Question 1 :
If {tex} 0.4 \hat { \mathrm { i } } + 0.7 \hat { \mathrm { j } } + \mathrm { c } \hat { \mathrm { k } } {/tex} is a unit vector, then the value of {tex} \mathrm { c } {/tex} is

Question 2 :
Two stones are projected from the same point with same speed making angles {tex} \left( 45 ^ { \circ } + \theta \right) {/tex} and {tex} \left( 45 ^ { \circ } - \theta \right) {/tex} with the horizontal respectively. If {tex} \theta \leq 45 ^ { \circ } , {/tex} then the horizontal ranges of the two stones are in the ratio of

Question 3 :
The angle which the velocity vector of a projectile thrown with a velocity {tex}v{/tex} at an angle {tex} \theta {/tex} to the horizontal will make with the horizontal after time {tex}t{/tex} of its being thrown up is:

Question 4 :
A stone is projected horizontally with velocity {tex}u{/tex} from a height {tex}\mathrm H{/tex}. It's time of flight is:

Question 5 :
An object, moving with a speed of {tex} 6.25 \mathrm { m } / \mathrm { s } {/tex}, is decelerated at a rate given by: {tex} \frac { d v } { d t } = - 2.5 \sqrt { v } {/tex} where {tex} v {/tex} is the instantaneous speed. The time taken by the object, to come to rest, would be

Question 6 :
The resultant of vectors {tex} \overrightarrow { \mathbf { P } } {/tex} and {tex} \overrightarrow { \mathbf { Q } } {/tex} is {tex} \overrightarrow { \mathbf { R } } {/tex}. On reversing the direction of {tex} \overrightarrow { \mathbf { Q } } {/tex}, the resultant vector becomes {tex} \overrightarrow { \mathbf { S } } {/tex}. Then, correct relation is

Question 7 :
A body falls freely from rest. It cover as much distance in the last second of its motion as covered in the first three second. The body has fallen for a time of :

Question 8 :
A projectilel can have the same range {tex} \mathrm { R } {/tex} for two angles of projection. If {tex} \mathrm { t } _ { 1 } {/tex} and {tex} \mathrm { t } _ { 2 } {/tex} be the times of flight in two cases, then what is the product of two times of flight?

Question 9 :
A particle crossing the origin of co-ordinates at time {tex} \mathrm { t } = 0 {/tex} moves in the {tex}\mathrm{xy}{/tex}-plane with a constant acceleration a in the {tex}\mathrm{y}{/tex}-direction. If its equation of motion is {tex} \mathrm { y } = \mathrm { bx } ^ { 2 } {/tex} ({tex}\mathrm{b}{/tex} is a constant), its velocity component in the {tex}\mathrm{x}{/tex}-direction is

Question 10 :
A truck travelling due north at {tex} 20 \mathrm { m } / \mathrm { s } {/tex} turns west and travels at the same speed. What is the change in velocity?