# CBSE Class 12 Mathematics Sample Paper Set N

See below CBSE Class 12 Mathematics Sample Paper Set N with solutions. We have provided CBSE Sample Papers for Class 12 Mathematics as per the latest paper pattern issued by CBSE for the current academic year. All sample papers provided by our Class 12 Mathematics teachers are with answers. You can see the sample paper given below and use them for more practice for Class 12 Mathematics examination.

1.

(a) is an empty set
(b) contains exactly one element
(c) contains exactly two elements
(d) contains more than two elements

C

2.

D

3. The sum of all real values of x satisfying the equation
(a) 3
(b) – 4
(c) 6
(d) 5

A

4.

(a) – 1
(b) 5
(c) 4
(d) 13

B

5. The system of linear equations

has a non-trivial solution for
(a) infinitely many values of λ
(b) exactly one value of λ
(c) exactly two values of λ
(d) exactly three values of λ

D

6. If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is
(a) 46th
(b) 59th
(c) 52nd
(d) 58th

D

7. If the number of terms in the expansion of

is 28, then the sum of the coefficients of all the terms in this expansion, is
(a) 64
(b) 2187
(c) 243
(d) 729

D

8. If the 2nd, 5th and 9th terms of a non-constant AP are in GP, then the common ratio of this GP is
(a)8/5
(b)4/3
(c) 1
(d)7/4

B

9. If the sum of the first ten terms of the series

(a) 102
(b) 101
(c) 100
(d) 99

B

10.

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

C

11.

B

12.

B

13. A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then
(a) 2 x = (π + 4)r
(b) (4 – π)x = πr
(c) x = 2r
(d) 2 x = r

C

14.

B

15.

B

16.

B

17. If a curve y = f ( x) passes through the point (1, – 1) and satisfies the differential equation, y(1 + xy)dx = x dy,then f (-1/2)is equal to
(a) – 2/5
(b) – 4/5
(c) 2/5
(d) 4/5

D

18. Two sides of a rhombus are along the lines,x – y + 1 = 0 and 7x – y – 5 = 0. If its diagonals intersect at (- 1, – 2), then which one of the following is a vertex of this rhombus?
(a) (- 3, – 9)
(b) (- 3, – 8)
(c)(1/3,-8/3)
(d) (-10/3,7/3)

C

19. The centres of those circles which touch the circle,x2+y2-8x-8y-4=0  externally and also touch the X-axis, lie on
(a) a circle
(b) an ellipse which is not a circle
(c) a hyperbola
(d) a parabola

D

20. If one of the diameters of the circle, given by the equation, x2+y2-4x+6y-12=0  is a chord of a circle S,whose centre is at (-3,2), then the radius ofS is
(a) 5√2
(b) 5 √3
(c) 5
(d) 10

B

21. Let P be the point on the parabola, y2 x 2 = 8 ,which is at a minimum distance from the centre C of the circle, x2+(y+6)2=1.  Then, the equation of the circle,passing through C and having its centre at P is

A

22. The eccentricity of the hyperbola whose length of the latusrectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is
(a)4/3
(b)4/√3
(c)2/√3
(d) √3

C

23. The distance of the point (1, – 5, 9) from the plane x – y + z = 5measured along the line x = y = z is
(a) 3√10
(b) 10√3
(c)10/√3
(d)20/3

B

24.

(a) 26
(b) 18
(c) 5
(d) 2

D

25.

(a)3π/4
(b)π/2
(c)2π/3
(d)5π/6

D

26. If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

D

27. Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd,then which of the following statements is not true?
(a) E1 and E2 are independent
(b) E2 and E3 are independent
(c) E1 and E3 are independent
(d) E1, E2 and E3 are independent

D

28. If 0 ≤ x < 2π, then the number of real values of x,which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0, is
(a) 3
(b) 5
(c) 7
(d) 9

C

29. A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30°. After walking for 10 min from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60°. Then, the time taken (in minutes) by him, from B to reach the pillar, is
(a) 6
(b) 10
(c) 20
(d) 5