PPSC Lecturer Mathematics Solved Paper-2011

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 Q.87  Evaluate  \lim_{x\rightarrow 0}(\frac{tanx}{x})^{\frac{3}{x^3}}   

(A) 0

(B) e

(C)  e^{\frac{1}{3}}

(D) e³ 

Check Answer
a

Q.88 If z=x^2 tan^{-1}(\frac{y}{x})-y^2 tan^{-1}(\frac{x}{y}),then\; \frac{\theta^2 z}{\theta x \theta y} is 

(A) \frac{x^2}{y^2}

(B)  \frac{x^2+y^2}{x^2-y^2}

(C)  \frac{x^2-y^2}{x^2+y^2}

(D) None of these

Check Answer
c

Q.89 The radius of curvature is

(A) Double the measure of curvature

(B) Square the curvature

(C) Reciprocal of curvature

(D) None of these 

Check Answer
c

Q.90  Suppose a and c are real numbers, c > 0, and f is defined on [-1, 1] by  f(x) =  \left\{\begin{matrix} x^a sin(x^{-e}) & (if\; x \neq 0)\\ 0 & (if\; x = 0) \end{matrix}\right.  f is continuous if and only if

(A) a\geq1 

(B) a>1

(C) a\geq0

(D) a>0

Check Answer
d




Q.91   The value of \int_{0}^{\infty}\frac{dx}{1+x^2}  is

(A)  \frac{\pi}{2}

(B)  \frac{\pi}{4}

(C)  \infty

(D)  0

Check Answer
a

Q.92  Which of the following function is a bijection from R to R.

(A) f(x) = x² +1

(B)  f(x) = x³

(C) f(x) = \frac{x^2+1}{x^2+2}  

(D) f(x) = x²

Check Answer
b

93. f(z) = \frac{1}{z} is not uniformly continuous in the region 

(A)  0\leq | z| \leq 1

(B)  0\leq | z| < 1

(C)  0< | z| < 1

(D)  0< | z| \leq 1

Check Answer
a

Q.94  f(z) = z³ + 3i is

(A) analytic everywhere except z = 3i

(B) analytic everywhere except z = -3i

(C) analytic everywhere except z = 0

(D) analytic everywhere

Check Answer
d

Q.95 If C is the circle | z| = 3, then  \oint_{c}^{}\frac{dz}{1+z^2}  is equal to

(A) 3

(B) 2

(C)  0

(D) 1

Check Answer
c

Q.96  The series    \sum_{n=0}^{\infty}\frac{n^1}{(2i)^n}   

(A) convergent

 (B) absolutely convergent

(C)  divergent

(D) none of these

Check Answer
c

Q.97  The radius of convergence of sinh Z is

(A) R = \infty

(B) R=0

(C) R= 1

(D) R = 2

Check Answer
a

Q.98  Four married couples have bought 8 seats in a concert. In how many different ways can they be seated if each couple is to sit together? (A) 24

(B) 96

(C) 384

(D) none of these

Check Answer
c

Q.99 A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting 2 tails and 1 head is

(A) 1/9

(B) 2/9

(C) 4/9

(D) none of these

Check Answer
d

100. If X represents the outcome when a die is tossed. Then the expected value of X is

(A) 1/2

(B) 5/2

(C) 7/2

(D)  3/2

Check Answer
d




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