JEE Main 2019 (Online) 12th January Morning Slot
Paper was held on Sat, Jan 12, 2019 3:30 AM
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Chemistry

1
Two solids dissociate as follows –
JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Chemical Equilibrium Question 73 English
The total pressure when both the solids dissociated simultaneously is -
2
The major product of the following reaction is –

JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 186 English
3
Mn2(CO)10 is an organometallic compound due to the presence of -
4
In a chemical reaction,

JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Chemical Equilibrium Question 74 English
the initial concentration of B was 1.5 times of the concentration of A, but the equilibrium concentrations of A and B were found to be equal. The equilibrium constant (K) for the aforesaid chemical reaction is -
5
The major product of the following reaction is

JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Hydrocarbons Question 115 English
6
The increasing order of reactivity of the following compounds towards reaction with alkyl halides directly is JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Compounds Containing Nitrogen Question 183 English 1

(A)

JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Compounds Containing Nitrogen Question 183 English 2

(B)

JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Compounds Containing Nitrogen Question 183 English 3

(C)

JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Compounds Containing Nitrogen Question 183 English 4

(D)

7
The standard electrode potential $${E^o }$$ and its temperature coefficient $$\left( {{{d{E^o }} \over {dT}}} \right)$$ for a cell are 2V and $$-$$ 5 $$ \times $$ 10$$-$$4 VK$$-$$1 at 300 K respectively.
The cell reaction is
Zn(s) + Cu2+ (aq) $$\buildrel \, \over \longrightarrow $$ Zn2+ (aq) + Cu(s)

The standard reaction enthalpy ($$\Delta $$rH$${^o }$$) at 300 K in kJ mol–1 is, [Use R = 8 JK–1 mol–1 and F = 96,000C mol–1]
8
Decomposition of X exhibits a rate constant of 0.05 $$\mu $$g/year. How many year are required for the decomposition of 5$$\mu $$g of X into 2.5 $$\mu $$g?
9
Among the following compounds most basic amino acid is -
10
The metal d-orbitals that are directly facing the ligands in K3[Co(CN)6] are -
11
The element with Z = 120 (not yet discovered) will be an/a -
12
The hardness of a water sample (in terms of equivalents of CaCO3) containing 10–3 M CaSO4 is (Molar mass of CaSO4 = 136 g mol–1)
13
Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A, then molecular weight of Y is -
14
50 mL of 0.5 M oxalic acid is needed to neutralize 25 mL of sodium hydroxide solution. The amount of NaOH in 50 mL of the given sodium hydroxide solution is -
15
For diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?
16
JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Alcohols, Phenols and Ethers Question 130 English
can not be prepared by -
17
The correct order for acid strength of compounds :

CH $$ \equiv $$ CH, CH3–C $$ \equiv $$ CH and CH2 = CH2 is as follows
18
In the following reaction, products A and B are –

JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 187 English
19
What is the work function of the metal if the light of wavelength 4000$$\mathop A\limits^ \circ $$ generates photoelectrons of velocity 6 $$ \times $$ 105 ms–1 from it ?
(Mass of electron = 9 $$ \times $$ 10–31 kg;
Velocity of light = 3 $$ \times $$ 108 ms$$-$$1
Plank's constant = 6.626 $$ \times $$ 10–34 Js;
Charge of electron = 1.6 $$ \times $$10–19 JeV–1)
20
The pair of metal ions that can give a spin only magnetic moment of 3.9 BM for the complex [M(H2O)6]Cl2, is -
21
Among the following four aromatic compounds, which one will have the lowest melting point ?
22
In the following reaction :

Aldehyde + Alcohol   $$\buildrel {HCl} \over \longrightarrow $$  Acetal

Aldehyde                    Alcohol
HCHO tBuOH
CH3CHO MeOH

The best combination is

Mathematics

1
If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :
2
A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of $${\left( {{2^{1/3}} + {1 \over {2{{\left( 3 \right)}^{1/3}}}}} \right)^{10}}$$ is :
3
Let f and g be continuous functions on [0, a] such that f(x) = f(a – x) and g(x) + g(a – x) = 4, then $$\int\limits_0^a \, $$f(x) g(x) dx is equal to :
4
If $${{z - \alpha } \over {z + \alpha }}\left( {\alpha \in R} \right)$$ is a purely imaginary number and | z | = 2, then a value of $$\alpha $$ is :
5
Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is :
6
In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :
7
The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 – x2 such that the rectangle lies inside the parabola, is :
8
If the vertices of a hyperbola be at (–2, 0) and (2, 0) and one of its foci be at (–3, 0), then which one of the following points does not lie on this hyperbola?
9
Let P(4, –4) and Q(9, 6) be two points on the parabola, y2 = 4x and let x be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of $$\Delta $$PXQ is maximum. Then this maximum area (in sq. units) is :
10
Consider three boxes, each containing, 10 balls labelled 1, 2, … , 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n1 < n2 < n3 is :
11
Let P = $$\left[ {\matrix{ 1 & 0 & 0 \cr 3 & 1 & 0 \cr 9 & 3 & 1 \cr } } \right]$$ and Q = [qij] be two 3 $$ \times $$ 3 matrices such that Q – P5 = I3.

