The area (in sq. units) of the region given by \(R=\left\{(x, y): \frac{y^2}{2} \leq x \leq y+4\right\}\) is

A bag contains 12 two rupee coins, 7 one rupee coins and 4 fifty paise coins. If three coins are selected at random, then the probability that the sum of the values of the three coins is not an integral multiple of a rupee is

The number of complex numbers z satisfying \(\bar{z}=i z^2\) is

The area (in sq. units) of the triangle formed by the tangent and normal to the ellipse \(9 x^2+4 y^2=72\) at the point \((2,3)\) with the \(X\)-axis is

Observe the following lists


Then the correct match for List I from List II is
A B C D

If the mean of a data $\overline{x}$ is $10$ and if all the observations are multiplied by $2$, then the mean of new data is

Find the value of \(k\) if \(\int \cos ^k(x) \sin (x) d x=\frac{-1}{4}\) \(\cos ^4(x)+c\)

Torque required to hold a small circular coil of $10$ turns, $2\times {10}^{-4}{ \mathrm{m}}^2$ area and carrying $0.5 \mathrm{A}$ current is the middle of a long solenoid of ${10}^3$ turns per meter carrying $3 \mathrm{A}$ current, with its axis perpendicular to the axis of the solenoid is

\(20 \mathrm{~mL}\) of \(\mathrm{Fe}^{2+}\) solution of certain concentration has completely reacted with \(20 \mathrm{~mL}\) of \(0.01 \mathrm{M} \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7\) in acidic medium. If \(20 \mathrm{~mL}\) of same \(\mathrm{Fe}^{2+}\) solution has reacted completely with \(20 \mathrm{~mL}\) of \(\mathrm{KMnO}_4\) solution in acid medium, the molarity of \(\mathrm{KMnO}_4\) solution is

Which of the following complex ions is most stable?

\(\mathrm{Cu}^{2+}\) does not form \(\mathrm{CuI}_2\). This is because \(\mathrm{Cu}^{2+}\)

The initial rates of decrease of \(\mathrm{I}_2\) in acetone - iodine reaction catalysed by \(\mathrm{H}^{+}\) are given in the table.
\(\begin{array}{|c|c|c|c|c|}
\hline \begin{array}{c}
\text { Experiment } \\
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{I}_2\right]} \\
\left(\mathrm{mol} \mathrm{L}^{-1}\right)
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{H}^{+}\right]} \\
\left(\mathrm{mol} \mathrm{L}^{-1}\right)
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]} \\
\left(\mathrm{mol} \mathrm{L}^{-1}\right)
\end{array} & \begin{array}{c}
\text { Initial rate of decrease of } \mathrm{I}_2 \\
\left(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\right)
\end{array} \\
\hline 1 & 0.01 & 0.1 & 0.1 & 0.096 \\
2 & 0.01 & 0.2 & 0.1 & 0.192 \\
3 & 0.02 & 0.2 & 0.1 & 0.192 \\
4 & 0.01 & 0.2 & 0.2 & 0.384 \\
\hline
\end{array}\)
The order with respect to \(\mathrm{I}_2, \mathrm{H}^{+}\), acetone and total order of the reaction respectively are:

A transformer works on the principle of