The storage battery of a car has an emf of 10 V. If the internal resistance of the battery is \( 0.2 \Omega \), then the maximum current that can be drawn from the battery is

If the least distance of distinct vision for a person is 50 cm, what should be the focal length of the reading spectacles for him ?

Match List-I with List-II (Symbols have their usual meanings)

List-I (Physical Quantity)	List-II (Expression)
(A) Current density	(I) \( \frac{e E \tau}{m} \)
(B) Drift velocity	(II) \( \frac{n e^2 \tau}{m} \)
(C) Conductivity	(III) \( \frac{e \tau}{m} \)
(D) Mobility	(IV) \( n e v_d \)

Choose the correct answer from the options given below:

In a series LCR circuit, the voltage across \(R\) is \(200 V, C=5 \mu F\), and \(R=2 k \Omega\). The resonant frequency \(\omega\) is \(1 0 0 ~ r a d / s\). At resonance, the voltage across \(L\) is:

The distance between a luminous object and the screen is 60 cm. A convex lens placed in between produces a three times magnified image on the screen. The focal length of the convex lens is:

When a transistor is used as an Amplifier, the phase difference between the input and the output signal voltage is

A capacitor charged from a 100 V d.c supply is found to have charge of 20 \(\mu\text{C}\). How much energy is stored in it ?

A radioactive material with half life of 6.25 years undergoes beta decay. How much fraction of material is decayed after 25 years:

False statement about Frenkel defect is:

The following reaction is an example of:

Microbes in human welfare Microbes are a very important component of life on earth. we use microbes and microbially derived products almost every day, like LAB to make curd, yeast to make bread, adding flavor and texture to cheese, producing antibiotics etc. The addition of LAB, improves the milk quality by increasing vit. B12. Cheese is one of the oldest food items in which microbes are used. For example, large holes in Swiss cheese are due to CO2 produced by the bacterium Propionibacterium sharmanii. 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. The greater the BOD of waste water, the more is its polluting potential. In anaerobic sludge digesters, bacteria produce a mixture of gases like methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as a source of energy. Biofertilisers are organisms that enrich the nutrient quality of the soil. The main sources of biofertilisers are bacteria, fungi and cyanobacteria. You have studied about the nodules on the roots of leguminous plants formed by the symbiotic association of Rhizobium. These bacteria fix atmospheric nitrogen into organic forms, which is used by the plant as a nutrient. Other bacteria can fix atmospheric nitrogen while free-living in the soil (examples Azospirillum and Azotobacter).
In anaerobic sludge digesters, the biogas produced by the bacteria, is composed of -

A proton moves with a velocity equal to \( \left( \frac{1}{20} \right)^{\text{th}} \) of velocity of light.
The associated de-Broglie wavelength is:

The value of \(\left|\begin{array}{ccc}7! & 8! & 9! \\ 8! & 9! & 10! \\ 9! & 10! & 11!\end{array}\right|\) is :