At temperature $T \ K$,the $rms$ speed of $CO_2$ gas is $x \ cm/s$. At what temperature (in $Kelvin$) will the $rms$ speed of nitrous oxide $(N_2O)$ be $4x \ cm/s$ (in $T$)?

$(\vec{a} \times \vec{b}) \times [(\vec{b} \times \vec{c}) \times (\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a})]$ is

$A$ circle of radius $4$,drawn on a chord of the parabola $y^2 = 8x$ as diameter,touches the axis of the parabola. Then,the slope of the chord is

Which of the following statements are true about acceleration due to gravity?
$(a)$ $g$ decreases in moving away from the centre if $r > R$
$(b)$ $g$ decreases in moving away from the centre if $r < R$
$(c)$ $g$ is zero at the centre of the Earth
$(d)$ $g$ decreases if the Earth stops rotating on its axis

The horizontal and vertical displacements $x$ and $y$ of a projectile at a given time $t$ are given by $x = 6t \text{ m}$ and $y = 8t - 5t^2 \text{ m}$. The range of the projectile in metres is

$A$ ball is thrown upward with an initial velocity $V_0$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m \gamma v^2$ (where $m$ is the mass of the ball,$v$ is its instantaneous velocity,and $\gamma$ is a constant). The time taken by the ball to rise to its zenith is: