PUNJAB PUBLIC SERVICE COMMISSION WRITTEN TEST FOR THE POST OF LECTURER IN MATHEMATICS 2015

Q.11 “Every bounded infinite set has at least one limit point” is the statement of

A. Heln-Borel Theorem

B. Welerstrass-Bolzano Theorem

C. Contor’s Intersection Theorem

D. None of these

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Simple theorem statement

Q.12 $\fn_cm \lim_{z \rightarrow 0}\frac{\overline{z}}{z}=$ _______________

A. $\fn_cm \frac{1+i}{1-i}$

B. 1

C. Does not exist

D. -1

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In process

Q.13 Cauchy-Riemann Equations in polar forms are

A. $\fn_cm \frac{\partial u}{\partial r}=\frac{1}{r}\frac{\partial v}{\partial \theta},\frac{\partial v}{\partial r}=-\frac{1}{r}\frac{\partial u}{\partial \theta}$

B. $\fn_cm \frac{\partial u}{\partial r}=-\frac{1}{r}\frac{\partial v}{\partial \theta},\frac{\partial v}{\partial r}=\frac{1}{r}\frac{\partial u}{\partial \theta}$

C. $\fn_cm \frac{\partial u}{\partial r}=-\frac{1}{r}\frac{\partial v}{\partial \theta},\frac{\partial v}{\partial r}=-\frac{1}{r}\frac{\partial u}{\partial \theta}$

D. $\fn_cm \frac{\partial u}{\partial r}=\frac{1}{r}\frac{\partial v}{\partial \theta},\frac{\partial v}{\partial r}=\frac{1}{r}\frac{\partial u}{\partial \theta}$