In the given diagram, if PQ = A, QR = B and RS = C, then PS equals

• A − B + C

• A + B − C

• A + B + C

• A − B − C

The magnitudes of a set of 3 vectors are given below. The set of vectors for which the resultant cannot be zero is

• 15, 20, 30

• 20, 20, 30

• 10, 20, 40

• 10, 10, 20

When a body is projected vertically up from the ground with certain velocity, its potential energy and kinetic energy at a point A are in the ratio 2 : 3. If the same body is projected with double the previous velocity, then at the same point A the ratio of its potential energy to kinetic energy is

• 9 : 1

• 2 : 9

• 1 : 9

• 9 : 2

A ball is dropped from the top of a tower of height 100 m and at the same time another ball is projected vertically upwards from ground with a velocity 25 ms^-1. Then, the distance from the top of the tower, at which the two balls meet is

• 68.4 m

• 48.4 m

• 78.4 m

• 18.4 m

45.

A particle has the position vector $\mathrm{r} = \hat{\mathrm{i}} - 2\hat{\mathrm{j}} + \hat{\mathrm{k}}$ and the linear momentum $\mathrm{p} = 2\hat{\mathrm{i}} - \hat{\mathrm{j}} + \hat{\mathrm{k}}$. Its angular momentum about the origin is

• $- \hat{\mathrm{i}} + \hat{\mathrm{j}} - 3\hat{\mathrm{k}}$

• $- \hat{\mathrm{i}} + \hat{\mathrm{j}} + 3\hat{\mathrm{k}}$

• $\hat{\mathrm{i}} - \hat{\mathrm{j}} + 3\hat{\mathrm{k}}$

• $\hat{\mathrm{i}} - \hat{\mathrm{j}} - 5\hat{\mathrm{k}}$

The vertical component of velocity of a projectile at its maximum height (u = velocity of projection, θ = angle of projection) is

• u sin θ

• u cos θ

• $\frac{\mathrm{u}}{\sin \mathrm{\theta }}$

• zero

From an elevated point P, a stone is projected vertically upwards when the stone reaches a distance h below P, its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection is

• $\frac{3}{5} \mathrm{h}$

• $\frac{5}{3} \mathrm{h}$

• $\frac{5}{7} \mathrm{h}$

• $\frac{2}{3} \mathrm{h}$

A particle describes uniform circular motion in a circle of radius 2 m, with the angular speed of 2 rad s^-1. The magnitude of the change in its velocity in $\frac{\mathrm{\pi }}{2}$ s is

• 0 ms^-1

• $2\sqrt{2} {\mathrm{ms}}^{-1}$

• 8 ms^-1

• 4 ms^-1

A body projected at an angle with the horizontal has a range 300 m. If the time of flight is 6 s, then the horizontal component of velocity is

• 30 ms^-1

• 50 ms^-1

• 40 ms^-1

• 45 ms^-1

The velocity-time graph for the vertical component of the velocity of a body thrown upwards from the ground and landing on the roof of a building is given in the figure. The height of the building is

• 50 m

• 40 m

• 20 m

• 30 m