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For the figure - 

1.  A+B=C
2.  B+C=A
3.  C+A=B
4.  A+B+C=0

A vector $\overrightarrow{\mathrm{A}}$ is directed along 30$°$ west of north direction and another vector $\overrightarrow{\mathrm{B}}$ along 15$°$ south of east. Their resultant cannot be in ______ direction.
1.  North
2.  East
3.  North-East
4.  South

Consider east as positive x-axis north as positive y-axis and vertically upward direction as z-axis. A helicopter first rises up to an altitude of 100 m than flies straight in north 500 m and then suddenly takes a turn towards east and travels 1000 m east. What is position vector of helicopter. (Take starting point as origin)
1.  $1000<mspace\; width="1em"></mspace>\hat{\mathrm{i}}-500<mspace\; width="1em"></mspace>\hat{\mathrm{j}}+100<mspace\; width="1em"></mspace>\hat{\mathrm{k}}$
2.  $1000<mspace\; width="1em"></mspace>\hat{\mathrm{i}}+500<mspace\; width="1em"></mspace>\hat{\mathrm{j}}-100<mspace\; width="1em"></mspace>\hat{\mathrm{k}}$
3.  $1000<mspace\; width="1em"></mspace>\hat{\mathrm{i}}+500<mspace\; width="1em"></mspace>\hat{\mathrm{j}}+100<mspace\; width="1em"></mspace>\hat{\mathrm{k}}$
4.  $-1000<mspace\; width="1em"></mspace>\hat{\mathrm{i}}+500<mspace\; width="1em"></mspace>\hat{\mathrm{j}}+100<mspace\; width="1em"></mspace>\hat{\mathrm{k}}$

A particle  is moving westward with a velocity ${\overrightarrow{\mathrm{v}}}_1=5<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}.$ Its velocity changed to ${\overrightarrow{\mathrm{v}}}_2=5<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$ northward. The change in velocity vector $\left(△\overrightarrow{\mathrm{V}}={\overrightarrow{\mathrm{v}}}_2-{\overrightarrow{\mathrm{v}}}_1\right)$ is
1.  $5\sqrt{2}<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$ towards north east
2.  5 m/s towards north west
3.  zero
4.  $5\sqrt{2}<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$ towards north west

Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?
1.  2, 4, 8
2.  4, 8, 16
3.  1, 2, 1
4.  0, 5, 1, 2

A man rows a boat with a speed of 18 km/hr in northwest direction. The shoreline makes an angle of 15$°$ south of west. Obtain the component of the velocity of the boat along the shoreline.
1.  9 km/hr
2.  18$\frac{\sqrt{3}}{2}$ km/hr
3.  18 cos 15$°$ km/hr
4.  18 cos 75$°$ km/hr

A bird moves from point (1, -2) to (4, 2). If the speed of the bird is 10 m/sec, then the velocity vector of the bird is:
1.  $5\left(\hat{\mathrm{i}}-2\hat{\mathrm{j}}\right)$
2.  $5<mspace\; width="1em"></mspace>\left(4\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right)$
3.  $0.6<mspace\; width="1em"></mspace>\hat{\mathrm{i}}+0.8<mspace\; width="1em"></mspace>\hat{\mathrm{j}}$
4.  $6<mspace\; width="1em"></mspace>\hat{\mathrm{i}}+8<mspace\; width="1em"></mspace>\hat{\mathrm{j}}$