If P and Q are two non-collinear unit vectors and if $\left|\mathrm{P} + \mathrm{Q}\right| = \sqrt{3}$ then the value of (P - Q)(2P + Q) will be

• 1

• 2

• $\frac{1}{2}$

• $\frac{3}{2}$

A gas bubble forms an explosion under water which oscillate with a period T ∝ p^aρ^bE^c, where p is the static pressure, ρ is the density ofwater and E is the total energy of explosion. Then, the values of a, b and c will be

• $- \frac{5}{6}, \frac{1}{2}, \frac{1}{3}$

• $\frac{2}{5}, \frac{1}{3}, \frac{1}{4}$

• $\frac{4}{5}, \frac{9}{8}, \frac{1}{2}$

• $\frac{3}{2}, \frac{1}{4}, \frac{5}{6}$

If a particle moves a distance x at a speed v₁ and comes back with speed v₂ , then the average speed and average velocity during this round trip will respectively be

• 0, v₁ + v₂

• $\frac{2{\mathrm{v}}_1{\mathrm{v}}_2}{{\mathrm{v}}_1 + {\mathrm{v}}_2}, 0$

• v₁ + v₂, 0

• v₁ − v₂, $\frac{2{\mathrm{v}}_1{\mathrm{v}}_2}{{\mathrm{v}}_1 + {\mathrm{v}}_2 }$

On an electron in an atom both electric and gravitational forces are collinear we neglect gravitational force (F_G) in comparision to electric force (F_E ), because

• F_E > F_G

• F_N > F_E

• F_E >> F_G

• F_N >> F_G

A metal block of mass 1 kg is resting on a frictionless horizontal plane. It is struck by a jet releasing water at a rate of 1 m/s and at a speed of 4 m/s. Then, the initial acceleration of the block will be

• 2 m/s²

• 8 m/s²

• 1 m/s²

• 4 m/s²

A body of mass 5 kg moves on a straight path as a function of time x = t³ − 12t. The force on the body at t = 5s will be

• 100 N

• 150 N

• 120 N

• 130 N

The potential energy of a certain spring when stretched through a distance x is 20 J. The amoµnt of work that must be done on this spring to stretch it through an additional distance $\frac{\mathrm{x}}{2}$ will be

• 20 J

• 25 J

• 5 J

• 15 J

8.

A flywheel of moment of inertia 0.4 kg-m² and radius 20 cm is free to rotate about a central axis. If a string is wrapped on its circumference and it is pulled with a force of 10 N, then the change in its angular velocity after 4 s will be

• 10 rad/s

• 20 rad/s

• 40 rad/s

• 5 rad/s

Three identical spheres of mass m each are placed at the corners of an equilateral triangle of side 1 m. Taking one of the corners as the origin, the position vector of centre of mass is

• $\frac{1}{2}\stackrel{\wedge }{\mathrm{i}} + \frac{\sqrt{3}}{2} \stackrel{\wedge }{\mathrm{j}}$

• $\frac{1}{2} \stackrel{\wedge }{\mathrm{i}} + \frac{1}{2\sqrt{3}} \stackrel{\wedge }{\mathrm{j}}$

• $\stackrel{\wedge }{\mathrm{i}} + \stackrel{\wedge }{\mathrm{j}}$

• $2\stackrel{\wedge }{\mathrm{i}} - \stackrel{\wedge }{\mathrm{j}}$

The driver of a truck travelling with a velocity v suddenly notice a brick wall infront of him at a distance r. How the driver avoid himself by crashing into the wall ?

• By speeding up the truck

• By applying a brake

• By slowing down the truck

• By taking a circular turn