If $A$ and $B$ are any two sets,then $A \cup (A \cap B)$ is equal to

$y=e^{a \sin ^{-1} x} \Rightarrow (1-x^2) y_{n+2}-(2 n+1) x y_{n+1}$ is equal to

Which of the following is $NOT$ a harmful effect of drug abuse?

$A$ coil is suspended in a uniform magnetic field with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil,it starts oscillating and is very difficult to stop. However,if an aluminium plate is placed near the coil,it stops. This is due to:

In order to double the frequency of the fundamental note emitted by a stretched string,the length is reduced to $\frac{3}{4}$ of the original length and the tension is changed. The factor by which the tension is to be changed is

If $f:R \to R$ and $g:R \to R$ are defined by $f(x) = 2x + 3$ and $g(x) = x^2 + 7$,then the values of $x$ such that $g(f(x)) = 8$ are