$A$ transistor-oscillator using a resonant circuit with an inductor $L$ (of negligible resistance) and a capacitor $C$ in series produces oscillations of frequency $f$. If $L$ is doubled and $C$ is changed to $4C$,the frequency will be

$\int_0^{\frac{\pi}{4}} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x=$

$A$ small fish $0.4\, m$ below the surface of a lake is viewed through a simple converging lens of focal length $3\, m$. The lens is kept at $0.2\, m$ above the water surface such that the fish lies on the optical axis of the lens. The image of the fish seen by the observer will be at (given $\mu_{water} = 4/3$):

The strength of an acid depends on its tendency to

Which of the following is absent in polluted water?

$A$ point object on the principal axis at a distance $15\, cm$ in front of a concave mirror of radius of curvature $20\, cm$ has a velocity of $2\, mm/s$ perpendicular to the principal axis. The velocity of the image at that instant will be.......$mm/s$.