As the switch $S$ is closed in the circuit shown in the figure,the current passing through it is ................ $A$.

The distance between the pair of lines $x^2+2 \sqrt{2} x y+2 y^2+4 x+4 \sqrt{2} y+1=0$ is:

Which of the following would produce a buffer solution when mixed in equal volumes?

$A$ conducting square loop of side $L$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. $A$ magnetic induction $B$,constant in time and space,pointing perpendicular and into the plane of the loop,exists everywhere with half the loop outside the field,as shown in the figure. The induced $emf$ is

For all values of $\theta$,the values of $3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)$ lie in the interval :

$A$ particle executes a simple harmonic motion of time period $T$. Find the time taken by the particle to go directly from its mean position to half the amplitude.