Please see below Class 12 Mathematics Sample Paper Set C with solutions. We have provided Class 12 Mathematics Sample Papers with solutions designed by Mathematics teachers for Class 12 based on the latest examination pattern issued by CBSE. We have provided the following sample paper for Class 12 Mathematics with answers. You will be able to understand the type of questions which can come in the upcoming exams.

CBSE Sample Paper for Class 12 Mathematics Set C

1. Area of triangle formed by the vertices (0, 0), (6, 0), (4, 3) is
(a) 6
(b) 9
(c) 18
(d) 24 

2. In a box containing 100 bulbs, 10 are faulty. The probability that from a sample of 5 bulbs none are defective.
(a) (1/10)⁵
(b) (9/10)⁵
(c) 9/10⁵
(d) 1/5

3. If 2 sec 2α = tan β + cot β then one of the values of (α+β) =
(a) p
(b) π/2
(c) π/4
(d) None of these 

4. The probability of getting the sum more than 7 when a pair of dice is tossed is
(a) 1/9
(b) 1/4
(c) 7/12
(d) 512 

5. 

(a) 5 (n – 3)
(b) 5 (n – 2)
(c) 5n
(d) 5 (2n – 9) 

6.

(a) ¹⁶C₇
(b) ¹⁷C₇
(c) ¹⁷C₈ 
(d) ¹⁶C₈   

7. If y = A sin ωt then d⁵y/dt⁵ =

8. 

(a) 5
(b) 6
(c) 7
(d) 8   

9.

(a) cos ⁻¹ (4/9)
(b) cos ⁻¹ (3/9)
(c) cos ⁻¹ (2/9)
(d) cos ⁻¹ (1/9)   

10. The contrapositive of (p∨ q)⇒r is
(a) r ⇒ (p ∨ q)
(b) ~ r ⇒ (p ∨ q)
(c) ~ r ⇒ ~ p ∧ ~ q
(d) p ⇒ (q ∨ r) 

11. If (2, 3, 5) are ends of the diameter of a sphere x2 + y2 + z2 – 6x – 12y – 2z + 20 = 0. Then coordinates of the other end are
(a) (4, 9, –3)
(b) (4, 3, 5)
(c) (4, 3, –3)
(d) (4, –3, 9) 

12. Three persons A, B, C throw a die in succession. The one getting ‘six’ wins. If A starts then the  probability of B winning is
(a) 36/91
(b) 25/91
(c) 41/91
(d) 30/91 

13. The eccentricity of the ellipse represented by
25x² + 16y² – 150x – 175 = 0 is
(a) 2/5
(b) 3/5
(c) 4/5
(d) 1/5 

14. If f(x) = | x – 2| and g(x) = f (f(x)) then for x > 10, g'(x) equal
(a) –1
(b) 0
(c) 1
(d) 2x – 4 

15. If a, b, c are in A.P., b, c, d are in G.P. and c, d, e are in H.P. then a, c, e are in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these 

16. The coefficient of x¹⁰ in the expansion of (3x² – 1/x²)¹⁵ is

17. The mean of discrete observations y₁, y₂, y₃,…,y_n is given by

18. 

19. The spheres x² + y² + z² + x + y + z –1 = 0 and ² + y² + z² + x + y + z – 5 = 0
(a) intersect in a plane
(b) intersect in five points
(c) do not intersect
(d) None of these 

20.

Statement-1 : I₁, I₂, I₃ . . . is an increasing sequence.
Statement-2 : ln x is an increasing function.
(a) Statement-1 is false, Statement-2 is true.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(d) Statement-1 is true, Statement-2 is false. 

21. Statement–1 : Range of f(x) = √4 – x² is [0, 2]
Statement–2 : f(x) is increasing for 0 ≤ x ≤ 2 and decreasing for – 2 ≤ x ≤ 0.
(a) Statement-1 is false, Statement-2 is true.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is true; Statement-2is not a correct explanation for Statement-1.
(d) Statement-1 is true, Statement-2 is false. 

22. Let x, y, z are three integers lying between 1 and 9 such that x 51, y 41 and z 31 are three digit numbers.
Statement-1 : The value of the determinant

Statement-2 : The value of a determinant is zero if the entries in any two rows (or columns) of the determinant are correspondingly proportional.
(a) Statement-1 is false, Statement-2 is true.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(d) Statement-1 is true, Statement-2 is false. 

23. Statement-1 : Slope of tangents drawn from (4, 10) to parabola y² = 9x are 1/4, 9/4
Statement-2 : Every parabola is symmetric about its directrix 
(a) Statement-1 is false, Statement-2 is true.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(d) Statement-1 is true, Statement-2 is false. 

24. 

(a) Statement-1 is false, Statement-2 is true.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(d) Statement-1 is true, Statement-2 is false. 

25. If AB = 0, then for the matrices   

(a) an odd multiple of π/2
(b) an odd multiple of p
(c) an even multiple of π/2 
(d) 0   

26. If f'(x) = (x – 1) (x – 2) (x – 3) then f(x) in monotonically increasing in
(a) x < 1
(b) x > 3, x < 1
(c) x > 3, 1 < x < 2
(d) x < 1, 2 < x < 3 

27. The area enclosed by the curve y = x⁵, the x-axis and the ordinates x = –1, x = 1 is
(a) 0
(b) 1/3
(c) 1/6
(d) None   

28. An inverted cone is 10 cm in diameter and 10 cm deep. Water is poured into it at the rate of 4cm³/min. When the depth of water level is 6 cm, then it is rising at the rate
(a) 9/4π cm³ /min.
(b) 1/4π cm³ /min.
(c) 1/9π cm³ /min.
(d) 4/9π cm³ /min. 

29. The equation of tangent to 4x² – 9y² = 36 which are perpendicular to straight line 5x + 2y – 10 = 0 are
(a) 5 (y–3) = 2(x – √117/2)
(b) 2y – |5x + 10– 2√18 = 0
(c) 2y – 5x – 10– 2√18 = 0
(d) None of these 

30. 

(a) √3
(b) 1/√3
(c) 3√3/2
(d) 1/2√3