# Sample Paper Class XII (Mathematics) Bihar Board 2010-11

**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) = 3x ^{2}
+ 5x + 7 in the interval [4, 3] is
**

**(A)**3

**0**

(B)

(B)

**2**

(C)

(C)

**1**

(D)

(D)

**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}=(d^{2}y/dx^{2})^{3}
is**

**(A)**1

**0**

(B)

(B)

**2**

(C)

(C)

**3**

(D)

(D)

**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

**y = sinx – c cos x**

(D)

(D)

**5. If 3i+ j–2k, –i+3j +4k and a i – 2 j – 6 k are coplanar then a =
**

**(A)**0

**4**

(B)

(B)

**–2**

(C)

(C)

**2**

(D)

(D)

**6. If f(x) = 8x ^{3} and g(x) = x^{1/3} then gof is**

**(A)**2x

**6x**

(B)

(B)

**8x**

(C)

(C)

**4x**

(D)

(D)

**Sample Paper Bihar Board Class XII Mathematics**

**(Set-3)**

**1. Value of c for lagrange's mean value theoren for the function f(x) = 3x ^{2}
+ 5x + 7 in the interval [4, 3] is
**

**(A)**3

**0**

(B)

(B)

**2**

(C)

(C)

**1**

(D)

(D)

**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}=(d^{2}y/dx^{2})^{3}
is**

**(A)**1

**0**

(B)

(B)

**2**

(C)

(C)

**3**

(D)

(D)

**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

**y = sinx – c cos x**

(D)

(D)

**5. If 3i+ j–2k, –i+3j +4k and a i – 2 j – 6 k are coplanar then a =
**

**(A)**0

**4**

(B)

(B)

**–2**

(C)

(C)

**2**

(D)

(D)

**6. If f(x) = 8x ^{3} and g(x) = x^{1/3} then gof is**

**(A)**2x

**6x**

(B)

(B)

**8x**

(C)

(C)

**4x**

(D)

(D)

**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 A**

^{2}–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) A

^{2}= 2A

(B) A

^{–1}exists

(C) |A| = 0

(D) None

**4. If y= cosecx (cot– ^{1}x) 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) = x ^{2}
– 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 y ^{2} = 4ax and its latus recturn is
(A)** 8a

^{2}/3 sq. units

**(B)**4a

^{2}/3 sq. units

**(C)**2a

^{2}/3 sq. units

**(D)**None of these

**2. (1-x ^{2})^{1/2}-(1-y^{2})^{1/2}=a (x-y)
then dy/dx equal to** (1-x

(A)

^{2}/1-y

^{2)}

**(B)**(1-y

^{2}/1-x

^{2)}

**(C)**(1-x

^{2}/1-y

^{2)1/2}

**(D)**(1-y

^{2}/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 x ^{3} = 8a^{2}y, a > 0 at the
point in the first quadrant is –2/3 then the point is** (a, 2a)

(A)

**(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

(A)

**(B)**4

**(C)**1

**(D)**2