Question 1 :
A projectile is thrown at an angle of {tex} 40 ^ { \circ } {/tex} with the horizontal and its range is {tex} R {/tex}, Another projectile is thrown at an angle {tex} 40 ^ { \circ } {/tex} with the vertical and its range is {tex} R _ { 2 } . {/tex} What is the relation between {tex} R _ { 1 } {/tex} and {tex} R _ { 2 } ? {/tex}

Question 2 :
If the resultant of the vectors {tex} 3 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } + 5 \hat { \mathrm { k } } {/tex} and {tex} 5 \hat { \mathrm { i } } + 3 \hat { \mathrm { j } } + 4 \hat { \mathrm { k } } {/tex} makes an angle {tex} \theta {/tex} with {tex} x {/tex} -axis, then {tex} \cos \theta {/tex} is

Question 3 :
The coordinates of a particle moving in {tex} \mathrm { x } - \mathrm { y } {/tex} plane at any instant of time {tex} \mathrm { t } {/tex} are {tex} \mathrm { x } = 4 \mathrm { t } ^ { 2 } ; \mathrm { y } = 3 \mathrm { t } ^ { 2 } . {/tex} The speed of the particle at that instant is

Question 5 :
If a vector {tex} 2 \hat { \mathrm { i } } + 3 \hat { \mathrm { j } } + 8 \hat { \mathrm { k } } {/tex} is perpendicular to the vector {tex} 4 \hat { \mathrm { j } } - 4 \hat { \mathrm { i } } + \alpha \hat { \mathrm { k } } , {/tex} then the value of {tex} \alpha {/tex} is

Question 6 :
Which of the following is/are correct?<br> I. {tex} \vec { A } \times \vec { B } = - \vec { B } \times A {/tex} <br>II. {tex} \vec { A } \times \vec { B } \neq \vec { B } \times A {/tex} <br>III. {tex} \vec { A } \times ( \vec { B } + \vec { C } ) = ( \vec { A } \times \vec { B } ) + \vec { C } {/tex}

Question 7 :
If {tex} \mathrm { t } _ { \mathrm { m } } {/tex} is the time taken by a projectile to achieve the maximum height, then the total time of flight {tex} \mathrm { T } _ { \mathrm { f } } {/tex} related to {tex} \mathrm { t } _ { \mathrm { m } } {/tex} as

Question 8 :
A stone tied to the end of a string of {tex} 1 \mathrm { m } {/tex} long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in {tex}44{/tex} seconds, what is the magnitude and direction of acceleration of the stone?

Question 9 :
A stone of mass {tex} m {/tex} is tied to a string of length {tex} \ell {/tex} and rotated in a circle with a constant speed {tex} v {/tex}, if the string is released the stone flies

Question 10 :
A particle moves so that its position vector is given by {tex} \overrightarrow { \mathrm { r } } = \cos \omega \mathrm { t } \hat { \mathrm { x } } + {/tex} sin {tex} \omega \mathrm { t } \hat { \mathrm { y } } . {/tex} Where {tex} \omega {/tex} is a constant. Which of the following is true?