A series LCR circuit with \( L = 5.0 \text{ H}, C = 80 \text{ } \mu\text{F} \) and \( R = 40 \text{ } \Omega \) is connected to a variable frequency 200 V source. The amplitude of current at the resonant frequency is

When a piece of metal is illuminated by monochromatic light of wavelength λ, the stopping potential for photoelectric current is 2.5 V0. When the same surface is illuminated by light of wavelength 1.5 λ, the stopping potential becomes V0. The value of threshold wavelength for photoelectric emission is:

Kirchhoff's second law for an electric network is based on:

Match List-I with List-II

List-I (EM Waves)	List-II (Production)
(A) Infra-red rays	(I) Electrons in atoms emit light when they move from one energy level to a lower level
(B) Visible light rays	(II) Radioactive decay of the nucleus
(C) Ultraviolet rays	(III) Vibration of molecules
(D) Gamma rays	(IV) Inner shell electrons in atoms moving from one energy level to a lower level

Choose the correct answer from the options given below:

A proton is projected with a speed of \( v = 4 \times 10^6 \text{ m s}^{-1} \) horizontally from east to west. A uniform magnetic field \( \vec{B} \) of strength \( B = 1.5 \times 10^{-3} \text{ T} \) exists in the vertically upward direction. What is the acceleration produced? (Use charge on the proton \( q = 1.6 \times 10^{-19} \text{ C} \) and mass of the proton \( m = 1.67 \times 10^{-27} \text{ kg} \))

Which of the following phenomena proves the particle nature of photon ?

Match List-I with List-II

List-I	List-II
(A) Light	(I) 1 mm to \(10^{-3} nm\)
(B) Infra-red	(II) 700 nm to 400 nm
(C) X-rays	(III) 400 nm to 1 nm
(D) UV rays	(IV) 1 mm to 700 nm

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:

Match List-I with List-II

List-I (Parameter of Magnetic Dipole)	List-II (Formula)
(A) Magnetic moment	(I) \( \mu_0 2m / (4\pi x^3) \)
(B) Magnetic field on the equatorial line	(II) \( m \times B \)
(C) Magnetic field on axial line	(III) \( IA \)
(D) External torque in magnetic field	(IV) [Missing/Constant]

Choose the correct answer from the options given below:

The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is:

Area of region bounded by the curves \(x=y^3, x=0\) between \(y=-1\) and \(y=2\) is :

Let \(R\) be a relation on the set of integers \(Z\) such that \(R=\left\{(a, b), a=2^k b, a, b, k \in Z\right\}\), then \(R\) is :

Conversion of freshly prepared precipitate into the colloidal solution is known as