An alpha particle is moving in a magnetic field \( (3\hat{i} + 2\hat{j}) \text{ T} \) with the velocity \( (7 \times 10^5 \hat{i}) \text{ m/s} \). The magnetic force acting on the particle is:

A square shaped wire loop of side L is carrying a current I. What is the magnetic field at the point of intersection of diagonals of the square wire loop ?

Select the correct option for the statements given below.
(A) The diffraction pattern is a superposition of waves originating from each point on a single slit.
(B) The interference pattern is the superposition of two waves originating from two narrow slits.
(C) The diffraction pattern in single slit has a central bright maximum brighter than other maxima.
(D) The interference in double slit has a number of equally spaced bright and dark bands.
Choose the correct answer from the options given below :

Rainbow is a phenomenon due to the combined effect of
(A) Interference
(B) Dispersion
(C) Reflection
(D) Refraction
(E) Scattering
Choose the correct answer from the options given below:

The kinetic energy of an electron in the H-atom in the second excited state is k units. Its total energy and potential energy, respectively, in the ground state will be

A uniformly charged sphere of \( 80 \text{ } \mu\text{C} \) and radius 2 cm is placed in air.
The electric field intensity at a point 20 cm from the center of the sphere is:

A charged particle moves along a circular path in a uniform magnetic field of 0.04 T with a velocity of \( 2 \times 10^5 \text{ m/s} \). The charge to mass ratio of the particle is \( 5 \times 10^7 \text{ C/kg} \). The radius of the circular path of the charged particle is:

Area (in sq. units) of the region bounded by the curves \(y = - 1, y = 2 x = y^3\) and \(x = 0\) is

If \(X+Y=\left(\begin{array}{ll}7 & 0 \\ 2 & 5\end{array}\right)\) and \(X-Y=\left(\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right)\), then \(X\) and \(Y\) are:

Heroin, commonly called as smack is a/an:

Transgenic animals are used to understand the contribution of genes in the development of diseases such as:

A wire carries a current of 2.0 A. The number of electrons crossing through its cross-section in 10 s will be

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 A\(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), 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.
If the equivalent conductivity of 1 M Phthalic acid is \(12.8 S cm ^2 eq ^{-1}\) and the limiting equivalent conductivities of the
hydrogen and Phthalate ions are 42 and \(288.42 S cm ^2 eq ^{-1}\), respectively, the degree of dissociation of Phthalic acid will be :