CBSE Class 12 Mathematics Sample Paper Set O

Sample Paper Class 12

1. Let P(4, – 4) and Q(9, 6) be two points on the parabola, y x 2 = 4 and let X be any point on the arc P O Q of this parabola, where O is the vertex of this parabola, such that the area of Δ P X Q is maximum. Then, this maximum area (in sq units) is
(a)125/2
(b)75/2
(c)625/4
(d)125/4

Answer

D

2. Consider three boxes, each containing 10 balls labelled 1, 2, …, 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box,(i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n1<n2<nis
(a) 82
(b) 120
(c) 240
(d) 164

Answer

B

3. Let y = y(x) be the solution of the differential equation,

(a) – e/2
(b) – e2/2
(c)e/4
(d)e2/4

Answer

C

4. The sum of the distinct real values of

(a) 2
(b) 0
(c) 1
(d) – 1

Answer

D

5. Let C1 and C2 be the centres of the circles x2+Y2-2X-2Y-2=0 and x2+Y2-6X-6Y+14=0 respectively.
If P andQ are the points of intersection of these circles, then the area (in sq units) of the quadrilateral PC1 QC2 is
(a) 8
(b) 4
(c) 6
(d) 9

Answer

B

6. If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β),then β equals
(a) 35/3
(b) – 5
(c) – 35/3
(d) 5

Answer

D

7. A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of

Answer

C

8. Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even, is
(a) 250 (250– )
(b) 250 -1
(c) 250 +1
(d) 2 100 -1

Answer

A

9. The maximum area (in sq. units) of a rectangle having its base on the X-axis and its other two vertices on the parabola, y = 12 – x2 such that the rectangle lies inside the parabola, is
(a) 36
(b) 20√2
(c)32
(d) 18√3

Answer

C

10.

Answer

A

11. 

(a) 4√2
(b) 4
(c) 8
(d) 8√2

Answer

C

12. An ordered pair (a, b) for which the system of linear equations
(1 + a)x + by + z = 2
ax + (1 + b)y + z = 3
ax + by + 2z = 2
has a unique solution, is
(a) (2, 4)
(b) (- 4, 2)
(c) (1, – 3)
(d) (-3, 1)

Answer

A

13. If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is
(a) 50
(b) 30
(c) 51
(d) 31

Answer

D

14.

Answer

B

15. The maximum value of 3 cosθ+5 sin (θ-π/6) for any real value of θ is
(a)√79/2
(b) √34
(c) √31
(d) √19

Answer

D

16. The area (in sq units) of the region bounded by the parabola, y = x2 + 2 and lines, y = x + 1, x = 0 and x = 3, is
(a)15/2
(b)17/4
(c)21/2
(d)15/4

Answer

A

17. 

Answer

D

18. If a variable line, 3x + 4y – λ = 0 is such that the two circles x2+Y2-2X-2Y+1=0 and x2+Y2-18X-2Y+78=0  are on its opposite sides, then the set of all values of λ is the interval
(a) [13, 23]
(b) (2, 17)
(c) [12, 21]
(d) (23, 31)

Answer

C

19. The perpendicular distance from the origin to the plane containing the two lines,

(a) 11√6
(b)11/√6
(c) 11
(d) 6 √11

Answer

B

20. If λ be the ratio of the roots of the quadratic equation in x,3m2x2+m(m-4)x+2=0,then the least value of m for which λ+1/λ=1,
(a) – 2 + √2
(b) 4 – 2 √3
(c) 4 – 3 √2
(d) 2 – √3

Answer

C

21. Considering  only the principal values of inverse functions, the set

(a) is an empty set
(b) is a singleton
(c) contains more than two elements
(d) contains two elements

Answer

B

22. If the vertices of a hyperbola be at (-2, 0) and (2,0) and one of its foci be at (-3, 0), then which one of the following points does not lie on this hyperbola?
(a) (2 √6, 5)
(b) (6, 5 √2)
(c) (4, √15)
(d) (- 6, 2 √10)

Answer

B

23. If z-α/z+α(α∈ R)is a purely imaginary number and|z| = 2, then a value of α is
(a) √2
(b)1/2
(c) 1
(d) 2 B

Answer

D

24.

(a) 10
(b) 135
(c) 9
(d) 15

Answer

A

25. In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to
(a)175/65
(b)225/65
(c)200/65
(d)150/65

Answer

A

26. Let S be the set of all points in (- π, π) at which the function,
f (x) = min {sin x, cos x} is not differentiable. Then, S is a subset of which of the following?

Answer

C

27. A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(- 1, 1, 2) and O(0, 0, 0). The angle between the faces O P Q and PQR is

Answer

C

28. The product of three consecutive terms of a GP is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an AP. Then, the sum of the original three terms of the given GP is
(a) 36
(b) 28
(c) 32
(d) 24

Answer

B

29.

(a) 156
(b) 301
(c) 283
(d) 303

Answer

D

30. Let f and g be continuous functions on [0, a] such that f (x) = f (a – x) and g(x) + g(a – x) = 4, then

Answer

C