The refractive index of air with respect to glass 2/3. The refractive index of diamond with respect to air is 2.4. What will be the refractive index of glass with respect to diamond?

Two resistance wires are of same material having length, l and 2l and area of cross-section, 4A and A respectively. When they are connected in parallel, their equivalent resistance can be expressed as

The extraordinary sparkling of an appropriately cut diamond is due to

Identify the incorrect statement(s) among the following:
when a dielectric medium is introduced between the plates of a charged capacitor:
(A) If a plate of dielectric constant k, thickness t is placed between the plates of a charged capacitor of area A and distance d, then the new capacitance will be \( \frac{A\varepsilon_0}{d - t(1 - 1/k)} \)
(B) The electric field between plates of the charged capacitor when the dielectric is introduced will be \( E = (E_0 - E_p) \)
(C) Dielectric constant of the dielectric placed between plates of charged capacitor will be \( k = \frac{E_0}{E_0 - E_p} \)
(D) Dielectric strength of the dielectric is the maximum value of the electric field which may be applied before its breakdown.
Choose the correct answer from the options given below :

Three concentric metallic spherical shells of radii \( R, 2R \), and \( 3R \) are given charges \( Q_1, Q_2 \) and \( Q_3 \), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells \( Q_1 : Q_2 : Q_3 \) is:

A coil having 'n' turns and resistance \( 'R' \, \Omega \) is connected with a galvanometer of resistance \( '4R' \, \Omega \). What is the induced current in the circuit when this combination (coil+galvanometer) is moved in time \( t \) from a magnetic flux \( \phi_1 \) to \( \phi_2 \) ?

When an electron of hydrogen atom is raised from the ground state to an excited state.

The value of \(\int_{0}^{\frac{\pi}{2}} \log \left( \frac{5 + 4 \sin x}{5 + 4 \cos x} \right) dx\) is:

Consider the function \(f(x)=x^3-3 x\). Then Match List-I with List-II:

List-I	List-II
(A) Point of local Maxima	(I) 1
(B) Point of local Minima	(II) -1
(C) Local maximum value	(III) 2
(D) Local minimum value	(IV) - 2

Choose the correct answer from the options given below:

In a compound microscope, the distance between objective lens and eye lens is always:

According to Alexander Zaitsev the most preferred product for dehydrohalogenation of 2-Bromopentane will be :

The specific conductance of a decinormal KCl solution is \(0.0121 ohm ^{-1} cm^{-1}\) and the resistance was found to be 56 ohm . Cell constant for the reaction will be

Consider the following hypothesis test :
\(H_0: \mu=15\)
\(H_a: \mu \neq 15\)
A sample of 50 provided a sample mean of 14.15 . If the sample standard deviation is 3 , then the value of the teat statistic in \(t\) - test is