The mass and volume of a body are found to be 5.00 ± 0.05 kg and 1.00 ± 0.05 m 3 respectively. Then the maximum possible percentage error in its density is

• 6 %

• 3 %

• 10 %

• 5 %

If F denotes force and t time, then in the equation F = at^-1 + bt², the dimensions of a and b respectively are

• [LT^-4] and [LT^-1]

• [LT^-1] and [LT^-4]

• [MLT^-4] and [MLT^-1]

• [MLT] and [MLT^-4]

A car moves a distance of 200 m. It covers first half of the distance at speed 60 kmh^-1 and the second half at speed v. If the average speed is 40 kmh^-1, the value of v is

• 30 kmh^-1

• 13 kmh^-1

• 60 kmh^-1

• 40 kmh^-1

A bus begins to move with an acceleration of 1 ms^-2. A man who is 48 m behind the bus starts running at 10 ms^-1 to catch the bus. The man will be able to catch the bus after 

• 6 s

• 5 s

• 8 s

• 7 s

A particle is moving with constant acceleration from A to B in a straight line AB. If u and v are the velocities at A and B respectively then its velocity at the midpoint C will be

• $\left(\frac{{\mathrm{u}}^2 + {\mathrm{v}}^2}{2\mathrm{u}}\right)$

• $\frac{\mathrm{u} + \mathrm{v}}{2}$

• $\frac{\mathrm{v} - \mathrm{u}}{2}$

• $\sqrt{\frac{{\mathrm{u}}^2 + {\mathrm{v}}^2}{2}}$

An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10 s apart is 30°, then the speed of the aircraft is

• 19.63 ms^-1

• 1963 ms^-1

• 108 ms^-1

• 196.3 ms^-1

Two projectiles A and B thrown with speeds in the ratio 1 : $\sqrt{2}$ acquired the same heights. If A is thrown at an angle of 45° with the horizontal, the angle of projection of B will be

• 0°6

• 60°

• 30°

• 45°

A particle crossing the origin of co-ordinates at time t = 0, moves in the xy-plane with a constant acceleration a in the y-direction. If its equation of motion is y = bx² (b is a constant), its velocity component in the x-direction is

• $\sqrt{\frac{2\mathrm{b}}{\mathrm{a}}}$

• $\sqrt{\frac{\mathrm{a}}{2\mathrm{b}}}$

• $\sqrt{\frac{\mathrm{a}}{\mathrm{b}}}$

• $\sqrt{\frac{\mathrm{b}}{\mathrm{a}}}$

A stationary bomb explodes into three pieces. One piece of 2 kg mass moves with a velocity of 8 ms^-1 at right angles to the other piece of mass 1 kg moving with a velocity of 12 ms^-1. If the mass of the third piece of 0.5 kg, then its velocity is 

• 10 ms^-1

• 20 ms^-1

• 30 ms^-1

• 40 ms^-1

A block at rest slides down a smooth inclined plane which makes an angle 60° with the vertical and it reaches the ground in t₁ seconds. Another block is dropped vertically from the same point and reaches the ground in t₂ seconds. Then the ratio of t₁ : t₂ is

• 1 : 2

• 2 : 1

• 1 : 3

• $1 : \sqrt{2}$