In a photoelectric experiment, a parallel beam of monochromatic light with the power of $200\text{W}$ is incident on a perfectly absorbing cathode of work function $6.25 \mathrm{eV}$. The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of $500\text{V}$ is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force $F=n\times {10}^{-4}\mathrm{ N}$ due to the impact of the electrons. The value of $n$ is __________. Mass of the electron \(\text{m}_\text e =9 \times 10^{-31} kg\) and \(1.0 eV =1.6 \times\) \(10^{-19}\text{ J}.\)

A ball of mass \((m) 0.5 \mathrm{~kg}\) is attached to the end of a string having length \((L) 0.5 \mathrm{~m}\). The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is \(324 \mathrm{~N}\). The maximum possible value of angular velocity of ball (in rad/s) is

Statement I The total translational kinetic energy of all the molecules of a given mass of an ideal gas is \(1.5\) times the product of its pressure and its volume.
Statement II The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

A biconvex lens of focal length \(f\) forms a circular image of radius \(r\) of sun in focal plane. Then, which option is correct?

The activity of a freshly prepared radioactive sample is \(10^{10}\) disintegrations per second, whose mean life is \(10^{-9} \mathrm{~s}\). The mass of an atom of this radioisotope is \(10^{-25} \mathrm{~kg}\). The mass (in \(\mathrm{mg}\) ) of the radioactive sample is

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A thermal power plant produces electric power of \(600 \mathrm{~kW}\) at \(4000 \mathrm{~V}\), which is to be transported to a place \(20 \mathrm{~km}\) away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with a power factor unity. All the currents and voltages mentioned are rms values.


Question:

If the direct transmission method with a cable of resistance \(0.4 \Omega \mathrm{km}^{-1}\) is used, the power dissipation (in %) during transmission is

A person blows into open-end of a long pipe. As a result, a high pressure pulse of air travels down the pipe.

When this pulse reaches the other end of the pipe,

Let \(X\) be a random variable, and let \(P(X=x)\) denote the probability that \(X\) takes the value \(x\). Suppose that the points \((x, P(X=x)), x=0,1,2,3,4\), lie on a fixed straight line in the \(x y\)-plane, and \(P(X=x)=0\) for all \(x \in \mathbb{R}-\{0,1,2,3,4\}\). If the mean of \(X\) is \(\frac{5}{2}\), and the variance of \(X\) is \(\alpha\), then the value of \(24 \alpha\) is ___

A straight line \(L\) through the point \((3,-2)\) is inclined at an angle \(60^{\circ}\) to the line \(\sqrt{3} x+y=1\). If \(L\) also intersects the \(X\)-axis, then the equation of \(L\) is

Match the statements of Column I with these in Column II.
[Note : Here \(z\) takes values in the complex plane and \(\operatorname{Im}(z)\) and \(\operatorname{Re}(z)\) denote respectively, the imaginary part and the real part of \(z\) ]

Column I	Column II
(A)The set of points \(z\) satisfying \(|z-i| z||=|z+i| z||\) is contained in or equal to	(p)an ellipse with eccentricity \(4 / 5\)
(B) The set of points \(z\) satisfying \(|z+4|+|z-4|=0\) is contained in or equal to	(q) the set of points \(z\) satisfying \(\operatorname{Im}(z)=0\)
(C) If \(|w|=2\), then the set of points \(z=w-\frac{1}{w}\) is contained in or equal to	(r) the set of points \(z\) satisfying \(|\operatorname{Im} z| \leq 1\)
(D) If \(|w|=1\), then the set of points \(z=w+\frac{1}{w}\) is contained in or equal to	(s) the set of points satisfying \(|\operatorname{Re} z| \leq 2\)
	(t) the set of points \(z\) satisfying \(|z| \leq 3\)

A normal with slope \(\frac{1}{\sqrt{6}}\) is drawn from the point \((0,-\alpha)\) to the parabola \(x^2=-4 a y\), where \(a>0\). Let \(L\) be the line passing through \((0,-\alpha)\) and parallel to the directrix of the parabola. Suppose that \(L\) intersects the parabola at two points \(A\) and \(B\). Let \(r\) denote the length of the latus rectum and \(s\) denote the square of the length of the line segment \(A B\). If \(r: s=1: 16\), then the value of 24ais ________.

Reaction of \(\mathbf{x}\) g of \(\mathrm{Sn}\) with \(\mathrm{HCl}\) quantitatively produced a salt. Entire amount of the salt reacted with \(\mathbf{y} g\) of nitrobenzene in the presence of required amount of \(\mathrm{HCl}\) to produce \(1.29 \mathrm{~g}\) of an organic salt (quantitatively).
(Use Molar masses (in \(\mathrm{g} \mathrm{mol}^{-1}\) ) of \(\mathrm{H}, \mathrm{C}, \mathrm{N}, \mathrm{O}, \mathrm{Cl}\) and \(\mathrm{Sn}\) as \(1,12,14,16,35\) and 119 , respectively).
The value of $\mathrm{y}$ is_________ .

A point object is placed at distance of \(20 \mathrm{~cm}\) from a thin planoconvex lens of focal length \(15 \mathrm{~cm}\). The plane surface of the lens is now silvered. The image created by the system is at