The area (in square units) of the circle which touches the lines $4x + 3y = 15$ and $4x + 3y = 5$ is

If the $x$-coordinate of a point $P$ on the line joining the points $Q(2, 2, 1)$ and $R(5, 1, -2)$ is $4$,then the $z$-coordinate of $P$ is

Let $P$ be a plane passing through the points $(2,1,0), (4,1,1)$ and $(5,0,1)$ and $R$ be any point $(2,1,6)$. Then the image of $R$ in the plane $P$ is

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,what is its new time period in seconds?

There is some change in length when a $33000 ~N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} ~m^2$. The change of temperature required to produce the same elongation,if the steel rod is heated,is (The modulus of elasticity is $3 \times 10^{11} ~N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ} C$). (in $^{\circ} C$)

If the charge on the capacitor is increased by $2 \ C$,the energy stored in it increases by $21 \%$. The original charge on the capacitor is: (in $C$)