Two wires of the same material have lengths in the ratio $1:2$ and their radii are in the ratio $1:\sqrt{2}$. If they are stretched by applying equal forces,the increase in their lengths will be in the ratio:

If the altitudes of a triangle are in arithmetic progression,then the sides of the triangle are in

Two trains travelling on the same track are approaching each other with equal speeds of $40\, m/s$. The drivers of the trains begin to decelerate simultaneously when they are just $2.0\, km$ apart. Assuming the decelerations to be uniform and equal,the value of the deceleration to barely avoid collision should be.........$m/s^2$.

$A$ carrier signal $60 \sin(2\pi \times 10^6 t)$ is used to modulate an audio signal $15 \sin(300\pi t)$. The depth of modulation is .........$\%$.

The major product of the following reaction is

If $f(x) = \sqrt{\frac{x - \sin x}{x + \cos^2 x}}$,then $\lim_{x \to \infty} f(x)$ is