Identify the unit vector in the following?

(a)

\(\hat { i } +\hat { j } \)

(b)

\(\frac { \hat { i } }{ \sqrt { 2 } } \)

(c)

\(\hat { k } -\frac { \hat { j } }{ \sqrt { 2 } } \)

(d)

\(\frac { \hat { i } +\hat { j } }{ \sqrt { 2 } } \)

If the velocity is \(\overrightarrow { v } =2\hat { i } +{ t }^{ 2 }\hat { j } -9\overrightarrow { k } \), then the magnitude of acceleration at t = 0.5s is

(a)

1 ms^-2

(b)

2 ms^-2

(c)

zero

(d)

-1 ms^-2

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

(a)

(b)

(c)

(d)

A ball is dropped from some height towards the ground. Which one of the following represents the correct motion of the ball?

(a)

(b)

(c)

(d)

Two objects are projected at angles 30° and 60° respectively with respect to the horizontal direction. The range of two objects are denoted as R_30° and R_30°. Choose the correct relation from the following

(a)

R_30° = R_60°

(b)

R_30° = 4R_60°

(c)

R_30° =\(\frac{R_{60°}}{2}\)

(d)

R_30° = 2R_60°

The angle between A i +j and B = i - j is ______________.

(a)

45°

(b)

90°

(c)

-45°

(d)

180°

Consider the quantities pressure, power, energy, impulse, charge. Out of these, the only vector quantity is _______________.

(a)

pressure

(b)

power

(c)

impulse

(d)

charge

Distance is a scalar quantity and ______________ is a vector.

(a)

Speed

(b)

Length

(c)

Time

(d)

Displacement

Choose the motion in two dimension from the following.

(a)

Motion of a train along a straight railway track

(b)

An object falling freely under gravity close to the Earth.

(c)

A particle moving along a curved path in a plane.

(d)

Flying of a kite on a windy day.

The displacement of particle is given by X = a_o + \(\frac{a_1t}{2}-\frac{2_2t^2}{3}\) What is its acceleration?

(a)

\(\frac{2a_2}{3}\)

(b)

\(-\frac{2a_2}{3}\)

(c)

a₂

(d)

zero

A man should hold his umbrella with vertical, when rain falls vertically with velocity \(\vec { { V }_{ R } } \) and man walks horizontally with velocity \(\vec{{V}_{M}}\) is _____________

(a)

\(tan^{-1}(\frac{\vec{V}_{M}}{\vec{V}_{R}})\)

(b)

\(tan^{-1}(\frac{\vec{V}_{R}}{\vec{V}_{M}})\)

(c)

tan^-1(V_R)

(d)

tan^-1(V_M)

The maximum range of a gun of horizontal terrain is 16 km. If g = 10ms², then muzzle velocity of a shell must be _____________

(a)

160 ms^-1

(b)

200 \(\sqrt{2}\) ms^-1

(c)

400 ms^-1

(d)

800 ms^-1

The path of the projectile, projected horizontally is _____________.

(a)

hyperbola

(b)

parabola

(c)

straight line

(d)

circle

A person performing a somersault is an example of__________motion.

(a)

circular

(b)

vibratory

(c)

linear

(d)

rotational

Resultant of the 2 vector is maximum when angle between them is _____________

(a)

90°

(b)

180°

(c)

0°

(d)

270°

The dot product of two vectors is _____________

(a)

commutative

(b)

associative

(c)

unit-commutative

(d)

none of the three

If for two vectors \(\bar A,\bar B\) \(\bar A\times\bar B=0\) then the vectors are ____________

(a)

perpendicular to each other

(b)

parallel to each other

(c)

act at an angle 60°

(d)

act at an angle 30°

Two vectors \(\bar A\) and \(\bar B\) are such that \(\bar A \times\bar B=\bar C\) and A = B = C then angle between  \(\bar A\) and \(\bar B\) is: _______________

(a)

120°

(b)

90°

(c)

60°

(d)

30°

The expression for time of flight of a projectile is t_f = _____________

(a)

\(\frac{\sin\theta}{g}\)

(b)

\(\frac{u\sin\theta}{g}\)

(c)

\(\frac{u\sin\theta}{2g}\)

(d)

\(\frac{2u\sin\theta}{2g}\)

During a projectile motion if the maximum height equals the horizontal range, then the angle of projection with the horizontal is ______________.

(a)

tan^-1(1)

(b)

tan^-1(2)

(c)

tan^-1(3)

(d)

tan^-1(4)