PPSC Lecturer Mathematics Solved Paper-2011

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Q. 75   Let f(x) = \frac{x+5}{(x-1)(x-2)}   Then range of f is

(A) Set of all real numbers R

(B) R-(1, 2}

(C)  R^{+}   

(D)  R^{-}  

Check Answer
a

Q.76  The value of \int_{0}^{1}xe^ydx is

(A) -1 

(B) 1

(C) c

(D) 2c

Check Answer
b

Q.77 The solution of the congruence 4x = 5 (mod 9) is

 (A) x= 6(mod 9)

(B) x= 7(mod 9)   

(C) x=8(mod 9)

(D) x= 2(mod 9)

Check Answer
c

78. The series  x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\frac{x^{4}}{4}+...    is convergent for 

(A) | x | < 1 only

(B) | x|\leq  1

(C) -1 < x\leq  1  

(D) all real values of x

Check Answer
a

Q.78  The general solution of the differential equation (x² + y²) dx- 2xdy 0 is

(A)  x² – cx- y² = 0, where c is an arbitrary constant

(B) (x- y)² = cx, where c is an arbitrary constant

(C) x+y+ 2xy = C, where c is an arbitrary constant

(D) y = x² – 2x + C, where cis an arbitrary constant

Check Answer
a

Q.79  Let f be defined on R by setting f(x) = x, if x is rational and f (x) = 1- x if x is irrational. Then 

(A) f is continuous on R

(B) f is continuous only at x = \frac{1}{2}

(C) f is continuous everywhere except at x = \frac{1}{2}

(D) f is discontinuous everywhere

Check Answer
a




Q.80  The differential equation ydx – 2xdy = 0 represents

(A) a family of straight lines

(B) a family of parabola

(C) a family of hyperbolas

(D) a family of circles

Check Answer
b

Q.81  A particular integral of the differential equation (D² + 4)y=x is

(A) xc^{-2x}

(B) x cos 2x

(C) x sin 2x

(D)  \frac{x}{4}

Check Answer
d

Q.82  The area of the cardioid r= a(1 + cos0) is equal to

(A) 4\pi a^{2}

(B) 8\pi a

(C)  \frac{3\pi a}{4}

(D)  2\pi a^{2}

Check Answer
c

Q. 84. The value of {\sqrt{3}} sin x + cos x ill be greatest when x is equal to

(A)  \frac{\pi}{2}

(B)    \frac{\pi}{4}

(C)    \frac{\pi}{6}

(D)  \frac{\pi}{8}

Check Answer
b

Q.85  If a particle in equilibrium is subjected to four forces F_1=21- 5j + 6k, F_2 =1+31-7k, F_3 = 21 – 21-3k and F_4 then F_4 equal to

(A)-5i + 4j + 4k

(B) 5i – 4j- 4k

(C) 3i-2j-k

(D) 3i +j – 10k

Check Answer
a

Q.86  The function f(x) = |x|+|x-1| is

(A) Continuous and differentiable for x = 0, x =1 

(B)  Continuous but not differentiable for x = 0, x = 1

(B)  Discontinuous but differentiable for x = 0, x = 1

(D) Neither continuous nor differentiable for x = 0, x-1

Check Answer
b
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