AIEEE 2006

Paper was held on
Sat, Apr 29, 2006 9:30 AM

## Chemistry

How many moles of magnesium phosphate Mg3(PO4)2 will contain 0.25 mole of oxygen atoms?

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Density of a 2.05M solution of acetic acid in water is 1.02 g/mL The molality of the solution is

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According to Bohr's theory, the angular momentum of an electron in 5th orbit is

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Uncertainty in the position of an electron (mass = 9.1 $$\times$$ 10-31 kg) moving with a velocity 300 ms-1, accurate up

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Which of the following sets of ions represents a collection of isoelectronic species?

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Following statements regarding the periodic trends of chemical reactivity of the alkali metals and the
halogens are give

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Which of the following molecules/ions does not contain unpaired electrons?

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In which of the following molecules/ions are all the bonds not equal?

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The decreasing values of bond angles from NH3 (106o) to SbH3 (91o
) down group-15 of the periodic table is due to

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An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If Ti is the
initial temperatu

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($$\Delta H - \Delta U$$) for the formation of carbon monoxide (CO) from its elements at 298 K is : (R = 8.314 J K–1 mol

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The standard enthalpy of formation $$\Delta _fH^o$$ at 298 K for methane, CH4(g), is –74.8 kJ mol–1. The additional info

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The enthalpy changes for the following processes are listed below :
Cl2(g) = 2Cl(g), 242.3 kJ mol–1
I2(g) = 2I(g), 151

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Phosphorus pentachloride dissociates as follows, in a closed reaction vessel
PCl5 (g) $$\leftrightharpoons$$ PCl3 (g) +

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The equilibrium constant for the reaction
SO3 (g) $$\leftrightharpoons$$ SO2 (g) + $$1 \over 2$$ O2 (g)
is Kc = 4.9 $$

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Given the data at 25oC,
Ag + I- $$\to$$ AgI + e- , Eo = 0.152 V
Ag $$\to$$ Ag+ + e-, Eo = -0.800 V
What is the value of

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The ionic mobility of alkali metal ions in aqueous solution is maximum for :

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The increasing order of stability of the following free radicals is

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Increasing order of stability among the three main conformations (i.e. Eclipse, Anti, Gauche) of
2-fluoroethanol is

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CH3Br + Nu- $$\to$$ CH3 - Nu + Br- The decreasing order of the rate of the above reaction with nucleophiles (Nu–) A to D

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In Langmuir’s model of adsorption of a gas on a solid surface

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Total volume of atoms present in a face-centre cubic unit cell of a metal is (r is atomic radius) :

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Among the following mixtures, dipole-dipole as the major interaction, is present in

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18 g of glucose (C6H12O6) is added to 178.2 g of water. The vapour pressure of water for this aqueous solution at 100oC

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The molar conductivities $$ \wedge _{NaOAc}^o$$ and $$ \wedge _{HCl}^o$$ and at infinite dilution in water at 25oC are

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Which of the following chemical reactions depicts the oxidizing behaviour of H2SO4?

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Resistance of a conductivity cell filled with a solution of an electrolyte of concentration 0.1 M is 100$$\Omega $$.
The

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A reaction was found to be second order with respect to the concentration of carbon monoxide. If the
concentration of ca

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In the transformation of $${}_{92}^{238}U$$ to $${}_{92}^{234}U$$, if one emission is an α-particle, what should be the

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Rate of a reaction can be expressed by Arrhenius equation as:
$$$k = A\,{e^{ - E/RT}}$$$
In this equation, E represents

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The following mechanism has been proposed for the reaction of NO with Br2 to form NOBr:
NO(g) + Br2 (g) $$\leftrighthar

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The increasing order of the first ionization enthalpies of the elements B, P, S and F (lowest first) is :

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Which of the following statements is true?

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What products are expected from the disproportionation reaction of hypochlorous acid?

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The “spin-only” magnetic moment [in units of Bohr magneton, (µB)] of Ni2+ in aqueous solution would
be : (Atomic number

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Lanthanoid contraction is caused due to :

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The IUPAC name for the complex [Co(NO2)(NH3)5]Cl2 is

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Nickel (Z = 28) combines with a uninegative monodentate ligand X– to form a paramagnetic complex [NiX4]2− . The number o

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In Fe(CO)5, the Fe – C bond possesses :

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How many EDTA (ethylenediaminetetraacetic acid) molecules are required to make an octahedral
complex with a Ca2+ ion?

