AIEEE 2004

Paper was held on
Sat, Apr 24, 2004 9:30 AM

## Chemistry

6.02 $$\times$$ 1020 molecules of urea are present in 100 ml of its solution. The concentration of urea solution is (Avo

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To neutralise completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H3PO3), the volume of 0.1 M aqueous KOH so

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The ammonia evolved from the treatment of 0.30 g of an organic compound for the estimation of nitrogen was passed in 100

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Which of the following sets of quantum numbers is correct for an electron in 4f orbital?

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Consider the ground state of Cr atom (Z = 24). The number of electrons with the azimuthal quantum numbers, l = 1 and 2 a

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The wavelength of the radiation emitted when in a hydrogen atom electron falls from infinity to stationary state 1, woul

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Which one of the following sets of ions represents the collection of isoelectronic species? (Atomic nos. : F = 9, Cl = 1

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Which one of the following ions has the highest value of ionic radius?

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Among Al2O3, SiO2, P2O3 and SO2 the correct order of acid strength is

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The formation of the oxide ion O2-(g) requires first an exothermic and then an endothermic
step as shown below
O(g) + e

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The correct order of bond angles (smallest first) in H2S, NH3, BF3 and SiH4 is

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The bond order in NO is 2.5 while that in NO+ is 3. Which of the following statements is true for these two species?

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The states of hybridization of boron and oxygen atoms in boric acid (H3BO3) are respectively

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Which one of the following has the regular tetrahedral structure?
(Atomic nos : B = 5, S = 16, Ni = 28, Xe = 54)

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The maximum number of 90° angles between bond pair of electrons is observed in

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As the temperature is raised from 20°C to 40°C, the average kinetic energy of neon atoms
changes by a factor of which of

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In Van der Waals equation of state of the gas law, the constant ‘b’ is a measure of

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An ideal gas expands in volume from 1$$\times$$10-3 m3 to 1 $$\times$$ 10-2 m3 at 300 K against a constant pressure of 1

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The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 kJ mol-1
respectively. The enthalpy of fo

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The conjugate base of H2PO4- is :

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What is the equilibrium expression for the reaction
P4 (s) + 5O2 $$\leftrightharpoons$$ P4O10 (s)?

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For the reaction, CO(g) + Cl2(g) $$\leftrightharpoons$$ COCl2(g) the $${{{K_p}} \over {{K_c}}}$$ is equal to :

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The equilibrium constant for the reaction N2(g) + O2(g) $$\leftrightharpoons$$ 2NO(g) at temperature T is
4 $$\times$$ 1

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The molar solubility (in ol L-1) of a sparingly soluble salt MX4 is "s". The corresponding solubility product is Ksp. 's

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One mole of magnesium nitride on the reaction with an excess of water gives :

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Which one of the following has the minimum boiling point?

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Which one the following does not have sp2 hybridized carbon?

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Which of the following compound is not chiral?

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Consider the acidity of the carboxylic acids:
(a) PhCOOH
(b) o – NO2C6H4COOH
(c) p – NO2C6H4COOH
(d) m – NO2C6H4COOH

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Which of the following will have meso-isomer also?

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Identify the correct statements regarding enzymes

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For which of the following parameters the structural isomers C2H5OH and CH3OCH3 would
be expected to have the same value

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Which of the following liquid pairs shows a positive deviation from Raoult’s law?

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Which one of the following aqueous solutions will exhibit highest boiling point?

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Which one of the following statements is false?

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In a hydrogen – oxygen fuel cell, combustion of hydrogen occurs to :

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Consider the following Eo values
$$E_{F{e^{3 + }}/F{e^{2 + }}}^o$$ = 0.77 V;
$$E_{S{n^{2 + }}/S{n}}^o$$ = -0.14 V
Under

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The standard e.m.f of a cell, involving one electron change is found to be 0.591 V at 25oC.
The equilibrium constant of

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The limiting molar conductivities Λ° for NaCl, KBr and KCl are 126, 152 and 150 S cm2 mol-1 respectively. The Λ° for NaB

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In a cell that utilises the reaction Zn(s) + 2H+
(aq) $$\to$$ Zn2+(aq) + H2(g) addition of H2SO4 to cathode compartment,

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The $$E_{{M^{3 + }}/{M^{2 + }}}^o$$ values for Cr, Mn, Fe and Co are – 0.41, +1.57, + 0.77 and +1.97 V
respectively. Fo

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In a first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15
minutes. The time taken

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The rate equation for the reaction 2A + B $$\to$$ C is found to be: rate k[A][B]. The correct
statement in relation to t

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Consider the following nuclear reactions
$${}_{92}^{238}M \to {}_Y^XN + 2{}_2^4He$$
$${}_Y^XN \to {}_B^AL + 2{\beta ^ +

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The half – life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the
mass remaining after

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Which one of the following ores is best concentrated by froth – floatation method?

