A light source of wavelength \(\lambda\) illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength \(\frac{\lambda}{2}\), then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV )

In \(5\, minutes,\) a body cools from \(75^{\circ} {C}\) to \(65^{\circ} {C}\) at room temperature of \(25^{\circ} {C}\). The temperature of body at the end of next \(5\, minutes\) is \(......\,{ }^{\circ} {C} .\)

Match List-I with List-II.

List-I (Relation)		List-II (Law)
A.	\(\oint \overrightarrow{ E } \cdot \overrightarrow{ d } l =-\frac{ d }{ dt } \oint \overrightarrow{ B } \cdot \overrightarrow{ d a}\)	I.	Ampere's circuital law.
B.	\(\oint\) B. \(\vec{d} l=\mu_0\left(1+\epsilon_0 \frac{d \phi_E}{d t}\right)\)	II.	Faraday's laws of electromagnetic induction.
C.	\(\oint \overrightarrow{ E } . \overrightarrow{ d a}=\frac{1}{\epsilon_0} \int \rho dv\)	III.	Ampere-Maxwell law
D.	\(\oint \overrightarrow{ B } \cdot \overrightarrow{ d } l =\mu_0 I\)	IV.	Gauss's law of electrostatics

Choose the correct answer from the options given below :

In a double slit experiment, at a certain point on the screen the path difference between the two interfering waves is \(\frac{1}{8} ^{th}\) of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is

In a physical balance working on the principle of moments, when \(5\, mg\) weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

A point charge \(q = 1\ \mu\text{C}\) is located at a distance \(2\text{ cm}\) from one end of a thin insulating wire of length \(10\text{ cm}\) having a charge \(Q = 24\ \mu\text{C}\), distributed uniformly along its length, as shown in figure. Force between \(q\) and wire is _______ N.
(Use \(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\text{ N}\cdot\text{m}^2/\text{C}^2\))

The electric field in an electromagnetic wave is given as \(\vec{E}=20 \sin \omega\left(t-\frac{x}{c}\right) \vec{j} NC ^{-1}\) Where \(\omega\) and \(c\) are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of \(5 \times 10^{-4}\, m ^3\) will be \(.....\times 10^{-13}\,J\) (Given \(\varepsilon_0=8.85 \times 10^{-12}\,C ^2 / Nm ^2\) )

What is the minimum energy required to launch a satellite of mass \(m\) from the surface of a planet of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2R\)?

An emf of \(20\; \mathrm{V}\) is applied at time \(\mathrm{t}=0\) to a circuit containing in series \(10\; \mathrm{mH}\) inductor and \(5 \;\Omega\) resistor. The ratio of the currents at time \(\mathrm{t}=\infty\) and at \(t=40\; s\) is close to : (Take \(e^{2}=7.389\) )

The area of cross-section of a large tank is \(0.5 \; m ^{2}\). It has a narrow opening near the bottom having area of cross-section \(1 \; cm ^{2}\). A load of \(25 \; kg\) is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is \(40 \; cm\) above the bottom, will be \(\dots \; cms ^{-1}\). \(\left[\right.\) Take \(\left.g =10 \; ms ^{-2}\right]\)

Effective capacitance of parallel combination of two capacitors \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\) is \(10\; \mu \mathrm{F}\). When these capacitors are individually connected to a voltage source of \(1\; \mathrm{V},\) the energy stored in the capacitor \(\mathrm{C}_{2}\) is \(4\) times that of \(\mathrm{C}_{1}\). If these capacitors are connected in series, their effective capacitance will be