List of top Mathematics Questions on Limits and derivations asked in CUET (PG)

The function f(z) defined by $f(z)= \begin{cases}     \frac{Re(z)}{z}       & z\neq0\\     0  & z=0   \end{cases}$then which one of the following is true?

Which one of the following is not correct?

Match List-I and List-II

LIST I		LIST II
A.	$\lim\limits_{x\rightarrow0}(1+sinx)^{2\cot x}$	I.	e-1/6
B.	$\lim\limits_{x\rightarrow0}e^x-(1+x)/x^2$	II.	e
C.	$\lim\limits_{x\rightarrow0}(\frac{sinx}{x})^{1/x^2}$	III.	e2
D.	$\lim\limits_{x\rightarrow\infty}(\frac{x+2}{x+1})^{x+3}$	IV.	½

Choose the correct answer from the options given below:

Given below are two statements:
Statement I: The sum of the series 2{7^-1+3^-17^-3 +5^-1.7^-5 +....} is log_e($\frac{4}{3}$).
Statement II: The value of e always lies between 2 and 3.
In the light of the above Statements, choose the most appropriate answer from the options given below :