A conducting circular loop is placed in a uniform magnetic field of \( B = 0.5 \text{ T} \), with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at the rate of \( \frac{dr}{dt} = 4 \text{ mm/s} \). When the radius of the loop is \( r = 4 \text{ cm} \), the induced emf in the loop is

A 12 V battery connected to a 6 \( \Omega \), 10 mH coil through a switch drives a constant current in the circuit. The switch is suddenly opened. Assuming that it took 1 ms to open the switch, the average emf induced across the coil would be

Match List-I with List-II

List-I	List-II
(A) Rutherford	(I) Nuclear model of atom
(B) A.H. Becquerel	(II) Plum-Pudding Model of atom
(C) Niels Bohr	(III) Radioactivity
(D) J.J. Thomson	(IV) Hydrogen atom model

Choose the correct answer from the options given below :

The magnetic field in a plane electromagnetic wave is given by \( B = 3 \times 10^{-7} \sin(1.5z + 5 \times 10^{8}t) \text{ T} \), where \( z \) is in meter and \( t \) is in second. The wavelength of the wave is: (Take \( \pi = 3 \))

If \(I_0\) is the intensity of the central diffraction band in the single slit diffraction experiment, then the intensity of the band when the slit width is doubled will be :

A wire is stretched to increase its length by 4 times. The resistance of the wire will :

The critical angle is maximum when light travels from

The slope of the normal to the curve \(y^2=16 x\) at the point \((1,4)\) is :

Any function \(f(x)\) is an increasing function in \([a, b]\) if:
(A) \(\forall x_1, x_2 \in[a, b], f\left(x_1\right) \geq f\left(x_2\right)\) if \(x_1 < x_2\)
(B) \(\forall x_1, x_2 \in[a, b], f\left(x_1\right) \geq f\left(x_2\right)\) if \(x_1 > x_2\)
(C) \(\forall x_1, x_2 \in[a, b], f\left(x_1\right) \leq f\left(x_2\right)\) if \(x_1 < x_2\)
(D) \(\forall x_1, x_2 \in[a, b], f\left(x_1\right) < f\left(x_2\right)\) if \(x_1 > x_2\)
Choose the correct answer from the options given below :

Which of the following pairs of solutions are isotonic?

When light passes from air to glass, then

We use microbes and microbially derived products almost every day. Bacteria called lactic acid bacteria (LAB) grow in milk to convert it into curd. The dough, which is used to make bread, is fermented by yeast called Saccharomyces cerevisiae. Microbes are used to produce industrial products like lactic acid, acetic acid and alcohol, which are used in a variety of processes in the industry. However, certain bacteria, which grow anaerobically on cellulosic material, produce large amount of methane along with CO2 and H2. These bacteria are collectively called methanogens, and one such common bacterium is Methanobacterium. These bacteria are commonly found in the anaerobic sludge during sewage treatment. Microbes are also used for commercial and industrial production of certain chemicals like organic acids, alcohols and enzymes.
Examples of acid producers are Aspergillus niger (a fungus) of citric acid. You are familiar with the commonly used antibiotic Penicillin. Do you know that Penicillin was the first antibiotic to be discovered, and it was a chance discovery? 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.
Which one of the following statements is not true with respect to microbes?

After the completion of replication, each DNA molecule will have one parental strand and one newly synthesized strand. This scheme is known as: