If the galvanometer G does not show any deflection in the circuit shown, the value of R is given by:

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of a closed pipe having the same length is:

Light travels a distance x in time t_1 in air and 10x in time t_2 in another denser medium. What is the critical angle for this medium?

If $\oint \mathbf{E} \cdot d\mathbf{S} = 0$ over a surface, then:

A 12 V, 60 W lamp is connected to the secondary of a step-down transformer, whose primary is connected to ac mains of 220 V. Assuming the transformer to be ideal, what is the current in the primary winding?

The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is proportional to:

The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly : (surface tension of soap solution = 0.03 N m$^{-1}$)

The magnitude and direction of the current in the following circuit is:

The work function of Caesium (Cs), Potassium (K), and Sodium (Na) are 2.14 eV, 2.30 eV, and 2.75 eV respectively. If incident electromagnetic radiation has an energy of 2.20 eV, which of these photosensitive surfaces may emit photoelectrons?

The net magnetic flux through any closed surface is:

In a plane electromagnetic wave traveling in free space, the electric field component oscillates sinusoidally at a frequency of $2.0 \times 10^{10} Hz$ and amplitude 48 V/m. Then the amplitude of oscillating magnetic field is: (Speed of light in free space $= 3 \times 10^{8} m/s)$

Given below are two statements:$\newline$Statement I: Photovoltaic devices can convert optical radiation into electricity.$\newline$Statement II: Zener diode is designed to operate under reverse bias in breakdown region.$\newline$In the light of the above statements, choose the most appropriate answer from the options given below:

A bullet is fired from a gun at the speed of 280 m/s in the direction $30^\circ$ above the horizontal. The maximum height attained by the bullet is $( g = 9.8 m/s^{2}, \sin 30^\circ = 0.5):$

An electric dipole is placed at an angle of $30^\circ$ with an electric field of intensity $2 \times 10^5 NC^{-1}.$ It experiences a torque equal to 4 Nm. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.

For Young's double slit experiment, two statements are given below:$\newline$Statement I: If the screen is moved away from the plane of slits, angular separation of the fringes remains constant.$\newline$Statement II: If the monochromatic source is replaced by another monochromatic source of larger wavelength, the angular separation of fringes decreases.$\newline$In the light of the above statements, choose the correct answer from the options given below:

A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:

A metal wire has mass $(0.4 \pm 0.002)$ g, radius $(0.3 \pm 0.001)$ mm and length $(5 \pm 0.02)$ cm. The maximum possible percentage error in the measurement of density will nearly be:

An AC source is connected to a capacitor C. Due to decrease in its operating frequency:

Resistance of a carbon resistor determined from colour codes is $(22000 \pm 5 \% \Omega)$ The colour of the third band must be:

A Carnot engine has an efficiency of 50% when its source is at a temperature $327^\circ C.$ The temperature of the sink is:

The angular acceleration of a body, moving along the circumference of a circle, is:

In a series LCR circuit, the inductance L is 10 mH, capacitance C is $1\mu F$ and resistance R is $100 \Omega.$ The frequency at which resonance occurs is:

A full wave rectifier circuit consists of two p-n junction diodes, a centre-tapped transformer, capacitor and a load resistance. Which of these components remove the ac ripple from the rectified output?

A vehicle travels half the distance with speed $v$ and the remaining with speed $2v.$ Its average speed is:

In hydrogen spectrum, the shortest wavelength in the Balmer series is $\lambda.$ The shortest wavelength in the Brackett series is:

The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is:

The half-life of a radioactive substance is 20 minutes. In how much time, the activity of the substance drops to $\frac{1}{16}$ of its initial value?

Two bodies of mass $m$ and $9m$ are placed at a distance $R.$ The gravitational potential on the line joining the bodies where the gravitational field equals zero will be ($G$ = gravitational constant):

The potential energy of a long spring when stretched by 2 cm is $U.$ If the spring is stretched by 8 cm, potential energy stored in it will be:

For the following logic circuit, the truth table is:

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 (g = 10 m/s^2).

The radius of the innermost orbit of hydrogen atom is $5.3 \times 10^{-11} m.$ What is the radius of third allowed orbit of hydrogen atom?

A bullet from a gun is fired on a rectangular wooden block with velocity $u.$ When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}.$ Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:

The net impedance of circuit (as shown in figure) will be:

A satellite is orbiting just above the surface of the earth with period $T.$ If $d$ is the density of the earth and $G$ is the universal constant of gravitation, the quantity $\frac{3Gd}{\pi}$ represents:

A very long conducting wire is bent in a semi-circular shape from A to B as shown in the figure. The magnetic field at point P for steady current configuration is given by:

The resistance of platinum wire at 0°C is $2\Omega$ and $6.8\Omega$ at 80°C. The temperature coefficient of resistance of the wire is:

10 resistors, each of resistance $R$ are connected in series to a battery of emf $E$ and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased $n$ times. The value of $n$ is:

The $x-t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2s$ is:

A wire carrying a current I along the positive x-axis has length L. It is kept in a magnetic field $\vec{B} = (2\hat{i} + 3\hat{j} - 4\hat{k})$ T. The magnitude of the magnetic force acting on the wire is:

In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)?

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 m/s. The ball strikes the water surface after 4s. The height of the bridge above the water surface is (Take $g = 10$ m/s$^2$):

Two thin lenses are of the same focal lengths ($f$), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be:

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight W attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is:

An electric dipole is placed as shown in the figure. The electric potential (in $10^2 V$) at point P due to the dipole is ($\varepsilon_0$ = permittivity of free space and $K = \frac{1}{4 \pi \varepsilon_0}$):

The temperature of a gas is $-50^\circ C.$To what temperature the gas should be heated so that the rms speed is increased by 3 times?

The magnetic energy stored in an inductor of inductance $4 \mu H$ carrying a current of 2 A is:

The equivalent capacitance of the system shown in the following circuit is:

The venturi-meter works on: