The de-Broglie wavelength of a particle accelerated with $150 \ V$ potential is $10^{-10} \ m$. If it is accelerated by $600 \ V$ potential difference,its wavelength will be ........... $\mathring{A}$.

$A$ homogeneous solid cylinder of length $L$ $(L < H/2)$,cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the figure. The lower density liquid is open to the atmosphere having pressure $P_0$. Then,the density $D$ of the solid is given by:

The value of ${\log _3}4 \times {\log _4}5 \times {\log _5}6 \times {\log _6}7 \times {\log _7}8 \times {\log _8}9$ is:

Which of the following statements is incorrect?

$A$ gaseous mixture consists of $16 \, g$ of helium and $16 \, g$ of oxygen. The ratio $(C_p / C_v)$ of the mixture is

Let $PQ$ and $RS$ be tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $2r$ equals