The half life of a radioactive substance is 20 s. The time taken for its sample to decay \( \frac{7}{8} \)th of the initial value is:

In the depletion layer of a reverse biased p-n junction, the :

Energy and momentum of a photon is given by the expressions, energy \(E=h \nu\), and momentum \(p=h / \lambda\), respectively, where \(\nu\) is the frequency of photon, \(h\) is Plank's constant and \(\lambda\) is the wavelength of the photon. On the basis of the above statement, choose the option which is equal to the velocity of light ?

For a medium with permittivity \( (\epsilon) \) and permeability \( (\mu) \), the speed of light \( (v) \) is given by :

Under the influence of a uniform magnetic field, a charged particle moves with a constant speed \( v \) in a circle of radius \( r \). The time period of the revolution of the particle :

In the circuit shown below, \(C_1 = 6 \mu F\), \(C_2 = 3 \mu F\) and battery \(B = 40 V\). Initially, switch \(A_1\) is opened and the switch \(A_2\) is closed. Now switch \(A_2\) is opened and \(A_1\) is closed. The charge on \(C_2\) will be

Given below are two statements :
Statement (I) : In a ground wave communication system, low frequency signal (< 2 MHz) can be transmitted.
Statement (II) : If frequency is high then it will induce electrical signal on the surface of the earth and so attenuation takes place.
In the light of the above statements, choose the most appropriate answer from the options given below :

The electric field E associated with an electromagnetic wave is given by \( E = E_0 \sin(kx - \omega t) \). The speed of the wave is

Identify the role of deoxyribonucleoside triphosphates in DNA replication.
A. Initiate replication.
B. Act as substrate.
C. Provide energy for polymerisation.
D. Activate ligases.
Choose the correct answer from the options given below:

Which of the following bond in DNA strand is broken by the action of restriction enzyme?

The equation of the line (in Cartesian form) which passes through the point \((-2,4,5)\) and parallel to the line given by \(\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}\) is:

Read the passage carefully and answer the Questions
Molar conductivity \(\left(\Lambda_m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases
with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar conductivity \(\left(\Lambda_m^0\right)\). For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\left(\Lambda_m^0\right)\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per
molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law
finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
The unit of constant A is :

The value of the determinant \(\begin{vmatrix} 3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & 1 \end{vmatrix}\) is: