A swimmer swims a distance d upstream in 4 s and swims an equal distance downstream in 2 s. The ratio of swimmer's speed in still water to the speed of river water will be:

1.  $\frac{6}{5}$

2.  $\frac{3}{1}$

3.  $\frac{5}{3}$

4.  $\frac{4}{3}$

A particle starts from (-1, 0) in the x-y plane along a straight path making an angle of 60° with the X-axis. Which of the following will not be the coordinate through which the particle will pass?

(1) (0, $\sqrt{3}$)

(2) (1, 2$\sqrt{3}$)

(3) (2, 3$\sqrt{3}$)

(4) (4, 4$\sqrt{3}$)

An aeroplane flies \(400\) m north and then \(300\) m west and then flies \(1200\) m upwards. Its net displacement is:

A projectile is thrown with an initial velocity (${\mathrm{v}}_{\mathrm{x}}\hat{\mathrm{i}}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{v}}_{\mathrm{y}}\hat{\mathrm{j}}$)m/s. Consider horizontal direction and vertical direction as x and y axes respectively. If the range of the projectile is double the maximum height, then $\frac{{\mathrm{v}}_{\mathrm{y}}}{{\mathrm{v}}_{\mathrm{x}}}$ is

(1) 4

(2) 3

(3) 2

(4) 1

A car is moving on a circular track at a speed of 20 m/s having a radius of 100 m. If it starts decelerating uniformly at the rate of $3<mspace\; width="1em"></mspace>\mathrm{m}/{\mathrm{s}}^2$, the angle made by the resultant acceleration with the direction of its instantaneous velocity is:

(1) 37°

(2) 127°

(3) 53°

(4) 143°

An object is moving on a circular path of the radius r with constant speed v. The average acceleration of the object, after it has travelled three and a half rounds, is

1.  $\frac{2{\mathrm{v}}^2}{\mathrm{\pi r}}$

2.  $\frac{4{\mathrm{v}}^2}{3\mathrm{\pi r}}$

3.  $\frac{4{\mathrm{v}}^2}{7\mathrm{\pi r}}$

4.  $\frac{2{\mathrm{v}}^2}{7\mathrm{\pi r}}$

A sprinkler is deployed to irrigate the garden. The speed of water-jet from the sprinkler is u. The maximum area which can be irrigated by the sprinkler is

1.  $\frac{{\mathrm{\pi }}^2{\mathrm{u}}^2}{\mathrm{g}}$

2.  $\frac{{\mathrm{\pi u}}^2}{\mathrm{g}}$

3.  $\frac{{\mathrm{\pi u}}^2}{{\mathrm{g}}^2}$

4.  $\frac{{\mathrm{\pi u}}^4}{{\mathrm{g}}^2}$

Which of the following is an appropriate expression for the radius of curvature of a projectile at the highest point? (R $\to$ Range of projectile)

(1) $\frac{\mathrm{R}}{2}<mspace\; width="1em"></mspace>\cot <mspace\; width="1em"></mspace>\mathrm{\theta }$

(2) $\frac{\mathrm{R}}{2}<mspace\; width="1em"></mspace>\tan <mspace\; width="1em"></mspace>\mathrm{\theta }$

(3) 2R cot $\mathrm{\theta }$

(4) 2R tan $\mathrm{\theta }$

The coordinates of a particle moving in the x-y plane vary with time according to the following relation:

$\mathrm{x}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\frac{\mathrm{B}}{\mathrm{t}}$, $\mathrm{y}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\mathrm{A}\sqrt{\mathrm{t}}$.

The locus of the particle is:

(1) Parabola

(2) Circle

(3) Eclipse

(4) Hyperbola