Three identical coils C₁, C₂, and C₃ are closely placed such that they share a common axis. C₂ is exactly midway. C₁ carries current I in anti-clockwise direction while C₃ carries current I in clockwise direction. An induced current flows through C₂ will be in clockwise direction when

A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field $\overrightarrow{E}$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is _______ . (g: acceleration due to gravity)

The electric field in a region is given by $\overrightarrow{E}=Ax\hat{i}+By\hat{j},$where A = 10 V/m² and B = 5 V/m². If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is _______V.

The volume of an ideal gas increases 8 times and temperature becomes (1/4)th of initial temperature during a reversible change. If there is no exchange of heat in this process (ΔQ = 0), then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :

Consider an equilateral prism (refractive index √2). A ray of light is incident on its one surface at a certain angle i. If the emergent ray is found to graze along the other surface, then the angle of refraction at the incident surface is close to _______.

Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at 100 °C and 40 °C respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperatures at junction points B and E are (close to) :

A cylindrical tube AB of length l, closed at both ends contains an ideal gas of 1 mol having molecular weight M. The tube is rotated in a horizontal plane with constant angular velocity ω about an axis perpendicular to AB and passing through the edge at end A, as shown in the figure. If P_A and P_B are the pressures at A and B respectively, then the relation between P_A and P_B is equal to:(Consider the temperature is same at all points in the tube)

The minimum frequency of photon required to break a particle of mass 15.348 amu into 4α particles is __________ kHz.

[mass of He nucleus = 4.002 amu, 1 amu = 1.66 x 10^-27 kg, h = 6.6 x 10^-34J.s, and c = 3 x 10⁸]

Net gravitational force at the centre of a square is found to be F₁ when four particles having mass М, 2М, 3M, and 4M are placed at the four corners of the square as shown in the figure, and it becomes F₂ when the positions of 3M and 4M are interchanged. If the ratio F₁/F₂ = α/√5, then the value of α is:

Find the correct combination of A, B, C, and D inputs that can cause the LED to glow.

Given below are two statements:
Statement I: Pressure of fluid is exerted only on a solid surface in contact as the fluid pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to the interior, results in surface tension.
In the light of the above statements, choose the correct answer from the options given below.

A projectile is thrown upward at an angle of 60° with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45° with the horizontal. The initial speed of the projectile is _______ m/s.

A meter bridge with two resistances R₁ and R₂, as shown in the figure, was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P, when a 16 Ω resistance is connected in parallel to R₂. The values of resistances R₁ and R₂ are ____ and ____ respectively.

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ________ m/s.

XPQY is a vertical smooth long loop having a total resistance R, where PX is parallel to QY, and the separation between them is l. A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L (L > l) and mass m is made to slide down from rest under gravity as shown in the figure. The terminal speed acquired by the rod is ___________  m/s. (g is acceleration due to gravity)

Six point charges are kept 60° apart from each other on the circumference of a circle of radius R as shown in the figure. The net electric field at the centre of the circle is _______ .

(ε₀ is the permittivity of free space)

7.9 MeV α-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) __________ m.

[$\frac{1}{4\mathrm{\pi }{\in }_0}=9\times {10}^{9}N{m}^2/C^2$ and electron charge = 1.6 x 10^-19]

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is _________ kg.m².