The primary and secondary coils of a transformer have $50$ and $1500$ turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi = \phi_0 + 4t$,where $\phi$ is in webers,$t$ is time in seconds,and $\phi_0$ is a constant,the output voltage across the secondary coil is ...... $volts$.

At $300 K$ , an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height $(h)$ of the solution $($density $=1.00 g cm ^{-3} )$ where h is equal to $2.00 cm$ . If the concentration of the dilute solution of the macromolecule is $2.00 g dm ^{-3}$, the molar mass of the macromolecule is calculated to be $X \times 10^4 g mol ^{-1}$. The value of $X$ is $...$ .
Use : Universal gas constant $(R)=8.3 J K ^{-1} mol^{-1}$ and acceleration due to gravity $( g )=10 m s ^{-2}$

The $AT/GC$ ratio in human beings is (where $A=$ adenine,$T=$ thymine,$G=$ guanine,$C=$ cytosine).

$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel,then the value of $d$ is

Aluminium reacts with $NaOH$ and forms compound '$X$'. If the coordination number of aluminium in '$X$' is $6$,the correct formula of $X$ is

Four massless springs whose force constants are $2k, 2k, k$ and $2k$ respectively are attached to a mass $M$ kept on a frictionless plane (as shown in the figure). If the mass $M$ is displaced in the horizontal direction,then the frequency of oscillation of the system is: