# Unseen Passage

For Class 4 to Class 12

# Class 12 Mathematics Sample Paper Set O

Please see below Class 12 Mathematics Sample Paper Set O 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 O

1. The positive value of λ for which the coefficient of x2 in the expression

(a) 3
(b) √5
(c) 2 √2
(d) 4

D

2.

C

3. With the usual notation, in ΔABC, if ∠A + ∠B = 120°, a = √3 + 1and b = √3 – 1, then the ratio ∠A : ∠B, is
(a) 7 : 1
(b) 3 : 1
(c) 9 : 7
(d) 5 : 3

A

4. Let a = (λ- 2) a + b and b = (4λ – 2) a + 3b be two given vectors where vectors a and b are non-collinear. The value of λ for which vectors α and β are collinear, is
(a) 4
(b) -3
(c) 3
(d) -4

D

5. A helicopter is flying along the curve given by y – x3/2 =  7, (x≥0). A soldier positioned at the point (1/2,7) wants to shoot down the helicopter when it is nearest to him. Then, this nearest distance is
(a)1/3√7/3
(b)√5/6
(c)1/6√7/3
(d)12

C

6. The value of

where [t]denotes the greatest integer less than or equal to t, is
(a)1/12(7π – 5)
(b)1.12(7π + 5)
(c)3/10(4π – 3)
(d)3/20(4π – 3)

A

7. If the probability of hitting a target by a shooter in any shot, is 1/3 , then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than 5/6 is
(a) 6
(b) 3
(c) 5
(d) 4

C

8. Two sides of a parallelogram are along the lines, x + y = 3 and x – y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is
(a) (3, 6)
(b) (2, 6)
(c) (2, 1)
(d) (3, 5)

A

9. The value of

(a)1/1024
(b)1/2
(c)1/512
(d)1/256

C

10. Let N be the set of natural numbers and two functions f and g be defined as f, g : N →N such that

(a) one-one but not onto
(b) onto but not one-one
(c) both one-one and onto
(d) neither one-one nor onto

B

11.

then, K is equal to
(a) 224
(b) 225 -1
(c) 225
(d) (25)2

C

12. Let f be a differentiable function

(a) does not exist
(b) exists and equals 4/7
(c) exists and equals 0
(d) exists and equals 4

D

13. Let A=

Then, the minimum value of det (A)/b is
(a) – √3
(b) -2 √3
(c) 2 √3
(d) √3

C

14. Let z=

R(z) and I (z) respectively denote the real and imaginary parts of z, then
(a) R(z) > 0 and I (z) > 0
(b) I (z) = 0
(c) R(z) < 0 and I (z) > 0
(d) R(z) = – 3

B

15. Two vertices of a triangle are (0, 2) and (4, 3). If its orthocentre is at the origin,then its third vertex lies in which quadrant?
(a) Fourth
(b) Third
(c) Second
(d) First

C

16.

where C is a constant of integration,
then f (x) is equal to
(a) – 4 x3-1
(b) 4x3+1
(c) – 2x3-1
(d) – 2x3+1

A

17. The value of

(a)23/22
(b)21/19
(c)19/21
(d)22/23

B

18. The tangent to the curve, y= xex2 passing through the point (1, e) also passes through the point
(a) (4/ 2e)
(b)(3,6e)
(c) (2,3e)
(d)(5/3,2e)

A

19. On which of the following lines lies the point of intersection of the line, x – 4/2 = y – 5/2 = z-3/1 and the plane, x + y + z = 2 ?

D

20. Let f : (-1, 1) → R be a function defined by f (x) = max {- lxl , – 1 – x2 }.
If K be the set of all points at which f is not differentiable, then K has exactly
(a) three elements
(b) five elements
(c) two elements
(d) one element A

21. The curve amongst the family of curves represented by the differential equation, (x2-y2) dx+ 2xydy  = 0, which passes through (1, 1), is
(a) a circle with centre on the Y-axis
(b) a circle with centre on the X-axis
(c) an ellipse with major axis along the Y-axis
(d) a hyperbola with transverse axis along the X-axis.

B

22.

(a) 24/25
(b)18/25
(c)6/25
(d)4/5

A

23. The number of values of q ∈(0, π) for which the system of linear equations
x + 3y + 7z = 0,
-x + 4y + 7z = 0,
(sin 3θ)x + (cos2 θ)y + 2z = 0
has a non-trivial solution, is two
(a) Two
(b) three
(c) four
(d) one

A

24. The plane which bisects the line segment joining the points (-3, – 3, 4) and (3, 7, 6) at right angles, passes through which one of the following points ?
(a) (4, – 1, 7)
(b) (2, 1, 3)
(c) (-2, 3, 5)
(d) (4, 1, – 2)

D

25. If mean and standard deviation of 5 observations x1,x2,x3,x4,x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2,… x5  and – 50 is equal to
(a) 507.5
(b) 586.5
(c) 582.5
(d) 509.5

A

26. Let a1,a2,a3…,a10 be in GP with ai > 0 for i = 1, 2, …..,10 and S be the set of pairs (r, k), r, k ∈N (the set of natural numbers) for which//26
(a) 4
(b) 2
(c) 10
(d) infinitely many

D

27. Consider the following three statements:
P : 5 is a prime number.
Q : 7 is a factor of 192.
R : LCM of 5 and 7 is 35.
Then, the truth value of which one of
the following statements is true ?

B

28 The length of the chord of the parabola x2 = 4y having equation x – √2y + 4 √2 = 0 is
(a) 8√2
(b) 2√11
(c) 3√2
(d) 6√3

D

29. If the area of an equilateral triangle inscribed in the circle, x2+y2+10x+12y+c=0  is 27√3 sq units, then c is equal to
(a) 20
(b) – 25
(c) 13
(d) 25

D

30. The value of λ such that sum of the squares of the roots of the quadratic equation, x2+(3-λ) x+ 2  =λ has the least value is
(a)4/9
(b) 1
(c)15/8
(d) 2