# CBSE Class 12 Mathematics Sample Paper Set L

See below CBSE Class 12 Mathematics Sample Paper Set L 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. Given a sequence of 4 numbers, first three of which are in GP and the last three are in AP with common difference six. If first and last terms of this sequence are equal, then the last term is
(a) 16
(b) 8
(c) 4
(d) 2

B

2. Statement I The only circle having radius √10 and a diameter along line 2x + y = 5 is x2+y2-6x+2y=0
Statement II  2x + y = 5 is a normal to the circle x2 +Y2-6X+2Y=0
(a) Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

D

3. If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle 60° on the circumference of the first circle, then the radius of the arc is
(a) √3
(b)1/2
(c) 1
(d) 2

A

4. If the image of point P(2, 3) in a line L is Q(4, 5), then the image of point R(0, 0) in the same line is
(a) (2, 2)
(b) (4, 5)
(c) (3, 4)
(d) (7, 7)

D

5. Consider the system of equations x + ay = 0, y + az = 0 and z + ax = 0. Then, the set of all real values of ‘a’ for which the system has a unique solution is
(a) R – {1}
(b) R – {- 1}
(c) {1, – 1}
(d) {1, 0, – 1}

B

6. A common tangent to the conics x2=6Y AND 2X2-4Y2=9is
(a) x – y = 3/2
(b) x + y = 1
(c) x + y = 9/2
(d) x – y = 1

A

7.

Then, the number of non-singular matrices in the set S is
(a) 27
(b) 24
(c) 10
(d) 20

D

8.

B

9. Let A(- 3, 2) and B(- 2,1) be the vertices of a DABC. If the centroid of this D lies on the line 3x + 4y + 2 = 0, then the vertex C lies on the line
(a) 4x + 3y + 5 = 0
(b) 3x + 4y + 2 = 0
(c) 4x + 3y + 3 = 0
(d) 3x + 4y + 5 = 0

B

10. Let ABC be a triangle with vertices at points A(2, 3, 5), B(- 1, 3, 2) andC(λ, 5, µ) in three dimensional space. If the median through A is equally inclined with the axes, then (λ, µ) is equal to
(a) (10, 7)
(b) (7, 5)
(c) (7,10)
(d) (5, 7)

C

11. In the integral

constant, then A is equal to
(a) – 1/16
(b)1/16
(c)1/8
(d) – 1/8

A

12. The equation of the curve passing through the origin and satisfying the differential equation

D

13.

A

14. Let f : [- 2, 3] →[0, ∞) be a continuous function such that f (1- x) = f (x) for all x∈[- 2, 3].
If R1 is the numerical value of the area of the region bounded by y = f (x), x = – 2, x = 3 and the axis of x and

(a) 3R1 = 2R2
(b) 2R1 = 3R2
(c) R1 R2
(d) R1 = 2R2

D

15.

(a)1/2
(b)3√3/2
(c) 3
(d)3/2

D

16.

(a) F, F
(b) T, T
(c) T, F
(d) F, T

C

17. If the events A and B are mutually exclusive events such that P (A) =3X+1/3 and P(B)=1-X/4, then the set of possible values of x lies in the interval

C

18. The equation of a plane through the line of intersection of the planes x + 2y = 3, y – 2z + 1= 0, and perpendicular to the first plane is
(a) 2x – y – 10z = 9
(b) 2x – y + 7z = 11
(c) 2x – y + 10z = 11
(d) 2x – y – 9z = 10

C

19. If for positive intergers r > 1, n > 2, the coefficients of the (3r)th and (r + 2)th powers of x in the expansion of (1+x) 2n are equal, then n is equal to
(a) 2r + 1
(b) 2r – 1
(c) 3r
(d) r + 1

A

20. 20

B

21. A spherical balloon is being inflated at the rate of 35 cc/min. The rate of increase in the surface area (in cm2/min) of the balloon when its diameter is 14 cm, is
(a) 10
(b) √10
(c) 100
(d) 10√10

A

22.

(a) A = B
(b) A ⊄ B
(c) B ⊄ A
(d) A ⊂ B and B – A ≠ Φ

B

23.

Statement I z is a real number.
Statement II Principal argument of z is π/3
(a) Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; statement II is false.
(d) Statement I is false; Statement II is true.

D

24. Consider the function

(a) Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

B

25.

(a) [15,19)
(b) (- ∞,12)
(c) [12,15)
(d) [19, ∞)

D

26. In a set of 2 nobservations, half of them are equal to ‘a’ and the remaining half are equal to ‘- a’. If the standard deviation of all the observations is 2; then the value of|a| is
(a) 2
(b) 2
(c) 4
(d) 2 √2

A

27. The value of 12+ 32+ 52+…. + 252 is
(a) 2925
(b) 1469
(c) 1728
(d) 1456

A

28. If an equation of a tangent to the curve,

(a) 1
(b) 2
(c) π/4
(d) π/2

D

29. 5-digit numbers are to be formed using 2, 3, 5, 7, 9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000, then p :q is
(a) 6 : 5
(b) 3 : 2
(c) 4 : 3
(d) 5 : 3