# Class 12 Mathematics Sample Paper With Solutions Set M

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

1. The shortest distance between the line y = x and the curve y2=x- = – 2 is
(a) 2
(b)7/8
(c)7/√2
(d) 11/4√2

C

2.

(a) 4√2
b) √2
(c) 2 √2
(d) 4

A

3. The greatest value of c∈R for which the system of linear equations
x -cy – cz = 0,
cx -y + cz = 0,
cx + cy – z = 0
has a non-trivial solution, is
(a) -1
(b)1/2
(c) 2
(d) 0

B

4. The contrapositive of the statement ‘‘If you are born in India, then you are a citizen of India’’, is
(a) If you are not a citizen of India, then you are not born in India.
(b) If you are a citizen of India, then you are born in India.
(c) If you are born in India, then you are not a citizen of India.
(d) If you are not born in India, then you are not a citizen of India.

A

5. All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is
(a) 180
(b) 175
(c) 160
(d) 162

A

6.

(a) π/32
(b) 0
(c)π/64
(d)π/16

C

7. If cos(α + β) = 3/5, sin(α – β) = 5/13 and 0<α,β<π/4,then tan(2a) is equal to
(a)63/52
(b)63/16
(c)21/16
(d)33/52

B

8. The sum of the coefficients of all even degree terms is x in the expansion of

(a) 29
(b) 32
(c) 26
(d) 24

D

9.

(where,C is a constant of integration )
(a) 2x + sin x + 2 sin 2x + C
(b) x + 2sin x + 2 sin 2x + C
(c) x + 2sin x + sin 2x + C
(d) 2x + sin x + sin 2x + C

C

10. The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is
(a) 45
(b) 49
(c) 48
(d) 40

C

11. The equation of a plane containing the line of intersection of the planes 2x – y – 4 = 0 and y + 2z – 4 = 0 and passing through the point (1, 1, 0) is
(a) x – 3y – 2z = -2
(b) 2x – z = 2
(c) x – y – z = 0
(d) x + 3y + z = 4

C

12. The magnitude of the projection of the vector

on the vector perpendicular to the plane containing the vectors

is
(a)√3/2
(b) √6
(c) 3 √6
(d)√3/2

D

13. The sum of the squares of the lengths of the chords intercepted on the circle, x2+y2=16 by the lines, x + y = n,n ∈N, where N is the set of all natural numbers, is
(a) 320
(b) 105
(c) 160
(d) 210

D

14. Let A and B be two non-null events such that A Ì B. Then, which of the following statements is always correct.
(a) P(A /B) = P(B) – P(A)
(b) P(A/B) ≥ P(A)
(c) P(A/B) ≤ P(A)
(d) P(A/B) = 1

B

15. If a and β are the roots of the equation x2-2x+2=0,  then the least value of n for which a

1 is
(a) 2
(b) 5
(c) 4
(d) 3

C

16. The area (in sq units) of the region

is
(a)53/6
(b) 8
(c)59/6
(d)26/3

C

17. If S1 and S2 are respectively the sets of local minimum and local maximum points of the function, f (x) =9x4+12x3 -36x2+25,x∈ R, then

C

18.

D

19. The sum of the series

(a) 226
(b) 225
(c) 223
(d) 224

B

20. The sum of the solutions of the equation

(a) 9
(b) 12
(c) 4
(d) 10

D

21. If the tangents on the ellipse 4x2+y2=8 at the points (1,2)  and (a, b) are perpendicular to each other, then a2 is equal to
(a)128/17
(b)64/17
(c)4/17
(d)2/17

D

22. Let y = y(x) be the solution of the differential equation,

(a)1/4
(b)1/2
(c) 1
(d)1/16

D

23. The sum of all natural numbers ‘n’ such that 100 < n < 200 and HCF (91,n)>1 is
(a) 3203
(b) 3303
(c) 3221
(d) 3121

D

24. The length of the perpendicular from the point (2, – 1, 4) on the straight line, x+3/10=y-2/-7=z/1 is
(a) greater than 3 but less than 4
(b) less than 2
(c) greater than 2 but less than 3
(d) greater than 4

A

25. A point on the straight line,3x + 5y = 15 which is equidistant from the coordinate axes will lie only in
(c) I and II quadrants
(d) I, II and IV quadrants

C

26. Let O(0, 0) and A(0, 1) be two fixed points, then the locus of a point P such that the perimeter of DAOP is 4, is
(a) 8 x2 -9y2+9y=18
(b) 9x2-8y2+8y=16
(c) 9x2+8y2-8y=16
(d) 8x2+9y2-9y=18

C

27.

B

28.

(a) 2f (x)
(b) 2 2 f (x )
(c) (f (x))2
(d) -2f (x)

A

29. Let f : [0, 2]→ R be a twice differentiable function such that

(a) increasing on (0, 1) and decreasing on (1, 2)
(b) decreasing on (0, 2)
(c) decreasing on (0, 1) and increasing on (1, 2)
(d) increasing on (0, 2)