JEE Main 2018 (Online) 15th April Morning Slot
Paper was held on Sun, Apr 15, 2018 3:30 AM
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Chemistry

1
The reagent(s) required for the following conversion are :

JEE Main 2018 (Online) 15th April Morning Slot Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 208 English
2
The major product of the following reaction is :

JEE Main 2018 (Online) 15th April Morning Slot Chemistry - Alcohols, Phenols and Ethers Question 143 English
3
Which of the following will not exist in zwitter ionic form at pH=7 ?
4
Which of the following will most readily give the dehydrohalogenation product ?
5
The main reduction product of the following compound with NaBH4 in methanol is :

JEE Main 2018 (Online) 15th April Morning Slot Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 209 English
6
The increasing order of nitration of the following compounds is :

JEE Main 2018 (Online) 15th April Morning Slot Chemistry - Compounds Containing Nitrogen Question 200 English
7
The correct match between items of List-I and List-II is :

List - I List - II
(A) Coloured impurity (P) Steam distilation
(B) Mixture of o-nitrophenol
and p-nitrophenol
(Q) Fractional distilation
(C) Crude Naphtha (R) Charcoal treatment
(d) Mixture of glycerol
and sugars
(S) Distillation under
reduced pressure
8
Which of the following is the correct structure of Adenosine?
9
JEE Main 2018 (Online) 15th April Morning Slot Chemistry - Chemical Bonding & Molecular Structure Question 192 English
In hydrogen azide (above) the bond orders of bond (I) and (II) are :
10
An ideal gas undergoes a cyclic process as shown in Figure.

JEE Main 2018 (Online) 15th April Morning Slot Chemistry - Thermodynamics Question 161 English
$$\Delta $$UBC = $$-$$5 kJ mol-1, qAB = $$2$$ kJ mol-1, WAB = $$-$$5 kJ mol-1, WCA = 3 kJ mol-1. Heat absorbed by the system during process $$CA$$ is :
11
The IUPAC name of the following compound is :

JEE Main 2018 (Online) 15th April Morning Slot Chemistry - Basics of Organic Chemistry Question 208 English
12
The decreasing order of bond angles in BF3, NH3, PF3 and I3- is :
13
When an electric currents passed through acidified water, 112 mL of hydrogen gas at N.T.P. was collected at the cathode in 965 seconds. The current passed, in ampere, is :
14
The correct combination is :
15
Identify the pair in which the geometry of the species is $$T$$-shape and square - pyraidal, respectively :
16
In graphite and diamond, the percentage of p-characters of the hybrid orbitals in hybridisation are respectively :
17
For Na+, Mg2+, F- and O2-; the correct order of increasing ionic radii is :
18
Which of the following is a Lewis acid?
19
In the molecular orbital diagram for the molecular ion, N2+, the number of electrons in the $$\sigma $$2pz molecular orbital is :
20
For which of the following reactions, $$\Delta $$H is equal to $$\Delta $$U?
21
Ejection of the photoelectron from metal in the photoelectric experiment can be stopped by applying 0.5 V when the radiation of 250 nm is used. The work function of the metal is :
22
N2O5 decomposes to NO2 and O2 and follows first order kinetics. After 50 minutes, the pressure inside the vessel increases from 50 mmHg to 87.5 mmHg. The pressure of the gaseous mixture after 100 minute at constant temperature will be :
23
In which of the following reactions, an increase in the volume of the container will favour the formation of products?
24
A sample of $$NaCl{O_3}$$ is converted by heat to $$NaCl$$ with a loss of $$0.16$$ $$g$$ of oxygen. The residue is dissolved in water and precipitated as $$AgCl.$$ The mass of $$AgCl$$ (in $$g$$) obtained will be : (Given : Molar mass of $$AgCl=143.5$$ $$g$$ $$mo{l^{ - 1}}$$)
25
The minimum volume of water required to dissolve 0.1 g lead (II) chloride to get a saturated solution (Ksp of PbCl2 = 3.2 $$ \times $$ 10-8 atomic mass of Pb = 207 u ) is :

