jee-advanced 2003 Q9

jee-advanced · India · screening Chain Rule Limit Evaluation Involving Composition or Substitution
9. If $\lim _ { ( x \rightarrow 0 ) } ( ( ( a - n ) n x - \tan x ) \sin n x ) / x ^ { 2 } = 0$, where $n$ is non zero real number, then $a$ is equal to:
(a) 0
(b) $( n + 1 ) / n$
(c) $n$
(d) $n + 1 / n$
The line $\frac { x - 4 } { 1 } = \frac { y - 2 } { 1 } = \frac { z - k } { 2 }$ lies completely in the plane $2 x - 4 y + z = 7$ for
9. If $\lim _ { ( x \rightarrow 0 ) } ( ( ( a - n ) n x - \tan x ) \sin n x ) / x ^ { 2 } = 0$, where $n$ is non zero real number, then $a$ is equal to:\\
(a) 0\\
(b) $( n + 1 ) / n$\\
(c) $n$\\
(d) $n + 1 / n$\\