Class 12 Mathematics Sample Paper With Solutions Set L

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

Question 1. 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

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

Question 3. The value of

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

Question 4.

(a) ¹⁶C₇
(b) ¹⁷C₇
(c) ¹⁷C₈
(d) ¹⁶C₈

Question 5. The angle between the two lines (x+1)/2 = (y+3)/2 = (z – 4)/-1 & (x – 4)/1 = (y+4)/2 = (z+1)/2 is
(a) cos^-1(4/9)
(b) cos^-1(3/9)
(c) cos^-1(2/9)
(d) cos^-1(1/9)

Question 6. The contrapositive of (p ∨ q) ⇒ r is
(a) r ⇒ (p ∨ q)
(b) ~ r ⇒ (p ∨ q)
(c) ~ r ⇒ ~ p Ù ~ q
(d) p ⇒ (q ∨ r)

Question 7. If (2, 3, 5) are ends of the diameter of a sphere x² + y² + z² – 6x – 12y – 2 + 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)

Question 8. 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

Question 9. 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

Question 10. The coefficient of x10 in the expansion of (3×2 − 1/x2)15 is
(a) (15!/10!5!)3¹⁰
(b) – (15!/10!5!)3¹⁰
(c) – 15!3⁵/10!5!
(d) (15!/7!8!)3⁸

Question 11. The mean of discrete observations y₁, y₂, y₃,…,yn is given by

Question 12.

Question 13. The spheres x² +y² + z² + x + y +z – 1 = 0 and x² + 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

Question 14. The domain of the function f (x) = exp√(5x -3- 2x²) is
(a) [3/2, ∞)
(b) [1, 3/2]
(c) (–∞, 1]
(d) (1, 3/2)

Question 15. The value of the determinant

(a) sin x = 0
(b) cos x = 0
(c) a = 0
(d) cos x = (1 + a²)/2a

Question 16. If AB = 0, then for the matrices

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

Question 17. 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

Question 18. 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

Question 19. 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

Question 20.

(a) √3
(b) 1/√3
(c) 3√3/2
(d) 1/2√3

Question 21. The probability of getting the sum more than 7 when a pair of dice is tossed is _________.

Question 22. 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 _________.

Question 23. The eccentricity of the ellipse represented by 25x² + 16y² – 150x – 175 = 0 is _________.

Question 24. If 1/1⁴ + 1/2⁴ + 1/3⁴ + …….. + ∞ = π⁴/90, then the value of 1/1⁴ + 1/3⁴ + 1/5⁴ + …….. + ∞ = π^y/k, then k is _________.

Question 25. The area enclosed by the curve y = x⁵, the x-axis and the ordinates x = –1, x = 1 in sq. units is _________.