Isogamous condition with non-flagellated gametes is found in:

$\sin ^{-1}\left(\sin \frac{7 \pi}{6}\right) = $

The natural frequency of an $L-C$ circuit is $1,25,000 \text{ cycles/s}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case,the frequency decreases by $25 \text{ kHz}$. The value of $K$ is

If $\cos (A-B)=3/5$ and $\tan A \tan B=2$,then which one of the following is true?

The point of contact of the circles $x^2+y^2+2x+2y+1=0$ and $x^2+y^2-2x+2y+1=0$ is

The shortest distance between the line $y - x = 1$ and the curve $x = y^2$ is: