Which of the following gives the correct expression for potential gradient in terms of the resistivity ( \(\rho\) ) of the wire?

Which of the following is not based on total internal reflection?

A storage battery of EMF 10 V and internal resistance 1 \( \Omega \) is being charged by a 120 V dc supply using a series resistor of 21 \( \Omega \). What is the terminal voltage of the battery during charging ?

The power factor of an RL circuit is \( \frac{1}{2} \). If the frequency of a.c. is doubled, the power factor will be :

Rohit has been given two converging lenses of focal lengths 1.25 cm and 5 cm, respectively to design a compound microscope. If it is desired to have a magnification of 30, what would be the separation between the objective and the eyepiece when the final image is formed at the least distance of distinct vision?

Arrange the following electromagnetic waves in increasing order of their wavelengths.
(A) Visible Light
(B) Microwave
(C) X rays
(D) Infra-red rays
Choose the correct answer from the options given below:

Three charges are arranged at the corner of a square ABCD of side a. At A (+q), at B (-q), and at C(+q) in coulomb. Find the work needed to bring + q to point D of the square when given other charges at A, B and C are fixed.

The characteristic oxidation state of Lanthanoids is +3, but Ce shows +4 oxidation state because…
(A) It has variable ionization enthalpy
(B) It has a tendency to attain noble gas configuration
(C) It has a tendency to attain \(f^0\) configuration
(D) It resembles \(\mathrm{Pb}^{4+}\)

The function \(f(x)=x^3\), is increasing for:

In the method of least squares, we find trend values using:

Read the following passage carefully and answer the given questions. During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
Statins, used as blood-cholesterol lowering agents are produced by -

A doctor is to visit a patient.
The probabilities that he comes by train, bus, scooter or other means are
\(\frac{3}{10}, \frac{1}{5}, \frac{1}{10}\) and \(\frac{2}{5}\) respectively.
The probabilities that he will be late are
\(\frac{1}{4}\) if he comes by train,
\(\frac{1}{3}\) if he comes by bus,
\(\frac{1}{12}\) if he comes by scooter.
If he comes by other means of transport, he will not be late.
When he arrives, he arrives late.
The probability that he comes by bus is:

Let \(A=\left[a_{i j}\right]_{n \times n}\) and \(B=\left[b_{i j}\right]_{n \times n}\).
Then which of the following is/are true?
(A) \(A B=B A\)
(B) \((A B)^{-1}=B^{-1} A^{-1}\)
(C) \((A B)^T=B^T A^T\)
(D) \(A B=0 \Rightarrow A=0\) or \(B=0\)
Choose the correct answer from the options given below :