The document contains instructions for a math exam for Class XII. It states that the paper contains 50 multiple choice questions (MCQs), and to darken the appropriate circle on the answer sheet. Each correct answer receives 4 marks, incorrect answers receive -1 mark, and unattempted questions receive 0 marks. It wishes the student good luck for their bright future.

1. MATHS MIND 2013
CLASS XII
Name ………………………………………………………………………………
Roll No. ………………………………………………………………………………
School ………………………………………………………………………………
INSTRUCTIONS
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 The paper comprises of 50 M.C.Q.’s.
 Darken the appropriate circle in the O.M.R. sheet.
Each correct answer will give you 4 marks, each incorrect answer will give you ‘ –1‘ and there is no mark for
an unattempted question.
 Best wishes to you for a bright future.
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1. If 4 cos -1x + Sin-1x = 휋, then value of x i s
(a) √3
2
(b)
1
√2
(c)
−1
2
(d)none of these
2. Let R be a relation in Z defined by aRb i f and only i f ab ≥ 0 for all a,b ∈ Z. Then R i s:
(a) Only Reflexive (b) Only Symmetric (c) Only Transitive (d) Equivalence
2푥 0
푥 푥
3. If A=[
1 0
−1 2
] and A-1= [
], then x=
(a) 1 (b)2 (c) 1/2 (d) none of these
4. The di fferential equation of family of lines passing through origin is:
(a) x
푑푦
푑푥
+y=0 (b)
푑푦
푑푥
=y (c)
푑푦
푑푥
= x (d) x
푑푦
푑푥
- y=0
5. Let A be any m × n matrix, then A2 can be found only when
(a) m> n (b)m < n (c) m = n (d) None of these
6. If there is an error of a% in measuring the edge of a cube, then percentage error in i ts surface area is
(a) 2a % (b) a/2 % (c) 3a% (d) None of these
7. If f(x) i s differentiable in the interval [2,5 ] where f(2) = 1/5 and f(5) = 1/2, then there exist a number c, 2<c<5 for whi ch f’(c)=
(a)
1
2
(b)
1
5
(c)
1
10
(d)0
8. If y = tan-1(
푠푖푛푥+푐표푠푥
푐표푠푥−푠푖푛푥
), then
푑푦
푑푥
is equal to
(a) 1/2 (b) 1 (c) 0 (d) 3/2
9. If 푎⃗ and 푏 ⃗⃗⃗⃗are the unit vectors inclined at an angle 휃, then the value of |푎⃗ -푏⃗⃗| is
(a) 2 s in휃/2 (b) 2 s in휃 (c) 2cos 휃/2 (d)2cos 휃
10. Some positions of a dice are given below.
Which number i s opposite to 4?

2. (a) 1 (b) 2 (c) 3 (d) 6
11. The value of ∫ 푥(1 − 푥) 1 99
0 푑푥 i s
(a)
1
10100
(b)
11
10100
(c)
1
10010
(d)none of these
12. If A i s a finite s et having n elements, then no. of relations which can be defined in A i s
(a) n 2 (b) 2 n (c)
2
2n (d) nn
13. Q+ i s the s et of all positive rational numbers with the binary operator * defined by a * b =
푎푏
2
, then inverse of 3 i s
(a) 4/3 (b) 2 (c) 1/3 (d) 2/3
휋
0 i s =
(a) 0 (b) 1 (c) 2 (d) 휋
14. ∫ | cos 푥|푑푥
15. If 푎⃗. 푖̂ = 4, then (푎⃗ x 푗)̂ . (2푗 ̂- 3푘̂) =
(a) 12 (b) 2 (c) 0 (d) -12
16. Value of [푖̂ 푗 ̂푘̂] + [푘̂ 푗 ̂푖̂] + [푗 ̂푖̂ 푘̂] =
(a) 0 (b) 1 (c) 3 (d) -1
17. Out of 15 ti cke ts 1, 2, …….. 15, thre e a re drawn at random. The chances that numbers on them are in AP i s
(a)
9
39
(b)
9
15
(c)
13
261
(d)
7
65
18. A speaks truth in 75% cases & B speaks truth in 80% cases. The probability that they contradict each other in a statement is:
(a) 7/20 (b) 13/20 (c) 3/5 (d) 2/5
19. If y=e3logx , then
푑푦
푑푥
is equal to
(a)
e3logx
푥
(b)
3e3logx
2푥
(c)3x2 (d)None of these
20. The re is a herd consisting of cows, oxen a nd 45 he ns. Ea ch 15 of the group a re gove rned by a ‘gwala’. The number of oxen is twice
the number of cows and the number of heads is 186 less than the number of legs (including the gwala). The total number of gwalas
is
(a) 5 (b) 6 (c) 9 (d) 15
21. If Cos (2Sin-1x) = 1/9, then x i s equal to
(a)
2
3
(b)
−2
3
(c) ∓
2
3
(d)None of these
1 1
1 1
22. If A= [
], then A100 i s equal to
(a) 2100A (b) 299A (c)2101A (d)None of these
23. A. Adj A i s equal to
(a) I (b)|A|n (c)|A|Ι (d) Zero
푒
1 i s equal to
(a) 0 (b) 1 (c) e-1 (d) e+1
24. ∫ 푙표푔푥 푑푥
25. Area between the parabolas y2 = 4x and x2 = 4y i s (in square units)
(a)
4
3
(b)
1
3
(c)
8
3
(d)
16
3
26. The probability for a randomly chosen month to have its 10th day as Sunday is
(a)
1
84
(b)
10
12
(c)
10
84
(d)
1
7
27. If 훼 , 훽, 훾 are the angles that a l ine makes withn the coordinate axes, then Sin2훼 + Sin2훽+ Sin2훾 = k, where k i s
(a) 0 (b) 1 (c) 2 (d) 3
28. The di stance between the planes 2x – 3y + 6z +8 = 0 & 4x – 6y + 12z + 8 = 0 i s

