AIEEE 2003

Paper was held on
Sat, Apr 26, 2003 9:30 AM

## Chemistry

What volume of hydrogen gas at 273 K and 1 atm pressure will be consumed in obtaining 21.6 g of elemental boron (atomic

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25 ml of a solution of barium hydroxide on titration with a 0.1 molar solution of hydrochloric acid gave a litre value o

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The number of d-electrons retained in Fe2+ (At no of Fe = 26) ion is

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The orbital angular momentum for an electron revolving in an orbit is given by $$\sqrt {l(l + 1)} {h \over {2\pi }}$$. T

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Which one of the following groupings represents a collection of isoelectronic species? (At. nos. : Cs : 55, Br : 35)

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In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following

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The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 meters per second is approximately

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According to the Periodic Law of elements, the variation in properties of elements is related to their

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Which one of the following is an amphoteric oxide?

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An ethar is more volatile than an alcohol having the same molecular formula. This is due to

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Which one of the following pairs of molecules will have permanent dipole moments for both members

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The pair of species having identical shapes for molecules of both species is

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Which one of the following compounds has the smallest bond angle in its molecule?

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According to the kinetic theory of gases, in an ideal gas, between two successive collisions of a gas molecule travels

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The internal energy change when a system goes from state A to B is 40 kJ/mole. If the system goes from A to B by a rever

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In an irreversible process taking place at constant T and P and in which only pressure-volume work is being done, the ch

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The enthalpy change for a reaction does not depend upon

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The correct relationship between free energy change in a reaction and the corresponding equilibrium constant Kc is

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If at 298 K the bond energies of C - H, C - C, C = C and H - H bonds are respectively 414, 347, 615 and 435 kJ/mol, the

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The solubility in water of a sparingly soluble salt AB2 is 1.0 $$\times$$ 10-5 mol L-1. Its solubility product number wi

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Which one of the following statements is not true?

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Consider the reaction equilibrium
2 SO2 (g) + O2 (g) $$\leftrightharpoons$$ 2 SO3 (g); $$\Delta H^o$$ = -198 kJ
One the

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For the reaction equilibrium
N2O4 (g) $$\leftrightharpoons$$ 2NO2 (g)
the concentrations of N2O4 and NO2 at equilibrium

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When rain is accompanied by a thunderstorm, the collected rain water will have a pH value

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In curing cement plasters water is sprinkled from time to time. This helps in

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The solubilities of carbonates decrease down the magnesium group due to a decrease in

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The substance not likely to contain CaCO3 is

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Which one of the following process will produce hard water?

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The IUPAC name of CH3COCH(CH3)2 is

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In the anion HCOO$$-$$
the two carbon-oxygen bonds are found to be of equal length. What is the reason for it?

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The general formula CnH2nO2 could be for open chain

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On mixing a certain alkane with chlorine and irradiating it with ultravioletlight, it forms only one
monochloroalkane. T

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Butene-1 may be converted to butane by reaction with

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Which one of the following characteristics is not correct for physical adsorption?

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How many unit cells are present in a cubeshaped ideal crystal of NaCl of mass 1.00 g?
[Atomic masses: Na = 23, Cl = 35.5

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A pressure cooker reduces cooking time for food because

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In a 0.2 molal aqueous solution of a weak acid HX the degree of ionization is 0.3. Taking kf for water as 1.85, the free

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If liquids A and B form an ideal solution

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Standard reduction electrode potentials of three metals A,B&C are respectively +0.5 V, -3.0 V & -1.2 V. The
redu

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For a cell reaction involving a two-electron change, the standard e.m.f. of the cell is found to be 0.295 V at 25oC. The

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When during electrolysis of a solution of AgNO3 9650 coulombs of charge pass through the electroplating
bath, the mass o

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For the redox reaction Zn(s) + Cu2+(0.1 M) $$\to$$ Zn2+(1M) + Cu(s) taking place in a cell, $$E_{cell}^o$$ is 1.10 volt

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Several blocks of magnesium are fixed to the bottom of a ship to

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The radionucleide $${}_{90}^{234}Th$$ undergoes two successive $$\beta$$ -decays followed by one $$\alpha$$-decay. The a

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The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of
it rem

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In respect of the equation k = Ae-Ea/RT in chemical kinetics, which one of the following statements is correct?

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The rate law for a reaction between the substances A and B is given by Rate = k[A]n [B]m On doubling the concentration o

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For the reaction system:
2NO(g) + O2(g) $$\to$$ 2NO2(g) volume is suddenly reduce to half its value by increasing the p

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Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that
graphite

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Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The
explanation for it i

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Which one of the following substances has the highest proton affinity?

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What may be expected to happen when phosphine gas is mixed with chlorine gas?

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For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass
over a liqu

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Glass is a

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What would happen when a solution of potassium chromate is treated with an excess of dilute nitric acid?

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The atomic numbers of vanadium (V), Chromium (Cr), manganese (Mn) and iron (Fe) are respectively 23, 24, 25 and 26. Whic

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Which one of the following nitrates will leave behind a metal on strong heating?

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Ammonia forms the complex ion [Cu(NH3)4]2+ with copper ions in alkaline solutions but not in acidic solutions. What is t

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The radius of La3+ (Atomic number of La = 57) is 1.06 Å. Which one of the following given values will be
closest to the

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One mole of the complex compound Co(NH3)5Cl3, gives 3 moles of ions on dissolution in water. One mole of the same comple

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In the coordination compound, K4[Ni(CN)4], the oxidation state of nickel is

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Bottles containing C6H5l and C6H5CH2I lost their original labels. They were labelled A and B for testing A and B were se

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During dehydration of alcohols to alkenes by heating with conc. H2SO4 the initiation step is

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When CH2 = CH - COOH is reduced with LiAlH4, the compound obtained will be

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The correct order of increasing basic nature for the bases NH3, CH3NH2 and (CH3)2 NH is

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Ethyl isocyanide on hydrolysis in acidic medium generates

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Which of the following could act as a propellant for rockets?

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Complete hydrolysis of cellulose gives

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Nylon threads are made of

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Which one of the following statements is correct?

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Among the following four structures $$i$$ to $$iv,$$
it is true that

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The reduction in atomic size with increase in atomic number is a characteristic of elements of

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The atomic numbers of Vanadium (V), Chromium (cr), Manganese (Mn) and Iron (Fe), respectively, $$23,24,25$$ and $$26$$.

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The reaction of chloroform with alcoholic $$KOH$$ and p-toluidine forms

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The reason for double helical structure of $$DNA$$ is operation of

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A red solid is insolvable in water. However it becomes soluble if some $$K{\rm I}$$ is added to water. Heating the red s

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## Mathematics

If $$z$$ and $$\omega $$ are two non-zero complex numbers such that $$\left| {z\omega } \right| = 1$$ and $$Arg(z) - Arg

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Let $${Z_1}$$ and $${Z_2}$$ be two roots of the equation $${Z^2} + aZ + b = 0$$, Z being complex. Further , assume that

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If $${\left( {{{1 + i} \over {1 - i}}} \right)^x} = 1$$ then

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If the sum of the roots of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the sum of the squares of their re

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The value of '$$a$$' for which one root of the quadratic equation
$$$\left( {{a^2} - 5a + 3} \right){x^2} + \left( {3a

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The number of real solutions of the equation $${x^2} - 3\left| x \right| + 2 = 0$$ is

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The real number $$x$$ when added to its inverse gives the minimum value of the sum at $$x$$ equal to

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If $$x$$ is positive, the first negative term in the expansion of $${\left( {1 + x} \right)^{27/5}}$$ is

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The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

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The number of integral terms in the expansion of $${\left( {\sqrt 3 + \root 8 \of 5 } \right)^{256}}$$ is

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A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five

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If $${}^n{C_r}$$ denotes the number of combination of n things taken r at a time, then the expression $$\,{}^n{C_{r + 1}

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The sum of the serier $${1 \over {1.2}} - {1 \over {2.3}} + {1 \over {3.4}}..............$$ up to $$\infty $$ is equal t

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A square of side a lies above the $$x$$-axis and has one vertex at the origin. The side passing through the origin makes

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If the pair of straight lines $${x^2} - 2pxy - {y^2} = 0$$ and $${x^2} - 2qxy - {y^2} = 0$$ be such that each pair bisec

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If $${x_1},{x_2},{x_3}$$ and $${y_1},{y_2},{y_3}$$ are both in G.P. with the same common ratio, then the points $$\left(

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Locus of centroid of the triangle whose vertices are $$\left( {a\cos t,a\sin t} \right),\left( {b\sin t, - b\cos t} \rig

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If the equation of the locus of a point equidistant from the point $$\left( {{a_{1,}}{b_1}} \right)$$ and $$\left( {{a_{

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If the two circles $${(x - 1)^2}\, + \,{(y - 3)^2} = \,{r^2}$$ and $$\,{x^2}\, + \,{y^2} - \,8x\, + \,2y\, + \,\,8\,\, =

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The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the c

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The normal at the point$$\left( {bt_1^2,2b{t_1}} \right)$$ on a parabola meets the parabola again in the point $$\left(

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The foci of yhe ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$$ and the hyperbola $${{{x^2}} \over {144}}

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If $$f\left( y \right) = {e^y},$$ $$g\left( y \right) = y;y > 0$$ and
$$F\left( t \right) = \int\limits_0^t {f\left(

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If $$f\left( x \right) = {x^n},$$ then the value of
$$f\left( 1 \right) - {{f'\left( 1 \right)} \over {1!}} + {{f''\lef

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Let $$f\left( x \right)$$ be a polynomial function of second degree. If $$f\left( 1 \right) = f\left( { - 1} \right)$$

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The sum of the radii of inscribed and circumscribed circles for an $$n$$ sided regular polygon of side $$a, $$ is

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In a triangle $$ABC$$, medians $$AD$$ and $$BE$$ are drawn. If $$AD=4$$,
$$\angle DAB = {\pi \over 6}$$ and $$\angle A

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If in a $$\Delta ABC$$ $$a\,{\cos ^2}\left( {{C \over 2}} \right) + c\,{\cos ^2}\left( {{A \over 2}} \right) = {{3b} \ov

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The trigonometric equation $${\sin ^{ - 1}}x = 2{\sin ^{ - 1}}a$$ has a solution for

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If the function $$f\left( x \right) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1,$$ where $$a>0,$$ attains its maximum and minim

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If $$A = \left[ {\matrix{
a & b \cr
b & a \cr
} } \right]$$ and $${A^2} = \left[ {\matrix{
\alpha

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If $$1,$$ $$\omega ,{\omega ^2}$$ are the cube roots of unity, then
$$\Delta = \left| {\matrix{
1 & {{\omega ^

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If the system of linear equations
$$x + 2ay + az = 0;$$ $$x + 3by + bz = 0;\,\,x + 4cy + cz = 0;$$
has a non - zero so

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The area of the region bounded by the curves $$y = \left| {x - 1} \right|$$ and $$y = 3 - \left| x \right|$$ is

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Let $$f(x)$$ be a function satisfying $$f'(x)=f(x)$$ with $$f(0)=1$$ and $$g(x)$$ be a function that satisfies $$f\left(

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If $$f\left( {a + b - x} \right) = f\left( x \right)$$ then $$\int\limits_a^b {xf\left( x \right)dx} $$ is equal to

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The value of the integral $$I = \int\limits_0^1 {x{{\left( {1 - x} \right)}^n}dx} $$ is

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The solution of the differential equation
$$\left( {1 + {y^2}} \right) + \left( {x - {e^{{{\tan }^{ - 1}}y}}} \right){{

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The degree and order of the differential equation of the family of all parabolas whose axis is $$x$$-axis, are respectiv

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Events $$A, B, C$$ are mutually exclusive events such that $$P\left( A \right) = {{3x + 1} \over 3},$$ $$P\left( B \righ

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The mean and variance of a random variable $$X$$ having binomial distribution are $$4$$ and $$2$$ respectively, then $$P

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Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A select

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Let $$\overrightarrow u = \widehat i + \widehat j,\,\overrightarrow v = \widehat i - \widehat j$$ and $$\overrightarro

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The vectors $$\overrightarrow {AB} = 3\widehat i + 4\widehat k\,\,\& \,\,\overrightarrow {AC} = 5\widehat i - 2\wi

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The shortest distance from the plane $$12x+4y+3z=327$$ to the sphere $${x^2} + {y^2} + {z^2} + 4x - 2y - 6z = 155$$ is

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The two lines $$x=ay+b,z=cy+d$$ and $$x = a'y + b',z = c'y + d'$$ will be perpendicular, if and only if

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The lines $${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$ and $${{x - 1} \over k} = {{y - 4} \over 2}

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$$\overrightarrow a \,,\overrightarrow b \,,\overrightarrow c $$ are $$3$$ vectors, such that $$\overrightarrow a + \o

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The radius of the circle in which the sphere
$${x^2} + {y^2} + {z^2} + 2x - 2y - 4z - 19 = 0$$ is cut by the plane
$$x

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A tetrahedron has vertices at $$O(0,0,0), A(1,2,1) B(2,1,3)$$ and $$C(-1,1,2).$$ Then the angle between the faces $$OAB$

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If $$\left| {\matrix{
a & {{a^2}} & {1 + {a^3}} \cr
b & {{b^2}} & {1 + {b^3}} \cr
c & {

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Consider points $$A, B, C$$ and $$D$$ with position
vectors $$7\widehat i - 4\widehat j + 7\widehat k,\widehat i - 6\wi

