# Class 12 Mathematics Sample Paper With Solutions Set O

Please refer to Class 12 Mathematics Sample Paper With Solutions Set O below. These Class 12 Mathematics Sample Papers will help you to get more understanding of the type of questions expected in the upcoming exams. All sample guess papers for Mathematics Class 12 have been designed as per the latest examination pattern issued by CBSE. Please practice all CBSE Sample Papers for Mathematics in Standard 12.

## Sample Paper Class 12 Mathematics With Solutions Set O

1. Let f (x)

x∈ R,where a, b and d are non-zero real constants. Then,
(a) f is an increasing function of x
(b) f is is not a continuous function of x
(c) f is a decreasing function of x
(d) f is neither increasing nor decreasing function of x

A

2. Let K be the set of all real values of x,where the function f (x) = sin|x|-|x| + 2(x – p)cos|x|is not differentiable.
Then, the set K is equal to
(a) {0}
(b) Φ (an empty set)
(c) {π}
(d) {0, π}

B

3. Let z be a complex number such that |z|+ z = 3 + i (where i = √- 1).
Then,|z|is equal to
(a)√34/3
(b)5/3
(c)√41/4
(d)5/4

B

4. Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression

(a)1/2
(b) 1
(c)1/4
(d)m+n/6 m n

C

5.

(a) injective only
(b) both injective as well as surjective
(c) not injective but it is surjective
(d) neither injective nor surjective

D

6.

(a) 12.25
(b) 12.50
(c) 12.00
(d) 12.75

A

7. Let A and B be two invertible matrices of order 3×3. If det(ABAT) = 8 and det(AB-1 ) = 8, then det (BA-1 B T) is equal to
(a) 1
(b)1/4
(c)1/16
(d) 16

C

8. The integral

C

9. The area (in sq units) in the first quadrant bounded by the parabola, y = x2 + 1, the tangent to it at the point (2, 5) and the coordinate axes is
(a)14/3
(b)187/24
(c)8/3
(d)37/24

D

10. If 19th term of a non-zero AP is zero,then its (49th term) : (29th term) is
(a) 1 : 3
(b) 4 : 1
(c) 2 : 1
(d) 3 : 1

D

11. If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x – 5y = 15, then 2α – 3β is equal to
(a) 17
(b) 7
(c) 5
(d) 12

B

12. A circle cuts a chord of length 4 a on the X-axis and passes through a point on the Y-axis, distant 2b from the origin. Then, the locus of the centre of this circle, is
(a) a parabola
(b) an ellipse
(c) a straight line
(d) a hyperbola

A

13.

where q is a real number and q ≠ 1. if

(a) 2100
(b) 202
(c) 200
(d) 299

A

14. All x satisfying the inequality
(cot– 1 x)2 – 7(cot– 1 x ) +  10> 0, lie in the interval
(a) (-∞, cot 5) ∪ (cot 2, ∞)
(b) (cot 5, cot 4)
(c) (cot 2, ∞)
(d) (- ∞, cot 5) ∪ (cot 4, cot 2)

C

15. The number of functions f from {1, 2,3, … , 20} onto {1, 2, 3, … , 20} such that f (k) is a multiple of 3, whenever k is a multiple of 4, is
(a) (15)! x 6!
(b) 56 x 15
(c) 5! x 6!
(d) 65x (15)!

A

16. Let the length of the latus rectum of an ellipse with its major axis along X-axis and centre at the origin, be 8.
If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?
(a) (4 √2, 2 √3)
(b) (4 √3, 2 √2)
(c) (4 √2,  2√2)
(d) (4 √3, 2 √3)

B

17. Let α and β be the roots of the quadratic equation x x2 q q q q sin(sin2cos ) cos

B

18.

(a) – (a + b + c)
(b) – 2(a + b + c)
(c) 2(a + b + c)
(d) abc

B

19. The solution of the differential equation, dy/dx = (x – y)2, when y(1) = 1, is

D

20. Contrapositive of the statement “If two numbers are not equal, then their squares are not equal” is
(a) If the squares of two numbers are not equal, then the numbers are not equal.
(b) If the squares of two numbers are equal, then the numbers are equal.
(c) If the squares of two numbers are not equal, then the numbers are equal.
(d) If the squares of two numbers are equal, then the numbers are not equal.

B

21.

(a) 0
(b) 1
(c) 4
(d) 2

B

22. A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then (mean of X /standard deviation of X) is equal to
(a)4√3
(b) 4
(c) 3√2
(d) 4 √3

D

23. If the area of the triangle whose one vertex is at the vertex of the parabola,y2+4(x-a2)=0  and the other two vertices are the points of intersection of the parabola andY-axis, is 250 sq units, then a value of ‘a’ is
(a) 5 √5
(b) 5
(c) 5 (21/3
(d) (10)2/3

B

24. Two lines x-3/1=y+1/3=z-6/-1 and x +5/7=y-2/-6=z-3/4 intersect at the point R. The reflection of R in the xy-plane has coordinates
(a) (2, – 4, – 7)
(b) (2, – 4, 7)
(c) (- 2, 4, 7)
(d) (2, 4, 7)

A

25.

where C is a constant of integration,then f (x) is equal to
(a)2/3(x+2)
(b)1/3(x+4)
(c)2/3(x-4)
(d)1/3(x + 1)

B

26. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is
(a)13/12
(b) 2
(c)13/8
(d)13/6

A

27. Let S = {1, 2,…, 20}. A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Then, the probability that a randomly chosen subset of S is ‘‘nice’’, is
(a)6/220
(b)4/220
(c)7/220
(d)5/220

D

28. If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is
(a) 3x + 5y – 13 = 0
(b) 3x – 5y + 7 = 0
(c) 5x – 3y + 1 = 0
(d) 5x + 3y – 11 = 0

C

29.

respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle 3/√2 sum of all possible values of β is
(a) 1
(b) 3
(c) 4
(d) 2