Solved papers for JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Afternoon)

JEE Main Paper (Held on 10-4-2019 Afternoon) Total Questions - 90

1) A bullet of mass 20 g has an initial speed of \[1m{{s}^{-1}},\] just before it starts penetrating a mud wall of thickness 20 cm. if the wall offers a mean resistance of \[2.5\times {{10}^{2}}N,\] the speed of the bullet after emerging from the other side of the wall is close to:                             [JEE Main 10-4-2019 Afternoon]

A)

\[0.4m{{s}^{-1}}\]

B)

              \[0.1m{{s}^{-1}}\]

C)

\[0.3m{{s}^{-1}}\]

D)

\[0.7m{{s}^{-1}}\]

View Answer
2) The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used? [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{{{b}^{2}}c}{a}\]

B)

\[\frac{{{b}^{2}}}{ac}\]

C)

\[\frac{a}{c}\]

D)

\[\frac{b}{c}\]

View Answer
3) The magnitude of the magnetic field at the center of an equilateral triangular loop of side 1m which is carrying a current of 10 A is : \[[\text{Take}\,{{\mu }_{0}}=4\pi \times {{10}^{-7}}N{{A}^{-2}}]\] [JEE Main 10-4-2019 Afternoon]

A)

\[18\mu T\]

B)

\[3\mu T\]

C)

\[1\mu T\]

D)

\[9\mu T\]

View Answer
4) A submarine experiences a pressure of \[5.05\times {{10}^{6}}\]Pa at a depth of \[{{d}_{1}}\]in a sea. When it goes further to a depth of \[{{d}_{2}},\]it experiences a pressure of \[8.08\times {{10}^{6}}Pa.,\]Then\[{{d}_{2}}-{{d}_{1}}\]is approximately (density of water \[={{10}^{3}}kg/{{m}^{3}}\]and acceleration due to gravity \[=10m{{s}^{-2}}\]) [JEE Main 10-4-2019 Afternoon]

A)

500 m

B)

400 m

C)

300 m

D)

600 m

View Answer
5) A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be : [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{3m}{\pi }\]

B)

\[\frac{4m}{\pi }\]

C)

\[\frac{2m}{\pi }\]

D)

\[\frac{m}{\pi }\]

View Answer
6) The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit? [JEE Main 10-4-2019 Afternoon]

A)

1.16 mm

B)

0.90 mm

C)

1.36 mm

D)

1.00 mm

View Answer
7) A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet?

[Given : Mass of planet \[=8\times {{10}^{22}}kg;\]

Radius of planet \[=2\times {{10}^{6}}m,\]

Gravitational constant

\[G=6.67\times {{10}^{11}}\]\[\text{ }N{{m}^{2}}/k{{g}^{2}}\]]

[JEE Main 10-4-2019 Afternoon]

A)

9

B)

11

C)

13

D)

17

View Answer
8) A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (Take velocity of sound in air is 350 m/s) [JEE Main 10-4-2019 Afternoon]

A)

857 Hz

B)

807 Hz

C)

750 Hz

D)

1143 Hz

View Answer
9) A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by : [JEE Main 10-4-2019 Afternoon]

A)

\[2\pi \sqrt{\frac{L}{\sqrt{{{g}^{2}}+{{\left( \frac{qE}{m} \right)}^{2}}}}}\]

B)

\[2\pi \sqrt{\frac{L}{\sqrt{g+\left( \frac{qE}{m} \right)}}}\]

C)

\[2\pi \sqrt{\frac{L}{\left( g-\begin{matrix} qE \\ m \\ \end{matrix} \right)}}\]

D)

\[2\pi \sqrt{\frac{L}{\left( {{g}^{2}}-\begin{matrix} {{q}^{2}}{{E}^{2}} \\ {{m}^{2}} \\ \end{matrix} \right)}}\]

View Answer
10) Light is incident normally on a completely absorbing surface with an energy flux of \[25Wc{{m}^{-2}}.\]if the surface has an area of \[25c{{m}^{-2}},\]the momentum transferred to the surface in 40 min time duration will be : [JEE Main 10-4-2019 Afternoon]

A)

\[5.0\times {{10}^{3}}Ns\]

B)

\[3.5\times {{10}^{6}}Ns\]

C)

\[1.4\times {{10}^{6}}Ns\]

D)

\[6.3\times {{10}^{4}}Ns\]

