JEE Main 2018 (Online) 15th April Morning Slot

Paper was held on
Sun, Apr 15, 2018 3:30 AM

## Chemistry

The minimum volume of water required to dissolve 0.1 g lead (II) chloride to get a saturated solution (Ksp of PbCl2 = 3

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A sample of $$NaCl{O_3}$$ is converted by heat to $$NaCl$$ with a loss of $$0.16$$ $$g$$ of oxygen. The residue is disso

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In which of the following reactions, an increase in the volume of the container will favour the formation of products?

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N2O5 decomposes to NO2 and O2 and follows first order kinetics. After 50 minutes, the pressure inside the vessel increas

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When an electric currents passed through acidified water, 112 mL of hydrogen gas at N.T.P. was collected at the cathode

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Which of the following statements about colloids is False ?

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Ejection of the photoelectron from metal in the photoelectric experiment can be stopped by applying 0.5 V when the radia

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For which of the following reactions, $$\Delta $$H is equal to $$\Delta $$U?

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In the molecular orbital diagram for the molecular ion, N2+, the number of electrons in the $$\sigma $$2pz molecular orb

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Which of the following is a Lewis acid?

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For Na+, Mg2+, F- and O2-; the correct order of increasing ionic radii is :

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In graphite and diamond, the percentage of p-characters of the hybrid orbitals in hybridisation are respectively :

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Identify the pair in which the geometry of the species is $$T$$-shape and square - pyraidal, respectively :

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The correct combination is :

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A white sodium salt dissolves readily in water to give a solution which is neutral to litmus. When silver nitrate soluti

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The decreasing order of bond angles in BF3, NH3, PF3 and I3- is :

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Xenon hexafluoride on partial hydrolysis produces compounds 'X' and 'Y' . Compounds 'X' and 'Y' and the oxidation state

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The IUPAC name of the following compound is :

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Which of the following arrangements shows the schematic alignment of magnetic moments of antiferromagnetic substance ?

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An ideal gas undergoes a cyclic process as shown in Figure.
$$\Delta $$UBC = $$-$$5 kJ mol-1, qAB = $$2$$ kJ mol-1, WAB

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In hydrogen azide (above) the bond orders of bond (I) and (II) are :

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Which of the following is the correct structure of Adenosine?

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The correct match between items of List-I and List-II is :
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.tg td{fon

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The increasing order of nitration of the following compounds is :

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The main reduction product of the following compound with NaBH4 in methanol is :

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Which of the following will most readily give the dehydrohalogenation product ?

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The copolymer formed by addition polymerization of styrene and acrylonitrile in the presence of peroxide is :

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Which of the following will not exist in zwitter ionic form at pH=7 ?

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The major product of the following reaction is :

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The reagent(s) required for the following conversion are :

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## Mathematics

Consider the following two binary relations on the set A = {a, b, c} :
R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a

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If $$\lambda $$ $$ \in $$ R is such that the sum of the cubes of the roots of the equation,
x2 + (2 $$-$$ $$\lambda $$)

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The set of all $$\alpha $$ $$ \in $$ R, for which w = $${{1 + \left( {1 - 8\alpha } \right)z} \over {1 - z}}$$ is purely

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Let $$A$$ be a matrix such that $$A.\left[ {\matrix{
1 & 2 \cr
0 & 3 \cr
} } \right]$$ is a scalar m

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Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y $$-$$ z = 3
3x + 2

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If n is the degree of the polynomial,
$${\left[ {{2 \over {\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8} + $$

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If x1, x2, . . ., xn and $${1 \over {{h_1}}}$$, $${1 \over {{h_2}}}$$, . . . , $${1 \over {{h_n}}}$$ are two A.P..s such

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n$$-$$digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct

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If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

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If $$f\left( x \right) = \left| {\matrix{
{\cos x} & x & 1 \cr
{2\sin x} & {{x^2}} & {2x} \cr

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If x2 + y2 + sin y = 4, then the value of $${{{d^2}y} \over {d{x^2}}}$$ at the point ($$-$$2,0) is :

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Let S = {($$\lambda $$, $$\mu $$) $$ \in $$ R $$ \times $$ R : f(t) = (|$$\lambda $$| e|t| $$-$$ $$\mu $$). sin (2|t|),

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If $$f\left( {{{x - 4} \over {x + 2}}} \right) = 2x + 1,$$ (x $$ \in $$ R $$-$${1, $$-$$ 2}), then $$\int f \left( x \ri

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If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (

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The area (in sq. units) of the region
{x $$ \in $$ R : x $$ \ge $$ 0, y $$ \ge $$ 0, y $$ \ge $$ x $$-$$ 2 and y

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The value of the integral
$$\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {{{\sin }^4}} x\left( {1 + \log \left( {{{2

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In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y

