Four equal charges \(Q\) are placed at the four corners of a square of side 'a'. Work done in removing a charge \(-Q\) from its centre to infinity is :

A potential difference of 3 V is applied across a conductor of resistance \(1.5 \Omega\).
The number of electrons flowing through it in one second would be:
(Given charge of an electron, \(e=1.6 \times 10^{-19} C\) )

If the electric field is given by \((6\hat{i} + 3\hat{j} + 4\hat{k}) \text{ V/m}\). The electric flux through a surface of area \(20 \text{ m}^2\) lying in Y-Z plane would be (in V-m).

A metal wire under constant potential difference, when heated, shows that the drift velocity of the electron :

Four diode connections are given below. Identify the diagram in which the diode is forward biased.
(A)

(B)

(C)

(D)

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Electric potential on an equitorial plane of an electric dipole is taken as zero. This is based on

In the context of the Photoelectric effect, identify the statements which support quantum nature of light.
(A) The electric charge of photoelectrons is quantized
(B) The maximum kinetic energy of photoelectrons depends on the frequency of the incident light, but is independent of its intensity
(C) The photoelectric emission is an instantaneous process without any apparent time lag, even when the incident radiation is made exceedingly dim
(D) There is a minimum frequency of light below which no photoelectrons are emitted
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An electric dipole consists of charges \( \pm 2 \times 10^{-6} \, \text{C} \), separated by a distance of 2 mm. It is placed on the right side near a long line charge of density \( 4 \times 10^{-4} \, \text{C m}^{-1} \). The negative charge of dipole is at a distance of 2 cm from the line charge as shown in figure. A positive charge (+2q) is placed on the left at 2 cm at point C. Given \( q = 2 \times 10^{-8} \, \text{C} \).

(A) Force \( |F_A| \) exerted on negative charge at point A due to line charge
(B) Force \( |F_B| \) exerted on positive charge at point B due to line charge
(C) Net force on the dipole \( |F_{net}| \) due to line charge
(D) Force \( |F_C| \) exerted on charge +2q at point C due to line charge
If the forces \( |F_A|, |F_B|, |F_C|, |F_{net}| \) are arranged in decreasing order, then:
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A nematode, Meloidogyne incognitia infects the roots of _______ and causes a great reduction in yield.

A piece of ancient wood shows an activity of 3.9 disintegrations per second per gram of C\(^{14}\). The age of wood, if half life of C\(^{14}\) is 5568 years, and activity of fresh C\(^{14}\) is 15.6 disintegrations per second per gram, is (take \(\log_e 2 = 0.693\)).

Match List-I and List-II

List-I	List-II
A. Phenol + CH3Cl is presence of anhy AlCl 3	I. Salicylaldehyde
B. Phenol + Br2 water	II. 2,4,6 -Tribromophenol
C. Phenol + CH3Cl/OH	III. Salicylic acid
D. Phenol + CO2 \(/ NaOH\)	IV. p-cresol

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The linear programming problem: Minimise \(Z=3 x+2 y\)
Subject to constraints: \(x+y \geq 8, \quad 3 x+5 y \leq 15, \quad x \geq 0, y \geq 0\) has

\(\int \frac{\sqrt{\tan x}}{\sin x \cos x} d x\) equals :