Mathematics

1
n$$-$$digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :
2
If x1, x2, . . ., xn and $${1 \over {{h_1}}}$$, $${1 \over {{h_2}}}$$, . . . , $${1 \over {{h_n}}}$$ are two A.P..s such that x3 = h2 = 8 and x8 = h7 = 20, then x5.h10 equals :
3
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 + 2y + kz = 4
has a unique solution. Then S is :
4
Let $$A$$ be a matrix such that $$A.\left[ {\matrix{ 1 & 2 \cr 0 & 3 \cr } } \right]$$ is a scalar matrix and |3A| = 108.
Then A2 equals :
5
The set of all $$\alpha $$ $$ \in $$ R, for which w = $${{1 + \left( {1 - 8\alpha } \right)z} \over {1 - z}}$$ is purely imaginary number, for all z $$ \in $$ C satisfying |z| = 1 and Re z $$ \ne $$ 1, is :
6
If $$\lambda $$ $$ \in $$ R is such that the sum of the cubes of the roots of the equation,
x2 + (2 $$-$$ $$\lambda $$) x + (10 $$-$$ $$\lambda $$) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :
7
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, a)} and
R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}.
Then :
8
If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :
9
If the tangents drawn to the hyperbola 4y2 = x2 + 1 intersect the co-ordinate axes at the distinct points A and B then the locus of the mid point of AB is :
10
If tanA and tanB are the roots of the quadratic equation, 3x2 $$-$$ 10x $$-$$ 25 = 0, then the value of 3 sin2(A + B) $$-$$ 10 sin(A + B).cos(A + B) $$-$$ 25 cos2(A + B) is :
11
A box 'A' contains $$2$$ white, $$3$$ red and $$2$$ black balls. Another box 'B' contains $$4$$ white, $$2$$ red and $$3$$ black balls. If two balls are drawn at random, without eplacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is :
12
The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $$\lambda $$ and then each of them is decreased by 25, their mean remains the same. Then $$\lambda $$ is equal to :
13
If $$\overrightarrow a ,\,\,\overrightarrow b ,$$ and $$\overrightarrow C $$ are unit vectors such that $$\overrightarrow a + 2\overrightarrow b + 2\overrightarrow c = \overrightarrow 0 ,$$ then $$\left| {\overrightarrow a \times \overrightarrow c } \right|$$ is equal to :
14
Let y = y(x) be the solution of the differential equation $${{dy} \over {dx}} + 2y = f\left( x \right),$$

where $$f\left( x \right) = \left\{ {\matrix{ {1,} & {x \in \left[ {0,1} \right]} \cr {0,} & {otherwise} \cr } } \right.$$

If y(0) = 0, then $$y\left( {{3 \over 2}} \right)$$ is :
15
In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4. Then area of $$\Delta $$ ABC (in sq. units) is :
16
The value of the integral

$$\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {{{\sin }^4}} x\left( {1 + \log \left( {{{2 + \sin x} \over {2 - \sin x}}} \right)} \right)dx$$ is :
17
The area (in sq. units) of the region

{x $$ \in $$ R : x $$ \ge $$ 0, y $$ \ge $$ 0, y $$ \ge $$ x $$-$$ 2  and y $$ \le $$ $$\sqrt x $$}, is :
18
If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is :
19
If $$f\left( {{{x - 4} \over {x + 2}}} \right) = 2x + 1,$$ (x $$ \in $$ R $$-$${1, $$-$$ 2}), then $$\int f \left( x \right)dx$$ is equal to :
(where C is a constant of integration)
20
Let S = {($$\lambda $$, $$\mu $$) $$ \in $$ R $$ \times $$ R : f(t) = (|$$\lambda $$| e|t| $$-$$ $$\mu $$). sin (2|t|), t $$ \in $$ R, is a differentiable function}. Then S is a subset of :
21
If   x2 + y2 + sin y = 4, then the value of $${{{d^2}y} \over {d{x^2}}}$$ at the point ($$-$$2,0) is :
22
If $$f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|,$$ then $$\mathop {\lim }\limits_{x \to 0} {{f'\left( x \right)} \over x}$$

Physics

1
A monochromatic beam of light has a frequency $$v = {3 \over {2\pi }} \times {10^{12}}Hz$$ and is propagating along the direction $${{\widehat i + \widehat j} \over {\sqrt 2 }}.$$
It is polarized along the $$\widehat k$$ direction. The acceptable form for the magnetic field is :
2
JEE Main 2018 (Online) 15th April Morning Slot Physics - Current Electricity Question 290 English
In a meter bridge, as shown in the figure, it is given that resistance $$Y = 12.5\,\,\Omega $$ and that the balance is obtained at a distance $$39.5$$ $$cm$$ from end $$A$$ (by Jockey J). After interchanging the resistances $$X$$ and $$Y$$, a new balance point is found at a distance $${l_2}$$ from end $$A.$$ What are the value of $$X$$ and $${l_2}$$ ?
3
A particle is oscillating on the $$X$$-axis with an amplitude $$2$$ $$cm$$ about the point $${x_0} = 10\,cm,$$ with a frequency $$\omega $$. A concave mirror of local length $$5$$ $$cm$$ is placed at the origin (see figure).

JEE Main 2018 (Online) 15th April Morning Slot Physics - Geometrical Optics Question 188 English
Identify the correct statements.
4
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 $$\theta $$ that will produce maximum moment of the force about point $$A$$ is given by :

JEE Main 2018 (Online) 15th April Morning Slot Physics - Rotational Motion Question 190 English
5
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.

JEE Main 2018 (Online) 15th April Morning Slot Physics - Electrostatics Question 195 English
The electric flux through the square surface is
6
The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in $$15$$ $$s$$ and (ii) the time at which the car will catch up with the scooter are, respectively.