View Answer
11) Space between two concentric conducting spheres of radii a and \[b\left( b>a \right)\] is filled with a medium of resistivity\[\rho \]. The resistance between the two spheres will be : [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{\rho }{4\pi }\left( \frac{1}{a}-\frac{1}{b} \right)\]

B)

\[\frac{\rho }{2\pi }\left( \frac{1}{a}-\frac{1}{b} \right)\]

C)

\[\frac{\rho }{2\pi }\left( \frac{1}{a}+\frac{1}{b} \right)\]

D)

\[\frac{\rho }{4\pi }\left( \frac{1}{a}+\frac{1}{b} \right)\]

View Answer
12) A coil of self inductance 10 mH and resistance \[0.1\Omega \] is connected through a switch to a battery of internal resistance \[0.9\Omega .\]After the switch is closed, the time taken for the current to attain 80% of the saturation value is : (Take \[\ln 5=1.6\]) [JEE Main 10-4-2019 Afternoon]

A)

0.103 s

B)

0.016 s

C)

0.002 s

D)

0.324 s

View Answer
13) Water from a tap emerges vertically downwards with an initial speed of \[1.0m{{s}^{-1}}.\]The cross-sectional area of the tap is \[{{10}^{-4}}{{m}^{2}}.\] Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be: (Take \[g=10m{{s}^{-2}}\]) [JEE Main 10-4-2019 Afternoon]

A)

\[1\times {{10}^{5}}{{m}^{2}}\]

B)

\[5\times {{10}^{5}}{{m}^{2}}\]

C)

\[2\times {{10}^{5}}{{m}^{2}}\]

D)

\[5\times {{10}^{4}}{{m}^{2}}\]

View Answer
14) In the formula \[X=5Y{{Z}^{2}},X\] and \[Z\] have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units? [JEE Main 10-4-2019 Afternoon]

A)

\[[{{M}^{-2}}{{L}^{-2}}{{T}^{6}}{{A}^{3}}]\]

B)

\[[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}]\]

C)

\[[{{M}^{-3}}{{L}^{-2}}{{T}^{8}}{{A}^{4}}]\]

D)

\[[{{M}^{-2}}{{L}^{0}}{{T}^{-4}}{{A}^{-2}}]\]

View Answer
15) A 2 mW laser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is :

[Given Planck's constant \[h=6.6\times {{10}^{34}}Js,\] speed of light \[c=3.0\times {{10}^{8}}m/s\]]

[JEE Main 10-4-2019 Afternoon]

A)

\[2\times {{10}^{16}}\]

B)

\[1.5\times {{10}^{16}}\]

C)

\[5\times {{10}^{15}}\]

D)

\[1\times {{10}^{16}}\]

View Answer
16) When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by \[\Delta T.\]The heat required to produce the same change in temperature, at a constant pressure is : [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{7}{5}Q\]

B)

\[\frac{3}{2}Q\]

C)

\[\frac{5}{3}Q\]

D)

\[\frac{2}{3}Q\]

View Answer
17) A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5 s, is close to: [JEE Main 10-4-2019 Afternoon]

A)

\[4.0\times {{10}^{6}}Nm\]

B)

\[2.0\times {{10}^{5}}Nm\]

C)

\[1.6\times {{10}^{5}}Nm\]

D)

\[7.9\times {{10}^{6}}\text{ }Nm\]

View Answer
18) The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6V and the load resistance is \[{{R}_{L}}=4k\Omega .\]The series resistance of the circuit is \[{{R}_{i}}=1\,k\Omega .\]If the battery voltage \[{{V}_{B}}\]varies from 8V to 16V, what are the minimum and maximum values of the current through Zener diode? [JEE Main 10-4-2019 Afternoon]

A)

0.5 mA ; 6 mA

B)

0.5 mA ; 8.5 Ma

C)

1.5 mA ; 8.5 mA

D)

1 mA ; 8.5 mA

View Answer
19) In \[L{{i}^{++}},\]electron in first Bohr orbit is excited to a level by a radiation of wavelength\[\lambda .\] when the ion gets excited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of \[\lambda \]?