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If $$\overrightarrow u \,,\overrightarrow v $$ and $$\overrightarrow w $$ are three non-coplanar vectors, then $$\,\left

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Two systems of rectangular axes have the same origin. If a plane cuts then at distances $$a,b,c$$ and $$a', b', c'$$ fro

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The function $$f\left( x \right)$$ $$ = \log \left( {x + \sqrt {{x^2} + 1} } \right)$$, is

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A function $$f$$ from the set of natural numbers to integers defined by
$$$f\left( n \right) = \left\{ {\matrix{
{{{n

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If $$f:R \to R$$ satisfies $$f$$(x + y) = $$f$$(x) + $$f$$(y), for all x, y $$ \in $$ R and $$f$$(1) = 7, then $$\sum\li

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Domain of definition of the function f(x) = $${3 \over {4 - {x^2}}}$$ + $${\log _{10}}\left( {{x^3} - x} \right)$$, is

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$$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^4} + {3^4} + .... + {n^4}} \over {{n^5}}}$$ - $$\mathop {\lim }\limits

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The value of $$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {{{\sec }^2}tdt} } \over xsinx}$$ is

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If $$\mathop {\lim }\limits_{x \to 0} {{\log \left( {3 + x} \right) - \log \left( {3 - x} \right)} \over x}$$ = k, the v

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Let $$f(a) = g(a) = k$$ and their nth derivatives
$${f^n}(a)$$, $${g^n}(a)$$ exist and are not equal for some n. Further

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$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\left[ {1 - \tan \left( {{x \over 2}} \right)} \right]\left[ {1 - \sin

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If $$f(x) = \left\{ {\matrix{
{x{e^{ - \left( {{1 \over {\left| x \right|}} + {1 \over x}} \right)}}} & {,x \ne 0

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In an experiment with 15 observations on $$x$$, then following results were available:
$$\sum {{x^2}} = 2830$$, $$\sum

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The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of
the set is increased by

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## Physics

Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are

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The physical quantities not having same dimensions are

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A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the
same car is moving at a spee

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A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an
angle of $$30^\circ $$ with

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The co-ordinates of a moving particle at any time 't' are given by x = $$\alpha $$t3 and y = βt3. The speed to the parti

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A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $$49$$ $$N

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A light spring balance hangs from the hook of the other light spring balance and a block of mass $$M$$ $$kg$$ hangs from

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A marble block of mass $$2$$ $$kg$$ lying on ice when given a velocity of $$6$$ $$m/s$$ is stopped by friction in $$10$$

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A block of mass $$M$$ is pulled along a horizontal frictionless surface by a rope of mass $$m.$$ If a force $$P$$ is app

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A rocket with a lift-off mass $$3.5 \times {10^4}\,\,kg$$ is blasted upwards with an initial acceleration of $$10m/{s^2}

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Consider the following two statements:
$$A.$$$$\,\,\,\,\,\,$$ Linear momentum of a system of particles is zero
$$B.$$$$

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A spring of spring constant $$5 \times {10^3}\,N/m$$ is stretched initially by $$5$$ $$cm$$ from the unstretched positio

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A wire suspended vertically from one of its ends is stretched by attaching a weight of $$200N$$ to the lower end. The we

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A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $

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A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the

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A circular disc $$X$$ of radius $$R$$ is made from an iron plate of thickness $$t,$$ and another disc $$Y$$ of radius $

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Let $$\overrightarrow F $$ be the force acting on a particle having position vector $$\overrightarrow r ,$$ and $$\over

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The time period of satellite of earth is $$5$$ hours. If the separation between the earth and the satellite is increased

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The escape velocity for a body projected vertically upwards from the surface of earth is $$11$$ $$km/s.$$ If the body is

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Two spherical bodies of mass $$M$$ and $$5M$$ & radii $$R$$ & $$2R$$ respectively are released in free space wit

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Three forces start acting simultaneously on a particle moving with velocity, $$\overrightarrow v \,\,.$$ These forces ar

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A horizontal force of $$10$$ $$N$$ is necessary to just hold a block stationary against a wall. The coefficient of frict

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''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or conseq

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During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature.

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Which of the following parameters does not characterize the thermodynamic state of mattter?