3. (a)
12
7
(b)
4
√7
(c)
4
7
(d) None of these
29. The number of arbitrary constants in the general solution of a differential equation of order 4 are
(a) 4 (b) 2 (c) 3 (d) Ca n’t s ay
30. Observe carefully the two cogged wheels A and B:
After how many revolutions of A and of B respectively, will they be exactly in the same position again?
(a) 3,4 (b) 4,3 (c) 2,4 (d) 3,2
31. Integrating factor(I.F.) of the differential equation x
푑푦
푑푥
-y =2x2 i s
(a) 푒 −푥 (b)푒 −푦 (c)
1
푥
(d) x
32. A & B throw a coin alternately ti ll one of them gets a head & wins the game. If A has the first throw; then the probability of winning
for A & B are respectively
(a)
1
4
,
3
4
(b)
1
3
,
2
3
(c)
2
3
,
1
3
(d)None of these
33. The function f(x)= x+ Cosx i s
(a) Always increasing (b) Always Decreasing (c) Increasing for certain range of x
(d) None of these
34. The local maximum value of
푙표푔푥
푥
0< x< ∞ is
(a)
1
푒
(b)-e (c)0 (d)e
35. Which of the following function is even?
(a) x3Sin3x (b) x2-|x|+x (c)
(1+2푥)2
2푥
(d)tan-1x
36. h(x)= e3x , g(x)= logx ; (x> 0), then (hog)(x) is
(a) 3x (b)x3 (c)log3x (d)None of these
37. A and B be two non zero square matrices. If AB is a null matrix, then
(a) A & B are s ingular (b)B i s non s ingular (c)A i s non singular (d)None of these
38. If √1 − 푥2 + √1 − 푦 2 = a(x-y) ; then
푑푦
푑푥
i s
1−푥2
1−푦2 (c) √1−푦2
1−푥2 (d)None of these
(a) √(1 − 푥2 )(1 − 푦 2) (b)√
푎
0 i s equal to
39. If f(a-x)=f(x) ; then ∫ 푥 푓(푥)푑푥
(a)
푎
2
푎
표 (b) a ∫ 푓(푥) 푑푥
∫ 푓(푥) 푑푥
푎
표 (c)
1
2
푎
표 (d)None of these
∫ 푓(푥) 푑푥

4. 40. There is family of six persons P, Q, R, S, T and U. They are engineer, doctor, teacher, salesman, manager and lawyer. There a re two
married couples in the family. The manager is the gra ndfather of U, who is an engineer. R, the salesman is married to the lady
teacher. The doctor S i s married to the manager. Q i s the mother of U and T. How many male members are there in the family?
(a) 2 (b) 3 (c) 4 (d) data inadequate
41. If Sin-1x+Sin-1y+Sin-1z =
3휋
2
, then the value of x100+y100+z100 -
9
푥101 +푦101+푧101 i s
(a) 0 (b) 1 (c) 2 (d) 3
42. Equation of plane passing through (2,3,4) and parallel to plane x+2y+4z=5 i s
(a) x+2y+4z=24 (b) x+2y+4z=20 (c) x+2y+4z=3 (d) x+2y+4z=10
43. Angl e between the line
푥−2
3
=
푦−3
4
=
푧−4
5
and plane i s 2x-2y+z =5 i s
(a) Sin-1(
10
6√5
) (b) Sin-1(
4
5√2
) (c) Sin-1(√2
10
) (d) Sin-1(
2√2
5
)
1
0 dx i s equal to
44. Value of ∫ tan−1 (
2푥−1
1+푥−푥2 )
(a) 1 (b)0 (c)-1 (d)
휋
4
45. If |
6푖 −3푖 1
4 3푖 −1
2 3 푖
| = x+iy , then
(a) x=3, y=1 (b) x=1, y=3 (c) x=0,y=3 (d) x=0, y=0
46. If each element of 3×3 matrix A i s multiplied by three, then determinant of newly formed matrix is
(a) 3 detA (b) 9 detA (c) (detA)3 (d) 27 detA
47. ∫
√푡푎푛푥
푠푖푛푥 푐표푠푥
dx i s equal to
(a) 2√푐표푡푥 + c (b)
1
2 √푡푎푛푥 + c (c)2√푡푎푛푥 + c (d)None of these
48. Smaller area bounded by the circle x2+y2=4 and the line x+y=2 i s (in suare units)
(a) 2(휋-2) (b) 휋-2 (c)2휋-1 (d)2(휋 +2)
49. The angle between the lines
푥−2
3
=
푦+1
−2
=
푧−2
0
and
푥−1
1
=
2푦+3
3
=
푧+5
2
is
(a)
휋
2
(b)
휋
3
(c)
휋
6
(d)None of these
50. A i s 100 days elder to B, B i s 100 weeks and a day younger than C, C i s 200 weeks and 2 days elder to D. D i s 1000 days elder to E. If
E was born on Monday, A was born on
(a) sunday (b) monday (c) tuesday (d) none of these