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Which among the following factors is the most important in making fluorine the strongest
oxidizing halogen?

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Beryllium and aluminium exhibit many properties which are similar. But the two elements
differ in :

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Which one the following statement regarding helium is incorrect?

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Excess of KI reacts with CuSO4 solution and then Na2S2O3 solution is added to it. Which of the statements is incorrect f

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Aluminium chloride exists as dimer, Al2Cl6 in solid state as well as in solution of non-polar
solvents such as benzene.

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Cerium (Z = 58) is an important member of the lanthanoids. Which of the following
statements about cerium is incorrect?

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Which one of the following complexes in an outer orbital complex?

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Coordination compound have great importance in biological systems. In this context which of
the following statements is

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Which one the following has largest number of isomers? (R = alkyl group, en = ethylenediamine)

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The coordination number of central metal atom in a complex is determined by :

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The correct order of magnetic moments (spin only values in B.M.) among is :
(Atomic numbers: Mn = 25; Fe = 26, Co =27)

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Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN– ion
towards metal spe

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The compound formed on heating chlorobenzene with chloral in the presence concentrated
sulphuric acid is

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On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant
solution is

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Which of the following undergoes reaction with 50% sodium hydroxide solution to give the
corresponding alcohol and acid?

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Which one of the following reduced with zinc and hydrochloric acid to give the corresponding
hydrocarbon?

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Acetyl bromide reacts with excess of CH3MgI followed by treatment with a saturated solution
of NH4Cl given

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Which base is present in RNA but not in DNA?

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Insulin production and its action in human body are responsible for the level of diabetes. This
compound belongs to whic

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The smog is essentially caused by the presence of :

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The compound formed in the positive test for nitrogen with the Lassaigne solution of an
organic compound is

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Which of the following is the strongest base ?

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Amongst the following compounds, the optically active alkane having lowest molecular mass is

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Rate of the reaction
is fastest when $$Z$$ is

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The $$IUPAC$$ name of the compound is

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What type of crystal defect is indicated in the diagram below?

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Among the following compounds which can be dehydrated very easily is

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Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?

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The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin butt

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## Mathematics

Let $$\alpha ,\,\beta $$ be such that $$\pi < \alpha - \beta < 3\pi $$.
If $$sin{\mkern 1mu} \alpha + \sin \be

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If $$u = \sqrt {{a^2}{{\cos }^2}\theta + {b^2}{{\sin }^2}\theta } + \sqrt {{a^2}{{\sin }^2}\theta + {b^2}{{\cos }^2}

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A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis.
If the angle $$\beta \,$$, which it mak

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Let z and w be complex numbers such that $$\overline z + i\overline w = 0$$ and arg zw = $$\pi $$. Then arg z equals :

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If $$z = x - iy$$ and $${z^{{1 \over 3}}} = p + iq$$, then
$${{\left( {{x \over p} + {y \over q}} \right)} \over {\left

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If $$\,\left| {{z^2} - 1} \right| = {\left| z \right|^2} + 1$$, then z lies on :

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Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

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If $$\left( {1 - p} \right)$$ is a root of quadratic equation $${x^2} + px + \left( {1 - p} \right) = 0$$ then its ro

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If one root of the equation $${x^2} + px + 12 = 0$$ is 4, while the equation $${x^2} + px + q = 0$$ has equal roots,
t

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How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

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Let $$S(K)$$ $$ = 1 + 3 + 5... + \left( {2K - 1} \right) = 3 + {K^2}.$$ Then which of the following is true

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The coefficient of the middle term in the binomial expansion in powers of $$x$$ of $${\left( {1 + \alpha x} \right)^4}$$

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The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

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The coefficient of $${x^n}$$ in expansion of $$\left( {1 + x} \right){\left( {1 - x} \right)^n}$$ is

