General
✓✗A ball is projected from the ground at angle θ. Its horizontal range is R and its maximum height is H. The angle of projection is
- \( \tan^{-1}\left(\dfrac{H}{R}\right) \)
- \( \tan^{-1}\left(\dfrac{2H}{R}\right) \)
- \( \tan^{-1}\left(\dfrac{4H}{R}\right) \)
- \( \tan^{-1}\left(\dfrac{R}{4H}\right) \)
General
✓✗A ball is projected with 10 m/s at 45°. Its horizontal range is (g = 10 m s−2)
- 5 m
- \( 5\sqrt{2} \) m
- 10 m
- 20 m
General
✓✗The angle between \( \vec{A} = \hat{i} + \hat{j} \) and \( \vec{B} = \hat{j} + \hat{k} \) is
- 30°
- 60°
- 45°
- 90°
General
✓✗A vector multiplied by −2 gives a vector that is
- twice as long and in the same direction
- half as long and in the opposite direction
- twice as long and in the opposite direction
- perpendicular to the original vector
General
✓✗If the angle between the vectors \( \vec{A} \) and \( \vec{B} \) is θ, the value of the product \( (\vec{B}\times\vec{A})\cdot\vec{A} \) is equal to
- \( BA^2\sin\theta \)
- \( BA^2\sin\theta\cos\theta \)
- \( BA^2\cos\theta \)
- zero
General
✓✗Two cars move at 30 km/h, one due east and the other due north. The magnitude of the velocity of one relative to the other is
- 60 km/h
- \( 30\sqrt{2} \) km/h
- 30 km/h
- zero
General
✓✗Assertion: A body moving in a circle with constant speed has no acceleration.
Reason: Acceleration is the rate of change of speed.
Reason: Acceleration is the rate of change of speed.
- Both Assertion and Reason are true and Reason is the correct explanation of Assertion
- Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
- Assertion is true but Reason is false
- Both Assertion and Reason are false
General
✓✗A particle moves with velocity \( \vec{v} = 2t\,\hat{i} + 3\hat{j} \) m/s starting from the origin. The equation of its path is
- \( y = 3x \)
- \( x^2 + y^2 = 9 \)
- \( x = \dfrac{y^2}{9} \)
- \( y = \dfrac{x^2}{9} \)
General
✓✗The relative velocity of A with respect to B is defined as
- \( \vec{v}_A + \vec{v}_B \)
- \( \vec{v}_A\times\vec{v}_B \)
- \( \vec{v}_A - \vec{v}_B \)
- \( \vec{v}_B - \vec{v}_A \)
General
✓✗A particle moves in a circle of radius 5 cm with constant speed and a time period of \( 0.2\pi \) s. The acceleration of the particle is
- 25 m s−2
- 36 m s−2
- 15 m s−2
- 5 m s−2
General
✓✗The ratio of the angular speeds of the minute hand and the hour hand of a watch is
- 12 : 1
- 60 : 1
- 1 : 12
- 1 : 60
General
✓✗Statement I: In two-dimensional motion with constant acceleration, the path can be a straight line.
Statement II: If the initial velocity is parallel to the acceleration, the motion is along a straight line.
Choose the correct answer.
Statement II: If the initial velocity is parallel to the acceleration, the motion is along a straight line.
Choose the correct answer.
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
General
✓✗The angular speed of the second hand of a clock is
- \( 2\pi \) rad/s
- \( \dfrac{\pi}{30} \) rad/s
- \( \dfrac{\pi}{1800} \) rad/s
- \( \dfrac{\pi}{60} \) rad/s
General
✓✗Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is
- \( \dfrac{a}{\sqrt{v^2 + v_1^2}} \)
- \( \dfrac{a}{v + v_1} \)
- \( \dfrac{a}{v - v_1} \)
- \( \sqrt{\dfrac{a^2}{v^2 - v_1^2}} \)
General
✓✗The position vector of a particle is \( \vec{r} = 3t\,\hat{i} + 4t\,\hat{j} \) m. Its speed is
- 12 m/s
- 1 m/s
- 7 m/s
- 5 m/s