# Sample Paper Class 12 Mathematics Set O

**1. Slope of a line passing through P (2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is**

## Answer

C

**2. If f (x) is a non-zero polynomial of degree four, having local extreme points at x = – 1, 0, 1, then the set S = {x ∈ R : f (x) = f (0)} contains exactly**

(a) four rational numbers

(b) two irrational and two rational numbers

(c) four irrational numbers

(d) two irrational and one rational number

## Answer

D

**3. Four persons can hit a target correctly with probabilities 1/2,1/3,1/4 and 1/8 respectively. If all hit at the target independently, then the probability that the target would be hit, is**

(a)1/192

(b)25/32

(c)7/32

(d)25/192

## Answer

B

**4.**

(a) 2

(b) 4

(c) 3

(d) 16

## Answer

C

**5. If the line x – 1/2=y+1/3=z-2/4 meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is**

(a) 7 / 2

(b) 9 / 2

(c) √5 / 2

(d) 2√5

## Answer

B

**6. If the line y = mx + 7 √3 is normal to the hyperbola x2/24-y2/18=1 then a value of m is**

(a)3/5

(b)√152

(c)2/√5

(d)√5/2

## Answer

C

**7. If a tangent to the circle x ^{2}+y^{2}=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is**

(a) x

^{2}+y

^{2}-2x

^{2}y

^{2}=0

(b) x

^{2}+y

^{2}-2xy=0

(c) x

^{2}+y

^{2}-4x

^{2}y

^{2}=0

(d)x

^{2}+y

^{2}-16x

^{2}y

^{2}=0

## Answer

C

**8. If the function f : R- {1, – 1}→ A defined by f (x)= x ^{2}/1-x^{2} is surjective, then A is equal to**

(a) R – {-1}

(b) [0, ∞)

(c) R – [-1, 0)

(d) R – (-1, 0)

## Answer

C

**9. The value of**

(a) π – 1/2

(b) π – 2/8

(c) π – 1/4

(d) π – 2/4

## Answer

C

**10. If one end of a focal chord of the parabola, y ^{2} = 16 is at (1, 4), then the length of this focal chord is**

(a) 22

(b) 25

(c) 24

(d) 20

## Answer

B

**11. The solution of the differential equation x dy/dx+2y=x ^{2}(x≠0) with y(1) = 1, is**

## Answer

A

**12. All the points in the set**

(a) circle whose radius is 2.

(b) straight line whose slope is -1.

(c) circle whose radius is 1.

(d) straight line whose slope is 1.

## Answer

C

**13. If the function f defined on (π/6, π/3) by **

**continuous, then k is equal to**

(a)1/2

(b) 2

(c) 1

(d)1/√2

## Answer

A

**14. Let S = {θ ∈[-2π, 2π] : 2cos ^{2} θ + 3sinθ = 0}, then the sum of the elements of S is**

(a) 2π

(b) π

(c)5π/3

(d)13π/6

## Answer

C

**15. If the tangent to the curve, y = x ^{3} + ax – b at the point (1, – 5) is perpendicular to the line,-x + y + 4 = 0, then which one of the following points lies on the curve ?**

(a) (-2, 2)

(b) (2, – 2)

(c) (-2, 1)

(d) (2, – 1)

## Answer

B

**16. If the standard deviation of the numbers -1, 0, 1, k is 5 where k > 0,then k is equal to**

(a)2√10/3

(b) 2 √6

(c) 4√5/3

(d) √6

## Answer

B

**17. Let p, q ∈R. If 2 – √3 is a root of the quadratic equation, x ^{2}+ px+ q = 0, then**

(a) q2-4p-16=0

(b) p

^{2}-4q-12=0

(c) p2-4q+12=0

(d) q

^{2}+4p+14=0

## Answer

B

**18. A plane passing through the points (0, – 1, 0) and (0, 0, 1) and making an angle π/4 with the plane y – z + 5 = 0, also passes through the point**

(a) ( √2, 1, 4)

(b) (- √2, 1, – 4)

(c) (- √2, – 1, – 4)

(d) ( √2, – 1, 4)

## Answer

A

**19 .**

## Answer

B

**20. Let f (x) = 15 – lx – 10l ; x ∈R. Then,the set of all values of x, at which the function, g(x) = f (f (x)) is not differentiable, is**

(a) {5, 10, 15, 20}

(b) {5, 10, 15}

(c) {10}

(d) {10, 15}

## Answer

B

**21. Let S be the set of all values of x for which the tangent to the curve y = f (x) = x ^{3-}x^{2}-2x at(x,y) is parallel to the line segment joining the points (1, f (1)) and (-1, f (-1)), then S is equal to**

(a){1/3,-1}

(b){1/3,1}

(c) {-1/3,1}

(d) {-1/3,-1}

## Answer

C

**22. For any two statements p and q, the negation of the expression**

## Answer

A

**23. If the fourth term in the binomial**

(a) 8 ^{-2}

(b) 8^{3}

(c) 8

(d) 8^{2 }

## Answer

D

**24. The value of**

## Answer

D

**25. Let α and β be the roots of the equation x2 +x+1 = 0. Then, for y≠ 0 in R,**

(a) y(y^{2} – 1)

(b) y (y^{2} – 3)

(c) y_{3} – 1

(d) y^{3}

## Answer

D

**26. The area (in sq units) of the region**

A = {(x, y) : x2 ≤ y ≤ x+2}

(a)13/6

(b)9/2

(c)31/6

(d)10/3

## Answer

B

**27. The integral**

** equal to (here C is a constant of integration)**

## Answer

B

**28. A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3** females, then

(a) m = n = 68

(b) m + n = 68

(c) m = n = 78

(d) n = m – 8

## Answer

C

**29. Let the sum of the first n terms of a non-constant AP a _{1},a_{2},a_{3}…. be 50n+n(n-7/2 A, where A is a constant. If d is the common difference of this AP, then the ordered pair (d, a_{50} ) is equal to**

(a) (A, 50 + 46A)

(b) (50, 50 + 45A)

(c) (50, 50 + 46A)

(d) (A, 50 + 45A)

## Answer

A

**30. **

## Answer

B