡ãi mKj E ¸‡jv GKm‡½ †i‡L mKj [2002-2003]

A¶i¸‡jvi web¨v‡mi msL¨v- (A) 60 (B) 65 (C)

[2010-2011] 70 (D) 75

15. eviwU eB‡qi g‡a¨ cuvPwU eB KZ cKÖ v‡i evQvB Kiv hvq hv‡Z

(A) 1680 (B) 15120 (C) wbw`©ó `By wU eB me©`v ev` _v‡K ?

277200 (D) 1512 [2004-2005]

08. cwÖ Zevi cÖ_g Ges †k‡l U †i‡L CALCULUS kãwUi (A) 120 (B) 225 (C)

A¶i¸‡jv‡K KZfv‡e mvRv‡bv hv‡e ? 252 (D) 128

16. 6 Rb QvÎ Ges 5 Rb QvÎx †_‡K 5 R‡bi GKwU KwgwU MVb Ki‡Z

[2011-2012,2005-2006] n‡e hv‡Z AšÍZ GKRb QvÎ I GKRb QvÎx AšÍf©³y _v‡K| KZ

(A) 180 (B) 280 (C) cKÖ v‡i G KwgwU MVb Kiv †h‡Z cv‡i

?

90 (D) 360 [2005-2006]

09. ¯^ieY¸© ‡jv‡K me mgq GK‡Î †i‡L KACHUA kãwUi eY©¸‡jv‡K (A) 360 (B) 160 (C)
mvRv‡bvi msL¨v n‡e–
410 (D) 455

17. SCHOOL kãwU n‡Z wZbwU A¶i wb‡q c„_Kfv‡e mvRv‡bvi msL¨v

[2012-2013]

(A) 24 (B) 72 [2007-2008]

(C) 144 (A) 10 (B) 14 (C)

(D) 8 4 (D) 15
10. 1, 2, 3, 4, 5, 6 I 7 †_‡K cybivew„ Z Qvov wZb A‡¼i msL¨v MVb Kiv
18. 6 Rb QvÎ Ges 5 Rb QvÎx †_‡K 5 R‡bi GKwU KwgwU MVb Ki‡Z

n‡e hv‡Z AšÍZ GKRb QvÎ I GKRb QvÎx _v‡K| KZ wewfbœ

n‡j KqwU msL¨vi gvb 100 †_‡K 500 Gi cKÖ v‡i G KwgwU MVb Kiv hv‡e ?

g‡a¨? [2011-2012,2009-2010]

(A) 455 (B) 360 (C)

[2013-2014] 144 (D) 720

(A) 240 (B) 60 (C) 19. 4 Rb gwnjvmn 10 e¨w³i ga¨ †_‡K 5 R‡bi GKwU KwgwU MVb

120 (D) 480 Ki‡Z n‡e hv‡Z AšÍZ GKRb gwnjv AšÍf©y³ _vK‡e| KZ wewfbœ
11. COURAGE kãwUi eY¸© j wb‡q KZ¸wj web¨vm msL¨v wbY©q
cKÖ v‡i G KwgwU MVb Kiv †h‡Z cv‡i?

Kiv hvq †hb cÖ‡Z¨K web¨v‡mi cÖ_g GKwU ¯^ieY© _v‡K? [2014- [2013-2014]

2015] (A) 1440 (B) 246

(A) 720 (B) 2880 (C) (C) 120

180 (D) 5040 (D) 60

20. 6 Rb evjK Ges 5 Rb evwjKvi GKwU `j †_‡K KZ Dcv‡q 3 Rb

12. mvZRb Bs‡iR Ges PviRb gvwK©wb‡`i g‡a¨ †_‡K Qq R‡bi evjK Ges 2 Rb evwjKvi GKwU `j MVb Kiv †h‡Z cv‡i? [2015-
GKwU KwgwU MVb Ki‡Z n‡e| KwgwU‡Z Kgc‡¶ `By Rb gvwK©wb
_vK‡e GB k‡Z© KZfv‡e GUv MVb Kiv †h‡Z cv‡i ? 2016]

(A) 10 (B) 20

(C) 50 (D) 200

[2001-2002] 21. ‘calculus’ kãwUi me¸wj A¶i (we`¨gvb cby ivew„ Ëmn) GK‡Î wb‡q

(A) 350 (B) 371 (C) KZfv‡e mvRv‡bv hvq, †hb cÖ_g I †kl A¶i me©`v c nq? (00-01)

381 (D) 415 A. 720 B. 360 C. 180 D. 5040

13. PviRb gwnjv I QqRb ciy y‡li ga¨ n‡Z Pvi m`m¨ wewkó GKwU Soln: [C] 'Calculus' kãwU‡Z †gvU A¶i 8 wU, hv‡Z C, u, l Av‡Q `yBU

DcKwgwU KZ cÖKv‡i MVb Kiv hv‡e, hv‡Z GKRb wbw`©ó cyiyl K‡i| cÖ_g I †kl A¶i C n‡e weavq cÖ_g I †kl ¯’vb `wy U‡Z C Gi

me©`vB AšÍf©y³ n‡e| web¨vm = 1 Aewkó 6 wU ¯’v‡b Aewkó 6 wU A¶‡ii web¨vm = 6!

wKš‘ Bnv‡Z 2wU u I `yBwU l _vKvq web¨vm n‡e = 6! = 180
2!2!

[2002-2003]  wb‡Y©q web¨vm = 1  180 = 180

|

22. PviRb gwnjv I QqRb ciy ‡~ li ga¨ n‡Z Pvi m`m¨ wewkó GKwU DcKwgwU (iv) 4 1
KZ cÖKv‡i MVb Kiv hv‡e, hv‡Z GKRb wbw`©ó cyi~l me©`vB AšÍf©³~ n‡e-
KwgwU MV‡bi Dcvq = 6C1  5C4 + 6C2  5C3 + 6C3  5C2 + 6C4 

(02-03) 5C1 = 455
28. SCHOOL kãwU n‡Z wZbwU A¶i wb‡q c_„ Kfv‡e mvRv‡bv msL¨v
A. 504 B. 210 C. 126 D. 84

Soln: [D] A. 10 B. 14 C. 4 D. 15

KwgwU MV‡bi m¤¢ve¨ Dcvq ¸‡jv wbgiœ ƒc: [GKRb wbw`©ó cyiæl me©`vB Soln: [B]