Then $${{{q_{21}} + {q_{31}}} \over {{q_{32}}}}$$ is equal to :
12
If $$\lambda $$ be the ratio of the roots of the quadratic equation in x, 3m2x2 + m(m – 4)x + 2 = 0, then the least value of m for which $$\lambda + {1 \over \lambda } = 1,$$ is
13
An ordered pair ($$\alpha $$, $$\beta $$) for which the system of linear equations
(1 + $$\alpha $$) x + $$\beta $$y + z = 2
$$\alpha $$x + (1 + $$\beta $$)y + z = 3
$$\alpha $$x + $$\beta $$y + 2z = 2
has a unique solution, is :
14
The maximum value of 3cos$$\theta $$ + 5sin $$\left( {\theta - {\pi \over 6}} \right)$$ for any real value of $$\theta $$ is :
15
Let S be the set of all points in (–$$\pi $$, $$\pi $$) at which the function, f(x) = min{sin x, cos x} is not differentiable. Then S is a subset of which of the following ?
16
The integral $$\int \, $$cos(loge x) dx is equal to : (where C is a constant of integration)
17
$$\mathop {\lim }\limits_{x \to \pi /4} {{{{\cot }^3}x - \tan x} \over {\cos \left( {x + {\pi \over 4}} \right)}}$$ is :
18
The area (in sq. units) of the region bounded by the parabola, y = x2 + 2 and the lines, y = x + 1, x = 0 and x = 3, is
19
For x > 1, if (2x)2y = 4e2x$$-$$2y,

then (1 + loge 2x)2 $${{dy} \over {dx}}$$ is equal to :
20
If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, $$\beta $$), then $$\beta $$ equals :
21
Considering only the principal values of inverse functions, the set
A = { x $$ \ge $$ 0: tan$$-$$1(2x) + tan$$-$$1(3x) = $${\pi \over 4}$$}
22
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :
23
Let y = y(x) be the solution of the differential equation, x$${{dy} \over {dx}}$$ + y = x loge x, (x > 1). If 2y(2) = loge 4 $$-$$ 1, then y(e) is equal to :

Physics

1
For the given cyclic process CAB as shown for a gas, the work done is :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Heat and Thermodynamics Question 322 English
2
The output of the given logic circuit is :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Semiconductor Question 158 English
3
The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 $$\mu $$m diameter of a wire is :
4
A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be :
5
What is the position and nature of image formed by lens combination shown in figure ? (f1, f2 are focal lengths)

JEE Main 2019 (Online) 12th January Morning Slot Physics - Geometrical Optics Question 171 English
6
A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx2 , is given by :
7
A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the following is a correct statement about the wave ?
8
In the figure shown, a circuit contains two identical resistors with resistance R = 5$$\Omega $$ and an inductance with L = 2mH. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is closed ?

JEE Main 2019 (Online) 12th January Morning Slot Physics - Alternating Current Question 141 English
9
In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Capacitor Question 119 English
10
A simple pendulum, made of a string of length $$\ell $$ and a bob of mass m, is released from a small angle $${{\theta _0}}$$. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle $${{\theta _1}}$$. Then M is given by :
11
In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation $${{dR} \over {d\ell }}$$ of its resistance R with length $$\ell $$ is $${{dR} \over {d\ell }}$$ $$ \propto $$ $${1 \over {\sqrt \ell }}$$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?

JEE Main 2019 (Online) 12th January Morning Slot Physics - Current Electricity Question 254 English
12
The galvanometer deflection, when key K1 is closed but K2 is open, equals $$\theta $$0 (see figure). On closing K2 also and adjusting R2 to 5$$\Omega $$, the deflection in galvanometer becomes $${{{\theta _0}} \over 5}.$$ . The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery] :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Current Electricity Question 256 English
13
A point source of light, S is placed at distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below. The distance over which the man can see the image of the light source in the mirror is

JEE Main 2019 (Online) 12th January Morning Slot Physics - Geometrical Optics Question 172 English
14
The position vector of the centre of mass $$\overrightarrow r {\,_{cm}}\,$$ of an asymmetric uniform bar of negligible area of crosssection as shown in figure is :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Center of Mass and Collision Question 95 English
15
Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is :
16
Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Electrostatics Question 177 English
17
A light wave is incident normally on a glass slab of refractive index 1.5. If 4 % of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propagating in the glass medium will be :
18
A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $${{{\lambda _A}} \over {{\lambda _B}}}$$ is close to :
19
A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and the of the outer cylinder is K2. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :
20
An ideal gas occupies a volume of 2m3 at a pressure of 3 $$ \times $$ 106 Pa. The energy of the gas is :
21
A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :
22
As shown in the figure, two infinitely long, identical wires are bent by 90o and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude of the magnetic field at O is 10–4 T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be ($$\mu $$0 = 4$$\pi $$ $$ \times $$ 10–7 NA–2) :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Magnetic Effect of Current Question 159 English
23
Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P1 and P2 respectively, then :
24
A particle of mass m moves in a circular orbit in a central potential field U(r) = $${1 \over 2}$$ kr2. If Bohr 's quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as :
25
Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length $$\ell $$ and mass m. The rod is pivoted at its centre 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Simple Harmonic Motion Question 109 English
26
A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction , and (ii) in the opposite direction is :
27
A proton and an $$\alpha $$-particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp : r$$\alpha $$ of the circular paths described by them will be ;
28
There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(t)) of the distribution as a function of its instantaneous radius R (t) is :
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