From the \(v\) - \(t\) graph shown. the ratio of distance to displacement in \(25\,s\) of motion

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.

The electric field of a plane electromagnetic wave is given by \(\overrightarrow{ E }= E _{0}(\hat{ x }+\hat{ y }) \sin ( kz -\omega t )\) Its magnetic field will be given by

The susceptibility of a paramagnetic material is \(99\) . The permeability of the material in \(Wb / A - m\) is : [Permeability of free space \(\left.\mu_{0}=4 \pi \times 10^{-7} Wb / A -m\right]\)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet.
In the light of the above statements, choose the correct answer from the options given below :

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \(2 \mathrm{~km} / \mathrm{s}\), the root mean square velocity of oxygen at the same condition in \(\mathrm{km} / \mathrm{s}\) is _______.

Two materials having coefficients of thermal conductivity \(3K\) and \(K\) and thickness \(d\) and \(3d\), respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are  \(\theta_2\) and \(\theta_1\) respectively  \(\left( {\theta _2} > {\theta _1} \right)\) . The temperature at the interface is

Given below are two statements: Statement \(I :\) \(PN\) junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement \(II :\) In the study of transistor, the amplification factor \(\beta\) indicates ratio of the collector current to the base current. In the light of the above statements, choose the correct answer from the options given below :

Two small spheres each of mass \(10 \,mg\) are suspended from a point by threads \(0.5 \,m\) long. They are equally charged and repel each other to a distance of \(0.20 \,m\). The charge on each of the sphere is \(\frac{ a }{21} \times 10^{-8} \, C\). The value of \(a\) will be ...... . \(\left[\right.\) Given \(\left.g=10 \,ms ^{-2}\right]\)

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) Earth has atmosphere whereas moon doesn't have any atmosphere. Reason \(R\) : The escape velocity on moon is very small as compared to that on earth. In the light of the above statement, choose the correct answer from the options given below :

Activities of three radioactive substances \(A , B\) and \(C\) are represented by the curves \(A, B\) and \(C,\) in the figure. Then their half-lives \(T _{\frac{1}{2}}( A ): T _{\frac{1}{2}}( B ): T _{\frac{1}{2}}( C )\) are in the ratio