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A carnot engine takes $$3 \times {10^6}$$ cal. of heat from a reservoir at $${627^ \circ }C,$$ and gives it to a sink at

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According to Newton's law of cooling, the rate of cooling of a body is proportional to $${\left( {\Delta \theta } \right

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The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

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A mass $$M$$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the

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Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring of spring constant $${k

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The displacement of particle varies according to the relation
$$x=4$$$$\left( {\cos \,\pi t + \sin \,\pi t} \right).$$

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The length of a simple pendulum executing simple harmonic motion is increased by $$21\% $$. The percentage increase in t

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A body executes simple harmonic motion. The potential energy $$(P.E),$$ the kinetic energy $$(K.E)$$ and total energy $$

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A metal wire of linear mass density of $$9.8$$ $$g/m$$ is stretched with a tension of $$10$$ $$kg$$-$$wt$$ between two r

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The displacement $$y$$ of a wave travelling in the $$x$$-direction is given by
$$$y = {10^{ - 4}}\,\sin \left( {600t -

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A tuning fork of known frequency $$256$$ $$Hz$$ makes $$5$$ beats per second with the vibrating string of a piano. The b

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If the electric flux entering and leaving an enclosed surface respectively is $${\phi _1}$$ and $${\phi _2},$$ the elect

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A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of th

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A thin spherical conducting shell of radius $$R$$ has a charge $$q.$$ Another charge $$Q$$ is placed at the center of th

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The work done in placing a charge of $$8 \times {10^{ - 18}}$$ coulomb on a condenser of capacity $$100$$ micro-farad is

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Three charges $$ - {q_1}, + {q_2}$$ and $$ - {q_3}$$ are placed as shown in the figure. The $$x$$-component of the force

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The length of a given cylindrical wire is increased by $$100\% $$. Due to the consequent decrease in diameter the change

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The length of a wire of a potentiometer is $$100$$ $$cm$$, and the $$e.$$ $$m.$$ $$f.$$ of its standard cell is $$E$$ vo

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The thermo $$e.m.f.$$ of a thermo -couple is $$25$$ $$\mu V/{}^ \circ C$$ at room temperature. A galvanometer of $$40$$

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An ammeter reads upto $$1$$ ampere. Its internal resistance is $$0.81$$ $$ohm$$. To increase the range to $$10$$ $$A$$ t

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The nagative $$Zn$$ pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by $$0.13g$$

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A $$3$$ volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current $

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A $$220$$ volt, $$1000$$ watt bulb is connected across a $$110$$ $$volt$$ mains supply. The power consumed will be

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A thin rectangular magnet suspended freely has a period of oscillation equal to $$T.$$ Now it is broken into two equal h

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A particle of mass $$M$$ and charge $$Q$$ moving with velocity $$\overrightarrow v $$ describe a circular path of radius

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A particle of charge $$ - 16 \times {10^{ - 18}}$$ coulomb moving with velocity $$10m{s^{ - 1}}$$ along the $$x$$-axis e

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A magnetic needle lying parallel to a magnetic field requires $$W$$ units of work to turn it through $${60^ \circ }.$$ T

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The magnetic lines of force inside a bar magnet

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Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

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In an oscillating $$LC$$ circuit the maximum charge on the capacitor is $$Q$$. The charge on the capacitor when the ener

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When the current changes from $$ + 2A$$ to $$-2A$$ in $$0.05$$ second, an $$e.m.f.$$ of $$8$$ $$V$$ is inducted in a coi

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The core of any transformer is laminated so as to

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Consider telecommunication through optical fibres. Which of the following statements is not true?

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To demonstrate the phenomenon of interference, we require two sources which emit radiation

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To get three images of a single object, one should have two plane mirrors at an angle of

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The image formed by an objective of a compound microscope is

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A strip of copper and another of germanium are cooled from room temperature to $$80K.$$ The resistance of

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Which of the following radiations has the least wavelength ?

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When a $${U^{238}}$$ nucleus originally at rest, decays by emitting an alpha particle having a speed $$'u',$$ the recoil

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The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to

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A radioactive sample at any instant has its disintegration rate $$5000$$ disintegrations per minute. After $$5$$ minutes

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A nucleus with $$Z=92$$ emits the following in a sequence:
$$$\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,\alpha ,\alpha

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Which of the following atoms has the lowest ionization potential ?

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The wavelengths involved in the spectrum of deuterium $$\left( {{}_1^2\,D} \right)$$ are slightly different from that of

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In the nuclear fusion reaction
$$${}_1^2H + {}_1^3H \to {}_2^4He + n$$$
given that the repulsive potential energy betwe

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Which of the following cannot be emitted by radioactive substances during their decay ?

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In the middle of the depletion layer of a reverse- biased $$p$$-$$n$$ junction, the

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Two identical photo-cathodes receive light of frequencies $${f_1}$$ and $${f_2}$$. If the velocities of the photo electr

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If the binding energy of the electron in a hydrogen atom is $$13.6eV,$$ the energy required to remove the electron from

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