AšÍf³y© ] SCHOOL kãwU‡Z †gvU 6 wU eY© Av‡Q Ges Gi g‡a¨ 2 wU 'O'| myZivs

Dcvq ciy æl (6) gwnjv (4) cÖwZev‡i 3 wU K‡i eY© wb‡q wbgœewY©Zfv‡e evQvB Kiv †h‡Z cv‡i:

(i) 4 0 i. 2 wU eY© Awfbœ Ges Aci 1 wU wfb|œ G‡¶‡Î evQvB msL¨v = 1  4C1 =

(ii) 3 1 4
ii. 3 wU eYB© wfb|œ G‡¶‡Î evQvB msL¨v = 5C2 = 10
(iii) 2 2
 wb‡Y©q evQvB msL¨v = 5C2 + 4C1= 14
(iv) 1 3 29. 6 Rb QvÎ Ges 5 Rb QvÎx †_‡K 5 R‡bi GKwU KwgwU MVb Ki‡Z n‡e

 KwgwU MV‡bi Dcvq = 5C3  4C0 + 5C2  4C1 + 5C1  4C2 + 5C0 hv‡Z AšÍZ GKRb QvÎ I GKRb QvÎx _v‡K| KZ wewfbœ cÖKv‡i G KwgwU

 4C3 = 10 + 40 + 30 + 4 = 84 MVb Kiv hv‡e?
23. 3, 5, 7, 8, 9 A¼¸wj GK ev GKvwaK evi e¨envi K‡i 7000 †_‡K eo
A. 455 B. 360 C. 144 D. 720
Pvi A¼ wewkó KZ¸wj msL¨v MVb Kiv hvq?
Soln: [A]

wb‡gvœ ³ m¤¢ve¨ Dcv‡q KwgwU MVb Kiv hvq-

A. 27 B. 81 C. 72 D. 56 Dcvq QvÎ (6) QvÎx (5)

Soln: [C] msL¨v¸‡jv 4 A¼ Øviv cY~ © Kivi Dcvq (i) 1 4

= 4P3 = 24  wb‡Y©q web¨vm = 3  24 = 72 (ii) 2 3
24. 5 Rb weÁvb I 3 Rb Kjv Abyl‡`i QvÎ †_‡K 4 R‡bi GKwU KwgwU MVb
(iii) 3 2
Ki‡Z n‡e hv‡Z AšÍZ GKRb weÁvb I GKRb Kjvi QvÎ _v‡K| KZ wewfbœ
(iv) 4 1

cÖKv‡i GB KwgwU MVb Kiv †h‡Z cv‡i- KwgwU MV‡bi Dcvq = 6C1  5C4 + 6C2  5C3 + 6C3  5C2 + 6C4 

A. 60 B. 65 C. 70 D. 75 5C1 = 455

Soln: [B] 30. cÖwZevi cÖ_‡g I †k‡l U †i‡L CALCULUS kãwUi A¶i¸‡jv‡K

KwgwU MV‡bi m¤¢ve¨ Dcq¸‡jv wbgœiƒc: KZfv‡e mvRv‡bv hv‡e?

Dcvq weÁv‡bi QvÎ (5) Kjvi QvÎ (3) A. 90 B. 180 C. 280 D. 360

Soln: [B] 'Calculus' kãwU‡Z †gvU A¶i 8 wU, hv‡Z C, u, l Av‡Q `By U

(i) 3 1 K‡i| cÖ_g I †kl A¶i C n‡e weavq cÖ_g I †kl ¯’vb `ywU‡Z C Gi

(ii) 2 2 web¨vm = 1 Aewkó 6 wU ¯’v‡b Aewkó 6 wU A¶‡ii web¨vm = 6!

(iii) 1 3 wKš‘ Bnv‡Z 2wU u I `yBwU l _vKvq web¨vm n‡e = 6! = 180
2!2!

 KwgwU MV‡bi Dcvq = 5C3  3C1 + 5C2  3C2 + 5C1  3C3 = 30 +  wb‡Y©q web¨vm = 1  180 = 180
31. 6 Rb QvÎ Ges 5 Rb QvÎx †_‡K 5 R‡bi GKwU KwgwU MVb Ki‡Z n‡e
30 + 5 = 65
25. eviwU eB‡qi g‡a¨ cuvPwU eB KZ cÖKv‡i evQvB Kiv hvq hv‡Z wbw`©ó `By wU hv‡Z AšÍZ GKRb QvÎ I GKRb QvÎx AšÍf©y³ _v‡K| KZ wewfbœ cÖKv‡i G

eB me©`v ev` _v‡K? KwgwU MVb Kiv †h‡Z cv‡i?

A. 120 B. 225 C. 252 D. 128 A. 160 B. 360 C. 410 D. 455

Soln: [C] †h‡nZ,z wbw`©ó `yBwU eB me©`v ev` _v‡K| Soln: [D]

 wb‡Y©q evQvB msL¨v = 10C5 = 252 wb‡gvœ ³ m¤¢ve¨ Dcv‡q KwgwU MVb Kiv hvq-
26. cÖwZevi cÖ_g Ges †k‡l u †i‡L calculus kãwUi A¶i¸‡jv‡K KZfv‡e
Dcvq QvÎ (6) QvÎx (5)
mvRv‡bv hv‡e?
(i) 1 4

A. 180 B. 280 C. 90 D. 360 (ii) 2 3

Soln: [A] 'Calculus' kãwU‡Z †gvU A¶i 8 wU, hv‡Z C, u, l Av‡Q `yBU (iii) 3 2

K‡i| cÖ_g I †kl A¶i C n‡e weavq cÖ_g I †kl ¯’vb `wy U‡Z C Gi (iv) 4 1
web¨vm = 1 Aewkó 6 wU ¯’v‡b Aewkó 6 wU A¶‡ii web¨vm = 6!
KwgwU MV‡bi Dcvq = 6C1  5C4 + 6C2  5C3 + 6C3  5C2 + 6C4 

wKš‘ Bnv‡Z 2wU u I `yBwU l _vKvq web¨vm n‡e = 6! = 180 5C1 = 455
2!2! 32. ¯^ieY©¸‡jv‡K me mgq GK‡Î †i‡L KACHUA kãwUi eY©¸‡jv‡K

 wb‡Y©q web¨vm = 1  180 = 180 mvRv‡bvi msL¨v n‡e-
27. 6 Rb QvÎ Ges 5 Rb QvÎx †_‡K 5 R‡bi GKwU KwgwU MVb Ki‡Z n‡e hv‡Z
A. 24 B. 72 C. 144 D. 8
AšÍZ GKRb QvÎ I GKRb QvÎx AšÍf©y³ _v‡K| KZ wewfbœ cÖKv‡i G KwgwU
Soln: [B] KACHUA kãwU‡Z †gvU eY© 6wU Ges ¯^ieY© 3wU, hv‡`i g‡a¨

