Match List I with List II

List I	List II
A. Rod rotated in uniform magnetic field	I. \( e = e_{0} \sin(\omega t) \)
B. Coil rotated in uniform magnetic field	II. \( e = Blv \)
C. Rod moved with linear velocity \( v \)	III. constant (for motional emf at constant \( v \))
D. Rectangular coil moved in magnetic field	IV. \( e = \frac{B\omega l^{2}}{2} \)

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Resolving power of a telescope can be increased by increasing:

If light of wavelength 412.5 nm is incident on each of the metals given below, which ones will show photoelectric emission ?

Metal	Work Function (eV)
Na	1.92
K	2.15
Ca	3.20
Mo	4.17

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When a deuteron is bombarded on \(^{16}_{8}\text{O}\) nucleus, an α-particle is emitted. Other product nucleus is:

The internal resistance of primary cell is \( 3 \Omega \). It generates a current of \( 0.3 \text{ A} \) in an external resistance of \( 22 \Omega \). The rate at which chemical energy is consumed in providing the current is:

Which of the following statements are correct?
(A) The electrostatic repulsive force between the protons can be greater than the nuclear force to bind the nucleons together inside a nucleus.
(B) The repulsive electrostatic force between protons in smaller nuclei is much smaller than the nuclear force between nucleons inside a nucleus.
(C) The gravitational force between nucleons is much smaller than the nuclear force between the nucleons inside a nucleus.
(D) The binding energy per nucleon between nucleons is almost constant because the nuclear force is a long range force.
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O2 molecules consists of two oxygen atoms. In the molecule, Nuclear force between the nuclei of two atoms.
(A) is not important because Nuclear forces are short ranged
(B) is as important as electrostatic force for binding the two atoms
(C) cancels the repulsive electrostatic force between the nuclei
(D) not important because oxygen nucleus have equal no. of neutrons and protons
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Maximum value of the objective function Z = 4x + 3y subject to the constraints \(x+y \geq 4, x \geq 4, y \geq 0\) exists at

The vector equation of the plane which is at a distance of 6 units from the origin and has \(2,-1,2\) as the direction ratios of normal to it, is :

Match List-l with List-ll

List-l (Organisms)	List-II (Products/Bioactive molecule)
(A) Trichoderma polysporum	(I) Citric acid
(B) Monascus purpureus	(II) Cyclosporin A
(C) Aspergillus niger	(III) Ethanol
(D) Saccharomyces cerevisiae	(IV) Statins

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Identify the correct statement(s) among the following:
(A) The time taken by a light wave is \( 5 \times 10^{-9} \text{ s} \) to travel a thickness of 1 cm of glass having refractive index 1.5.
(B) Two similar waves of amplitude 3 mm and 5 mm reach a point in the same phase. The resultant amplitude will be 8 mm.
(C) Two waves of amplitude 2 mm each reach a point with a phase difference of \( \pi/2 \). The resultant amplitude is zero.
(D) If one of the slits is closed in Young's double slit experiment, the interference pattern will disappear.
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The function \(f(x)=|x-3|, x \in R\) is:

A closed surface in vacuum encloses charges \( - q \) and \( + 3q \). Another charge \( - 2q \) lies out side the surface. The total electric flux over the surface is :