(Given : \[h=6.63\times {{10}^{34\text{ }}}Js;c=3\times {{10}^{8}}m{{s}^{1}}\])

[JEE Main 10-4-2019 Afternoon]

A)

9.4 nm

B)

12.3 nm

C)

10.8 nm

D)

11.4 nm

View Answer
20) A plane is inclined at an angle \[\alpha =30{}^\circ \]with a respect to the horizontal. A particle is projected with a speed \[u=2m{{s}^{-1}}\]from the base of the plane, making an angle \[\theta ={{15}^{o}}\]with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to : (Take \[g=10\,m{{s}^{-2}}\]) [JEE Main 10-4-2019 Afternoon]

A)

14 cm

B)

20 cm

C)

18 cm

D)

26 cm

View Answer
21) In free space, a particle A of charge \[1\mu C\]is held fixed at a point P. Another particle B of the same charge and mass \[4\mu g\]is kept at a distance of 1 mm from P. if B is released, then its velocity at a distance of 9 mm from P is : \[\left[ \text{Take}\frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}N{{m}^{2}}{{C}^{-2}} \right]\] [JEE Main 10-4-2019 Afternoon]

A)

\[2.0\times {{10}^{3}}m/s\]

B)

\[3.0\times {{10}^{4}}m/s\]

C)

\[1.5\times {{10}^{2}}m/s\]

D)

\[1.0\,m/s\]

View Answer
22) A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? (Take density of water \[={{10}^{3}}kg/{{m}^{3}}\]) [JEE Main 10-4-2019 Afternoon]

A)

65.4 kg

B)

87.5 kg

C)

30.1 kg

D)

46.3 kg

View Answer
23)             The time dependence of the position of a particle of mass \[m=2\]is given by \[\vec{r}(t)=2t\hat{i}-3{{t}^{2}}\hat{j}.\] Its angular momentum, with respect to the origin, at time \[t=2\]is : [JEE Main 10-4-2019 Afternoon]

A)

\[36\hat{k}\]

B)

\[-34(\hat{k}-\hat{i})\]

C)

\[48(\hat{i}+\hat{j})\]

D)

\[-48\hat{k}\]

View Answer
24) In an experiment, bras and steel wires of length 1m each with areas of cross section \[1m{{m}^{2}}\]are used. teh wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is : (Given, the Young's Modulus for steel and brass are respectively, \[120\times {{10}^{9}}\text{ }N/{{m}^{2}}\] and \[60\times {{10}^{9}}\text{ }N/{{m}^{2}}\]) [JEE Main 10-4-2019 Afternoon]

A)

\[0.2\times {{10}^{6}}\text{ }N/{{m}^{2}}\]

B)

\[4.0\times {{10}^{6}}\text{ }N/{{m}^{2}}\]

C)

\[1.8\times {{10}^{6}}\text{ }N/{{m}^{2}}\]

D)

\[1.2\times {{10}^{6}}\text{ }N/{{m}^{2}}\]

View Answer
25) Two blocks A and B of masses \[{{m}_{A}}=1kg\]and \[{{m}_{B}}=3kg\]are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is: (Take \[g=10\text{ }m/{{s}^{2}}\]) [JEE Main 10-4-2019 Afternoon]

A)

16 N

B)

40 N

C)

12 N

D)

8 N

View Answer
26) In a Young's double slit experiment, the ratio of the slit's width is 4:1. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be: [JEE Main 10-4-2019 Afternoon]

A)

\[{{(\sqrt{3}+1)}^{4}}:16\]

B)

\[9:1\]

C)

\[4:1\]

D)

\[25:9\]

View Answer
27) A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of \[\frac{7M}{8}\]and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let \[{{I}_{1}}\] be the moment of inertia of the disc about its axis and \[{{I}_{2}}\]be the moment of inertia of the new sphere about its axis. The ratio \[{{I}_{1}}/{{I}_{2}}\] is given by: [JEE Main 10-4-2019 Afternoon]

A)

185

B)

65

C)

285

D)

140

View Answer
28) The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz is : [JEE Main 10-4-2019 Afternoon]

A)

B)

C)

D)

View Answer
29) Two radioactive substances A and B have decay constants \[5\lambda \]and \[\lambda \]respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become\[{{\left( \frac{1}{e} \right)}^{2}}\]will be : [JEE Main 10-4-2019 Afternoon]

A)

\[1/4\lambda \]

B)

\[1/\lambda \]

C)

\[1/2\lambda \]

D)

\[2/\lambda \]

View Answer
30) One mole of an ideal gas passes through a process where pressure and volume obey the relation \[P={{P}_{0}}\left[ 1-\frac{1}{2}{{\left( \frac{{{V}_{0}}}{V} \right)}^{2}} \right].\] Here \[{{P}_{0}}\]and \[{{V}_{0}}\] are constants. Calculate the change in the temperature of the gas if its volume changes from \[{{V}_{0}}\] to \[2{{V}_{0}}\]. [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{1}{2}\frac{{{P}_{0}}{{V}_{0}}}{R}\]

B)

\[\frac{3}{4}\frac{{{P}_{0}}{{V}_{0}}}{R}\]

C)

\[\frac{5}{4}\frac{{{P}_{0}}{{V}_{0}}}{R}\]

D)

\[\frac{1}{4}\frac{{{P}_{0}}{{V}_{0}}}{R}\]

View Answer

31) The correct match between Item-I and Item-II is:

	Item-I		Item-II
[a]	High density polythene	(I)	Peroxide catalyst
[b]	Polyacreylonitrile	(II)	Condensation at high temperature & pressure
[c]	Novolac	(III)	Ziegler-Natta Catalyst
[d]	Nylon 6	(IV)	Acid or base catalyst

[JEE Main 10-4-2019 Afternoon]

\[\left( a \right)\to \left( III \right),\left( b \right)\to \left( I \right),\left( c \right)\to \left( II \right),\left( d \right)\to \left( IV \right)\]

\[\left( a \right)\to \left( IV \right),\left( b \right)\to \left( II \right),\left( c \right)\to \left( I \right),\left( d \right)\to \left( III \right)\]

\[\left( a \right)\to \left( II \right),\left( b \right)\to \left( IV \right),\left( c \right)\to \left( I \right),\left( d \right)\to \left( III \right)\]

\[\left( a \right)\to \left( III \right),\left( b \right)\to \left( I \right),\left( c \right)\to \left( IV \right),\left( d \right)\to \left( II \right)\]

View Answer

32) Which of the following is NOT a correct method of the preparation of benzylamine from cyanobenzene? [JEE Main 10-4-2019 Afternoon]

A)

\[(i)HCl/{{H}_{2}}O\]                       \[(ii)NaB{{H}_{4}}\]

B)

\[(i)LiAI{{H}_{4}}\]              \[(ii){{H}_{3}}{{O}^{+}}\]

C)

\[(i)SnC{{l}_{2}}+HC{{l}_{(gas)}}\]         \[(ii)NaB{{H}_{4}}\]

D)

\[{{H}_{2}}/Ni\]

View Answer
33) Which of these factors does not govern the stability of a conformation in acyclic compounds? [JEE Main 10-4-2019 Afternoon]

A)

Torsional strain

B)

Angle strain

C)

Steric interactions

D)

Electrostatic forces of interaction

View Answer
34) The difference between \[\Delta H\]and \[(\Delta H-\Delta U),\]when the combustion of one mole of heptane (1) is carried out at a temperature T, is equal to: [JEE Main 10-4-2019 Afternoon]

A)

3RT

B)

-3RT

C)

-4RT

D)

4RT

View Answer
35) For the reaction of\[{{H}_{2}}\]with\[{{I}_{2}},\]the rate constant is \[2.5\times {{10}^{-4}}d{{m}^{3}}mo{{l}^{-1}}{{s}^{-1}}\]at \[327{}^\circ C\] and \[1.0d{{m}^{3}}mo{{l}^{-1}}{{s}^{-1}}\]at \[527{}^\circ C.\]The activation energy for the reaction, in \[kJ\,mo{{l}^{-1}}\]is: \[\left( R=8.314J\text{ }{{K}^{1}}mo{{l}^{1}} \right)\] [JEE Main 10-4-2019 Afternoon]

A)

72

B)

166

C)

150

D)

59

View Answer

36) The correct statements among [a] to [b] are: [JEE Main 10-4-2019 Afternoon]

[a] saline hydrides produce \[{{H}_{2}}\]gas when reacted with \[{{H}_{2}}O\].

[b] reaction of \[LiA{{H}_{4}}\]with \[B{{F}_{3}}\]leads to \[{{B}_{2}}{{H}_{6}}.\]

[c] \[P{{H}_{3}}\] and \[C{{H}_{4}}\] are electron - rich and electron precise hydrides, respectively.

[d] \[HF\]and \[C{{H}_{4}}\]are called as molecular hydrides.

