$A$ block can slide on a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with an acceleration $a$,the acceleration of the block relative to the incline is:

The thermally most stable compound is:

The origin is translated to $(1,2)$. The point $(7,5)$ in the old system undergoes the following transformations successively.
$I$. Moves to the new point under the given translation of origin.
$II$. Translated through $2$ units along the negative direction of the new $X$-axis.
$III$. Rotated through an angle $\frac{\pi}{4}$ about the origin of the new system in the clockwise direction. The final position of the point $(7,5)$ is

$A$ bag contains $5$ black balls,$4$ white balls and $3$ red balls. If a ball is selected at random,the probability that it is a black or a red ball is:

In the given circuit,the readings of voltmeters $V_1$ and $V_2$ are $300 \, V$ each. The readings of the voltmeter $V_3$ and ammeter $A$ are respectively:

The line $\frac{x}{a} + \frac{y}{b} = 1$ moves in such a way that $\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{2c^2}$,where $a, b, c \in R_0$ and $c$ is a constant. Then,the locus of the foot of the perpendicular from the origin on the given line is -