\( P_1, P_2, P_3 \) are three Polaroid sheets; \( P_1 \) and \( P_3 \) are two crossed polaroids. What should be the angle between Polaroids \( P_1 \) and \( P_2 \), so that the value of \( I' = I_0/4 \)? (Where \( I' \) is intensity after \( P_2 \))

In the given circuit when steady current flows, the potential drop across the capacitor is:

The electric field vector of a plane electromagnetic wave oscillates sinusoidally at a frequency of \(4.5 \times 10^{10} \text{ Hz}\) in a medium with permittivity \(\epsilon_0\) and permeability \(\mu_0\). The wavelength of the wave is

Which of the following are not electromagnetic waves?
A. Gamma rays
B. Cathode rays
C. X-rays
D. \(\beta\)-rays
E. Radio waves
Choose the correct answer from the options given below:

Below given are some statements about electronic devices:
(A) Diodes can be used for rectifying an ac voltage.
(B) For semiconductors, band gap energy \( E_g > 3 \, eV \).
(C) By changing the external applied voltage, junction barriers can be changed.
(D) p-n junction is the 'key' to all semiconductor devices.
Choose the correct answer from the options given below:

Four capacitors are connected in the circuit as shown. The equivalent capacitance between P and Q will be :

The equivalent capacitance between P and Q will be :

Daily life phenomena based on scattering of light are
(A) Blue colour of sky
(B) Clouds appearing white
(C) Twinkling of stars
(D) Danger signals being red
Choose the correct answer from the options given below:

Two concentric coils, each of radius \( 2\pi \, \text{cm} \), are placed at right angles to each other. Currents of 3 A and 4 A respectively are flowing through the two coils. The magnetic induction at the center of the coils will be:

Which compound will exhibit the lowest boiling point ?

Out of 18 g of glucose, only 4.5 g is dissolved in water to obtain 40 mL of its aqueous solution. Find the molarity of this glucose solution.

The value of \(\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\tan x}+\sqrt{\cot x}} d x\) is:

The susceptibility of magnesium at 27°C is \( 1.2 \times 10^{-5} \). Its susceptibility at 200 K will be

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.
Citric acid is commercially obtained by Aspergillus niger, which is a: