AIEEE 2002

Paper was held on
Sat, Apr 27, 2002 9:30 AM

## Chemistry

With increase of temperature, which of these changes?

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In a compound C, H and N atoms are present in 9 : 1 : 3.5 by weight . Molecular weight of the compound is 108 g mol-1 .

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Number of atoms in 558.5 gram Fe (at. wt. of Fe = 55.85 g mol-1) is

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In a hydrogen atom, if energy of an electron in ground state is -13.6 eV, then that in the 2nd excited state is

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Uncertainty in position of a minute particle of mass 25 g in space is 10-5 m. What is the uncertainty in its velocity (i

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In which of the following species the interatomic bond angle is 109o28' ?

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Hybridisation of underline atom changes in

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Which of the following are arranged in an increasing order of their bond strengths?

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For an ideal gas, number of moles per litre in terms of its pressure P, gas constant R and temperature T is

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Value of gas constant R is

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Kinetic theory of gases proves

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If an endothermic reaction is non-spontaneous at freezing point of water and becomes feasible at its boiling point, then

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For the reactions
2C + O2 $$\to$$ 2CO2; $$\Delta H$$ = -393 J
2Zn + O2 $$\to$$ 2ZnO; $$\Delta H$$ = -412 J

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The heat required to raise the temperature of body by 1 K is called :

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A heat engine absorbs heat Q1 at temperature T1 and heat Q2 at temperature T2. Work done by the engine is J (Q1 + Q2). T

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1 M NaCL and 1 M HCL are present in an aqueous solution. The solution is

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Species acting as both Bronsted acid and base is :

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Let the solubility of an aqueous solution of Mg(OH)2 be x then its Ksp is :

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Change in volume of the system does not alter which of the following equilibria?

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For the reaction CO (g) + (1/2) O2 (g) $$\leftrightharpoons$$ CO2 (g), Kp/Kc is :

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KO2 (potassium super oxide) is used in oxygen cylinders in space and submarines because it :

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The metallic sodium disolves in liquid ammonia to form a deep blue coloured solution. The deep blue colour is due to for

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A metal M readily forms its sulphate MSO4, which is water-soluble. It forms its oxide MO which becomes inert on heating.

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Which of the following does not show geometrical isomerism?

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A similarity between optical and geometrical isomerism is that

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The functional group, which is found in amino acid is

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Arrangement of (CH3)3C-, (CH3)2CH-, CH3-CH2- when attached to benzyl or an unsaturated group in increasing order of indu

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Racemic mixture is formed by mixing two

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The reaction :
$${(CH)_3}C - Br\buildrel {{H_2}O} \over
\longrightarrow {(CH)_3}C - OH$$

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In which of the following species is the underlined carbon having sp3 hybridisation?

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What is the product when acetylene reacts with hypochlorous acid ?

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Which of these will not react with acetylene ?

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Na and Mg crystallize in BCC and FCC type crystals respectively, then the number of atoms of
Na and Mg present in the un

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The formation of gas at the surface of tungsten due to adsorption is the reaction of order :

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In a mixture of A and B, components show negative deviation when :

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Freezing point of an aqueous solution is (-0.186)oC. Elevation of boiling point of the same solution is Kb = 0.512 oC, K

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Conductivity (Seimen’s S) is directly proportional to area of the vessel and the concentration
of the solution in it and

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For the following cell with hydrogen electrodes at two different pressure p1 and p2. What will be the emf for the given

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EMF of a cell in terms of reduction potential of its left and right electrodes is :

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Which of the following reaction is possible at anode?

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When the sample of copper with zinc impurity is to be purified by electrolysis, the appropriate
electrodes are :

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Which of the following is a redox reaction ?

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Units of rate constant of first and zero order reactions in terms of molarity M unit are respectively

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For the reaction A + 2B $$\to$$ C, rate is given by R = [A] [B]2 then the order of the reaction is

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The differential rate law for the reaction H2 + I2 $$\to$$ 2HI is

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If half-life of a substance is 5 yrs, then the total amount of substance left after 15 years, when initial amount is 64

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The integrated rate equation is Rt = log C0 - log Ct . The straight line graph is obtained by
plotting

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$$\beta$$ - particle is emitted in radioactivity by

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Aluminium is extracted by the electrolysis of

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The metal extracted by leaching with a cyanide is

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Alum helps in purifying water by :

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In XeF2, XeF4, XeF6 the number of lone pairs of Xe are respectively :

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Which of the following statements is true?

