Photoelectric work function of a metal is 1 eV. Light of wavelength \( \lambda = 3000\text{\AA} \) falls on it. The photoelectrons come out with maximum kinetic energy of:

A diode having potential difference 0.5 V across its junction which does not depend on current, is connected in series with a resistance of \( 20 \Omega \) across a source. If 0.1 A current passes through the resistor, the voltage across the source is :

A p-n junction can act basically as

A spherical conducting shell of inner radius \( r_1 \) and outer radius \( r_2 \) has a charge \( Q \). A charge \( q \) is placed at the centre of the shell. The surface charge density on outer surface of the shell is :

Biot-Savart law indicates that the moving electrons (velocity \(\vec{v}\)) produce a magnetic field \(\vec{B}\) such that:

The magnetic flux (Φ) through the area of cross-section of a current-carrying coil is proportional to the current (i) i.e., Φ = Li.
(A) L is self-inductance of the coil
(B) The self-inductance of the coil does not depend on its geometry
(C) self-inductance is the electromagnetic analogue of mass in mechanics
(D) The self-inductance of the coil depends on the permeability of the medium inside coil
Choose the correct answer from the options given below:

The electric field is defined as \(\vec{E} = \lim_{q_0 \to 0} \frac{\vec{F}}{q_0}\) where \(q_0\) is the test charge and \(\vec{F}\) force on \(q_0\) due to the source charge. The meaning of \(\lim_{q_0 \to 0}\) is :

Ajesh has set up a sinking fund in order to have ₹ 10,00,000 after 10 years for his son's education. The amount should be set aside at the end of every 6 months into an account paying \(5\%\) per annum compounded half yearly is : [given \((1.025)^{20}=1.6386\) ]

Read the passage carefully and answer the questions
The osmotic pressure is one of the four colligative properties which depends on the number of particles of solute in the solution, irrespective of their nature. The osmotic pressure is equal to the product of concentration, gas constant and temperature. It is the most commonly used property for the determination of the molar mass of biomolecules. In many situations, the molecules get dissociated or associated when they are dissolved in a solvent, thereby changing the number of molecules in the solution. As a result, an abnormal molecular mass is obtained. The extent of dissociation or association is given by van't Hoff factor (i), which is the ratio of normal molar mass to abnormal molar mass. It is related with the degree of association or ionization. The introduction of van't Hoff factor in the osmotic pressure equation modifies the equation.
\[Itext\{Osmotic pressure\} ((Pi) \text\{of a solution does not depend upon\}\}]

Let \(e^y(x+1)=1\). Then which of the following are TRUE
(A) \(\frac{d^2 y}{d x^2}=-\frac{1}{(x+1)^2}\)
(B) \(\frac{d^2 y}{d x^2}=\left(\frac{d y}{d x}\right)^2\)
(C) \(\left.\frac{d^2 y}{d x^2}\right|_{x=0}=-1\)
(D) \(\left.\frac{d^2 y}{d x^2}\right|_{x=0}=1\)
(E) \(\left.\frac{d^2 y}{d x^2}\right|_{x=1}=\frac{1}{4}\)
Choose the correct answer from the options given below :

When a slab of insulating material 4 mm thick is introduced between the plates of a parallel plate capacitor of separation 4 mm, it is found that the distance between the plates has to be increased by 3.2 mm to restore the capacity to its original value. The dielectric constant of the material is :

The steps of PCR (Polymerase Chain Reaction) are given below. Arrange them in a correct sequence.
A. Extension of primers
B. Denaturation of DNA fragments by heating
C. Amplified DNA fragments
D. Annealing of primers
Choose the correct answer from the options given below:

A radioactive isotope phosphorous-32 has an initial activity \( 10 \mu \text{Ci} \) and has half life of \( 14 \text{ days} \). What is the activity of the source after \( 42 \text{ days} \) ?