Math 1st & 2nd - PDF Flipbook
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 = 05100 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 = 60 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 22 – 23 = –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 np,then the
Dimension Of Matrix A B is mp.
( + 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 = 11113 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 = 16000 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 = 1000 1011 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 45 = 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 mn Ges np 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. nm B. mn =
C. np D. pn E. mp
Soln: [E] A matrix Gi order mn I B matrix Gi order np n‡j 3xx22yy75
Solving x = 3, y = –2
AB Gi order mp.
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 23 Ges B matrix Gi order A–B = 13 2 4 2 2
4 6 3 7 = 2
33 | Avgiv Rvwb, A matrix Gi order mn I B matrix Gi order np 10
n‡j AB Gi order mp. So GLv‡b AB Gi order n‡e 23 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 23 35
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 XY = 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+2A11l 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 23 Ges 35 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 52 D. AB Gi gvÎv n‡e 33
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 k4
C. [6 4 3] D. [1 1 2]
Soln: [A] AB = [2 + 4 – 4 + 5 0 – 3] = [6 1 –3] β2 1
53. hw` A GKwU mn AvKv‡ii g¨vwU· Ges B GKwU n p AvKv‡ii g¨vwU·ª nq 61. 5 β4 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| xy x y
57. g¨vwU·ª A Gi gvÎv 24 Ges g¨vwU· B Gi gvÎv 43 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 yz
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 a4 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 xz z Gi gvb- y
y z yz
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 bc
= log yx log yz 1 1 log 2z = 0
67. b 1 c a Gi gvb n‡e-
1 1 log 3z
c 1 ab 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 bc abc 1 abc
Soln: [A] b 1 c a = a b c 1 a b c
c 1 ab abc 1 abc
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 α2 Gi gvb k~b¨ n‡j Gi gvb-
α4 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 xy 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 yz
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 bc 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 | ab 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 bc a abc 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 bc ab c abc c
79. b 1 c a Gi gvb KZ?
c 1 ab 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 bc a 1 abc 1 x yz
Soln: [B] b 1 c a = b 1 a b c c'3 = c1+c3
85. 1 y z x ?
c 1 ab c 1 abc 1 z xy
†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 yz 1 x xyz
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 xy 1 z xyz
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 yz = KZ? 94. 1 1 1 wbY©vqKwUi gvb 2 n‡j k Gi gvb-
1 y zx 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 xy 1 z xyz 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
Soln: [B] Dci A †f±‡ii Awf‡¶c n‡”Q-
F1 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]
ab
C. 7i 7j D. 3i 7 j 13. hw` a ˆi 2ˆj 3kˆ Ges bˆ 3ˆi ˆj 2kˆ nq, Z‡e Ges
4. SBoln: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±i؇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. cos1 4 B. cos1 2
25 25 A B .B -Gi gvb-
C. cos1 4 D. cos1 3 E. cos1 4 A. 2 B. 3 C. 4 D. 1
21 25 25 Soln: [D]
24. SBoln: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` ej؇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]
Soln: [A]
26. A i j k Ges B i j k †f±i؇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 -Gi 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]
|
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. SAoln: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›`y؇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)
Soln: [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. cos1 3 B. cos1 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. cos1(1) D. †KvbwUB bq 6. (2, –1), (a + 1, a – 3) I (a + 2, a) we›`y wZbwU mg‡iL n‡j a Gi
Soln:[B] gvb-
46. i j 2k Ges 2i 2j 4k †f±i؇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]
|
10. (1, 2) (4, 4) I (2, 8) h_vµ‡g wÎfR~ ABC Gi evû·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. 66.4 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]
|
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. 42 [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. (43, /6) B. (33, /6) A. 6 B. 8 C. 10 D. 12 [B]
C. (23, /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-
|
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 22 y 12 4 B. x 22 y 12 42
C. (1, 1) D. (1, 3) [C] C. x 22 y 12 4
57. wÎfz‡Ri kxl© we›`¸y wj h_vµ‡g (2, 5), (3, 6), (7, 4) n‡j,
†¶Îdj- D. x 22 y 12 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 cive˄ B. GKwU Dce˄
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. 2x5y+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‡iLv؇qi †Q`we›`y Ges
84. (–5, 7) I (3, – 1) we›`y؇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] †iLv؇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. 22
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. 2x
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‡iLv؇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‡iLv·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‡iLv؇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 †iLv؇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
2x
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. a1a2b1b2 =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 ؇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 – 53 = 0 D. 3x + y – 53 = 0
D. y + 5x + 0.5 = 0 E. †KvbwUB bq [B] E. x – 3y – 53 = 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 †iLv؇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 †iLv؇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]
|
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. xA¶ B. yA¶
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‡iLv؇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`vsk؇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
|
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 †iLv؇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 †iLv؇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 †iLv؇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 †iLv؇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 †iLv؇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?
|
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 †iLv؇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 †iLv؇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 †iLv؇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 †iLv؇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]
|
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›`y؇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 3x4y+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)
|
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›`y؇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„ ؇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
|
¯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?
|
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„ˇK
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. sin1(6 / 5) B. sin1(3/ 5)
C. 3x 2y = 3 D. 4x = 6 E. 3x + 2y = 3
Soln: [B] C. 2sin1(3/ 5) D. tan1(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„ˇK ¯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 mxy=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-
|
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. 32 GKK B. 23 GKK C. 52 GKK D. 25 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. 32 D. 32
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„ˇK ¯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›`y؇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| e˄ 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©-
|
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„ˇK 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 + y218x 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 [19971998]
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
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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. 3106 D. 3104 E. 7104 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 012C12 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 = 6nP3 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 r1 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 r1 B. n1C r C. nC r D. Cn1
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 Qv·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 Qv·K †Uwe‡ji cv‡k ewm‡q Zv‡`i gv‡S dv‡g©mx wefv‡Mi
Qv·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 Qv·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 Qv·K emv‡bv hvq 5! Dcv‡q| 106. n1p3 : 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] n1p3 : 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= nCnr 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 sin1 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]
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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)n4 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]
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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+tan25tan20-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(tan13) cosec2(cot15) -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 cot1x -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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