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Phenyl magnesium bromide reacts with methanol to give

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Fluorobenzene (C6H5F) can be synthesized in the laboratory

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Reaction of trans-2-phenyl-1-bromocyclopentane on reaction with alcoholic KOH produces

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HBr reacts with CH2 = CH – OCH3 under anhydrous conditions at room temperature to give

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The increasing order of the rate of HCN addition to compounds A – D is
(A) HCHO (B) CH3COCH3
(C) PhCOCH3 (D) PhCOPh

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The term anomers of glucose refers to

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The pyrimidine bases present in DNA are

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The $$IUPAC$$ name of the compound shown below is :

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The alkene formed as a major product in the above elimination reaction is

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The structure of the major product formed in the following reaction
is

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The structure of the compound that gives a tribromo derivative on treatment with bromine water is

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The electrophile involved in the above reaction is

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Among the following the one that gives positives iodoform test upon reaction with $${I_2}$$ and $$NaOH$$ is

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The correct order of increasing acid strength of the compounds

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A metal, $$M$$ forms chlorides in its $$+2$$ and $$+4$$ oxidation states. Which of the following statements about these

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## Mathematics

The number of values of $$x$$ in the interval $$\left[ {0,3\pi } \right]\,$$ satisfying the equation $$2{\sin ^2}x + 5\

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If $$0 < x < \pi $$ and $$\cos x + \sin x = {1 \over 2},$$ then $$\tan x$$ is :

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If $${z^2} + z + 1 = 0$$, where z is complex number, then value of $${\left( {z + {1 \over z}} \right)^2} + {\left( {{z^

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The value of $$\sum\limits_{k = 1}^{10} {\left( {\sin {{2k\pi } \over {11}} + i\,\,\cos {{2k\pi } \over {11}}} \right)}

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If the roots of the quadratic equation $${x^2} + px + q = 0$$ are $$\tan {30^ \circ }$$ and $$\tan {15^ \circ }$$, respe

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All the values of $$m$$ for which both roots of the equation $${x^2} - 2mx + {m^2} - 1 = 0$$ are greater than $$ - 2$$ b

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If $$x$$ is real, the maximum value of $${{3{x^2} + 9x + 17} \over {3{x^2} + 9x + 7}}$$ is

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At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 c

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If the expansion in powers of $$x$$ of the function $${1 \over {\left( {1 - ax} \right)\left( {1 - bx} \right)}}$$ is $$

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For natural numbers $$m$$ , $$n$$, if $${\left( {1 - y} \right)^m}{\left( {1 + y} \right)^n}\,\, = 1 + {a_1}y + {a_2}{y

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If $${{a_1},{a_2},....{a_n}}$$ are in H.P., then the expression $${{a_1}\,{a_2} + \,{a_2}\,{a_3}\, + .... + {a_{n - 1}}\

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Let $${a_1}$$, $${a_2}$$, $${a_3}$$.....be terms on A.P. If $${{{a_1} + {a_2} + .....{a_p}} \over {{a_1} + {a_2} + .....

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A straight line through the point $$A (3, 4)$$ is such that its intercept between the axes is bisected at $$A$$. Its equ

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If $$\left( {a,{a^2}} \right)$$ falls inside the angle made by the lines $$y = {x \over 2},$$ $$x > 0$$ and $$y = 3x,

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If the lines $$3x - 4y - 7 = 0$$ and $$2x - 3y - 5 = 0$$ are two diameters of a circle of area $$49\pi $$ square units,

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Let $$C$$ be the circle with centre $$(0, 0)$$ and radius $$3$$ units. The equation of the locus of the mid points of th

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The locus of the vertices of the family of parabolas
$$y = {{{a^3}{x^2}} \over 3} + {{{a^2}x} \over 2} - 2a$$ is :

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In the ellipse, the distance between its foci is $$6$$ and minor axis is $$8$$. Then its eccentricity is :

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Angle between the tangents to the curve $$y = {x^2} - 5x + 6$$ at the points $$(2,0)$$ and $$(3,0)$$ is

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The set of points where $$f\left( x \right) = {x \over {1 + \left| x \right|}}$$ is differentiable is

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If $${x^m}.{y^n} = {\left( {x + y} \right)^{m + n}},$$ then $${{{dy} \over {dx}}}$$ is

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The function $$f\left( x \right) = {x \over 2} + {2 \over x}$$ has a local minimum at

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A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides havi

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If $$A$$ and $$B$$ are square matrices of size $$n\, \times \,n$$ such that
$${A^2} - {B^2} = \left( {A - B} \right)\le

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Let $$A = \left( {\matrix{
1 & 2 \cr
3 & 4 \cr
} } \right)$$ and $$B = \left( {\matrix{
a & 0

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$$\int\limits_0^\pi {xf\left( {\sin x} \right)dx} $$ is equal to

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$$\int\limits_{ - {{3\pi } \over 2}}^{ - {\pi \over 2}} {\left[ {{{\left( {x + \pi } \right)}^3} + {{\cos }^2}\left( {x

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The value of $$\int\limits_1^a {\left[ x \right]} f'\left( x \right)dx,a > 1$$ where $${\left[ x \right]}$$ denotes t

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The differential equation whose solution is $$A{x^2} + B{y^2} = 1$$
where $$A$$ and $$B$$ are arbitrary constants is of

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At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an a

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If $$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c = \overrightarrow a \times

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The values of a, for which the points $$A, B, C$$ with position vectors $$2\widehat i - \widehat j + \widehat k,\,\,\wi

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The image of the point $$(-1, 3,4)$$ in the plane $$x-2y=0$$ is :

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The two lines $$x=ay+b, z=cy+d;$$ and $$x=a'y+b' ,$$ $$z=c'y+d'$$ are perpendicular to each other if :

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Suppose a population A has 100 observations 101, 102,........, 200, and another
population B has 100 observations 151, 1

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Let $W$ denote the words in the English dictionary. Define the relation $R$ by
$R=\{(x, y) \in W \times W \mid$ the wor

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## Physics

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity
'v' that varies

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A mass of $$M$$ $$kg$$ is suspended by a weightless string. The horizontal force that is required to displace it until t

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A ball of mass $$0.2$$ $$kg$$ is thrown vertically upwards by applying a force by hand. If the hand moves $$0.2$$ $$m$$

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A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $$\omega

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A player caught a cricket ball of mass $$150$$ $$g$$ moving at a rate of $$20$$ $$m/s.$$ If the catching process is com

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A particle of mass $$100g$$ is thrown vertically upwards with a speed of $$5$$ $$m/s$$. The work done by the force of gr

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The potential energy of a $$1$$ $$kg$$ particle free to move along the $$x$$-axis is given by $$V\left( x \right) = \lef

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A bomb of mass $$16kg$$ at rest explodes into two pieces of masses $$4$$ $$kg$$ and $$12$$ $$kg.$$ The velocity of the $

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Consider a two particle system with particles having masses $${m_1}$$ and $${m_2}$$. If the first particle is pushed tow

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A thin circular ring of mass $$m$$ and radius $$R$$ is rotating about its axis with a constant angular velocity $$\omega

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Four point masses, each of value $$m,$$ are placed at the corners of a square $$ABCD$$ of side $$l$$. The moment of iner

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If the terminal speed of a sphere of gold (density $$ = 19.5\,\,kg/{m^3}$$) is $$0.2$$ $$m/s$$ in a viscous liquid (dens

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A wire elongates by $$l$$ $$mm$$ when a LOAD $$W$$ is hanged from it. If the wire goes over a pulley and two weights $$W

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The work of $$146$$ $$kJ$$ is performed in order to compress one kilo mole of gas adiabatically and in this process the

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Assuming the Sun to be a spherical body of radius $$R$$ at a temperature of $$TK$$, evaluate the total radiant powered i

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Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperatu

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A force of $$ - F\widehat k$$ acts on $$O,$$ the origin of the coordinate system. The torque about the point $$(1, -1)$

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Starting from the origin a body oscillates simple harmonically with a period of $$2$$ $$s.$$ After what time will its ki

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The maximum velocity of a particle, executing simple harmonic motion with an amplitude $$7$$ $$mm,$$ is $$4.4$$ $$m/s.$$

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A whistle producing sound waves of frequencies $$9500$$ $$Hz$$ and above is approaching a stationary person with speed $

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A string is stretched between fixed points separated by $$75.0$$ $$cm.$$ It is observed to have resonant frequencies of

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An electric dipole is placed at an angle of $${30^ \circ }$$ to a non-uniform electric field. The dipole will experience

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Two spherical conductors $$A$$ and $$B$$ of radii $$1$$ $$mm$$ and $$2$$ $$mm$$ are separated by a distance of $$5$$ $$c

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Two insulating plates are both uniformly charged in such a way that the potential difference between them is $${V_2} - {

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A thermocouple is made from two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is

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An electric bulb is rated $$220$$ volt - $$100$$ watt. The power consumed by it when operated on $$110$$ volt will be

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In a Wheatstone's bridge, three resistance $$P, Q$$ and $$R$$ connected in the three arms and the fourth arm is formed b

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The resistance of bulb filmanet is $$100\Omega $$ at a temperature of $${100^ \circ }C.$$ If its temperature coefficient

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The current $${\rm I}$$ drawn from the $$5$$ volt source will be

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Needles $${N_1}$$, $${N_2}$$ and $${N_3}$$ are made of ferromagnetic, a paramagnetic and a diamagnetic substance respect

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In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A

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A long solenoid has $$200$$ turns per $$cm$$ and carries a current $$i.$$ The magnetic field at its center is $$6.28 \ti

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Which of the following units denotes the dimension $${{M{L^2}} \over {{Q^2}}}$$, where $$Q$$ denotes the electric charge

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In an $$AC$$ generator, a coil with $$N$$ turns, all of the same area $$A$$ and total resistance $$R,$$ rotates with fre

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In a series resonant $$LCR$$ circuit, the voltage across $$R$$ is $$100$$ volts and $$R = 1\,k\Omega $$ with $$C = 2\mu

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The flux linked with a coil at any instant $$'t'$$ is given by
$$\phi = 10{t^2} - 50t + 250$$
The induced $$emf$$ at

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The refractive index of a glass is $$1.520$$ for red light and $$1.525$$ for blue light. Let $${D_1}$$ and $${D_2}$$ be

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An inductor $$(L=100$$ $$mH)$$, a resistor $$\left( {R = 100\,\Omega } \right)$$ and a battery $$\left( {E = 100V} \righ

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In a common base mode of a transistor, the collector current is $$5.488$$ $$mA$$ for an emitter current of $$5.60mA.$$ T

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The threshold frequency for a metallic surface corresponds to an energy of $$6.2$$ $$eV$$ and the stopping potential for

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An alpha nucleus of energy $${1 \over 2}m{v^2}$$ bombards a heavy nuclear target of charge $$Ze$$. Then the distance of

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The time taken by a photoelectron to come out after the photon strikes is approximately

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If the ratio of the concentration of electrons to that of holes in a semiconductor is $${7 \over 5}$$ and the ratio of c

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When $${}_3L{i^7}$$ nuclei are bombarded by protons, and the resultant nuclei are $${}_4B{e^8}$$, the emitted particles

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A solid which is not transparent to visible light and whose conductivity increases with temperature is formed by

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If the binding energy per nucleon in $${}_3^7Li$$ and $${}_2^4He$$ nuclei are $$5.60$$ $$MeV$$ and $$7.06$$ $$MeV$$ resp

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The $$'rad'$$ is the correct unit used to report the measurement of

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The $$rms$$ value of the electric field of the light coming from the Sun is $$720$$ $$N/C.$$ The average total energy de

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The circuit has two oppositively connected ideal diodes in parallel. What is the current following in the circuit?

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The energy spectrum of $$\beta $$-particles [ number $$N(E)$$ as a function of $$\beta $$-energy $$E$$ ] emitted from a

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In the following, which one of the diodes is reverse biased?

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The anode voltage of a photocell is kept fixed. The wavelength $$\lambda $$ of the light falling on the cathode is gradu

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If the lattice constant of this semiconductor is decreased, then which of the following is correct?

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