22. The area of bounded by the curves $y = \sqrt { } x , 2 y + 3 = x$ and $x$-axis in the $1 ^ { \text {st } }$ quadrant is :\\
(a) 9\\
(b) $27 / 4$\\
(c) 36\\
(d) 18

\section*{III askllTians ||}
\section*{Powered By IITians}
\begin{enumerate}
  \setcounter{enumi}{22}
  \item Coefficient of $t ^ { 24 }$ in $\left( 1 + t ^ { 2 } \right) ^ { 12 } \left( 1 + t ^ { 12 } \right) \left( 1 + t ^ { 24 } \right)$ is:\\
(a) $\quad { } ^ { 12 } \mathrm { C } _ { 6 } + 3$\\
(b) $\quad { } ^ { 12 } \mathrm { C } _ { 6 } + 1$\\
(c) $\quad { } ^ { 12 } \mathrm { C } _ { 6 }$\\
(d) $\quad { } ^ { 12 } \mathrm { C } _ { 6 } + 2$
  \item The value of ' $a$ ' so that the volume of parallelepiped formed by $\hat { i } + a \hat { j } + k , \hat { j } + a k$ and aî $+ k$ because minimum is:\\
(a) $\quad - 3$\\
(b) 3\\
(c) $1 / \sqrt { } 3$\\
(d) $\sqrt { } 3$
  \item If the system of equations $x + a y = 0 , a z + y = 0$ and $a x + z = 0$ has infinite solutions, then the value of $a$ is\\
(a) $\quad - 1$\\
(b) 1\\
(c) 0\\
(d) no real values
  \item If $y ( t )$ is a solution of $( 1 + t ) d y / d t - t y = 1$ and $y ( 0 ) = - 1$, then $y ( 1 )$ is equal to:\\
(a) $\quad - 1 / 2$\\
(b) $\mathrm { e } + \frac { 1 } { 2 }$\\
(c) $\mathrm { e } - \frac { 1 } { 2 }$\\
(d) $\quad 1 / 2$
  \item Tangent is drawn to ellipse $x ^ { 2 } / 27 + y ^ { 2 } = 1$ at $( 3 \sqrt { } 3 \cos \theta , \sin \theta )$ (where $\theta \hat { \mathrm { I } } ( 0$, $\Pi / 2$ ). Then the value of $\theta$ such that sum of intercepts on axes made by this tangent is minimum, is\\
(a) $\mathrm { p } / 3$\\
(b) $\quad p / 6$\\
(c) $\mathrm { p } / 8$\\
(d) $\mathrm { p } / 4$
  \item Orthocentre of triangle with vertices $( 0,0 ) , ( 3,4 )$ and $( 4,0 )$ is:\\
(a) $\quad ( 3,4 / 5 )$\\
(b) $( 3,12 )$\\
(c) $( 3,3 / 4 )$\\
(d) $( 3,9 )$
\end{enumerate}