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A particle is projected at an angle $\mathrm{\theta }$ with horizontal with an initial speed u. When it makes an angle $\mathrm{\alpha }$ with horizontal, its speed is
1.  u cos$\mathrm{\theta }$
2.  u cos$\mathrm{\theta }$ cos $\mathrm{\alpha }$
3.  $\frac{\mathrm{u} \mathrm{sin\theta }}{\sin \mathrm{\alpha }}$
4.  $\frac{\mathrm{u} \mathrm{cos\theta }}{\cos \mathrm{\alpha }}$

A ship A is moving westwards with a speed of 10 km h^-1 and a ship B, 100 km south of A is moving northwards with a speed of 10 km h^-1. The time after which the distance between them becomes the shortest, is:
1.  5 hr
2.  $5\sqrt{2} \mathrm{hr}$
3.  $10\sqrt{2} \mathrm{hr}$
4.  0 hr

Three particles moving with constant velocities ${\mathrm{V}}_1, {\mathrm{V}}_2 \mathrm{and} \hspace{0.17em}\mathrm{V}$ respectively as given as figure. After some time all three particles are in the same line, then relation among ${\mathrm{V}}_1, {\mathrm{V}}_2 \mathrm{and} \hspace{0.17em}\mathrm{V}$ is:
                             
1.  $\mathrm{V}={\mathrm{V}}_1+{\mathrm{V}}_2$
2.  $\mathrm{V}=\sqrt{{\mathrm{V}}_1{\mathrm{V}}_2}$
3.  $\mathrm{V}=\frac{{\mathrm{V}}_1{\mathrm{V}}_2}{{\mathrm{V}}_1+{\mathrm{V}}_2}$
4.  $\mathrm{V}=\frac{\sqrt{2}{\mathrm{V}}_1{\mathrm{V}}_2}{{\mathrm{V}}_1+{\mathrm{V}}_2}$

A river is flowing with a speed of 1 km/hr. A simmer wants to go to point 'C' starting from 'A'. He swims with a speed of 5km/hr, at an angle $\mathrm{\theta }$ with respect to the river. If AB=BC=400 m. Then-
                   
1.  time taken by the mass is 12 min
2.  time taken by the man is 8 min
3.  the value of $\mathrm{\theta }$ is 45$°$
4.  the value of $\mathrm{\theta }$ is 53$°$