Question 1 :
Consider the following controls in an automobile: gas pedal, brake, steering wheel. The controls in this list that cause an acceleration of the car are -
Question 2 :
If {tex} \vec { A } \times \vec { B } = \vec { B } \times \vec { A } , {/tex} then the angle between {tex} A {/tex} and {tex} B {/tex} is
Question 3 :
A projectile is projected with a kinetic energy K. Its range is R. It will have the minimum kinetic energy, after covering a horizontal distance equal to
Question 4 :
Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e8324389b1556ddf0294' height='37' width='15' > and the maximum height reached by it is 102 m. Then the maximum height reached by the other in metre is -
Question 5 :
A boat which has a speed of 5 m/s in still water crosses the river of width 25 m in 10 seconds. The boat is heading at an angle of α with downstream, where α is equal to
Question 6 :
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. Which of following statement is incorrect. <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd331da6d070c2abf803"/> <br><img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd334bec8070e4e14f3a"/>
Question 7 :
A projectile is fired at 30<sup>o</sup> with momentum p. Neglecting friction, the change in kinetic energy when it returns to the ground will be
Question 8 :
A river is flowing from west to east with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim, so as to take the shortest possible path to go to the south?
Question 9 :
The speed of a projectile when it is at its greatest height is <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e833b5f89758f2d4f1bb' height='35' width='15' > times its initial speed. The angle of projection is -
Question 10 :
A man can row a boat with speed {tex}4 \mathrm { km } / \mathrm { hr } {/tex} in still water. If the velocity of water in river is {tex}3 \mathrm { km } / \mathrm { km } {/tex} . The time taken to reach just opposite is (river width {tex} = {/tex} 500{tex} \mathrm { m } ) {/tex}
Question 11 :
Acceleration-time graph of a particle, starting from rest in straight line, is shown in adjacent figure, then <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd8f4bec8070e4e14fa2"/>
Question 12 :
The roadway bridge over a canal is in the form of a circular arc of radius 18 m. What is the greatest speed with which a motorcycle can cross the bridge without leaving the ground?
Question 13 :
The velocity of a body depends on time according to the equation <em>v</em> = 20 + 0.1<em>t</em><sup>2</sup>. The body is undergoing
Question 14 :
A particle located at <em>x</em> = 0 at time <em>t</em> = 0, starts moving along the positive <em>x</em>-direction with a velocity ‘<em>v’</em> that varies as {tex}v = \alpha\sqrt{x}{/tex}. The displacement of the particle varies with time as
Question 15 :
A particle is projected from ground with velocity {tex}\text{40}\sqrt{2}{/tex} m/s at 45<font face="Symbol">°</font>. At time <em>t</em> = 2 s:
Question 16 :
A particle is moving eastwards with a velocity of {tex} 4 \mathrm { m } / \mathrm { s } . {/tex} In 5{tex} \mathrm { s } {/tex} the velocity changes to 3{tex} \mathrm { m } / \mathrm { s } {/tex} northwards. The average acceleration in this time interval is
Question 17 :
Two bodies are projected at angles θ and (90 – θ) to the horizontal with the same speed. The ratio of their times of flight is
Question 18 :
One body is dropped, while a second body is thrown downward with an initial velocity of 1ms<sup>–1</sup> simultaneously. The separation between these is 1.8 m after a time
Question 19 :
A ball thrown by one player reaches the other in 2 sec. the maximum height attained by the ball above the point of projection will be about
Question 20 :
Two particles starting from a point on a circle of radius 4 m in horizontal plane move along the circle with constant speeds of 4 ms<sup>-1</sup> and 6 ms<sup>-1</sup> respectively in opposite directions. The particles will collide with each other after a time of :
Question 21 :
What is the average velocity during time interval <em>t</em> = 2 s to <em>t</em> = 5 s, in the following position time curve? <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd391da6d070c2abf809"/>
Question 22 :
A boy throws a water–filled balloon at an angle of 53<font face="Symbol">°</font> with a speed of 10 m/s. A car is advancing toward the boy at a constant speed of 5 m/s. If the balloon is to hit the car, how far away should the car be when the balloon is thrown? (<em>g</em> = 10 ms<sup>–2</sup>)
Question 23 :
A man running uniformly at 8 m/s is 16 m behind a bus when it starts accelerating at 2 ms<sup>–2</sup>. Time taken by him to board the bus is
Question 24 :
A body is moving from rest under constant acceleration and let <em>S</em><sub>1</sub> be the displacement in the first (<em>p</em> – 1) sec and <em>S</em><sub>2</sub> be the displacement in the first <em>p</em> sec. The displacement in (<em>p</em><sup>2</sup> − <em>p</em> + 1)<sup>th</sup> sec will be
Question 25 :
A particle can be projected with a given speed in two possible ways so as to make it pass through a point at a distance {tex} r {/tex} from the point of projection. The product of the times taken to reach this point in the two possible ways is then proportional to
Question 26 :
In the graph shown, <em>X</em>-axis represents time, then the <em>Y</em>-axis could represent <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd634bec8070e4e14f6b"/>
Question 27 :
A projectile is fired vertically upwards with an initial velocity <em>u</em>. After an interval of <em>T</em> seconds a second projectile is fired vertically upwards, also with initial velocity <em>u</em>. The correct statement is
Question 28 :
A body starts from origin and moves along <em>x</em> axis such that at any instant velocity is <em>v<sub>t</sub></em> = 4<em>t</em><sup>3</sup> – 2<em>t</em> where <em>t</em> is in second and <em>v<sub>t</sub></em> is in ms<sup>–1</sup>. The acceleration of the particle when it is 2 m from the origin is
Question 29 :
Consider the quantities : pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are
Question 30 :
A road is 5 m wide. Its radius of curvature is {tex}20 \sqrt { 6 } \mathrm { m } {/tex} . The outer edge is above the inner edge by a distance of {tex} \mathrm { f } {/tex} {tex} 1 \mathrm { m } {/tex} . This road is most suited for a speed {tex} \left( g = 10 \mathrm { ms } ^ { - 2 } \right) {/tex}
Question 31 :
A projectile is fired with velocity u making angle θ with the horizontal. What is the change in velocity when it is at the highest point
Question 32 :
A body of mass 0.5 kg is projected under gravity with a speed of 98 m/s at an angle of 30<sup>o</sup> with the horizontal. The change in momentum (in magnitude) of the body is
Question 33 :
A ball rolls off the top of a stair way with a horizontal velocity of 4.5 m/s. If each step is 0.2 m high and 0.3 m broad, then the ball will strike the n<sup>th</sup> step where n is equal to : (g = 10 m/s<sup>2</sup>)
Question 34 :
A flowerpot falls off a window sill and falls past the window below. It takes 0.5 s to pass through a 2.0 m high window. Find how high is the window sill from the top of the window? <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e5794389b1556ddf0004' height='134' width='84' >
Question 35 :
The position of a particle as a function of time is {tex} \vec { r } = 4 \sin 2 \pi t \hat { i } + 4 \cos 2 \pi t \hat { j } {/tex} (where {tex} t {/tex} is time in second). Path of this particle will be