BITSAT Mock Test Paper

The velocity v of water waves depends on their wavelength λ, the density of water ρ, and the acceleration due to gravity g. Using dimensional analysis, which expression correctly relates these quantities?

A particle starts at $x = 0$ and $t = 0$, moving along the positive x-direction with a velocity that varies as $v = a\sqrt{x}$, where $a$ is a constant. How does the displacement of the particle depend on time?

A train accelerates from rest at a constant rate $α$ for distance $x_1$ and time $t_1$. It then retards to rest at a constant rate $β$ for distance $x_2$ and time $t_2$. Which relation between these quantities is correct?

An ant crawls up a hemispherical surface very slowly. The coefficient of friction between the ant and the surface is $\frac{1}{3}$. If the line joining the center of the hemispherical surface to the ant makes an angle $α$ with the vertical, what is the maximum possible value of $α$?

A block of weight 5 N is pushed against a vertical wall by a force of 12 N. The coefficient of friction between the wall and the block is 0.6. What is the magnitude of the force exerted by the wall on the block?

A vertical spring with force constant $k$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically onto the spring, compressing it by a distance $d$. What is the net work done in this process?

A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular velocity is $ω$. What maximum height does its center of mass rise to?

Two rods $P$ and $Q$ of the same length and diameter have thermal conductivity ratio 2:3 and are joined end to end. If the temperature at one end of $P$ is 100°C and at one end of $Q$ is 0°C, what is the temperature at the interface?

A square wire frame of size L is dipped in a liquid. On taking it out, a membrane is formed. If the surface tension of the liquid is T, what is the force acting on the frame?

A liquid is kept in a cylindrical vessel rotating along its axis, leading to the liquid rising at the sides. If the vessel's radius is 0.05 m and the rotation speed is 2 rad/s, what is the difference in the liquid's height between the center and the sides?

An ideal gas expands such that $pT^2 = constant$. What is the coefficient of volume expansion of the gas?

What is the ratio of the speed of sound in nitrogen gas to that in helium gas, both at 300 K?

A point mass oscillates along the X-axis according to the law $x = x_0 cos(ωt - \frac{π}{4})$. If the acceleration of the particle is written as $a = A cos(ωt + δ)$, what are the values of A and δ?

A Gaussian surface A encloses charged particles in free space (Given: $q_1 = -14 nC, q_2 = 78.85 nC, q_3 = -56 nC$). What is the electric flux for surface A?

A sphere of radius 4 cm is suspended within a hollow sphere of radius 6 cm. The inner sphere is charged to a potential of 3 esu. When the outer sphere is earthed, what is the charge on the inner sphere?

Six identical capacitors are joined in parallel and charged to a potential difference of 10 V. Then they are separated and connected in series, with the positive plate of one connected to the negative plate of the next. What is the potential difference between the free plates?

In the given figure constructed from a uniform wire of resistance 1 × 10⁻² Ω/m, where length AB is 2 m, what is the resistance between points A and B?

In the circuit where a resistor R is connected to a 15V source in series with a 2Ω resistor, if the power dissipated in the circuit is 150 W, what is the value of R?

The oscillating frequency of a cyclotron is 10 MHz. If the radius of its dees is 0.5 m, what is the kinetic energy of a proton accelerated by the cyclotron?