[c] and [d] only

[a], [b] and [c] only

[a], [b], [c] and [d]

[a], [c] and [d] only

View Answer

37) The increasing order of nucleophilicity of the following nucleophiles is :

[a]\[C{{H}_{3}}CO_{2}^{\Theta }\]

[b]\[{{H}_{2}}O\]

[c]\[C{{H}_{3}}SO_{3}^{\Theta }\]

[d]\[\overset{\Theta }{\mathop{O}}\,H\]

[JEE Main 10-4-2019 Afternoon]

[b] < [c] < [a] < [d]

[a] < [d] < [c] < [b]

[d] < (a] < [c] < [b]

[b] < [c] < [d] < [a]

View Answer

38) Number of stereo centers present in linear and cyclic structures of glucose are respectively : [JEE Main 10-4-2019 Afternoon]

A)

4 & 5

B)

5 & 5

C)

4 & 4

D)

5 & 4

View Answer
39) A hydrated solid X on heating initially gives a monohydrated compound Y. Y upon heating above 373K leads to an anhydrous white powder Z. X and Z, respectively, are: [JEE Main 10-4-2019 Afternoon]

A)

Washing soda and soda ash.

B)

Washing soda and dead burnt plaster.

C)

Baking soda and dead burnt plaster.

D)

Baking soda and soda ash.

View Answer
40) The number of pentagons in \[{{C}_{60}}\]and trigons (triangles) in white phosphorus, respectively, are: [JEE Main 10-4-2019 Afternoon]

A)

12 and 3

B)

20 and 4

C)

12 and 4

D)

20 and 3

View Answer
41) The correct order of the first ionization enthalpies is: [JEE Main 10-4-2019 Afternoon]

A)

\[Mn<Ti<Zn<Ni\]

B)

\[Ti<Mn<Ni<Zn\]

C)

\[Zn<Ni<Mn<Ti\]

D)

\[Ti<Mn<Zn<Ni\]

View Answer
42) The correct option among the following is : [JEE Main 10-4-2019 Afternoon]

A)

Colloidal particles in lyophobic sols can be precipiated by electrophoresis.

B)

Brownian motion in colloidal solution is faster the viscosity of the solution is very high.

C)

Colloidal medicines are more effective because they have small surface area.

D)

Addition of alum to water makes it unfit for drinking.

View Answer
43) Points I, II and III in the following plot respectively correspond to (\[{{V}_{mp}}:\]most probable velocity) [JEE Main 10-4-2019 Afternoon]

A)

\[{{V}_{mp}}\]of\[{{N}_{2}}(300K);\]\[{{V}_{mp}}\]of\[{{H}_{2}}(300K);\]\[{{V}_{mp}}\]of \[{{O}_{2}}(400K)\]

B)

\[{{V}_{mp}}\]of\[{{H}_{2}}(300K);\]\[{{V}_{mp}}\]of\[{{N}_{2}}(300K);\]\[{{V}_{mp}}\]of\[{{O}_{2}}(400K)\]

C)

\[{{V}_{mp}}\]of\[{{O}_{2}}(400K);\]\[{{V}_{mp}}\]of\[{{N}_{2}}(300K);\]\[{{V}_{mp}}\]of\[{{H}_{2}}(300K)\]

D)

\[{{N}_{2}}(300K);\]\[{{V}_{mp}}\]of\[{{O}_{2}}(400K);\]\[{{V}_{mp}}\]of\[{{H}_{2}}(300K)\]

View Answer
44) The INCORRECT statement is : [JEE Main 10-4-2019 Afternoon]

A)

the spin-only magnetic moments of \[{{[Fe{{({{H}_{2}}O)}_{6}}]}^{2+}}\] and \[{{[Cr{{({{H}_{2}}O)}_{6}}]}^{2+}}\]are nearly similar.

B)

the spin-only magnetic moment of \[{{[Ni{{(N{{H}_{3}})}_{4}}{{({{H}_{2}}O)}_{2}}]}^{2+}}\]is \[2.83BM.\]

C)

the gemstone, ruby, has \[C{{r}^{3+}}\]ions occupying the octahedral sites of beryl.

D)

the color of \[{{[CoCl{{(N{{H}_{3}})}_{5}}]}^{2+}}\]is violet as it absorbs the yellow light.

