The lines $ax^2+2hxy+by^2=0$ are at right angles if

The work done in moving an object from the origin to a point whose position vector is $r = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$ by a force $F = 2 \hat{i} - \hat{j} - \hat{k}$ is:

$A$ set of defective observation weights is used by a student to find the mass of an object using a physical balance. $A$ large number of readings will reduce:

In a potentiometer experiment,the balancing length with a cell is $240\,cm$. On shunting the cell with a resistance of $2\,\Omega$,the balancing length becomes $120\,cm$. The internal resistance of the cell is ................... $\Omega$.

If $a \sin^2 \theta + b \cos^2 \theta = c$,then $\tan^2 \theta$ is equal to

The string of a pendulum of length $l$ is displaced through $90^o$ from the vertical and released. Then,the minimum strength of the string in order to withstand the tension as the pendulum passes through the mean position is