"In the nuclear reaction below, a neutron hits a uranium nucleus.
\( n + ^{235}_{92}\text{U} \rightarrow ^{a}_{54}\text{Xe} + ^{94}_{b}\text{Sr} + 2n \)
The values of a and b are respectively :

If a particle is dropped from a height X. The de-Broglie wavelength of the particle as a function of height is proportional to :

The equivalent resistance between the points a and c of the network shown in the figure, would be
(Here each resistance is equal to r.)

A copper ball of density 8 g/cc and 1 cm diameter, immersed in oil of density 0.8 g/cc, remains suspended in an electric field of 600\(\pi\) V/m. The charge on the ball is :

A coil having area A is placed in a magnetic field. The field is perpendicular to the plane of the coil. When the magnetic field changes from \( B_0 \) to \( 4B_0 \) in a time interval t, the magnitude of emf induced in the coil will be :

Two charged conducting spheres of radii a and b are connected by a wire. The ratio of the electric fields at their surfaces respectively, is

Which of the following statements are correct?
(A) According to wave theory, energy carried by a wave depends on the amplitude of the wave, not on the speed of wave propagation
(B) For a given frequency, intensity of light in the photon picture is determined by the number of photons crossing a unit area
(C) At a large distance from the source, a small portion of the spherical wave can be approximated by a plane wave
(D) the reflected and refracted light both have different frequencies than the incident frequency
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (EM waves)	List-II (Application)
(A) Infrared	(I) diagnostic tool in medicine
(B) X-rays	(II) water purification
(C) UV rays	(III) communication radar
(D) Microwaves	(IV) improving visibility in foggy days

Choose the correct answer from the options given below:

In a linear programming problem, the linear constraints are as follows :
\(x-3 y \geq 0, y \geq 0,0 \leq x \leq 6 \)
where \(z=x+2 y\)
Which of the following statement/s is/are correct ?
(A) The feasible region is not the first quadrant
(B) The feasible region is unbounded in the first quadrant
(C) The feasible region is bounded in the first quadrant
(D) The feasible region is a triangular region
(E) The maximum value of \(z\) is 10
Choose the correct answer from the options given below :

If the radii of curvature of the faces of a double convex lens are 10 cm and 15 cm, respectively and its refractive index is 1.5, the focal length of the lens in air is

The term "biodiversity" was popularised by:

The letter "D" in D-(+)-glucose signifies

Read the passage carefully and answer the questions
The resistance ( \(R\) ) of an object is given by the expression \(R=\rho \frac{l}{A}\)
The inverse of \(R\) is called conductance and the inverse of \(\rho\) is called conductivity or specific conductance represented by \(\kappa\).
The conductivity depends upon the nature of the material (insulator, semiconductor or conductor) and the temperature of the substance.
Similarly, the conductance due to the ions present in the solution. (ionic conductance) depends upon the nature of the electrolyte, size of ions, the nature of the solvent and the temperature.
Molar conductivity ( \(\Lambda _{ m }\) ) of a solution at a given concentration is the conductance of volume \(V\) containing one mole of electrolyte kept between two electrodes of area \(A\) and unit distance apart.
It is given by the expression.\(A_m=\kappa V .\)
Molar conductivity increases with decrease in concentration and when concentration approaches sero, it is called limiting molar conductivity.
The decrease is linear for a strong electrolyte. However, for a weak electrolyte the change is gradual at higher concentrations and sharp near zero concentration.
Using limiting molar conductivity values of strong electrolytes we can calculate the limiting molar conductivity of weak electrolytes using Kohlrausch law of independent migration of ions.
From molar conductivity and limiting molar conductivity we can determine the degree of dissociation \(\left(\frac{\Lambda_m}{\Lambda_m^0}\right)\) and the ionisation constant of a weak acid.
The limiting molar conductivity values for \(HCl , NaCl\) and \(CH _3 COONa\) are \(425.9,126.4\) and \(91.0 S cm ^2 mol^{-1}\), respectively.
Calculate the limiting molar conductivity value for acetic acid.