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Number of sigma bonds in P4O10 is :

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In case of nitrogen, NCl3 is possible but not NCl5 while in case of phosphorous, PCl3 as well as
PCl5 are possible. It i

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Oxidation number of Cl in CaOCl2 (bleaching powder) is :

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When KMnO4 acts as an oxidising agent and ultimately forms [MnO4]-2, MnO2, Mn2O3, Mn+2
then the number of electrons tran

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Most common oxidation states of Ce (cerium) are :

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Which of the following ions has the maximum magnetic moment?

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A square planar complex is formed by hybridisation of which atomic orbitals ?

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The most stable ion is :

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CH3 - Mg - Br is an organometallic compound due to :

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What is B?

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When primary amine reacts with chloroform in ethanoic KOH then the product is

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Polymer formation from monomers starts by

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RNA is different from DNA because RNA contains

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How do we differentiate between Fe3+ and Cr3+ in group III?

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When H2S is passed through Hg2S we get :

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Which of the following compounds has wrong $$IUPAC$$ name ?

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Following types of compounds (as $$I, II$$ )
are studied in terms of isomerism in :

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The correct order of ionic radius is

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$$C{e^{ + 3}},\,\,L{a^{ + 3}},\,\,P{m^{ + 3}}\,\,$$ and $$Y{b^{ + 3}}\,\,$$ have ionic radial in the increasing order

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Picric acid is :

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The compound
is used as

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The type isomerism present in nitropentammine chromium $$\left( {{\rm I}{\rm I}{\rm I}} \right)$$ chloride is :

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Acetylene does not react with :

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For a cell given below
$$
\begin{aligned}
\mathrm{Ag}^{+}+\mathrm{e}^{-} & \longrightarrow \mathrm{Ag}; E^{\circ}=x

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## Mathematics

The period of $${\sin ^2}\theta $$ is

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The number of solution of $$\tan \,x + \sec \,x = 2\cos \,x$$ in $$\left[ {0,\,2\,\pi } \right]$$ is

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Which one is not periodic?

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z and w are two nonzero complex numbers such that $$\,\left| z \right| = \left| w \right|$$ and Arg z + Arg w =$$\pi $$

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If $$\left| {z - 4} \right| < \left| {z - 2} \right|$$, its solution is given by :

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The locus of the centre of a circle which touches the circle $$\left| {z - {z_1}} \right| = a$$ and$$\left| {z - {z_2}}

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If $$\alpha \ne \beta $$ but $${\alpha ^2} = 5\alpha - 3$$ and $${\beta ^2} = 5\beta - 3$$ then the equation having $

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Product of real roots of equation $${t^2}{x^2} + \left| x \right| + 9 = 0$$

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Difference between the corresponding roots of $${x^2} + ax + b = 0$$ and $${x^2} + bx + a = 0$$ is same and $$a \ne b,$

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If $$p$$ and $$q$$ are the roots of the equation $${x^2} + px + q = 0,$$ then

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If $$a,\,b,\,c$$ are distinct $$ + ve$$ real numbers and $${a^2} + {b^2} + {c^2} = 1$$ then $$ab + bc + ca$$ is

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$$r$$ and $$n$$ are positive integers $$\,r > 1,\,n > 2$$ and coefficient of $$\,{\left( {r + 2} \right)^{th}}$$ t

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The coefficients of $${x^p}$$ and $${x^q}$$ in the expansion of $${\left( {1 + x} \right)^{p + q}}$$ are

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The positive integer just greater than $${\left( {1 + 0.0001} \right)^{10000}}$$ is

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If the sum of the coefficients in the expansion of $$\,{\left( {a + b} \right)^n}$$ is 4096, then the greatest coefficie

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Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are :

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Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number

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Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers ar

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If $${a_n} = \sqrt {7 + \sqrt {7 + \sqrt {7 + .......} } } $$ having $$n$$ radical signs then by methods of mathematica

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The sum of integers from 1 to 100 that are divisible by 2 or 5 is :

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If 1, $${\log _9}\,\,({3^{1 - x}} + 2),\,\,{\log _3}\,\,({4.3^x} - 1)$$ are in A.P. then x equals

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l, m, n are the $${p^{th}}$$, $${q^{th}}$$ and $${r^{th}}$$ term of a G.P all positive, $$then\,\left| {\matrix{
{\lo

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The value of $$\,{2^{1/4}}.\,\,{4^{1/8}}.\,{8^{1/16}}...\infty $$ is

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Fifth term of a GP is 2, then the product of its 9 terms is

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Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is

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$${1^3} - \,\,{2^3} + {3^3} - {4^3} + ... + {9^3} = $$

