If h is the Planck's constant, then the momentum of the photon having frequency \(v\) is represented by

The energy released in fusion reaction \( ^2_1H + ^2_1H \rightarrow ^3_2He + n \) where Binding Energy of \( ^2_1H = 2.23 \text{ MeV} \) and of \( ^3_2He = 7.73 \text{ MeV} \), would be

Match List-I with List-II

List-I (Physical quantity)	List-II (Formula)
(A) Current sensitivity of galvanometer	(I) \( \frac{\mu_0 I}{2R} \)
(B) Magnetic field at the centre of a circular coil	(II) \( \frac{NAB}{kR} \)
(C) magnetic field due to a long straight wire carrying a current	(III) \( \frac{NAB}{k} \)
(D) Voltage sensitivity of galvanometer	(IV) \( \frac{\mu_0 I}{2\pi R} \)

Choose the correct answer from the options given below:

A bar magnet when suspended horizontally and perpendicular to earth's field experiences a torque of \( 3 \times 10^{-4} \text{ N m} \). The Magnetic moment of the magnet would be: (take horizontal component of Earth's magnetic field at the place \( 0.4 \times 10^{-4} \text{ T} \))

A square loop is placed near a long straight current carrying wire as shown in figure. If the loop is moved away from the wire

If a capacitor is connected in an ac circuit, what is the phase relationship between current and potential difference applied across the capacitor ?

Calculate the Ratio of Range of Transmitting antenna of height 64 m to the receiving antenna of height 16 m :

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?

The degree of the differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3=\left(\frac{d^3 y}{d x^3}\right)^2\) is :

The amount of radioactive substance left after \(75\) hours,
when \(100\) g of it is taken initially, will be:
(Half-life of the radioactive substance is \(15\) hours)

If \(\left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|\), where \(a, b\) and \(c\) are non zero constants, then the value of \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\) is

A double stranded DNA has 30\% of Thymine. The percentage of Guanine in it would be:

Ultra pure silicon can be obtained by