In a circuit, resistance \( R_1 \) is connected in series with the parallel combination of resistances \( R_2 \) and \( R_3 \). The currents passing through the resistances \( R_1, R_2 \) and \( R_3 \) are \( I_1, I_2 \) and \( I_3 \), respectively. What will be the ratio \( \frac{I_3}{I_1} \) of currents in terms of the resistances connected in the circuit?

Match List-I with List-II

List-I (Electric Field)	List-II (Expression)
(A) Field due to an infinitely long straight uniformly charged wire	(I) \(\sigma\left(2 \varepsilon_0\right)^{-1}\)
(B) Field due to a uniformly charged thin spherical shell (inside the shell)	(II)\(q\left(4 \pi \varepsilon_0 r^2\right)^{-1}\)
(C) Field due to a uniformly charged infinite plane sheet	(III) \(\lambda\left(2 \pi \varepsilon_0 r\right)^{-1}\)
(D) Field due to a uniformly charged thin spherical shell (outside the shell)	(IV) zero

Choose the correct answer from the options given below:

Transverse nature of electromagnetic waves are/is evident by:
A. Interference
B. Dispersion
C. Polarisation
D. Diffraction
Choose the correct answer from the options given below:

By increasing the temperature, resistivity of a conductor and a semiconductor

What will be the minimum length of antenna required to transmit a radio signal of frequency 10 MHz ?

If the temperature of a metallic conductor is increased, then the product of resistivity and conductivity

The energy equivalent of 5 g of substance is

A tightly wound 100 turn coil of radius 5 cm is carrying a certain amount of current. The magnitude of the magnetic field at the center of the coil is \( 2\pi \times 10^{-4} \, T \). The value of current flowing through the coil is

Read the passage carefully and answer the questions
Nearly all the transition elements display typical metallic properties such as high tensile strength, ductility, malleability, high thermal and electrical conductivity and metallic lustre. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. They have high enthalpies of atomization. lons of the same charge in a given series show progressive decrease in radius with increasing atomic number. However, the variation within a series is quite small. The filling of 4f before 5d orbital results in a regular decrease in atomic radii called Lanthanoid contraction which essentially compensates for the expected increase in atomic size with increasing atomic number. The net result of the lanthanoid contraction is that the second and the third d series exhibit similar radii (e.g., Zr 160 pm, Hf 159 pm) and have very similar physical and chemical properties. There is an increase in ionisation enthalpy along each series of the transition elements from left to right. The first ionisation enthalpy, in general, increases, but the magnitude of the increase in the second and third ionisation enthalpies for the successive elements, is much higher along a series. One of the notable features of a transition elements is the great variety of oxidation states these may show in their compounds.
Among \(\mathrm{Cr}(\mathrm{Z}=24), \mathrm{Co}(\mathrm{Z}=27), \mathrm{Mn}(\mathrm{Z}=25)\) and \(\mathrm{Fe}(\mathrm{Z}=26)\); which will show the maximum variety of oxidation states?

The figure is showing the technique of gel electrophoresis. The matrix used in this technique is made out of:

Read the paragraph given below and answer the question.
Insulin used for diabetes was earlier extracted from slaughtered cattle and pigs. Insulin from an animal source, though caused some patients to develop allergy or other type of reactions. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked bridges. In mammals, including human, insulin is synthesised as a pro-hormone.
Bonds which link 'A' and 'B' peptide chains of human insulin are

Which of the following enzymes join the sticky ends in recombinant DNA technology?

A pipe A can fill a tank in 4 hours. There are two outlet pipes, B and C, from the tank which can empty it in 8 and 10 hours respectively. If all the three pipes are opened simultaneously, how long will it take to fill the tank?