If the angle between the pair of lines $2x^2 + 2hxy + 2y^2 - x + y - 1 = 0$ is $\tan^{-1}(3/4)$ and $h$ is a positive rational number,then the point of intersection of these two lines is

$A$ metallic ring connected to a rod oscillates freely like a pendulum. If now a magnetic field is applied in a horizontal direction so that the pendulum now swings through the field,the pendulum will

$A$ radioactive sample $S_1$ having an activity of $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ can be

The voltage of an $ac$ source varies with time according to the equation $V = 100 \sin(100 \pi t) \cos(100 \pi t)$,where $t$ is in seconds and $V$ is in volts. Then:

The direction ratios of the two lines $AB$ and $AC$ are $1, -1, -1$ and $2, -1, 1$. The direction ratios of the normal to the plane $ABC$ are