jee-main 2025 Q68

jee-main · India · session2_08apr_shift2 Exponential Functions Limit Evaluation
Q68. $\lim _ { x \rightarrow 0 } \frac { e - ( 1 + 2 x ) ^ { \frac { 1 } { 2 x } } } { x }$ is equal to
(1) 0
(2) $\frac { - 2 } { e }$
(3) e
(4) $e - e ^ { 2 }$
Q69. If the variance of the frequency distribution
$x$$c$$2 c$$3 c$$4 c$$5 c$$6 c$
$f$211111

is 160 , then the value of $c \in N$ is
(1) 7
(2) 8
(3) 5
(4) 6
Q68. $\lim _ { x \rightarrow 0 } \frac { e - ( 1 + 2 x ) ^ { \frac { 1 } { 2 x } } } { x }$ is equal to\\
(1) 0\\
(2) $\frac { - 2 } { e }$\\
(3) e\\
(4) $e - e ^ { 2 }$

Q69.\\
If the variance of the frequency distribution

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
$x$ & $c$ & $2 c$ & $3 c$ & $4 c$ & $5 c$ & $6 c$ \\
\hline
$f$ & 2 & 1 & 1 & 1 & 1 & 1 \\
\hline
\end{tabular}
\end{center}

is 160 , then the value of $c \in N$ is\\
(1) 7\\
(2) 8\\
(3) 5\\
(4) 6