If the de Broglie wavelengths for a proton and an \(\alpha\)-particle are equal, then the ratio of their velocities respectively will be :

A uniformly charged sphere of \( 80 \text{ } \mu\text{C} \) and radius 2 cm is placed in air.
The electric field intensity at a point 20 cm from the center of the sphere is:

An alternating voltage \( V = V_0 \sin(\omega t + \pi/2) \) is applied across an ac circuit. As a result, a current \( I = I_0 \sin(\omega t + \pi/6) \) flows in it. The power factor of the circuit is

Which of the following statements are correct:
A. In semiconductor diodes carriers are generated by photo-excitation.
B. When the photo diode is illuminated with light with energy (E) > Energy gap (Eg) of the semiconductor, then electron-holepairs are generated.
C. Photovoltaic devices convert electricity into optical radiation.
D. Photodiode can be used as a photodetector to detect optical signal.
E. Zener diode specification should be taken as per the required output voltage.
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Match List - I with List - II.

List - I	List - II (Physical Quantity) (S.I. Unit)
(A) Electric Field intensity	(I) Coulomb/metre
(B) Electric dipole moment	(II) Newton (metre)\(^2\)/Coulomb
(C) Linear charge density	(III) Newton/Coulomb
(D) Electric flux	(IV) Coulomb - metre

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Which of the following particles/rays is emitted in a radioactive decay in which neither the atomic number nor the mass number changes?

An equiconvex lens has a focal length of 20 cm and its radius of curvature is 30 cm. Its refractive index is

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Electrochemistry is the study involving two types of processes. One type involves the production of electricity from the energy released during a spontaneous chemical reaction. Galvanic cells like Daniel cells are used to produce electricity from the redox reaction. Nernst equation of a galvanic cell gives the relation between the standard cell potential and the concentration of the species involved in the redox reaction. The second type of study involves the cells in which electrical energy is used to bring about the chemical reactions in a non-spontaneous process. The conductance of electrolytic solution depends on many factors including the nature of the electrolyte and the dimensions of the electrolytic cell.
Faraday's laws of electrolysis are related to:

Hole is-

A series LCR circuit is connected to a 220 V variable frequency (a.c) supply. If L = 20 mH, \( C = 800/\pi^2 \, \mu \text{F} \) and R = 110 \( \Omega \). The frequency of the source, for which the average power absorbed by the circuit is maximum will be:

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Alcohols and phenols are formed when a hydrogen atom in a hydrocarbon, aliphatic and aromatic respectively is replaced by -OH group. These are further classified on the basis of number of hydroxy groups and according to the hybridization of the carbon atom \(sp ^2\) or \(sp ^3\) to which the -OH group is attached. They find applications in industry as well as in day-to-day life. One of the most commercially obtained alcohol also known as wood spirit is obtained by destructive distillation of wood. Both alcohols and phenols are acidic in nature. The acidity of alcohols and phenols vary according to the nature of substituent(s) attached to them. Alcohols and phenols react with carboxylic acids, acid chlorides and acid anhydrides to form esters. Introduction of acetyl group in alcohols and phenols is called acetylation. Phenol undergo electrophilic aromatic substitution reaction because the -OH activates the benzene ring. It undergoes nitration, halogenation and sulphonation reactions.
Which of the following compound lacks a phenolic group?

The following table gives the lenght, diameter and appiled potential difference of four copper wires, A, B, C, D, across their ends. Arrange the wires in correct order of the increasing electric field.

Wire	Length	Diameter	Potential difference
(A) Wire A	l	3d	V
(B) Wire B	2l	d	V
(C) Wire C	3l	2d	2V
(D) Wire D	3l	2d	V

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For what distance is ray optics a good approximation when the aperture is 3 mm wide and the wavelength is 500 nm?