MVb Kiv †h‡Z cv‡i? 2wU A|

A. 360 B. 160 C. 410 D. 455 3wU ¯^ieY©‡K 1wU ai‡j †gvU eY© nq 4wU

Soln: [D]  eM©¸‡jv mvRv‡bv msL¨v = 4!  3! = 72 [†h‡nZz 2wU A, ZvB 2! Øviv
2!
wb‡gvœ ³ m¤¢ve¨ Dcv‡q KwgwU MVb Kiv hvq-
fvM Kiv n‡q‡Q]
Dcvq QvÎ (6) QvÎx (5)
33. COURAGE kãwUi eY¸© wj wb‡q KZ¸wj web¨vm msL¨v wbY©q Kiv hvq
(i) 1 4 †hb cÖ‡Z¨K web¨v‡mi cÖ_‡g GKwU ¯^ieY© _v‡K?

(ii) 2 3 A. 720 B. 2880 C. 180 D. 5040

(iii) 3 2

|

Soln: [B] COURAGE kãwU‡Z †gvU eY© 7wU Ges ¯^ieY© 4wU| 1g  †gvU msL¨v = 4 p2 + 5 p4 = 6 + 5 = 11
42. e¨ÄbeY¸© ‡jv †KejgvÎ we‡Rvo ¯’v‡b †i‡L 'EQUATION' kãwUi
¯’vbwU ¯^ieY© Øviv ci~ Y Kiv hvq 4P1 cÖKv‡i| evwK 6wU Ni 6wU eY© Øviv

c~iY Kivi Dcvq 6 A¶i¸‡jv‡K mvRv‡bv hvq-

wb‡Y©q web¨vm = 4P1  6 = 2880 A. 2840 ways B. 2880 ways
34. "PERMUTATION" kãwUi eY©¸wji †Kvb ¯^ie‡Y©i Ae¯’vb cwieZ©b
C. 880 ways D. 2480 ways
bv K‡i KZ iK‡g cby we©b¨vm Kiv †h‡Z cv‡i|
Soln: [B] Equation kãwU‡Z †gvU eY© 8 wU, e¨Äb eY© 3 wU, ¯^ieY© 5 wU|

A. 359 B. 720 12345678

C. 719 D. 358 E. None

Soln:[A],GLv‡b e¨ÄbeY© Av‡Q 6wU, T Av‡Q 2wU | 4 wU Ae¯’vb we‡Rvo (cÖ_g, Z…Zxq, cÂg, mßg)

 cybwe©b¨vm Kiv hv‡e 6! – 1 = 359 Dcv‡q| myZivs, 3wU e¨ÄbeY©‡K 4 wU we‡Rvo ¯’v‡b mvRv‡bvi Dcvq = 4 P3 Ges
2! evKx 5 wU ¯’v‡b 5 wU ¯^ieY© mvRv‡bv hvq = 5! fv‡e|

35. 0, 3, 5, 6, 8 A¼¸‡jv w`‡q †Kvb A‡¼i cybivew„ Ë bv K‡i 4000 Gi †P‡h  †gvU web¨vm msL¨v = 4 P3  5! = 2880
eo KZ¸‡jv msL¨v MVb Kiv hvq? 43. cÖwZevi cÖ_‡g I †k‡l u †i‡L calculus kãwUi A¶i¸wj‡K KZfv‡e

A. 144 B. 192 C. 168 D. None mvRv‡bv hv‡e?

Soln:[C], 5, 6, 8, 1g ¯’v‡b emvbv hvq 3p1 = 3 fv‡e | msL¨vwU 4 A‡¼i

n‡j, A. 90 B. 280 C. 360 D. 180

evwK 3wU ¯’v‡b 4wU A¼ emv‡bv hvq = 4p3 fv‡e| msL¨vwU 5 A‡¼i n‡j, 5 Soln: [D]Same as DU 01
wU ¯’v‡b 5wU A¼ emv‡bv hvq fv‡e |cÖ_g ¯’v‡b 0 _5vK‡e Ggb web¨vm = 44. e¨ÄbeY¸© ‡j†K †KejgvÎ we‡Rvo ¯’v‡b †i‡L 'EQUATION' kãwUi
4  †gvU web¨vm = 3p1  4p3 + ( –5 ) 4= 168
36. GKwU `kf~‡Ri †KŠwYK we›`¸y ‡jvi ms‡hvM †iLvi mvnvh¨ KZ¸‡jv KY© Uvbv A¶i¸‡jv hZfv‡e mvRv‡bv hvq Zvi msL¨v-( 08-09)

A. 2840 B. 2880 C. 880 D. 2480

†h‡Z cv‡i? [BUET 06-07] Soln: [B] Same as JNU 01
45. "MATHEMATICS' kãwUi eY¸© ‡jv‡K KZ cÖKv‡i mvRv‡bv hvq?

A. 20 B. 35 C. 45 D. 25 A. 11! 11! 11! 11!
8 B. C. D.
Soln:[C], 10wU †KŠwYK we›`iy †h †Kvb `ywU h³y n‡Z cv‡i 10p2 Dcv‡q|
3! 4! 6!
 K‡Y©i msL¨v = 10 p2 – 10 = 35
Soln: [A] "MATHEMATICS" kãwU‡Z †gvU 11 wU A¶i Av‡Q|

37. 6 Rb evjK I 4 Rb evwjKv n‡Z 5 Rb‡K GKwU wbw`©ó †Kv‡m© fwZi© Rb¨ G‡`i g‡a¨ M Av‡Q 2 wU, T Av‡Q 2 wU I A Av‡Q 2 wU|

evQvB Ki‡Z cv‡i| wVK 2 Rb evwjKv‡K †i‡L evQvB cÖwµqvwU‡K KZ fv‡e  me¸wj A¶i jBqv †gvU web¨vm msL¨v = 11! = 11!
MVb Kiv †h‡Z cv‡i| 2!2!2! 8

A. 110 B. 120 C. 125 D. 130 46. CALCULUS kãwUi A¶i¸wj‡K KZfv‡e mvRv‡bv hv‡e †hb me©`v U

Soln:[C], ïiæ‡Z Ges †k‡l _v‡K?

evQvB Kivi Ecvq 6p3  4 p2 = 120 A. 280 B. 180 C. 360 D. 90

38. `wy U fv‡Mi cÖ‡Z¨K fv‡M 5wU K‡i †gvU 10wU cÖkœ n‡Z GKRb cix¶v_©x‡K Soln: [B] Same as DU 01

6wU cÖ‡kiœ DËi w`‡Z n‡e| †Kvb fvM †_‡K 4wUi †ekx cÖ‡kiœ DËi Kiv 47. 6 Rb QvÎ Ges 5 Rb QvÎx †_‡K 5 R‡bi GKwU KwgwU MVb Ki‡Z n‡e
wbwl×| H cix¶v_x© KZ Dcv‡q cÖkœ¸‡jv evQvB Ki‡Z cvi‡e?
hv‡Z AšÍZ GKRb QvÎ I GKRb QvÎx _v‡K| KZ wewfbœ cÖKv‡i GB KwgwU

A. 200 B. 300 C. 270 D. 410 MVb Kiv †h‡Z cv‡i-

Soln[A] 1g fvM2q fvM A. 455 B. 360 C. 210 D. 192

42 Soln: [A] Same as DU 07
48. CALCULUS kãwU A¶i¸wj‡K KZfv‡e mvRv‡bv hv‡e †hb me©`v U
33

24 ïiæ‡Z Ges †k‡l _v‡K?
 cÖkœ¸‡jv evQvB Kivi †gvU Dcvq msL¨v
A. 280 B. 180 C. 360 D. 90

= 5 p4  5 p2 + 5 p3  5 p3 + 5 p2  5 p4 = 200 Soln: [B] `wy U u †K cÖv‡šÍi `yB cv‡k †i‡L evwK 6wU eY©‡K †hLv‡b 2wU c I
39. Ljy bv kn‡ii †Uwj‡dvb b¤^i 72, 73 ev 76 w`‡q ïiæ Ges 6 AsK wewkó
2wU L Av‡Q| Zv‡K mvRv‡bvi msL¨v = 6! =180.
nB‡j †gvU m¤¢ve¨ ms‡hvM msL¨v KZ? 2! 2!

A. 106 B. 104 49. INTERNET kãwUi A¶i¸wj n‡Z cÖwZev‡i 4wU K‡i eY© wb‡q †gvU

C. 3106 D. 3104 E. 7104 KZfv‡e evQvB Kiv hv‡e?

Soln:[C] A. 56 B. 48 C. 26 D. 36
D. 6
40. 7wU e¨vÄbeY© I 3wU ¯^ieY© n‡j KqwU kã MVb Kiv hv‡e †hLv‡b 3wU Soln: [C]

e¨vÄYeY© I 2wU ¯^ieY© _v‡K| 50. nC6 n C8 n‡j n Gi gvb-

A. 120 B. 25200 A. 2 B. 14 C. 8

C. 4200 D. 25000 E. None Soln: [B]

Soln:[E], kã MVb Kivi Dcvq 7 p3  3 p2 =1260 51. web¨vm I mgv‡e‡ki g‡a¨ mwVK m¤úK© †KvbwU?

41. 'THESIS' kãwUi eY¸© wj n‡Z cÖwZevi 4wU eY© wb‡q MwVZ mgv‡ek msL¨v A. m Pr  m!m Cr m Pr m Cr
r!
wbY©q Ki| B. 

A. 10 B. 11 C. 9 D. None C. m!m Pr m Cr D. m Pr  r!m Cr

Soln:[B], evQvB Kiv hvq-

1| 2wU Awfbœ Ges 2wU wfbœ G‡¶‡Î evQvB msL¨v = 1  4 p2 Soln: [D]
2| 4wU Awfbœ G‡¶‡Î evQvB msL¨v = 5 p4
52. CRICKET kãwUi A¶i¸wj‡K GK m‡½ wb‡q hZ cÖKv‡i mvRv‡bv hvq

Zvi msL¨v

|

A. 7! B. 2.7! 7! D. 6! Soln: [C]
Soln: [C] C. 64. ECONOMICS kãwUi eY©¸‡jv‡K GK‡Î wb‡q KZfv‡e mvRv‡bv hvq?

2 A. 90720 B. 362880
C. 5040 D. 1260
Soln: [E] E. †KvbwU mZ¨ bq

53. `yBwU we‡kl c¯y ÍK‡K GK‡Î bv †i‡L 7wU wewfbœ c¯y ÍK‡K hZ cÖKv‡i mvRv‡bv 65. n C12 n C8 n‡j, n Gi gvb-
hvq, Zvi msL¨v

A. 5.6! B. 6.5! C. 2.6! 6! A. 4 B. 8
Soln: [A] D.
C. 12 D. 16 E. 20
2

54. 12C 012C12 Gi gvb KZ? Soln: [E]

66. Failure k‡ãi A¶i¸wj‡K KZ fv‡e mvRv‡bv hvq? ( 09-10)

A. 12 B. 0 A. 2040 B. 3040

C. 1 D.  E. †KvbwU mZ¨ bq C. 4040 D. 5040 E. 6040

Soln: [B]Using calculator Soln: [D]

55. cÖ_g 14wU ¯^vfvweK e‡M©i †hvMdj KZ? 67. ¯^ieY©¸‡jv‡K †Rvo¯’v‡b †i‡L ARTICLE k‡ãi eY©¸‡jv KZ Dcv‡q

A. 950 B. 1000 mvRv‡bv hvq?

C. 1015 D. 1050 E. 1060 A. 144 B. 360 E. 840
D. 576
Soln: [C] C. 480
56. ‘Equation’ kãwUi A¶i¸wj †_‡K Pvi A¶i wewkó wewfbœ kã MVb Kiv Soln: [A]

n‡jv. G‡`i KZ¸‡jv‡Z ‘q’ eZ©gvb _vK‡e wKš‘ ‘n’ eZ©gvb _vK‡e bv? 68. n C6 n C8 n‡j 16Cn  ? ( 09-10)

A. 450 B. 480 A. 12 B. 80

C. 420 D. 500 E. 600 C. 120 D. 140 E. ï× DËi †bB

Soln: [B] Soln: [C]

57. CHITTAGONG kãwUi A¶i ¸wj‡K GK ms‡M wb‡q hZ cÖKv‡i 69. n C12 n C8 n‡j 22Cn Gi gvb:

mvRv‡bv hvq, Zvi msL¨v n‡e A. 213 B. 431

A. 10 ! B. 8 ! C. 331 D. 312 E. 231

C. 10! D. 48 ! E. 410 ! Soln: [E]
4
70. n C8 n C12 n‡j n C19 Gi gvb n‡”Q- ( 10-11)
Soln: [C]
A. 1 B. 20
58. 'PARALLEL' kãwUi A¶i¸‡jvi me¸‡jv GK‡Î wb‡q KZ cÖKv‡i
C. 25 D. 49 E. 72
mvRv‡bv hvq?
Soln: [B]
A. 40320 B. 120
71. hw` n P4  6 n P3 nq, Zvn‡j n Gi gvb n‡e-
C. 3360 D. 360 E. 720
A. 9 B. 6
Soln: [C] C. 10 D. 7 E. †KvbwUB b‡n.

59. hw` n C12 n C8 nq Z‡e 22 Cn = ? Soln: [A]
72. ‘PROPORTION’ Gi web¨vm msL¨v KZ?
A. 241 B. 221

C. 231 D. 230 E. 220 A. 151000 B. 151300

Soln: [C] C. 151200 D. 151100 E. †KvbwUB b‡n.
60. "COMMERCE" kãwUi A¶i¸wji me¸wj GK‡Î wb‡q KZ cÖKvi
Soln: [C]

mvRv‡bv hvq? 73. 10 Rb QvÎ cÖ‡Z¨K Rb cÖ‡Z¨K Rb‡K GKwU K‡i †Mvjvc dzj w`‡j †gvU

A. 8! B. 7! KZwU †Mvjvc djz jvM‡e?

C. 6! D. 5! E. 4! A. 10 wU B. 20wU

Soln: [B] C. 100wU D. 90wU E. 91 wU
61. n msL¨K e¯‘ n‡Z †h †Kvb msL¨K wRwbm w`‡q web¨vm msL¨v n‡e?
Soln: [D]

A. n B. nn 74. CHATTAGRAM kãwUi A¶i¸wj‡K GKms‡M wb‡q KZ cÖKv‡i

mvRv‡bv hv‡e?

C. nn-1 D. nn+1 n L10 B. L0

E. A.

2 4

Soln: [A] C. L10 D. L4 10
62. cÖ‡Z¨KwU AsK †Kej GKevi e¨envi K‡i 8, 9, 7, 6, 3, 2 AsK¸‡jv Øviv
E.
wZb AsK wewkó KZ¸‡jv wfbœ wfbœ msL¨v MVb Kiv hv‡e?
4

A. 130 B. 140 10!
Correct Ans:
C. 120 D. 60 E. 240
2!3!
Soln: [C] 75. `kwU †gnMwb Ges AvUwU MR©b Pviv †_‡K `yÕwU †gnwMwb Ges `yÕwU MR©b Pviv

63. ‘Degree’ kãwUi A¶i¸‡jv †_‡K †h †Kvb 4wU A¶i cÖ‡Z¨Kevi wb‡q KZ KZ wewfbœ fv‡e jvMv‡bv m¤¢e?

cÖKv‡i evQvB Kiv †h‡Z cv‡i? A. 72 B. 1260

A. 5 B. 6 C. 3060 D.5060 E.96

C. 7 D. 8 E. 9 Soln: [B] 10c2  8c2 = 1260.

|

76. "HATHAZARI" kãwUi A¶i¸wj w`‡q KZ cÖKvi web¨vm n‡e? A.1440 B. 2160 C. 720 D. †KvbwUB bv

A. |9 B. |9  |3 Soln: [D]
|2
87. 12 wU evû wewkó GKwU eûf‚‡Ri K‡Y©i msL¨v ( 06-07)

|9 |9 A. 66 B. 60 C. 12 D. 54
C. E.
D. |4 Soln: [D] K‡Y©i msL¨v = 12C2 – 12 = 54
|2  |3 |4
88. `kfy‡Ri K‡Y©i msL¨v :

Soln: [C] "HATHAZARI" †Z †gvU 9wU A¶i Av‡Q| Gi g‡a¨ A. 45 B. 35 C. 50 D. 40
Soln: [B]
2wU H I 3wU A Av‡Q|
 K‡Y©i msL¨v = 10C2 – 10 = 35
 wb‡Y©q web¨vm msL¨v = 9! 89. 8 Rb e¨w³ †_‡K 5 m`‡m¨i GKwU KwgwU MVb Ki‡Z n‡e hv‡Z 3 Rb
2! 3!
we‡kl e¨w³i AšÍZc‡¶ GKRb _vK‡e. Giƒc KwgwUi msL¨v-
77. hw` n C5 n C7 nq, Z‡e n C11 Gi gvb KZ?
A. 15 B. 55 C. 46 D. 48

A. 10 B. 12 Soln: [B]
KwgwU MV‡bi m¤¢ve¨ Dcvq¸‡jv wbgœiƒc:
C. 16 D. 28 E. 25

Soln: [B] n C5 n C7  nCn – 5 = nC7  n –5 = 7 Dcvq Awe‡kl e¨w³ (5) we‡kl kw³ (3)
 n = 12
(1) 4 1
 12c11 = 12.
78. 'ASSASSINATION' kãwUi A¶i¸‡jv w`‡q KZwU web¨vm ˆZix Kiv (ii) 3 2

hvq Zvi msL¨v wbiƒcY Ki? (ii) 2 3

A. 13! B. 13  KwgwU MV‡bi Dcvq 5C4  3C1 + 5C3  3C2 + 5C2  3C3
3!
= 15 + 30 + 10 = 55

C. 13 D. 13 13! 90. 1, 3, 5, 7 I 8 Øviv KZ¸wj msL¨v evbv‡bv hvq hviv 300 †_‡K eo Ges
3!4!2! 3 E.
700 †_‡K †QvU n‡e?
36 16
A. 16 B. 8 C. 24 D. 12
Soln: [E] †gvU eY© 13wU| A 3wU, S 4wU, I 2wU, N 2 wU|
Soln: [C] †h‡nZz msL¨v¸‡jv 300 †_‡K eo Ges 700 †_‡K †QvU n‡e

 web¨vm msL¨v = 13! = 13! †m‡nZz msL¨v¸‡jv 3 A¼ wewkó Ges (3 I 5) Øviv ïiæ n‡e, hv Kivi Dcvq
4! 2! 36  16
3! 2! = 2 P1 = 2;

79. Calculus kãwUi me eY© GK‡Î wb‡q cÖ_g I †kl A¶i ‘U’ †i‡L KZ Avevi, Aewkó 2 wU ¯’vb Aewkó 4 wU A¼ Øviv c~Y© Kivi Dcvq = 4 P2 =

cÖKv‡i mvRv‡bv hvq? 12
 wb‡Y©q web¨vm = 2  12 = 24
A. 180 B. 181 C. 175 D. 190 91. `By Rb ÔNÕ BDwb‡Ui cix¶v_©x‡K cvkvcvwk bv ewm‡q mvZRb ÔKÕ BDwb‡Ui
cix¶v_©x I cuvPRb ÔNÕ BDwb‡Ui cix¶v_©x‡K GK jvB‡b KZ cÖKv‡i
Soln: [A] Same as DU 01 mvRv‡bv hvq?

80. hw` nP4 = 6nP3 nq Z‡e n Gi gvb:

A. 8 B. 7 C. 9 D. 6

Soln: [C] nP4 = 6  nP3 A. 7!7p5 B. 7!8p5 C. 7!7p8 D. †KvbwUB bq
 n (n – 1) (n – 2) (n – 3) = 6n (n – 1) (n – 2) Soln: [B] K BDwb‡Ui 7 Rb cix¶v_©x‡K GK jvB‡b 7! Dcv‡q mvRv‡bv
hvq|
n=9

81. nC12 = nC8 n‡j n Gi gvb:

A. 20 B. 8 C. -12 D. 2nCr-1 K BDwb‡Ui 7 Rb cix¶v_©xi gv‡S 8 wU dvKv ¯’vb Av‡Q| GB 8 wU dvKv
Soln: [A] ¯’v‡b N-BDwb‡Ui 5 Rb cix¶v_x©‡K emv‡j Zviv KL‡bvB cvkvcvwk _vK‡e
bv|
82. 12 evû wewkó GKwU eûf‡z Ri K‡Y©i msL¨v:

A. 12 B. 24 C. 54 D. 36  8 wU dvKv ¯’v‡b N-BDwb‡Ui 5 Rb cix¶v_x©‡K 8P5 Dcv‡q mvRv‡bv hvq|

Soln: [C] K‡Y©i msL¨v = 12C2 – 12 = 54  †gvU mvRv‡bv msL¨v = 7!  8 P5
92. GKwU †Uwbm Uzbv© ‡g‡›U 150 Rb †L‡jvqvo Av‡Q. GKRb †L‡jvqvo GKwU
83. nC r nC r1 Gi mgvb †KvbwU?
g¨vP nvi‡jB Uzb©v‡g›U †_‡K we`vq †bq. Ubz ©v‡g‡›U KZwU g¨vP †Ljv n‡q‡Q?
A. nC r1 B. n1C r C. nC r D. Cn1
r 1

Soln: [B] A. 75 B. 76 C. 149 D. 150

84. 8 Rb †jvK cÖ‡Z¨‡K cÖ‡Z¨‡Ki mv‡_ Kig`©b Ki‡j Kig`©‡bi msL¨v n‡e- Soln: [C]

A. 28 B. 8 C. 16 D. 24 93. wekw¦ e`¨vjq fwZ© cix¶vq 4 †Q‡j I 2 Rb †g‡q‡K GK mvwi‡Z emv‡bv

Soln: [A]  Kig`©‡bi msL¨v = 8C2 = 28 n‡e| KZfv‡e emv‡bv m¤¢e †hb †g‡q `Ry b memgq cvkvcvwk e‡m?

85. ZIGZAG kãwUi A¶i¸‡jv‡K †gvU KZRb wfbœ wfbœ AvKv‡i mvRv‡bv A. 60 B. 120

hvq? C. 240 D. 360 E. 270

A. 720 B. 1440 C. 360 D. 180 Soln: [B] `wy U †g‡q‡K GKwU ai‡j †gvU †Q‡j †g‡q 5 Rb| 5 Rb‡K

Soln: [D] ZIGZAG kãwU‡Z †gvU eY© 6 wU hv‡Z G I Z Av‡Q `yBwU GKmvwi‡Z 5! = 120 cÖKv‡i emv‡bv hvq|

K‡i| 94. `yBRb dv‡gm© x wefv‡Mi QvÎ‡K GK‡Î bv ewm‡q 5 Rb imvq‡bi QvÎ I 5

 kãwUi eY©¸‡jvi me¸wj GK‡Î wb‡q mvRv‡bv msL¨v = 6! = 180 Rb dv‡g©mx wefv‡Mi QvÎ KZ iK‡g GKwU †Uwe‡ji cv‡k Avmb wb‡Z cv‡i?
2!2!
A. 2880 B. 2840 C. 2480 D. 2440

86. 0, 1, 2, 3, 4, 5, 6, GB AsK¸‡jv Øviv †Kvb AsK cybive„wË bv K‡i 3000 Soln: [A]

Ges 60000 Gi gv‡S †gvU KqwU wfbœ wfbœ msL¨v wjLv hv‡e? 5 Rb imvq‡bi QvÎ‡K †Uwe‡ji cv‡k ewm‡q Zv‡`i gv‡S dv‡g©mx wefv‡Mi

QvÎ‡K emv‡j `By Rb dv‡g©mx wefv‡Mi QvÎ GK‡Î _vK‡e bv|

|

GKRb‡K wbw`©ó a‡i 5 Rb imvq‡bi QvÎ‡K †Uwe‡ji cv‡k 4! Dcv‡q C. 9 D. †KvbwUB bq
emv‡bv hvq| Soln: [A]
Zv‡`i gv‡S dv‡g©mx wefv‡Mi QvÎ‡K emv‡bv hvq 5! Dcv‡q| 106. n1p3 : n+1p3 = 5:12 n‡j n Gi gvb n‡e-

 †gvU web¨vm msL¨v = 4!  5! = 2880 A. 6 B. 7 C. 8 D. 9
95. CALCULUS kãwUi eY©¸‡jvi me¸‡jv GK‡Î wb‡q KZ cÖKv‡i mvRv‡bv
Soln: [C] n1p3 : n+1p3 = 5:12
hvq †hb 1g I †kl A¶i U _v‡K? (RU 08-09)  12(n–1) (n–2) (n–3) = 5(n + 1) n(n–1)

A. 180 B. 360 C. 81 D. 420  12 (n–2) (n–3) = 5n (n + 1)

Soln: [A] 'Calculus' kãwU‡Z †gvU A¶i 8 wU, hv‡Z C, U, L Av‡Q  12n2 – 60n + 72 = 5n2 + 5n

`By U K‡i| cÖ_g I †kl A¶i C n‡e weavq cÖ_g I †kl ¯’vb `ywU‡Z C Gi  7n2 – 65n + 72 = 0

web¨vm = 1 | Aewkó 6 wU ¯’v‡b Aewkó 6 wU A¶‡ii web¨vm = 6! = 180 9
7
96. GKRb Qv‡Îi 10 Rb mncvVx Av‡Q| Zvi g‡a¨ 4 Rb evÜex| †m KZ  n = 8,

Dcv‡q Zv‡`i‡K cÖwZ MÖæ‡c 5 Rb‡K `vIqvZ Ki‡Z cv‡i †hLv‡b Aek¨B 2 107. 16C4 Gi gvb n‡e-

Rb evÜex _vK‡e?