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Let y = y(x) be the solution of the differential equation $${{dy} \over {dx}} + 2y = f\left( x \right),$$ where $$f\left

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A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, $$y - 4x + 3 = 0,$$ then its radiu

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If the tangents drawn to the hyperbola 4y2 = x2 + 1 intersect the co-ordinate axes at the distinct points A and B then t

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Two parabolas with a common vertex and with axes along x-axis and $$y$$-axis, respectively intersect each other in the f

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If $$\beta $$ is one of the angles between the normals to the ellipse, x2 + 3y2 = 9 at the points (3 cos $$\theta $$, $$

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A variable plane passes through a fixed point (3,2,1) and meets x, y and z axes at A, B and C respectively. A plane is d

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An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z $$-$$ 1 = 0 and 5x + 8

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If $$\overrightarrow a ,\,\,\overrightarrow b ,$$ and $$\overrightarrow C $$ are unit vectors such that $$\overrightarr

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The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $$\lambda $$ and then e

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A box 'A' contains $$2$$ white, $$3$$ red and $$2$$ black balls. Another box 'B' contains $$4$$ white, $$2$$ red and $$3

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If tanA and tanB are the roots of the quadratic equation, 3x2 $$-$$ 10x $$-$$ 25 = 0, then the value of 3 sin2(A + B) $$

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An aeroplane flying at a constant speed, parallel to the horizontal ground, $$\sqrt 3 $$ kmabove it, is obsered at an el

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If (p $$ \wedge $$ $$ \sim $$ q) $$ \wedge $$ (p $$ \wedge $$ r) $$ \to $$ $$ \sim $$ p $$ \vee $$ q is false, then the

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## Physics

A given object takes n times more time to slide down a $${45^ \circ }$$ rough inclined plane as it takes to slide down a

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A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two

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An automobile, travelling at $$40\,$$ km/h, can be stopped at a distance of $$40\,$$ m by applying brakes. If the same a

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The relative error in the determination of the surface area of sphere is $$\alpha $$. Then the relative error in the de

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Take the mean distance of the moon and the sun from the earth to be $$0.4 \times {10^6}$$ km and $$150 \times {10^6}$$ k

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A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids

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A Carnot's engine works as a refrigerator between $$250$$ K and $$300$$ K. It receives $$500$$ cal heat from the reservo

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One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperat

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A body of mass $$M$$ and charge $$q$$ is connected to spring of spring constant $$k.$$ It is oscillating along $$x$$-di

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A tuning fork vibrates with frequency $$256$$ $$Hz$$ and gives one beat per second with the third normal mode of vibrati

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Light of wavelength $$550$$ $$nm$$ falls normally on a slit of width $$22.0 \times {10^{ - 5}}$$ $$cm.$$ The angular pos

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A monochromatic beam of light has a frequency $$v = {3 \over {2\pi }} \times {10^{12}}Hz$$ and is propagating along the

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A planoconvex lens becomes an optical system of $$28$$ $$cm$$ focal length when its plane surface is silvered and illumi

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The energy required to remove the electron from a singly ionized Helium atom is $$2.2$$ times the energies required to r

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Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength

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A solution containing active cobalt $${^{60}_{27}}Co$$ having activity of $$0.8$$ $$\mu Ci$$ and decay constant $$\lambd

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In a common emitter configuration with suitable bias, it is given that $${R_L}$$ is the load resistance and $${R_{BE}}$

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In a screw gauge, $$5$$ complete rotations of the screw cause it to move a linear distance of $$0.25$$ $$cm.$$ There are

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The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travell

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A charge $$Q$$ is placed at a distance $$a/2$$ above the center of the square surface of edge a as shown in the figure.

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A force of $$40$$ $$N$$ acts on a point $$B$$ at the end of an $$L$$-shaped object, as shown in the figure. The angle $$

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A particle is oscillating on the $$X$$-axis with an amplitude $$2$$ $$cm$$ about the point $${x_0} = 10\,cm,$$ with a fr

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In a meter bridge, as shown in the figure, it is given that resistance $$Y = 12.5\,\,\Omega $$ and that the balance is

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A Helmholtz coil has a pair of loops, each with $$N$$ turns and radius $$R$$. They are placed coaxially at distance $$R$

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The $$B$$-$$H$$ curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solended with $$

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In the given circuit all resistances are of value $$R$$ $$ohm$$ each. The equivalent resistance between $$A$$ and $$B$$

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The number of amplitude modulted broadcast stations that can be accomodated in a $$300$$ $$kHz$$ band width for the high

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An ideal capacitor of capacitance $$0.2\,\mu F$$ is charged to a potential difference of $$10$$ $$V.$$ The charging batt

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A uniform rod $$AB$$ is suspended from a point $$X,$$ at a variable distance $$x$$ from $$A$$, as shown, To make the rod

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The equivalent capacitance between $$A$$ and $$B$$ in the circuit given below, is :

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