Which of the following is the energy of a possible excited state of hydrogen ? ............ \(\mathrm{eV}\)

Given below are two statements . Statement \(I :\) In \(CuSO _{4} .5 H _{2} O , Cu - O\) bonds are present. Statement \(II :\) In \(CuSO _{4} .5 H _{2} O\), ligands coordinating with \(Cu\) \((II)\) ion are \(O\)-and \(S\)-based ligands. In the light of the above statements, choose the correct answer from the options given below

The bond angle \(H-X-H\) is the greatest in the compound

The correct sequential order of the reagents for the given reaction is.

The addition of \(HI\) in the presence of peroxide catalyst does not follow anti-Markovnikov's rule because

A perfect gas \((0.1 \mathrm{~mol})\) having \(\overline{\mathrm{C}}_{\mathrm{v}}=1.50 \mathrm{R}\) (independent of temperature) undergoes the above transformation from point 1 to point 4. If each step is reversible, the total work done (w) while going from point 1 to point 4 is \((-)\) ________ J (nearest integer) \(\left[\right.\) Given : \(\left.\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]\)

Benzyl isocyanide can be obtained by: Choose the correct answer from the options given below:

The ratio \((R)\) of output resistance \(r_0\), and the input resistance \(r_i\) in measurements of input and output characteristics of a transistor is typically in the range

Let the abscissae of the two points \(P\) and \(Q\) be the roots of \(2 x ^{2}- rx + p =0\) and the ordinates of \(P\) and \(Q\) be the roots of \(x^{2}-s x-q=0\). If the equation of the circle described on \(PQ\) as diameter is \(2\left( x ^{2}+ y ^{2}\right)-11 x -14 y -22=0\), then \(2 r+s-2 q+p\) is equal to

A particle of mass \('{m}'\) is moving in time \('t'\) on a trajectory given by \(\overrightarrow{{r}}=10 \alpha {t}^{2}\, \hat{{i}}+5 \beta({t}-5)\, \hat{{j}}\) Where \(\alpha\) and \(\beta\) are dimensional constants. The angular momentum of the particle becomes the same as it was for \({t}=0\) at time \({t}=\) .....\(seconds.\)

The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is \(9 : 4\). The mass of the planet is \(\frac{1}{9}^{th}\) of that of the Earth. If \('R'\) is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)

Which of the following are correct expression for torque acting on a body?
A. \(\vec{\tau}=\vec{r}\times\vec{L}\)
B. \(\vec{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}})\)
C. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \frac{\mathrm{d} \mathrm{p}}{\mathrm{dt}}\)
D. \(\vec{\tau}=\mathrm{I} \vec{\alpha}\)
E. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}\)
( \(\overrightarrow{\mathrm{r}}=\) position vector; \(\overrightarrow{\mathrm{p}}=\) linear momentum;
\(\overrightarrow{\mathrm{L}}=\) angular momentum; \(\vec{\alpha}=\) angular acceleration;
\(I=\) moment of inertia; \(\vec{F}=\) force; \(t=\) time)
Choose the correct answer from the options given below :

If the earth suddenly shrinks to \(\frac{1}{64}\) th of its original volume with its mass remaining the same, the period of rotation of earth becomes \(\frac{24}{ x } h\). The value of \(x\) is \(.......\)