The horizontal range of a projectile fired at an angle of $15^\circ$ is $50~\text m.$ If it is fired with the same speed at an angle of $45^\circ,$ its range will be:
1. $60~\text m$
2. $71~\text m$
3. $100~\text m$
4. $141~\text m$ 

In a two-dimensional motion, instantaneous speed $v_0$ is a positive constant. Then which of the following is necessarily true?

In a two-dimensional motion, instantaneous speed $v_0$ is a positive constant. Then which of the following is necessarily true?

A particle slides down a frictionless parabolic track starting from rest at point $A$. Point $B$ is at the vertex of the parabola and point $C$ is at a height less than that of point $A$. After $C$, the particle moves freely in the air as a projectile. If the particle reaches the highest point at $P$, then,

The following are four different relations about displacement, velocity and acceleration for the motion of a particle in general.

The incorrect options is/are:

For a particle performing uniform circular motion,

Choose the correct statement/s:

Two particles are projected in the air with speed $v_0$, at angles $\theta_1$ and $\theta_2$ to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then:

Choose the correct option:
1. (a), (c), (d)
2. (a), (c)
3. (b), (c), (d)
4. (a), (b)