JEE Main 2018 (Online) 15th April Morning Slot Physics - Motion in a Straight Line Question 92 English
7
In a screw gauge, $$5$$ complete rotations of the screw cause it to move a linear distance of $$0.25$$ $$cm.$$ There are $$100$$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $$4$$ main scale divisions and $$30$$ circular scale divisions. Assuming negligible zero error, the thickness of the wire is :
8
Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength are $${\lambda _1}$$ and $${\lambda _2},$$ their de Broglie wavelength in the frame of reference attached to their center of masses :
9
The energy required to remove the electron from a singly ionized Helium atom is $$2.2$$ times the energies required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is :
10
A planoconvex lens becomes an optical system of $$28$$ $$cm$$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.

If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig-B, it acts like an optical system of focal length $$10$$ $$cm.$$ The refractive index of the material of lens is :

JEE Main 2018 (Online) 15th April Morning Slot Physics - Geometrical Optics Question 189 English
11
A Helmholtz coil has a pair of loops, each with $$N$$ turns and radius $$R$$. They are placed coaxially at distance $$R$$ and the same current $${\rm I}$$ flows through the loops in the same direction. $$P,$$ midway between the centers $$A$$ and $$C$$, is given by [Refer to figure given below] :

JEE Main 2018 (Online) 15th April Morning Slot Physics - Magnetic Effect of Current Question 176 English
12
Light of wavelength $$550$$ $$nm$$ falls normally on a slit of width $$22.0 \times {10^{ - 5}}$$ $$cm.$$ The angular position of the second minima from the central maximum will (in radians) :
13
A tuning fork vibrates with frequency $$256$$ $$Hz$$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $$340\,m{s^{ - 1}}$$)
14
A body of mass $$M$$ and charge $$q$$ is connected to spring of spring constant $$k.$$ It is oscillating along $$x$$-direction about its equilibrium position, taken to be at $$x=0,$$ with an amplitude $$A$$. An electric field $$E$$ is applied along the $$x$$-direction. Which of the following statements is correct ?
15
One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, $${27^ \circ }C.$$ The work done on the gas will be :
16
A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $${\rho _1}$$ and $${\rho _2}$$ $$\left( {{\rho _1} > {\rho _2}} \right),$$ fill half the circle. The angle $$\theta $$ between the radius vector passing through the common interface and the vertical is :
17
Take the mean distance of the moon and the sun from the earth to be $$0.4 \times {10^6}$$ km and $$150 \times {10^6}$$ km respectively. Their masses are $$8 \times {10^{22}}$$ kg and $$2 \times {10^{30}}$$ kg respectively. The radius of the earth is $$6400$$ km. Let $$\Delta {F_1}$$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $$\Delta {F_2}$$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $${{\Delta {F_1}} \over {\Delta {F_2}}}$$ is :
18
The relative error in the determination of the surface area of sphere is $$\alpha $$. Then the relative error in the determination of its volume is :
19
An automobile, travelling at $$40\,$$ km/h, can be stopped at a distance of $$40\,$$ m by applying brakes. If the same automobile is travelling at $$80\,$$ km/h, the minimum stopping distance, in metres, is (assume no skidding) :
20
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 equal masses. The first mass moves in a circular orbit of radius $${R \over 2},$$ and the other mass, in a circular orbit of radius $${3R \over 2}$$. The difference between the final and initial total energies is :
21
A given object takes n times more time to slide down a $${45^ \circ }$$ rough inclined plane as it takes to slide down a perfectly smooth $${45^ \circ }$$ incline. The coefficient of kinetic friction between the object and the incline is :
22
The equivalent capacitance between $$A$$ and $$B$$ in the circuit given below, is :

JEE Main 2018 (Online) 15th April Morning Slot Physics - Capacitor Question 133 English
23
JEE Main 2018 (Online) 15th April Morning Slot Physics - Rotational Motion Question 189 English
A uniform rod $$AB$$ is suspended from a point $$X,$$ at a variable distance $$x$$ from $$A$$, as shown, To make the rod horizontal, a mass $$m$$ is suspended from its end $$A.$$A$$ set of $$(m,x)$$ values is recorded. The appropriate variables that give a straight line, when plotted, are :
24
An ideal capacitor of capacitance $$0.2\,\mu F$$ is charged to a potential difference of $$10$$ $$V.$$ The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $$0.5$$ $$mH.$$ The current at a time when the potential difference across the capacitor is $$5$$ $$V,$$ is :
25
In the given circuit all resistances are of value $$R$$ $$ohm$$ each. The equivalent resistance between $$A$$ and $$B$$ is :

JEE Main 2018 (Online) 15th April Morning Slot Physics - Current Electricity Question 289 English
26
The $$B$$-$$H$$ curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solended with $$1000$$ turns/cm. The current that should be passed in the solended to demagnetise the ferromagnet completely is :

JEE Main 2018 (Online) 15th April Morning Slot Physics - Magnetic Properties of Matter Question 54 English
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