BITSAT 2018 Solved Paper

Four point charges Q, -q, 2q, and 2Q are positioned at the corners of a square. What relationship between Q and q makes the electric potential zero at the square's center?

Two long, parallel wires separated by a distance of 2d carry equal currents in the same direction. The magnetic field B at a distance x from the midpoint on the perpendicular bisector is:

In the provided circuit, with components having standard meanings and the cell having EMF E, the switch X is initially connected to Y for a long time, then switched to Z. What is the maximum charge on capacitor C at any later time?

A point object is placed in front of a glass rod with a spherical end having a radius of curvature of 30 cm. Where will the image be formed?

In Young's double-slit experiment with $\lambda = 500 \text{nm}$, $d = 1 \text{mm}$, and $D = 1 \text{m}$, what is the minimum distance from the central maximum for which the intensity is half of the maximum intensity?

In a common emitter amplifier with an input resistance of 3 Ω and a load resistance of 24 Ω, if β = 0.6, what is the voltage gain?

Given that the acceleration due to gravity on the Moon's surface is 1/6 that of Earth and the Moon's diameter is 1/4 that of Earth, what is the ratio of the escape velocities on Earth to the Moon?

Given vectors $\vec{P} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ and $\vec{Q} = \hat{j} - 2\hat{k}$, what is the magnitude of their resultant vector?

A particle of mass m executes simple harmonic motion (SHM) with amplitude a and frequency ν. What is the average kinetic energy during its motion from the position of equilibrium to the end?

What is the dipole moment of the described charge distribution?

At a certain location, the Earth's horizontal and vertical components of the magnetic field are equal. What is the angle of dip at that place?

The third line of the Balmer series for an ion equivalent to a hydrogen atom has a wavelength of 108.5 nm. What is the ground state energy of an electron of this ion?

The binding energy per nucleon of $^{10}X$ is 9 MeV, and that of $^{11}X$ is 7.5 MeV, where X represents an element. What is the minimum energy required to remove a neutron from $^{11}X$?

If c = velocity of light, g = acceleration due to gravity, and P = atmospheric pressure are fundamental quantities, what are the dimensions of length?

A boy running on a horizontal road at 8 km/h observes rain falling vertically. Increasing his speed to 12 km/h, he observes the rain making a 30° angle with the vertical. What is the rain's actual speed with respect to the ground?

A hunter aims his gun and fires a bullet directly at a monkey on a tree. At the instant the bullet leaves the barrel, the monkey drops from the tree. Which statement regarding the situation is correct, assuming no air resistance?

A particle of mass m₁ moving with velocity v collides with a mass m₂ at rest. After the collision, they stick together. What happens to the velocity of the combined system immediately after the collision?

If the ratio of specific heats of a gas, $C_P / C_V$ is 1.66, what type of gas is it most likely to be?

Two oscillators are started simultaneously in the same phase. After 50 oscillations of one oscillator, they are out of phase by π (half an oscillation). What is the approximate percentage difference in their frequencies?

A juggler continuously throws four balls, releasing one ball every interval. If each ball leaves his hand with a speed of 20 m/s, what are the heights of the other balls in the air when one ball leaves his hand (assuming g = 10 m/s²)?

If a stone of mass 0.05 kg is thrown out of a train window moving at a constant speed of 100 km/h, what is the magnitude of the net force acting on the stone?