# Class 12 Mathematics Sample Paper With Solutions Set N

Please refer to Class 12 Mathematics Sample Paper With Solutions Set N 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 N

1. If for some x ∈R, the frequency distribution of the marks obtained by 20 students in a test is

Then, the mean of the marks is
(a) 3.0
(b) 2.8
(c) 2.5
(d) 3.2

B

2. If Q(0, – 1, – 3) is the image of the  point P in the plane 3x – y + 4z = 2 and R is the point (3, – 1, – 2) , then the area (in sq units) of Δ PQR is
(a) √91/2
(b) 2 √13
(c)√9/14
(d) √65/2

A

3. If the circles

intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for
(a) no values of K
(b) exactly one value of K
(c) exactly two values of K
(d) infinitely many values of K

A

4.

A

5.

C

6 If a directrix of a hyperbola centred at the origin and passing through the point (4, – 2 √3) is 5x = 4 √5 and its eccentricity is e, then

D

7. If the line x – 2y = 12 is tangent to the ellipse x2/a2+y2/b2= 1at the point (3,-9/2), then the length of the latusrectum of the ellipse is
(a) 8√ 3
(b) 9
(c) 5
(d) 12√2

B

8. If α and β are the roots of the quadratic equation,

A

9. The number of 6 digits numbers that can be formed using the digits 0, 1, 2,5, 7 and 9 which are divisible by 11 and no digit is repeated, is
(a) 60
(b) 72
(c) 48
(d) 36

A

10.

(a) 64
(b) 76
(c) 98
(d) 38

B

11. ABC is a triangular park with AB = AC = 100m. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are cot-1 (3√2 )  and cosec-1 (2√2) respectively, then the height of the tower (in m) is
(a) 25
(b) 20
(c) 10 √5
(d)1003√3

B

12.

C

13. The region represented by|x – y|≤ 2
and|x + y|≤ 2 is bounded by a
(a) rhombus of side length 2 units
(b) rhombus of area 8 √2 sq units
(c) square of side length 2 2 units
(d) square of area 16 sq units

C

14.

B

15. If the length of the perpendicular from the point (β, 0, β) (β ≠ 0) to the line,

equal to
(a) 2
(b) – 2
(c) – 1
(d) 1

C

16.

C

17.

C

18.

(a)4/3
(b)3/8
(c)3/2
(d)8/3

D

19.

(a) 2|sin x| = 3 sin y
(b) sin x =|sin y|
(c) sin x = 2 sin y
(d) 2 sin x = sin y

B

20. The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, – 3), then its radius is
(a) 3√2
(b) 2√2
(c) 2
(d) 3

B

21. Let A(3, 0, -1), B (2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the mid-point of AC. If G divides BM in the ratio 2 : 1, then cos (∠ OA) (O being the origin) is equal to
(a) 1/√15
(b)1/2√15
(c)1/√30
(d)1/6 √10

A

22. Which one of the following Boolean expressions is a tautology ?
(a) (p v q) Ú (p v ~ q)
(b) (p ∧ q) Ú (p ∧ ~ q)
(c) (p v q) Ù (p v ~ q)
(d) (p v q) ∧ (~ p ∧ ~ q)

A

23. Let f : R→ R be differentiable at c∈R and f (c) = 0. If g(x) =|f (x)|, then at x = c, g is
(a) not differentiable
(b) differentiable if f ‘ (c) ≠ 0
(c) not differentiable if f ‘ (c) = 0
(d) differentiable if f’  (c) = 0

D

24. If the coefficients of x2 and x3 are both zero, in the expansion of the expression (1 ) + ax + bx2 (1- 3x )15 in powers of x, then the ordered pair (a, b) is equal to
(a) (28, 315)
(b) (- 21, 714)
(c) (28, 861)
(d) (- 54, 315)

A

25.

(a) 680
(b) 600
(c) 660
(d) 620

C

26. Assume that each born child is equally likely to be a boy or a girl. If two families have two children each,then the conditional probability that all children are girls given that at least two are girls; is
(a)1/17
(b)1/12
(c)1/10
(d)1/11

D

27. If the system of linear equations
x + y + z = 5
x + 2y + 2z = 6
x + 3y + λz = µ,(λ,µ ∈R),
has infinitely many solutions, then the value of λ + µ is
(a) 7
(b) 12
(c) 10
(d) 9

C

28.

is continuous at x = 0 , then the ordered pair (p, q) is equal to

D

29.

30. The value of//3 [sin 2x (1+ cos 3x )] dx,where [t]denotes the greatest integer function, is
(a) – π
(b) 2π
(c) – 2π
(d) π