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Let $${{T_r}}$$ be the rth term of an A.P. whose first term is a and common difference is d. If for some positive intege

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If $${S_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}}} \,\,and\,\,{t_n} = \sum\limits_{r = 0}^n {{r \over {{}^n{C_r}

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The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + ....\,is\,{{n{{(n + 1

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The sum of series $${1 \over {2\,!}} + {1 \over {4\,!}} + {1 \over {6\,!}} + ........$$ is

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The equation of the straight line passing through the point $$(4, 3)$$ and making intercepts on the co-ordinate axes who

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Let $$A\left( {2, - 3} \right)$$ and $$B\left( {-2, 1} \right)$$ be vertices of a triangle $$ABC$$. If the centroid of

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If the sum of the slopes of the lines given by $${x^2} - 2cxy - 7{y^2} = 0$$ is four times their product $$c$$ has the v

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If one of the lines given by $$6{x^2} - xy + 4c{y^2} = 0$$ is $$3x + 4y = 0,$$ then $$c$$ equals :

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A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter

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If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference $$10\,\pi $$, then the e

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If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = 4$$ orthogonally, then the locus o

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Intercept on the line y = x by the circle $${x^2}\, + \,{y^2} - 2x = 0$$ is AB. Equation of the circle on AB as a diamet

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If $$a \ne 0$$ and the line $$2bx+3cy+4d=0$$ passes through the points of intersection of the parabolas $${y^2} = 4ax$$

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The eccentricity of an ellipse, with its centre at the origin, is $${1 \over 2}$$. If one of the directrices is $$x=4$$,

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If $$x = {e^{y + {e^y} + {e^{y + .....\infty }}}}$$ , $$x > 0,$$ then $${{{dy} \over {dx}}}$$ is

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A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank

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The sides of a triangle are $$\sin \alpha ,\,\cos \alpha $$ and $$\sqrt {1 + \sin \alpha \cos \alpha } $$ for some $$0 &

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A point on the parabola $${y^2} = 18x$$ at which the ordinate increases at twice the rate of the abscissa is

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A function $$y=f(x)$$ has a second order derivative $$f''\left( x \right) = 6\left( {x - 1} \right).$$ If its graph pass

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If $$2a+3b+6c=0$$, then at least one root of the equation
$$a{x^2} + bx + c = 0$$ lies in the interval

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The normal to the curve x = a(1 + cos $$\theta $$), $$y = a\sin \theta $$ at $$'\theta '$$ always passes through the fix

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Let $$A = \left( {\matrix{
1 & { - 1} & 1 \cr
2 & 1 & { - 3} \cr
1 & 1 & 1 \cr

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Let $$A = \left( {\matrix{
0 & 0 & { - 1} \cr
0 & { - 1} & 0 \cr
{ - 1} & 0 & 0 \c

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If $${a_1},{a_2},{a_3},.........,{a_n},......$$ are in G.P., then the value of the determinant
$$\left| {\matrix{
{\

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If $$\int {{{\sin x} \over {\sin \left( {x - \alpha } \right)}}dx = Ax + B\log \sin \left( {x - \alpha } \right), + C,}

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$$\int {{{dx} \over {\cos x - \sin x}}} $$ is equal to

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$$\mathop {Lim}\limits_{n \to \infty } \sum\limits_{r = 1}^n {{1 \over n}{e^{{r \over n}}}} $$ is

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The value of $$I = \int\limits_0^{\pi /2} {{{{{\left( {\sin x + \cos x} \right)}^2}} \over {\sqrt {1 + \sin 2x} }}dx} $$

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The value of $$\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx} $$ is

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If $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} } $$ then

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If $$f\left( x \right) = {{{e^x}} \over {1 + {e^x}}},{I_1} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {x

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The area of the region bounded by the curves
$$y = \left| {x - 2} \right|,x = 1,x = 3$$ and the $$x$$-axis is :

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The differential equation for the family of circle $${x^2} + {y^2} - 2ay = 0,$$ where a is an arbitrary constant is :

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Solution of the differential equation $$ydx + \left( {x + {x^2}y} \right)dy = 0$$ is

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The mean and the variance of a binomial distribution are $$4$$ and $$2$$ respectively. Then the probability of $$2$$ suc

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The probability that $$A$$ speaks truth is $${4 \over 5},$$ while the probability for $$B$$ is $${3 \over 4}.$$ The pro

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A particle acted on by constant forces $$4\widehat i + \widehat j - 3\widehat k$$ and $$3\widehat i + \widehat j - \wide

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Distance between two parallel planes
$$\,2x + y + 2z = 8$$ and $$4x + 2y + 4z + 5 = 0$$ is :

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Let $$\overrightarrow u ,\overrightarrow v ,\overrightarrow w $$ be such that $$\left| {\overrightarrow u } \right| = 1,

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A line with direction cosines proportional to $$2,1,2$$ meets each of the lines $$x=y+a=z$$ and $$x+a=2y=2z$$ . The co-

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If $${\overrightarrow a ,\overrightarrow b ,\overrightarrow c }$$ are non-coplanar vectors and $$\lambda $$ is a real nu

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The intersection of the spheres
$${x^2} + {y^2} + {z^2} + 7x - 2y - z = 13$$ and
$${x^2} + {y^2} + {z^2} - 3x + 3y + 4z

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Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be non-zero vectors such that $$\left( {\overri

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If the straight lines
$$x=1+s,y=-3$$$$ - \lambda s,$$ $$z = 1 + \lambda s$$ and $$x = {t \over 2},y = 1 + t,z = 2 - t,$

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Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be three non-zero vectors such that no two of t

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The range of the function f(x) = $${}^{7 - x}{P_{x - 3}}$$ is

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If $$f:R \to S$$, defined by
$$f\left( x \right) = \sin x - \sqrt 3 \cos x + 1$$,
is onto, then the interval of $$S$$ is

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The graph of the function y = f(x) is symmetrical about the line x = 2, then

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The domain of the function
$$f\left( x \right) = {{{{\sin }^{ - 1}}\left( {x - 3} \right)} \over {\sqrt {9 - {x^2}} }}$$

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Let $$f(x) = {{1 - \tan x} \over {4x - \pi }}$$, $$x \ne {\pi \over 4}$$, $$x \in \left[ {0,{\pi \over 2}} \right]$$.

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If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$$, then

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Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of

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In a series of 2n observations, half of them equal $$a$$ and remaining half equal $$–a$$. If the
standard deviation of t

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Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ is :

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## Physics

Which one of the following represents the correct dimensions of the coefficient of viscosity?

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A ball is released from the top of a tower of height h meters. It takes T seconds to reach the
ground. What is the posit

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If $$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $$, then the angle beetw

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A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time
of flights in the two ca

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Which of the following statements is FALSE for a particle moving in a circle with a constant
angular speed?

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An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m.
If the car is going twice a

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A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point
and at the same instant p

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Two masses $${m_1} = 5kg$$ and $${m_2} = 4.8kg$$ tied to a string are hanging over a light frictionless pulley. What is

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A block rests on a rough inclined plane `making an angle of $${30^ \circ }$$ with the horizontal. The coefficient of sta

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A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for an

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A uniform chain of length $$2$$ $$m$$ is kept on a table such that a length of $$60$$ $$cm$$ hangs freely from the edge

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A force $$\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j + 2\overrightarrow k } \right)N$$ is ap

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A body of mass $$' m ',$$ acceleration uniformly from rest to $$'{v_1}'$$ in time $${T}$$. The instantaneous power deliv

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A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle,

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A machine gun fires a bullet of mass $$40$$ $$g$$ with a velocity $$1200m{s^{ - 1}}.$$ The man holding it can exert a m

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One solid sphere $$A$$ and another hollow sphere $$B$$ are of same mass and same outer radii. Their moment of inertia ab

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A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which on of the fol

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A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height $$x$$ from its surface. If $$g$$ is the

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If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mas

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The time period of an earth satellite in circular orbit is independent of

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Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circu

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A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is

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If two soap bubbles of different radii are connected by a tube

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Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta $$ with a velocity $$v.$$ The retardi

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One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with one mole of diatomic gas $$\left( {\gam

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If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio

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Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatures $$\left( {{T_1},{T_2}} \right),$$ vo

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Which of the following statements is correct for any thermodynamic system ?

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The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of therma

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The bob of a simple pendulum executes simple harmonic motion in water with a period $$t,$$ while the period of oscillati

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A particle at the end of a spring executes $$S.H.M$$ with a period $${t_1}$$. While the corresponding period for another

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The total energy of particle, executing simple harmonic motion is

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A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and has a natural angular frequency $${\omeg

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In forced oscillation of a particle the amplitude is maximum for a frequency $${\omega _1}$$ of the force while the ener

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The displacement $$y$$ of a particle in a medium can be expressed as, $$y = {10^{ - 6}}\,\sin $$ $$\left( {100t + 20x +

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Two spherical conductors $$B$$ and $$C$$ having equal radii and carrying equal charges on them repel each other with a f

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A charge particle $$'q'$$ is shot towards another charged particle $$'Q'$$ which is fixed, with a speed $$'v'$$. It appr

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Four charges equal to -$$Q$$ are placed at the four corners of a square and a charge $$q$$ is at its center. If the sys

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A charged oil drop is suspended in a uniform field of $$3 \times {10^4}$$ $$v/m$$ so that it neither falls nor rises. T

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The resistance of the series combination of two resistances is $$S.$$ When they are jointed in parallel the total resist

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An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the

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The total current supplied to the circuit by the battery is

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Time taken by a $$836$$ $$W$$ heater to heat one litre of water from $$10{}^ \circ C$$ to $$40{}^ \circ C$$ is

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In a meter bridge experiment null point is obtained at $$20$$ $$cm$$, from one end of the wire when resistance $$X$$ is

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Thermistors are usually made of

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The electrochemical equivalent of a metal is $${3.35109^{ - 7}}$$ $$kg$$ per Coulomb. The mass of the metal liberated at

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The thermo $$emf$$ of a thermocouple varies with temperature $$\theta $$ of the hot junction as $$E = a\theta + b{\the

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The Kirchhoff's first law $$\left( {\sum i = 0} \right)$$ and second law $$\left( {\sum iR = \sum E} \right),$$ where th

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A material $$'B'$$ has twice the specific resistance of $$'A'.$$ A circular wire made of $$'B'$$ has twice the diameter

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Curie temperature is the temperature above which

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A current $$i$$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any poin

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A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the c

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The magnetic field due to a current carrying circular loop of radius $$3$$ $$cm$$ at a point on the axis at a distance o

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The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration mag

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Two long conductors, separated by a distance $$d$$ carry current $${I_1}$$ and $${I_2}$$ in the same direction. They exe

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The materials suitable for making electromagnets should have

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Alternating current can not be measured by $$D.C.$$ ammeter because

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In an $$LCR$$ series $$a.c.$$ circuit, the voltage across each of the components, $$L,C$$ and $$R$$ is $$50V$$. The volt

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A coil having $$n$$ turns and resistance $$R\Omega $$ is connected with a galvanometer of resistance $$4R\Omega .$$ This

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In a uniform magnetic field of induction $$B$$ a wire in the form of a semicircle of radius $$r$$ rotates about the diam

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A metal conductor of length $$1$$ $$m$$ rotates vertically about one of its ends at angular velocity $$5$$ radians per

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In a $$LCR$$ circuit capacitance is changed from $$C$$ to $$2$$ $$C$$. For the resonant frequency to remain unchaged, th

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A plano convex lens of refractive index $$1.5$$ and radius of curvature $$30$$ $$cm$$. Is silvered at the curved surface

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The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index

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An electromagnetic wave of frequency $$v=3.0$$ $$MHz$$ passes from vacuum into a dielectric medium with permittivity $$

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The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-s

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The work function of a substance is $$4.0$$ $$eV.$$ The longest wavelength of light that can cause photo-electron emiss

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A radiation of energy $$E$$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

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According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a met

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An $$\alpha $$-particle of energy $$5$$ $$MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The d

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The binding energy per nucleon of deuteron $$\left( {{}_1^2\,H} \right)$$ and helium nucleus $$\left( {{}_2^4\,He} \righ

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A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $$2:1.$$ The ratio of their n

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When $$npn$$ transistor is used as an amplifer

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For a transistor amplifier in common emitter configuration for load impedance of $$1k\,\Omega $$ $$\left( {{h_{fe}} = 50

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A piece of copper and another of germanium are cooled from room temperature to $$77K,$$ the resistance of

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The manifestation of band structure in solids is due to

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When $$p$$-$$n$$ junction diode is forward biased then

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A light ray is incident perpendicularly to one face of a $${90^ \circ }$$ prism and is totally internally reflected at t

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