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If the chord y = mx + 1 of the circle $${x^2}\, + \,{y^2} = 1$$ subtends an angle of measure $${45^ \circ }$$ at the maj

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The centre of the circle passing through (0, 0) and (1, 0) and touching the circle $${x^2}\, + \,{y^2} = 9$$ is :

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The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $

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The centres of a set of circles, each of radius 3, lie on the circle $${x^2}\, + \,{y^2} = 25$$. The locus of any point

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Two common tangents to the circle $${x^2} + {y^2} = 2{a^2}$$ and parabola $${y^2} = 8ax$$ are :

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If $$y = {\left( {x + \sqrt {1 + {x^2}} } \right)^n},$$ then $$\left( {1 + {x^2}} \right){{{d^2}y} \over {d{x^2}}} + x{{

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The sides of a triangle are $$3x + 4y,$$ $$4x + 3y$$ and $$5x + 5y$$ where $$x$$, $$y>0$$ then the triangle is :

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In a triangle with sides $$a, b, c,$$ $${r_1} > {r_2} > {r_3}$$ (which are the ex-radii) then :

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$${\cot ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) - {\tan ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) = x,$$ the

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The maximum distance from origin of a point on the curve
$$x = a\sin t - b\sin \left( {{{at} \over b}} \right)$$
$$y =

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If $$2a+3b+6c=0,$$ $$\left( {a,b,c \in R} \right)$$ then the quadratic equation $$a{x^2} + bx + c = 0$$ has

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If $$a>0$$ and discriminant of $$\,a{x^2} + 2bx + c$$ is $$-ve$$, then
$$\left| {\matrix{
a & b & {ax + b}

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$$\int\limits_0^{10\pi } {\left| {\sin x} \right|dx} $$ is

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$${I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,dx} $$ then $$\,\mathop {\lim }\limits_{n \to \infty } \,n\left[ {{I_n}

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$$\int\limits_0^2 {\left[ {{x^2}} \right]dx} $$ is

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$$\int_{ - \pi }^\pi {{{2x\left( {1 + \sin x} \right)} \over {1 + {{\cos }^2}x}}} dx$$ is

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If $$y=f(x)$$ makes +$$ve$$ intercept of $$2$$ and $$0$$ unit on $$x$$ and $$y$$ axes and encloses an area of $$3/4$$ sq

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The area bounded by the curves $$y = \ln x,y = \ln \left| x \right|,y = \left| {\ln {\mkern 1mu} x} \right|$$ and $$y =

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The order and degree of the differential equation
$$\,{\left( {1 + 3{{dy} \over {dx}}} \right)^{2/3}} = 4{{{d^3}y} \ove

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The solution of the equation $$\,{{{d^2}y} \over {d{x^2}}} = {e^{ - 2x}}$$

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$$A$$ and $$B$$ are events such that $$P\left( {A \cup B} \right) = 3/4$$,$$P\left( {A \cap B} \right) = 1/4,$$
$$P\lef

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A dice is tossed $$5$$ times. Getting an odd number is considered a success. Then the variance of distribution of succes

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A problem in mathematics is given to three students $$A,B,C$$ and their respective probability of solving the problem is

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A plane which passes through the point $$(3,2,0)$$ and the line
$${{x - 4} \over 1} = {{y - 7} \over 5} = {{z - 4} \ove

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If $$\left| {\overrightarrow a } \right| = 4,\left| {\overrightarrow b } \right| = 2$$ and the angle between $${\overrig

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If $$\overrightarrow a \,\,,\,\,\overrightarrow b \,\,,\,\,\overrightarrow c $$ are vectors such that $$\left[ {\overrig

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If the vectors $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ from the sid

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If $$\left| {\overrightarrow a } \right| = 5,\left| {\overrightarrow b } \right| = 4,\left| {\overrightarrow c } \right|

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$$\overrightarrow a = 3\widehat i - 5\widehat j$$ and $$\overrightarrow b = 6\widehat i + 3\widehat j$$ are two vector

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If the vectors $$\overrightarrow c ,\overrightarrow a = x\widehat i + y\widehat j + z\widehat k$$ and $$\widehat b = \w

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The $$d.r.$$ of normal to the plane through $$(1, 0, 0), (0, 1, 0)$$ which makes an angle $$\pi /4$$ with plane $$x+y=3$

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In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the comple

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$$\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - \cos 2x} } \over {\sqrt 2 x}}$$ is

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The domain of $${\sin ^{ - 1}}\left[ {{{\log }_3}\left( {{x \over 3}} \right)} \right]$$ is

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$$\mathop {\lim }\limits_{x \to \infty } {\left( {{{{x^2} + 5x + 3} \over {{x^2} + x + 2}}} \right)^x}$$

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$$\mathop {\lim }\limits_{n \to \infty } {{{1^p} + {2^p} + {3^p} + ..... + {n^p}} \over {{n^{p + 1}}}}$$ is

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Let $$f(2) = 4$$ and $$f'(x) = 4.$$
Then $$\mathop {\lim }\limits_{x \to 2} {{xf\left( 2 \right) - 2f\left( x \right)} \

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$$\mathop {\lim }\limits_{x \to 0} {{\log {x^n} - \left[ x \right]} \over {\left[ x \right]}}$$, $$n \in N$$, ( [x] deno

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If $$f\left( 1 \right) = 1,{f^1}\left( 1 \right) = 2,$$ then
$$\mathop {\lim }\limits_{x \to 1} {{\sqrt {f\left( x \righ

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$$f$$ is defined in $$\left[ { - 5,5} \right]$$ as
$$f\left( x \right) = x$$ if $$x$$ is rational
$$\,\,\,\,\,\,\,\,\,\,

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f(x) and g(x) are two differentiable functions on [0, 2] such that
f''(x) - g''(x) = 0, f'(1) = 2, g'(1) = 4, f(2) = 3,

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If f(x + y) = f(x).f(y) $$\forall $$ x, y and f(5) = 2, f'(0) = 3, then
f'(5) is

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A triangle with vertices $$\left( {4,0} \right),\left( { - 1, - 1} \right),\left( {3,5} \right)$$ is :

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Locus of mid point of the portion between the axes of
$$x$$ $$cos$$ $$\alpha + y\,\sin \alpha = p$$ where $$p$$ is c

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If the pair of lines
$$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$$
intersect on the $$y$$-axis then :

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The pair of lines represented by
$$$3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0$$$
are perpendicular to each ot

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## Physics

Identify the pair whose dimensions are equal

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A ball whose kinetic energy E, is projected at an angle of $$45^\circ $$ to the horizontal. The kinetic energy of the ba

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From a building two balls A and B are thrown such that A is thrown upwards and B downwards ( both vertically with the s

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If a body looses half of its velocity on penetrating $$3$$ $$cm$$ in a wooden block, then how much will it penetrate mor

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A lift is moving down with acceleration $$a.$$ A man in the lift drops a ball inside the lift. The acceleration of the b

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When forces $${F_1},\,\,{F_2},\,\,{F_3}$$ are acting on a particle of mass $$m$$ such that $${F_2}$$ and $${F_3}$$ are m

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Two forces are such that the sum of their magnitudes is $$18$$ $$N$$ and their resultant is $$12$$ $$N$$ which is perpen

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A light string passing over a smooth light pulley connects two blocks of masses $${m_1}$$ and $${m_2}$$ (vertically). If

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Speeds of two identical cars are $$u $$ and $$4$$$$u $$ at the specific instant. The ratio of the respective distances i

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Three identical blocks of masses $$m=2$$ $$kg$$ are drawn by a force $$F=10.2$$ $$N$$ with an acceleration of $$0.6$$ $$

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A cylinder of height $$20$$ $$m$$ is completely filled with water. The velocity of efflux of water (in $$m{s^{ - 1}}$$)

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Initial angular velocity of a circular disc of mass $$M$$ is $${\omega _1}.$$ Then two small spheres of mass $$m$$ are a

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The minimum velocity (in $$m{s^{ - 1}}$$) with which a car driver must traverse a flat curve of radius 150 m and coeffic

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A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide

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A particle of mass $$m$$ moves along line PC with velocity $$v$$ as shown. What is the angular momentum of the particle

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Two identical particles move towards each other with velocity $$2v$$ and $$v$$ respectively. The velocity of center of m

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The kinetic energy needed to project a body of mass $$m$$ from the earth surface (radius $$R$$) to infinity is

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If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then

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The escape velocity of a body depends upon mass as

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Energy required to move a body of mass $$m$$ from an orbit of radius $$2R$$ to $$3R$$ is

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A spring of force constant $$800$$ $$N/m$$ has an extension of $$5$$ $$cm.$$ The work done in extending it from $$5$$ $$

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One end of a mass-less rope, which passes over a mass-less and friction-less pulley $$P$$ is tied to a hook $$C$$ while

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Which statement is incorrect?

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Infrared radiation is detected by

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Heat given to a body which raises its temperature by $${1^ \circ }C$$ is

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Which of the following is more close to a black body?

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If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

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Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

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Even Carnot engine cannot give $$100\% $$ efficiency because we cannot

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At what temperature is the $$r.m.s$$ velocity of a hydrogen molecule equal to that of an oxygen molecule at $${47^ \circ

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1 mole of a gas with $$\gamma = 7/5$$ is mixed with $$1$$ mole of a gas with $$\gamma = 5/3,$$ then the value of $$\ga

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Two spheres of the same material have radii $$1$$ $$m$$ and $$4$$ $$m$$ and temperatures $$4000$$ $$K$$ and $$2000$$ $$K

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Moment of inertia of a circular wire of mass $$M$$ and radius $$R$$ about its diameter is

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If a spring has time period $$T,$$ and is cut into $$n$$ equal parts, then the time period of each part will be

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In a simple harmonic oscillator, at the mean position

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A child swinging on a swing in sitting position, stands up, then the time period of the swing will

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length of a string tied to two rigid supports is $$40$$ $$cm$$. Maximum length (wavelength in $$cm$$) of a stationary wa

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A tuning fork arrangement (pair) produces $$4$$ beats/sec with one fork of frequency $$288$$ $$cps.$$ A little wax is pl

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Tube $$A$$ has bolt ends open while tube $$B$$ has one end closed, otherwise they are identical. The ratio of fundamenta

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A wave $$y=a$$ $$\sin \left( {\omega t - kx} \right)$$ on a string meets with another wave producing a node at $$x=0.$$

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When temperature increases, the frequency of a tuning fork

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On moving a charge of $$20$$ coulomb by $$2$$ $$cm,$$ $$2$$ $$J$$ of work is done, then the potential differences betwee

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If there are $$n$$ capacitors in parallel connected to $$V$$ volt source, then the energy stored is equal to

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A charged particle $$q$$ is placed at the centre $$O$$ of cube of length $$L(ABCDEFGH).$$ Another same charge $$q$$ is p

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If a charge $$q$$ is placed at the center of the line joining two equal charges $$Q$$ such that the system is in equilib

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Capacitance (in $$F$$) of a spherical conductor with radius $$1$$ $$m$$ is

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If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a

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A wire when connected to $$220$$ $$V$$ mains supply has power dissipation $${P_1}.$$ Now the wire is cut into two equal

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If in the circuit, power dissipation is $$150W,$$ then $$R$$ is

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If a current is passed through a spring then the spring will

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The mass of product liberated on anode in an electrochemical cell depends on (where $$t$$ is the time period for which

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If $${\theta _1},$$ is the inversion temperature, $${\theta _n}$$ is the neutral temperature, $${\theta _c}$$ is the te

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If an electron and a proton having same momentum enter perpendicular to a magnetic field, then

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If in a circular coil $$A$$ of radius $$R,$$ current $$I$$ is flowing and in another coil $$B$$ of radius $$2R$$ a curr

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The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its

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Wires $$1$$ and $$2$$ carrying currents $$i{}_1$$ and $$i{}_2$$ respectively are inclined at an angle $$\theta $$ to eac

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The power factor of $$AC$$ circuit having resistance $$(R)$$ and inductance $$(L)$$ connected in series and an angular v

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In a transformer, number of turns in the primary coil are $$140$$ and that in the secondary coil are $$280.$$ If current

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An astronomical telescope has a large aperture to

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Electromagnetic waves are transverse in nature is evident by

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If two mirrors are kept at $${60^ \circ }$$ to each other, then the number of images formed by them is

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Wavelength of light used in an optical instrument are $${\lambda _1} = 4000\mathop A\limits^ \circ $$ and $${\lambda _

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Which of the following is used in optical fibres?

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A conducting square loop of side $$L$$ and resistance $$R$$ moves in its plane with a uniform velocity $$v$$ perpendicul

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The inductance between $$A$$ and $$D$$ is

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If $$13.6$$ $$eV$$ energy is required to ionize the hydrogen atom, then the energy required to remove an electron from $

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At absolute zero, Si acts as

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Sodium and copper have work functions $$2.3$$ $$eV$$ and $$4.5$$ $$eV$$ respectively. Then the ratio of the wavelengths

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At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit
$$\eqali

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Formation of covalent bonds in compounds exhibits

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If $${N_0}$$ is the original mass of the substance of half-life period $${t_{1/2}} = 5$$ years, then the amount of subst

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By increasing the temperature, the specific resistance of a conductor and a semiconductor

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The energy band gap is maximum in

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The part of a transistor which is most heavily doped to produce large number of majority carriers is

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Which of the following are not electromagnetic waves?

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