Please refer to Class 12 Mathematics Sample Paper With Solutions Set L provided below. The Sample Papers for Class 12 Mathematics have been prepared based on the latest pattern issued by CBSE. Students should practice these guess papers for class 12 Mathematics to gain more practice and get better marks in examinations. The Sample Papers for Mathematics Standard 12 will help you to understand the type of questions which can be asked in upcoming examinations.

**1. The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to** **any question, is**

(a) ^{30} C7

(b)^{ 21}C_{8}

(c)^{ 21} C_{7}

(d)^{ 30 }C_{8 }

## Answer

C

**2. If the system of linear equations**

**is consistent and has infinite number of solutions, then**(a) a = 8, b can be any real number

(b) b = 15, a can be any real number

(c) a ∈R – {8} and b∈R – {15}

(d) a = 8, b = 15

## Answer

D

**3. Given sum of the firstnterms of an AP is 2n +3n ^{2}. Another**

**AP is formed with the same first term and double of the**

**common difference, the sum of n terms of the new AP is**

(a) n + 4n

^{2}

(b) 6n

^{2}– n

(c) n

^{2}+ 4n

(d) 3n+ 2n

^{2 }

## Answer

B

4. **Statement I** The function x^{2}(ex+e^{-x})increasing for all x > 0**Statement II** The function x^{2} e^{x} and x^{2} e^{-x} are increasing for all x > 0 and the sum of two increasing functions in any interval (a, b) is an increasing function in (a, b) (a) Statement I is true, Statement II is false

(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 true; Statement II is a correct explanation for Statement I

(d) Statement I is false, Statement II is true

## Answer

C

**5. Mean of 5 observations is 7. If four of these observations** **are 6, 7, 8, 10 and one is missing then the variance of all** **the five observations is**

(a) 4

(b) 6

(c) 8

(d) 2

## Answer

A

**6. The area of the region (in sq. units), in the first quadrant,** **bounded by the parabola y = 9x ^{2} and the lines x = 0, y = 1**

**and y = 4, is**

(a)7/9

(b)14/3

(c)7/3

(d)14/9

## Answer

D

**7. If the x-intercept of some line L is double as that of the line, 3x + 4y = 12 and the y-intercept of L is half as that of the same line, then the slope of L is**

(a) – 3

(b) – 3/8

(c) – 3/2

(d) – 3/16

## Answer

D

**8. The sum**

(a)7/2

(b)11/4

(c)11/2

(d)60/11

## Answer

C

**9. The integral**

(a) log2 √2

(b) log2

(c) 2 log2

(d) log √2

## Answer

A

**10. Let R = {(3, 3), (5, 5), (9, 9), (12,12), (5,12), (3, 9), (3,12) (3, 5)} be a relation on the set A = {3, 5, 9,12}. Then, R is**

(a) reflexive, symmetric but not transitive

(b) Symmetric, transitive but not reflexive

(c) an equivalence relation

(d) reflexive, transitive but not symmetric.

## Answer

D

**11.**

(a) 2

(b) √3

(c) √5

(d) 1

## Answer

C

**12. If the 7th term in the binomial expansion of**

(a) e^{2}

(b) e

(c)e/2

(d) 2 e

## Answer

B

**13. Statement I** The line x – 2y = 2 meets the parabola, y^{2} + 2x = 0 only at the point (- 2, – 2)**Statement II** The line y= mx-1/2m-1/2m(m≠0) is tangent to the parabola, y^{2}=-2x at the point -1/2m^{2}‘-1/m)

(a) Statement I is true, Statement II is false

(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 true; Statement II is a correct explanation for Statement I

(d) Statement I is false, Statement II is true

## Answer

B

**14. If a circle C passing through (4, 0) touches the circle** **x ^{2}+y^{2}+4x-6y-12=0, externally at a point (1, – 1), then the radius of the circle C is**

(a) 5

(b) 2√5

(c) 4

(d) √57

## Answer

A

**15. Let Q be the foot of perpendicular from the origin to the** **plane 4x – 3y + z + 13 = 0 and R be a point (- 1,1, – 6) on** **the plane. Then, length QR is**

(a) √14

(b)√19/2

(c) 3√7/2

(d)3/√2

## Answer

C

**16. Given two independent events, if the probability that** **exactly one of them occurs is 26/49 and the probability that** **none of them occurs is 15/49, then the probability of more** **probable of the two events is**

(a)4/7

(b)6/7

(c)3/7

(d)5/7

## Answer

A

**17. The statement p→ (q→ p) is equivalent to**

(a) p→ q

(b) p→ (p ν q)

(c) p→(p→ q)

(d) p→ (p ∧ q)

## Answer

B

**18. The maximum area of a right angled triangle with hypotenuse h is/// 18**

(a)h^{3}/2 √2

(b)h^{2}/2

(c)h^{2}/√2

(d)h^{2}/4

## Answer

D

**19. **

(a) – x

(b) x

(c) √1- x

(d) √1+ x

## Answer

B

**20. If two vertices of an equilateral triangle are A(- a, 0) and B(a, 0), a > 0, and the third vertexC lies above x-axis, then the equation of the circumcircle of Δ ABC is**

(a) 3x^{2}+3y^{2}-2√3ay=3a^{2}

(b) 3x^{2}+3y^{2}-2ay=3a^{2 }

(c) x^{2}+y^{2}-2ay=a^{2 }

(d) x^{2}+y^{2}-√3ay=a^{2 }

## Answer

A

**21. The acute angle between two lines such that the direction cosines 1, m, n of each of them satisfy the equations 1+ m + n = 0 and1 ^{1} + m^{2} – n^{2} = is**

(a) 15°

(b) 30°

(c) 60°

(d) 45°

## Answer

C

**22. Consider the differential equation**

**Statement I** The substitution z = y^{2} transforms the above equation into a first order homogenous differential equation.**Statement II** The solution of this differential equation is y^{2}e-y^{2/x}= C.

(a) Both Statement are false

(b) Statement I is true and Statement II is false

(c) Statement I is false and Statement II is true

(d) Both Statement are true

## Answer

D

**23. The number of solutions of the equation, sin ^{-1} = tan^{-1} x(in principal values) is**

(a) 1

(b) 4

(c) 2

(d) 3

## Answer

D

**24. **

## Answer

D

**25. If p, q, r are 3 real numbers satisfying the matrix equation,**

(a) – 3

(b) – 1

(c) 4

(d) 2

## Answer

A

**26. **

**then the angle between the vectors $a and $c is**

(a) π/4

(b)π/3

(c) π/6

(d)π/2

## Answer

B

**27. Let the equations of two ellipses be**

**then the length of the minor axis of ellipse E _{2} is**(a) 8

(b) 9

(c) 4

(d) 2

## Answer

C

**28. If α and β are roots of the equation x2+ px+3p/4=0,such that|a – β|= √10, then p belongs to the set**

(a) {2, – 5}

(b) {- 3, 2}

(c) {- 2, 5}

(d) {3, – 5}

## Answer

C

29. **Statement I** The number of common solution of the trigonometric equations 2 sin^{2} θ – cos2 θ = 0 and 2 cos^{2}θ -3 q – sinθ = θ in the interval [0, π ] is two.

**Statement II** The number of solutions of the equation, 2 cos2 θ -3 sinθ = 0 in the interval [0, π] is two.

(a) Statement I is true, Statement II is false

(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 true; Statement II is a correct explanation for Statement I

(d) Statement I is false, Statement II is true

## Answer

B

**30. Let f (x) = – 1+|x – 2|and g(x) = 1-|x|, then the set of all points where fog is discontinuous is**

(a) {0, 2}

(b) {0,1, 2}

(c) {0}

(d) an empty set

## Answer

D