The compound$(s)$ with $P - H$ bond$(s)$ is$(are)$
$(A) \ H _3 PO _4$ $(B) \ H _3 PO _3$ $(C) \ H _4 P _2 O _7$ $(D) \ H _3 PO _2$

If the frequency of light in a photoelectric experiment is doubled,the stopping potential will

For positive numbers $x, y, \text{ and } z$,the numerical value of the determinant $\left| \begin{array}{ccc} 1 & \log_x y & \log_x z \\ \log_y x & 1 & \log_y z \\ \log_z x & \log_z y & 1 \end{array} \right|$ is

$A$ large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water,the quantities of water flowing out per second from the two holes are the same. Then the value of $R$ is

Two particles $A$ and $B$ of masses $m$ and $2m$ are suspended from massless springs of force constants $K_1$ and $K_2$. During their oscillation,if their maximum velocities are equal,then the ratio of amplitudes of $A$ and $B$ is

Dividing the interval $[0,6]$ into $6$ equal parts and by using the trapezoidal rule, the value of $\int_0^6 x^3 dx$ is approximately: