Sample Paper Bihar Board Class XII Mathematics

(Set-1)

1. Derivative of X ^x with respect to x is
(A) x^x (log x + 1)
(B) x / x^x–1
(C) x. x^x
(D) (1 + log x)

2. The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference ?
(A) 2π cm/s
(B) 0.7 π cm/s
(C) 1.7π cm/s
(D) None of these

3. If x = a cos θ, y = b sin θ then find dy/dx =
(A) -b/a* cotθ
(B) 0
(C) b/a* tanθ
(D) -b/a* tanθ

4.ƒ1-sinx/cosx dx =

(A) tan x – sec x + c
(B) None of these
(C) tan x + sec x + c
(D) sec x – tan x + c

5.If E and F are events such that P (E/F) = P (F/E) then
(A) P (E) = P (F)
(B) E = F
(C) E ⊂ F but E ≠ F
(D) E ∩ F = φ

6. If P and Q are symmetric matrices of same order then PQ – QP is a
(A) Zero Matrix
(B) Identity Matrix
(C) Skew-symmetric Matrix
(D) Symmetric Matrix

Sample Paper Bihar Board Class XII Mathematics

(Set-2)

1. Value of c for lagrange's mean value theoren for the function f(x) = 3x² + 5x + 7 in the interval [4, 3] is
(A) 3
(B) 0
(C) 2
(D) 1

2. If |a^→+ b^→| =|a^→–b^→| then  the angle between a^→ and  b^→ is
(A) π/4
(B) π/6
(C) π/2
(D) 0

3. The order of the differential equation  1+(dy/dx)²=(d²y/dx²)³  is
(A) 1
(B) 0
(C) 2
(D) 3

4. The solution of the differential equation  dy/dn + y tanx=secx is

(A) y = tanx + cotx + c
(B) None of these
(C) y = sinx + c cos x
(D) y = sinx – c cos x

5. If  3i+ j–2k, –i+3j +4k and a i – 2 j – 6 k are coplanar then a =
(A) 0
(B) 4
(C) –2
(D) 2

6. If f(x) = 8x³ and g(x) = x^1/3 then gof is
(A) 2x
(B) 6x
(C) 8x
(D) 4x

Sample Paper Bihar Board Class XII Mathematics

(Set-3)

1. Value of c for lagrange's mean value theoren for the function f(x) = 3x² + 5x + 7 in the interval [4, 3] is
(A) 3
(B) 0
(C) 2
(D) 1

2. If |a^→+ b^→| =|a^→–b^→| then  the angle between a^→ and  b^→ is
(A) π/4
(B) π/6
(C) π/2
(D) 0

3. The order of the differential equation  1+(dy/dx)²=(d²y/dx²)³  is
(A) 1
(B) 0
(C) 2
(D) 3

4. The solution of the differential equation  dy/dn + y tanx=secx is

(A) y = tanx + cotx + c
(B) None of these
(C) y = sinx + c cos x
(D) y = sinx – c cos x

5. If  3i+ j–2k, –i+3j +4k and a i – 2 j – 6 k are coplanar then a =
(A) 0
(B) 4
(C) –2
(D) 2

6. If f(x) = 8x³ and g(x) = x^1/3 then gof is
(A) 2x
(B) 6x
(C) 8x
(D) 4x

Sample Paper Bihar Board Class XII Mathematics

(Set-4)

1. A Matrix has 18 elements, then possible orders of a matrix are
(A) 6
(B) 5
(C) 3
(D) 4

2. If   matrix A=3  1
                         -1   2    then A² –5A – 7I is
(A) diagonal matrix 
(B) an identity matrix
(C) zero matrix
(D) None of these

3. A =1    2
         2     4 then
(A) A² = 2A
(B) A^–1 exists 
(C) |A| = 0
(D) None

4. If  y= cosecx (cot–¹x) then dy/dx=
(A) x/(1-x^2)1/2
(B)- x/(1+x^2)1/2
(C)  x/(1+x^2)1/2
(D) None

5. The maximum value of (1/x)²
(A) 1/e^e
(B) (1/e)^1/e
(C) e
(D) e^e

6. The value of c of Rolle's theorem for the function f (x) = x² – 1 is interval [–1,1] is
(A)1/4
(B)1/2
(C)0
(D) None

Sample Paper Bihar Board Class XII Mathematics

(Set-5)

1. The area bounded by parabola y² = 4ax and its latus recturn is
(A) 8a²/3 sq. units
(B) 4a²/3 sq. units
(C)2a²/3 sq. units
(D) None of these

2. (1-x²)^1/2-(1-y²)^1/2=a (x-y)  then dy/dx equal to
(A) (1-x²/1-y²⁾
(B)(1-y²/1-x²⁾
(C)(1-x²/1-y^2)1/2
(D)(1-y²/1-x^2)1/2

3. If a relation R is reflexive, symmetric and transitive then the relation is
(A) Binary
(B) Conjugate
(C) Equivalence
(D) None of these

4. Slope of normal to the curve x³ = 8a²y, a > 0 at the point in the first quadrant is –2/3 then the point is
(A) (a, 2a)
(B) (a, a)
(C) (2a, –a)
(D) (2a, a)
5. Let A = {1, 2, 3} then number of equivalence relations containing (1, 2) is
(A) 3
(B) 4
(C) 1
(D) 2