$A$ mass $M \text{ kg}$ is suspended by a weightless string. The horizontal force required to hold the mass at $60^{\circ}$ with the vertical is

$\int \frac{1+\cos 4 x}{\cot x-\tan x} d x$ is equal to

$A$ constant voltage of $25 ~V$ is applied to a series $L-R$ circuit at $t=0$,by closing a switch. What is the potential difference across the resistor and the inductor at time $t=0$?

In which of the following pairs do both species have $sp^3$ hybridization?

The circuit diagram shows a logic combination with the states of outputs $X, Y$ and $Z$ given for inputs $P, Q, R$ and $S$ all at state $1$. When inputs $P$ and $R$ change to state $0$ with inputs $Q$ and $S$ still at $1$,the states of outputs $X, Y$ and $Z$ change to:

$A$ charged particle of mass $m$ and charge $q$ is released from rest in a uniform electric field $E$. Neglecting the effect of gravity,the kinetic energy of the charged particle after $t$ seconds is: