$A$ coil of $n$ turns and resistance $R \ \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time $t$ seconds through a magnetic flux change from $\phi_{1}$ to $\phi_{2}$. The induced current in the circuit is:

What is the molecular formula of the product formed when benzene is reacted with ethyl chloride in the presence of anhydrous aluminium chloride?

The solution of the differential equation $x y^2 d y - (x^3 + y^3) d x = 0$ is

The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

The binding energy of deuteron is $2.2\,MeV$ and that of $_2^4He$ is $28\,MeV$. If two deuterons are fused to form one $_2^4He$ nucleus, then the energy released is ......... $MeV$.

Two towers $A$ and $B$,each of height $20 \ m$,are situated a distance $200 \ m$ apart. $A$ body is thrown horizontally from the top of tower $A$ with a velocity $20 \ ms^{-1}$ towards tower $B$ and hits the ground at point $P$. Another body is thrown horizontally from the top of tower $B$ with a velocity $30 \ ms^{-1}$ towards tower $A$ and hits the ground at point $Q$. If a car starting from rest from point $P$ reaches point $Q$ in $10 \ s$,the acceleration of the car is . . . . . . . (Acceleration due to gravity $g = 10 \ ms^{-2}$) (in $ms^{-2}$)