Please refer to Class 12 Mathematics Sample Paper Set K with solutions below. The following CBSE Sample Paper for Class 12 Mathematics has been prepared as per the latest pattern and examination guidelines issued by CBSE. By practicing the Mathematics Sample Paper for Class 12 students will be able to improve their understanding of the subject and get more marks.

**1. If the lines x+1/2 = y-1/1 = z+1/3 and x+2/2 = y-k/3 = z/4 are coplanar, then the value of k is**

(a) 11/2

(b) -/1

(c) 9/2

(d) -9/2

## Answer

A

**2. Statement I The slope of the tangent at any point P on a parabola, whose axis is the axis of x and vertex is at the origin, is inversely proportional to the ordinate of the point P.****Statement II The system of parabolas y ^{2} =4ax 2**

**= 4 satisfies a differential equation of degree 1 and order 1.**

**(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

**3.**

(a) 2

(b) 5

(c) 3

(d) 1

## Answer

D

**4.**

## Answer

A

**5.**

## Answer

D

**6.**

(a) non-negative

(b) negative

(c) positive

(d) non-positive

## Answer

B

**7.**

## Answer

A

**8**.

(a) 41/11

(b) 121/1681

(c) 11/41

(d) 121/1861

## Answer

B

**9.** **Statement I** The equation x log x = 2-x is satisfied by at least one value of x lying between I and II.**Statement II** The function f (x) =x log x is an increasing function in [1,2] and g (x) = 2-x is a decreasing function in [1, 2] and the graphs represented by these functions intersect at a point in [1 , 2].

(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

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

## Answer

A

**10.**

## Answer

B

**11.** **The area bounded by the curve y= ln(x) and the lines y = 0, y= ln (3) and x=0 is equal to**

(a) 3

(b) 3 ln (3) -2

(c) 3 ln (3 )+2

(d) 2

## Answer

D

**12.** **The values of a for which one root of the equation x ^{2}-(a+1) x+a^{2}+ a-8 = 0 exceeds 2 and the other is lesser than 2, are given by**

(a) 3 < a <10

(b) a ≥ 10

(c) – 2<a<3

(d) a ≥-2

## Answer

C

**13.** **If the surface area of a sphere of radius r is increasing uniformly at the rate 8 cm ^{2} / s, then the rate of change of its volume is**

(a) constant

(b) proportional to √r

(c) proportional to r

^{2}

(d) proportional to r

## Answer

D

**14. The probability of a man hitting a target is 2/5 ×He fires at the target k times(k , a given number). Then the minimumk, so that the probability of hitting the target at least once is more than 7/10, is**

(a) 3

(b) 5

(c) 2

(d) 4

## Answer

A

**15. Equation of the line passing through the points of intersection of the parabola x ^{2}=8y and the ellipse**

x

^{2}/3 + y

^{2}= 1 is

(a) y – 3 = 0

(b) y + 3= 0

(c) 3y +1=0

(d) 3y-1=0

## Answer

D

**16.** **The sum of the series**

(a) 18/11

(b) 22/13

(c) 20/11

(d) 16/9

## Answer

C

**17.** **A value of x for which sin[cot ^{-1} (1+x)] =cos (tan^{-1}x) , is**

(a) -1/2

(b) 1

(c) 0

(d) 1/2

## Answer

A

**18.** **If a and c are positive real numbers and the ellipse**

## Answer

C

**19.** **The vector **

**to**

(a) b x a

(b) a

(c) a x b

(d) b

## Answer

C

**20.** **A light ray emerging from the point source placed at P( 1,3) is reflected at a point Q in the axis of x. If the reflected ray passes through the point R(6, 7), then the abscissa of Q is**

(a) 1

(b) 3

(c) 7/2

(d) 5/2

## Answer

D

**21. The mean of a data set consisting of 20 observations is 40.****If one observation 53 was wrongly recorded as 33, then the correct mean will be**

(a) 41

(b) 49

(c) 40.5

(d) 42.5

## Answer

A

**22.**

(a) R does not have an inverse.

(b) R is not a one to one function.

(c) R is an onto function.

(d) R is not a function.

## Answer

C

**23.**

## Answer

A

**24.**

## Answer

A

**25. **

(a) 7 : 16

(b) 7 : 64

(c) 1 : 4

(d) 1 : 32

## Answer

D

**26. **

(a) 1

(b) -1/2

(c) 2

(d) 0

## Answer

B

**27.**

## Answer

B

**28**. **Statement I** The statement A→ (B→ A) is equivalent to A→ (A v B) .**Statement II** The statement ////28 is a Tautology.

(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

**29. A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that in includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is**

(a) 40

(b) 41

(c) 16

(d) 32

## Answer

B

**30.**

## Answer

B