The dimensions of $\frac{\mathrm{a}}{\mathrm{b}}$ in the equation $\mathrm{p} = \frac{\mathrm{a} - {\mathrm{t}}^2}{\mathrm{bx}}$where, p is pressure, x is distance and and t is time, are

• [M²LT^-3]

• [MT^-2]

• [LT^-3]

• [ML³T^-1]

Three vectors satisfy the relation A . B = 0 and A . C = 0, then A is parallel to

• C

• B

• B × C

• B . C

A student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of 1 ms^-2,  the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is

• 8 ms^-1

• 5 ms^-1

• 12 ms^-1

• 10 ms^-1

4.

For a given velocity, a projectile has the same range R for two angles of projection if t₁ and t₂ are the time of flight in the two cases, then

• t₁t₂ ∝ R

• t₁t₂ ∝ R²

• ${\mathrm{t}}_1{\mathrm{t}}_2 \propto \frac{1}{{\mathrm{R}}^2}$

• ${\mathrm{t}}_1{\mathrm{t}}_2 \propto \frac{1}{\mathrm{R}}$

Weight of a body ofmass m decreases by 1 % when it is raised to height h above the earth's surface. If the body is taken to a depth h in a mine, change in its weight is

• 0.5 % decrease

• 2 % decrease

• 0.5 % decrease

• 1 % increase

Which of the following sets of concurrent forces may be in equilibrium ?

• F₁ = 3 N, F₂ = 5 N, F₃ = 1 N

• F₁ = 3 N, F₂ = 5 N, F₃ = 9 N

• F₁ = 3 N, F₂ = 5 N, F₃ = 6 N

• F₁ = 3 N, F₂ = 2 N, F₃ = 15 N

The displacement time graph of a particle executing SHM is as shown in the figure.

The corresponding force time graph of the particle is

Young's modulus of perfectly rigid body material is

• infinite

• zero

• 10 × 10¹⁰ / m²

• 1 × 10¹⁰ N/m²

An ideal monoatomic gas at 27°C is compressed adiabatically to 8/27 times of its present volume. The increase in temperature of the gas is

• 375°C

• 402°C

• 175°C

• 475°C

A sample of ideal monoatomic gas is taken round the cycle ABCA as shown in the figure. The work done during the cycle is

• 3 pV

• zero

• 9 pV

• 6 pV