$A$ vibratory motion is represented by $x = 2A \cos \omega t + A \cos (\omega t + \frac{\pi}{2}) + A \cos (\omega t + \pi) + \frac{A}{2} \cos (\omega t + \frac{3\pi}{2})$. The resultant amplitude of the motion is:

$A$ long solenoid of radius $2\, cm$ has $100\, turns/cm$ and carries a current of $5\, A$. $A$ coil of radius $1\, cm$ having $100\, turns$ and a total resistance of $20\, \Omega$ is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction,find the charge flown through the galvanometer.

If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle of $\frac{3 \pi}{4}$ with the positive $X$-axis,then the value of $f^{\prime}(3)$ is

$A$ small square loop of wire of side $l$ is placed inside a large square loop of side $L$ $(L \gg l)$. If the loops are coplanar and their centres coincide,the mutual inductance of the system is directly proportional to :

What is the current through an ideal $P-N$ junction diode shown in the figure below? (in $mA$)

The number of atoms/molecules contained in one face-centred cubic $(FCC)$ unit cell of a monoatomic substance is