A. 20 B. 36 C. 120 D. 240 A. 1820 B. 1620 C. 1380 D. 1460

Soln: [C] Soln: [A]

`vIqvZ †`Iqvi m¤¢ve¨ Dcvq wbgiœ ƒc: 108. ALGEBRA kãwUi eY©¸‡jv †_‡K cÖwZev‡i wZbwU K‡i wb‡q KZ¸‡jv
wfbœ wfbœ kã MVb Kiv hvq?
Dcvq eÜz (6) evÜex (4)

(i) 3 2 A. 135 B. 125 C. 140 D. 130

 `vIqvZ †`Iqvi Dcvq = 6C3  4C2 = 120 Soln: [A] ALGEBRA kãwU‡Z †gvU 7 wU eY© Av‡Q Ges Gi g‡a¨ 2 wU
97. npn Gi gvb KZ?
'A'|

A. 1 B. n! mgv‡ek web¨vm

C. n D. 0 (i) 2 wU A Ges 1 wU wfb:œ 1  5C1 = 5 5  3! = 15
2!
n! n! n!
Soln: [B] npn = (n – n)! = 0! = 1 = n! (ii) me wfbœ: 6C3 = 20 20  3! = 120  wfbœ
†gvU evQvB = 25 †gvU web¨vm = 135
98. ncn Gi gvb KZ?
wfbœ kã msL¨v = 135
A. 1 B. n! C. n D. 0 109. hw` nP4 = 6 nP3 nq Zvn‡j n Gi gvb n‡e-

Soln: [A]

99. 8, 9, 7, 6, 3, 2 Øviv wZb AsK wewkó KZ¸‡jv wfbœ wfbœ msL¨v MVb Kiv A. 9 B. 7

hvq? C. 12 D. 4

A. 6 B. 120 Soln: [A]

C. 6! D. 480 110. Parallel kãwUi A¶i¸‡jvi ¯^ieY©¸‡jv‡K GK‡Î †i‡L A¶i¸‡jv

Soln: [B]  †gvU wfbœ wfbœ mvRv‡bvi msL¨v = 6p3 = 120 hZiK‡g mvRv‡bv hvq?

100. 0! Gi gvb KZ? A. 361 B. 362

A. 1 B. 0 C.  D. †KvbwUB bq C. 359 D. 360
Soln: [A]
Soln: [D]
101. n Po Gi gvb-
A. 0 B. 1 C. –1 D. †KvbwUB bq 111. x = nCr Ges y= nCnr n‡j wb‡giœ †KvbwU wVK?

Soln: [B] A. x  y B. x>y

102. 6C4 6 C3 7 C3 Gi gvb- C. x  < 2) n‡j  Gi gvb-

A. 2 tan 2A B. 2 cot 2A C. 2 cos2 A D. 2sin2 A    2
Soln: [B] A. 6 B. 4 C. 3 D. 3

34. cot  sin1 1  -Gi gvb- Soln: [C]
 2
45. sin 65 + cos65 Gi gvb-

A. 2 cos20 B. 2 cos20 C. 2 sin20 D. 2sin20
Soln: [B]

|

46. ABC wÎf‡z Ri cos A + cosC = sin B n‡j C Gi gvb- A. 30 B. 60 C.0 D. 45

   Soln:[B]
A. 4 B. 3 C. 2 D. 6
58. cos + 3 sin = 2, (0 <  < 360) Gi gvb wbY©q Ki|

Soln: [C] A. 45 B. 60 C. 90 D. 120

sin + cos(–) Soln:[B]
sec(–) + tan 
47. hw` tan = 5 Ges cos abvZ¥K nq, Z‡e Gi 59. sin + cos = 2 n‡j  Gi gvb-
12
A. 30 B. 45 C. 60 D. None
gvb n‡e-
Soln:[B]
34 34 30 35
A. 39 B. 40 C. 39 D. 50 60. hw` sin–1 1 2a – cos–1 1 – b2 = 2tan–1 x: nq, Zvn‡j x Gi gvb
+ a2 1 + b2
Soln:[B],
n‡e:
48. hw` cot = 2 nq, Z‡e 10sin2 – 6tan2 Gi gvb n‡e-
1 + ab
A. 1 B. 3 C. 2 D. 0 A. a + b B. a – b

Soln:[D] C. a – b a–b
D. 1 + ab
49. hw` tan  = y nq, Z‡e x cos 2 + y sin 2 Gi gvb n‡e:
x Soln:[D]

A. 2x B. x + y C. x – y D. x 61. hw` sin–1x + sin–1y =  nq, Zvn‡j (x2 + y2) Gi gvb n‡”Q-
2
Soln:[D]

50. hw` cot  + cot β = a, tan  + tan β = b I  + β =  nq Z‡e A. 4 B. 3 C. 2 D. 1

cot  Gi gvb KZ? (KUET 10-11) Soln:[D]

11 1 1 62. mgvavb Ki: 2 tan–1 (cos x) = tan–1 (2 cosec x)
A. a + b a b
B. – A. n  (–1)n4 B. 2n 
3
1 1 1 1
C. a + b D. a – b E. b – a C. n   D. n  
3 4
Soln:[E]
Soln:[D]
51. hw` cotA cotB + cotB cotC + cotC cotA = 1 nq, Z‡e A + B
cos–1 sec–1 x Gi miwjKZ… gvb KZ?
+ C Gi gvb KZ? 63. sin tan y

 B.  3 D. 2 7 x2 – 2y2 2y2 – x2
A. 2 C. 2 E. 2 A. x B. x

Soln:[B] y2 – 2x2 y2 – 2x2
cos 27 – cos 63 C. y D. x
52. cos 27 + cos 63 = ?
2y2 – 2x2
A. sin 18 B. tan 18 E. y

C. cos 18 D. tan 15 E. cot 15 Soln:[B]
Soln:[B]
64. sec2 (tan–14) + tan2(sec–13) Gi gvb KZ?
53. cos + sin = 2 n‡j  Gi gvb- [02-03]
A. 5 B. 25 C. 7 D. None

A. 2n +   Soln:[B
4 B. (4n + 1) 2
65. hw` x = sin cos–1 y nq, Z‡e x2 + y2 Gi gvb n‡e-

–   A. 2 B. 1 C. –1 D. 0
3 6
C. (4n 1) D. n + Soln:[B],

Soln:[A] 66. (a + b + c) (b + c – a) = 3bc n‡j A †Kv‡bi gvb wbY©q Ki|

hw` y nq, Z‡e x cos 2 + y sin 2 Gi gvb n‡e: A. 30 B. 0 C. 60 D. 45
x
54. tan  = Soln:[C]

A. 2x B. x + y C. x – y D. x 67. GKwU wÎf‡~ Ri evû¸‡jv h_vµ‡g 5, 12 Ges 13 cm n‡j wÎf~RwU

Soln:[D] n‡e|

55. hw` tan2 + sec  = –1; 0 <  < 2 nq, Z‡e  Gi gvb n‡e- A. ¯’j~ ‡KvYx B. m²~ ‡KvYx

C. mg‡KvYx D. 60 †KvYx E. None

A.    3 Soln:[C]
B. 2 C. 4 D. 2

Soln:[A] 68. sin(780) cos(390) – sin (330) cos(–330)-Gi gvb-

56. hw` cot2 + cosec – 5 = 0 nq ZLb  abvZ¡K, Zvn‡j 0 <  <  A. 0 B. –1 1 D. 1
2 C.
2
Gi Rb¨  Gi gvb n‡e?
Soln: [D]

A. 0 B. 30 C. 45 D. 60 69. cot x – tan x = 2 mgxKi‡Yi mvaviY mgvavb-
Soln:[B]
4n 1 n n 4n 1
57. mgvavb Ki: tan 2 tan  = 1, 0 ≤  ≤  C.
2 A. B. D.
84 2 2

Soln: [A]

|

70. tan–16+tan–1 5 -Gi gvb-  B.   
7 A. C. D.

4 3 2

3 2 5  Soln: [D]
A. B. C. D.
84. tan(–15)-Gi gvb KZ?
4 4 4 4

Soln: [*] A. 2  2 B. 3  2 C. 2  3 D. 5
Soln: [C]
Correct Ans. option-G †bB| Correct Ans. 116.075

71. cos 198 + sin 432 + tan 168 + tan 12-Gi gvb- 85. sin  = 1 mgxKi‡Yi mvaviY mgvavb Kx?
2
 B. 1 C. 0 D. –1
A.
2
A. n + (1)n  B. 2n + 
Soln: [C] 4
4
72. cos + sin = 2 n‡j -Gi gvb- C. n  
D. 2n  
A. 2n  D. (2n–1) 4
B. (2n+1) C. 2n+ Soln: [A] 4

4

Soln: [C] 86. cos  = 12 n‡j tan  Gi gvb KZ?
13
73. sin(780) cos(390) – sin(330) cos(–300)-Gi gvb-

1 B. –1 C. 1 D.  1 13 B.  13 C. 25 D.  5
A. 2 A. 12 144 12

2 D. 2 12

Soln: [C] Soln: [D]

74. tan–1 1+ tan–1 2 + tan–1 3-Gi gvb- 87. Sin (4x+1) Gi e„Ëxq dvsk‡bi ch©vqKvj KZ?

A. 0 B.  C.  A. 2 B.  C.  D. 

2 42

75. 2 cos2  + 2 2 sin  = 3 n‡j -Gi gvb- Soln: [D]

A. 30 B. 45 C. 60 D. 120 88. Cos2θ  1 mgxKi‡Yi mvaviY mgvavb †KvbwU?
D. 1 2
Soln: [B]

76. cos  + i sin = KZ? A. 2   B.    C. 2   D.   
33 88
A. 0 B. i C. –1
Soln: [C] Soln: [C]

77. 2(cos2–sin2) = 3 n‡j -Gi gvb- 89. tan20+tan25+tan25tan20-Gi gvb KZ?

A. 2n/6 B. n/6 1
D.
C. 2n/12 D. n/12 A. 1 B. 0 C.  2
Soln: [D]
Soln: [A]
78. †KvbwU mwVK bq?
90. sec2(tan13)  cosec2(cot15) -Gi gvb KZ?
A. cosec(–)= –cosec B. sec(–)= –sec
C. cos(–)= cos() D. cot(–)= –cot() A. 36 B. 63 C. 1 D. 0
Soln: [B]
Soln: [A]
79. tan C-Gi ch©vqKvj-
91. tan (-1125) -Gi gvb KZ?

A. 2 B.  C. 3 D. 4 A. 1 B. -1 C.  1
Soln: [B] D.
2

80. sin75  sin15 mgvb- Soln: [B]
sin75  sin15
92. t = x + 1 GB mgxKiYwU †jLwPÎ n‡e (x  0)

1 1 A. B. C. D.
B. C.
A. 3 D. 2 tt tt
2 3

Soln: [A] O x O xO xO x

81. GKwU wÎfy‡Ri evû¸‡jv 13, 14 Ges 15 GKK n‡j wÎfRy wUi

†¶Îdj- Soln: [B]

A. 84 sq. units B. 88 sq. units 93. hw` cosφ  1 , 3π  φ  2π n‡j tanφ -Gi gvb n‡e-
D. 64 sq. units 22
C. 80 sq. units
Soln: [A] A.  3 B. 3 C. 3 / 2 D.  3 / 2

82. tan x-Gi ch©vqKvj- Soln: [A]

A. 2 B.  C. 3 D. 4 93. cos (sin-1x)= KZ ?

Soln: [B]

83. tan–1x+cot–1x = KZ? A. 1  x 2 B. x 2  1 C.  1  x2 D.  1 x2
Soln: [D]

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95. mwVK MvwYwZK A‡f`wU n‡”Q  105. tan cot1x -Gi gvb-

A. sin(   )  sin  B. sin(  )  sin  A. x B. 1
x
C. sin(  )   sin  D. sin(  )   sin 

Soln: [D] C. 1 D. x E. 1 x2
x2 1 1 x2
96. sinA  12 n‡j cosA-Gi gvb
13 Soln: [B]

5 B.  5 C.  5 D.  5 106.cosA + sinA = 2 CosA n‡j cosA –sinA n‡e-
A. 13 13 12
A. 2 sinA B. 2 sinA
13

Soln: [C] .

97. hw` tanθ   5 nq Z‡e cos -Gi gvb n‡e- C. 2SinA D. 2 sinA E. 5 sinA
12 Soln: [B]

A.  13 B. 5 C. 12 D.  12 E. 12 107.sin= 3 n‡j  Gi gvb n‡e (hLb 3600

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