Interference fringes may be observed due to the superposition of two light waves represented by :

A solenoid with \(2\times 10^4\) turns per meter, diameter 0.1 m, has a coil of 100 turns and 0.01 m radius placed inside. If solenoid current decreases from 4 A to 0 in 0.05 s, total charge through coil is :

Two waves of amplitudes 3 m and 2 m, respectively superimpose at a point in the same phase. The resultant amplitude would be

A charged particle with charge 0.01 C rotates on a circular path of radius 0.5 m , with velocity \(0.2 m / s\). What is the value of \(B\) at the center of the circle ?

In a pair of adjacent coils, if current in one coil changes from 0 A to 10 A in 0.25 s, causing a magnetic flux change of 15 Wb in the adjacent coil, the mutual inductance of the coils is :

The following experiment suggests that light propagates as waves

A Fraunhofer diffraction pattern due to a single slit of width 0.2 mm is being obtained on a screen placed at a distance of 2 m from the slit. The first minimum lies at 5 mm on either side of the central maximum on the screen. The wavelength of light is:

Match List-I with List-II

LIST-I (Function \(f(x)\))	LIST-II (Interval)
(A) \(f(x)=x|x|\)	(I) Decreases on (0, \(\infty\) )
(B) \(f(x)=x^2+2 x-5\)	(II) Increases on ( \(3, \infty\) )
(C) \(f(x)=x^2-6 x+9\)	(III) Decreases on \((-\infty,-1)\)
(D) \(f(x)=-x^2\)	(iv) Increases on \((-\infty, \infty)\)

Choose the correct answer from the options given below:

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.
The discovery of penicillin was a chance discovery by Alexander Fleming while working on:

Which of the following are autosomal recessive trait/ disorder?
(A) Thalassemia
(B) Haemophilia
(C) Sickle cell anaemia
(D) Phenylketonuria
Choose the correct answer from the options given below:

A needle of length 4.5 cm is placed vertically 12 cm away from a convex mirror of focal length 15 cm. The magnification of the image produced is

What is the unit of electric flux in terms of the base units of SI?

The rise and fall of share market is an example of