A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
An ideal monatomic gas of $ n $ moles is taken through a cycle $ WXYZW $ consisting of consecutive adiabatic and isobaric quasi-static processes, as shown in the schematic $ V-T $ diagram. The volume of the gas at $ W, X $ and $ Y $ points are, $ 64 \, \text{cm}^3 $, $ 125 \, \text{cm}^3 $ and $ 250 \, \text{cm}^3 $, respectively. If the absolute temperature of the gas $ T_W $ at the point $ W $ is such that $ n R T_W = 1 \, J $ ($ R $ is the universal gas constant), then the amount of heat absorbed (in J) by the gas along the path $ XY $ is 


Monocyclic compounds $ P, Q, R $ and $ S $ are the major products formed in the reaction sequences given below.
The product having the highest number of unsaturated carbon atom(s) is:
For the reaction sequence given below, the correct statement(s) is(are): 
Consider a reaction $ A + R \rightarrow Product $. The rate of this reaction is measured to be $ k[A][R] $. At the start of the reaction, the concentration of $ R $, $[R]_0$, is 10-times the concentration of $ A $, $[A]_0$. The reaction can be considered to be a pseudo first order reaction with assumption that $ k[R] = k' $ is constant. Due to this assumption, the relative error (in %) in the rate when this reaction is 40% complete, is ____. [$k$ and $k'$ represent corresponding rate constants]
Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.
Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,
F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic
This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.