Question 1 :
If vectors {tex} \overrightarrow { \mathrm { A } } {/tex} and {tex} \overrightarrow { \mathrm { B } } {/tex} are given by {tex} \overrightarrow { \mathrm { A } } = 5 \hat { \mathrm { i } } + 6 \hat { \mathrm { j } } + 3 \hat { \mathrm { k } } {/tex} and {tex} \overrightarrow { \mathrm { B } } = 6 \hat { \mathrm { i } } - 2 \hat { \mathrm { j } } - 6 \hat { \mathrm { k } } . {/tex} Which is/are of the following correct?

Question 2 :
A ball rolls off the top of a stairway horizontally with a velocity of {tex} 4.5 \mathrm { ms } ^ { - 1 } {/tex}. Each step is {tex} 0.2 \mathrm { m } {/tex} high and {tex}0.3 \mathrm { m } {/tex} wide. If {tex} \mathrm { g } {/tex} is {tex} 10 \mathrm { ms } ^ { - 2 } , {/tex} and the ball strikes the edge of {tex} n {/tex} th step, then {tex} n {/tex} is equal to

Question 3 :
Displacement (<em>s</em>) versus time (<em>t</em>) graphs of two particles moving in a straight line along <em>x</em>-axis are shown below. It can be stated that <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f16bda5bfef6349df00fcb8" /> <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f16bda5f1a5a149feab98a2" />

Question 4 :
A ball is thrown at different angles with the same speed {tex} u {/tex} and from the same point and it has the same range in both the cases. If {tex} y _ { 1 } {/tex} and {tex} y _ { 2 } {/tex} are the heights attained in the two cases, then {tex} y _ { 1 } + y _ { 2 } {/tex} is equal to<br>

Question 5 :
A body has an initial velocity of {tex} 3 \mathrm { m } / \mathrm { s } {/tex} and has an acceleration of {tex} 1 \mathrm { ms } ^ { - 2 } {/tex} normal to the direction of the initial velocity. Then its velocity {tex} 4 \mathrm { s } {/tex} after the start is

Question 6 :
A particle starts sliding down a frictionless inclined plane. If {tex} S _ { n } {/tex} is the distance travelled by it from time {tex} t = n - 1 {/tex} sec to {tex} t = n \sec , {/tex} the ratio {tex} S _ { n } / S _ { n + 1 } {/tex} is

Question 7 :
A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the vertical displacement-time graph is characterised by

Question 8 :
What is the magnitude of the upward force on the rider?

Question 10 :
A body is projected horizontally from the top of a tower with initial velocity {tex} 18 \mathrm { ms } ^ { - 1 } . {/tex} It hits the ground at angle {tex} 45 ^ { \circ } . {/tex} What is the vertical component of velocity when strikes the ground?