View Answer
45) For the reaction, \[2S{{O}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2S{{O}_{3}}(g),\]\[\Delta H=-57.2kJ\,mo{{l}^{-1}}\] and \[{{K}_{c}}=1.7\times {{10}^{16}}.\] Which of the following statement is INCORRECT? [JEE Main 10-4-2019 Afternoon]

A)

The equilibrium constant is large suggestive of reaction going to completion and so no catalyst is required.

B)

The equilibrium will shift in forward direction as the pressure increase.

C)

The equilibrium constant decreases as the temperature increases.

D)

The addition of inert gas at constant volume will not affect the equilibrium constant.

View Answer
46) The pH of a \[0.02M\,N{{H}_{4}}Cl\]solution will be [given \[{{K}_{b}}(N{{H}_{4}}OH)={{10}^{-5}}\]and \[log2=0.301\]] [JEE Main 10-4-2019 Afternoon]

A)

4.65

B)

5.35

C)

4.35

D)

2.65

View Answer
47) The noble gas that does NOT occur in the atmosphere is: [JEE Main 10-4-2019 Afternoon]

A)

He

B)

Ra

C)

Ne

D)

Kr

View Answer
48) 1 g of non-volatile non-electrolyte solute is dissolved in 100g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1:5. The ratio of the elevation in their boiling points,\[\frac{\Delta {{T}_{b}}(A)}{\Delta {{T}_{b}}(B)},\]is: [JEE Main 10-4-2019 Afternoon]

A)

5 : 1

B)

10 : 1

C)

1 : 5

D)

1 : 0.2

View Answer
49) Which one of the following graphs between molar conductivity \[({{\Lambda }_{m}})\]versus\[\sqrt{C}\]is correct? [JEE Main 10-4-2019 Afternoon]

A)

B)

C)

D)

View Answer
50) The correct statement is: [JEE Main 10-4-2019 Afternoon]

A)

zincite is a carbonate ore

B)

aniline is a froth stabilizer

C)

zone refining process is used for the refining of titanium

D)

sodium cyanide cannot be used in the metallurgy of silver

View Answer
51) The minimum amount of\[{{O}_{2}}(g)\]consumed per gram of reactant is for the reaction:

(Given atomic mass : \[Fe=56,O=16,\]\[Mg=24,P=31,C=12,H=1\])

[JEE Main 10-4-2019 Afternoon]

A)

\[{{C}_{3}}{{H}_{8}}(g)+5{{O}_{2}}(g)\to 3C{{O}_{2}}(g)+4{{H}_{2}}O(l)\]

B)

\[{{P}_{4}}(s)+5{{O}_{2}}(g)\to {{P}_{4}}{{O}_{10}}(s)\]

C)

\[4Fe(s)+3{{O}_{2}}(g)\to 2Fe{{O}_{3}}(s)\]

D)

\[2Mg(s)+{{O}_{2}}(g)\to 2MgO(s)\]

View Answer
52) Air pollution that occurs in sunlight is: [JEE Main 10-4-2019 Afternoon]

A)

oxidising smog

B)

acid rain

C)

reducing smog

D)

fog

View Answer
53) The major product 'Y' in the following reaction is: [JEE Main 10-4-2019 Afternoon]

A)

B)

C)

D)

View Answer
54) Compound\[A({{C}_{9}}{{H}_{10}}O)\]shows positive iodo form test. Oxidation of A with \[KMn{{O}_{4}}/KOH\]gives acid \[B({{C}_{8}}{{H}_{6}}{{O}_{4}}).\]Anhydride of B is used for the preparation of phenolphthalein. Compound A is :- [JEE Main 10-4-2019 Afternoon]

A)

B)

C)

D)

View Answer
55) The crystal filed stabilization energy (CFSE) of \[[Fe{{({{H}_{2}}O)}_{6}}]C{{l}_{2}}\]and \[{{K}_{2}}[NiC{{l}_{4}}],\]respectively, are :- [JEE Main 10-4-2019 Afternoon]

A)

\[-0.4{{\Delta }_{o}}\] and \[-0.8{{\Delta }_{t}}\]

B)

\[-0.4{{\Delta }_{o}}\]and \[-1.2{{\Delta }_{t}}\]

C)

\[-2.4{{\Delta }_{o}}\] and \[-1.2{{\Delta }_{t}}\]

D)

\[-0.6{{\Delta }_{o}}\] and \[-0.8{{\Delta }_{t}}\]

View Answer
56) The major product obtained in the given reaction is :- [JEE Main 10-4-2019 Afternoon]

A)



B)

C)



D)



View Answer
57) The highest possible oxidation states of uranium and plutonium, respectively, are :- [JEE Main 10-4-2019 Afternoon]

A)

6 and 4

B)

7 and 6

C)

4 and 6

D)

6 and 7

View Answer
58) In chromatography, which of the following statements is INCORRECT for \[{{R}_{f}}\]? [JEE Main 10-4-2019 Afternoon]

A)

\[{{R}_{f}}\]value depends on the type of chromatography.

B)

The value of \[{{R}_{f}}\] can not be more than one.

C)

Higher \[{{R}_{f}}\] value means higher adsorption.

D)

\[{{R}_{f}}\] value is dependent on the mobile phase.

View Answer
59) The major product 'Y' in the following reaction is:- [JEE Main 10-4-2019 Afternoon]

A)

B)

C)

D)

View Answer
60) The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are: [JEE Main 10-4-2019 Afternoon]

A)

Paschen and P fund

B)

Lyman and Paschen

C)

Brackett and Piund

D)

Balmer and Brackett

View Answer
61) The distance of the point having position vector \[-\hat{i}+2\hat{j}+6\hat{k}\] from the straight line passing through the point (2, 3, -4) and parallel to the vector, \[6\hat{i}+3\hat{j}-4\hat{k}\]is: [JEE Main 10-4-2019 Afternoon]

A)

\[7\]

B)

\[4\sqrt{3}\]

C)

\[2\sqrt{13}\]

D)

6

View Answer
62) If both the mean and the standard deviation of 50 observations \[{{x}_{1}},{{x}_{2}}....,{{x}_{50}}\] are equal to 16, then the mean of \[{{({{x}_{1}}-4)}^{2}},{{({{x}_{2}}-4)}^{2}},.....\]\[{{({{x}_{50}}-4)}^{2}}\]is : [JEE Main 10-4-2019 Afternoon]

A)

525

B)

380

C)

480

D)

400

View Answer
63) A perpendicular is drawn from a point on the line \[\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{1}\]to the plane \[x+y+z=3\] such that the foot of the perpendicular Q also lies on the plane \[xy+z=3.\]Then the co-ordinates of Q are : [JEE Main 10-4-2019 Afternoon]

A)

\[\left( 2,0,1 \right)\]

B)

\[\left( 4,0,1 \right)\]

C)

\[\left( 1,0,4 \right)\]

D)

\[\left( 1,0,2 \right)\]

View Answer
64) The tangent and normal to the ellipse \[3{{x}^{2}}+5{{y}^{2}}=32\]at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is : [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{14}{3}\]

B)

\[\frac{16}{3}\]

C)

\[\frac{68}{15}\]

D)

\[\frac{34}{15}\]

View Answer
65) Let\[\lambda \] be a real number for which the system of linear equations

\[x+y+z=6\]

\[4x+\lambda y\lambda z=\lambda 2\]

\[3x+2y4z=5\]

has infinitely many solutions. Then\[\lambda \]is a root of the quadratic equation.

[JEE Main 10-4-2019 Afternoon]

A)

\[{{\lambda }^{2}}-3\lambda -4=0\]

B)

\[{{\lambda }^{2}}-\lambda -6=0\]

C)

\[{{\lambda }^{2}}+3\lambda -4=0\]

D)

\[{{\lambda }^{2}}+\lambda -6=0\]

View Answer
66) The smallest natural number n, such that the coefficient of x in the expansion of\[{{\left( {{x}^{2}}+\frac{1}{{{x}^{3}}} \right)}^{n}}\]is \[^{n}{{C}_{23}},\]is : [JEE Main 10-4-2019 Afternoon]

A)

35

B)

38

C)

23

D)

58

View Answer
67) A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of \[50\text{ }c{{m}^{3}}/min.\]When the thickness of the ice is 5cm, then the rate at which the thickness (in cm/min) of the ice decreases, is : [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{1}{9\pi }\]

B)

\[\frac{5}{6\pi }\]

C)

\[\frac{1}{18\pi }\]

D)

\[\frac{1}{36\pi }\]

View Answer
68) If \[5x+9=0\]is the directrix of the hyperbola \[16{{x}^{2}}9{{y}^{2}}=144,\]then its corresponding focus is: [JEE Main 10-4-2019 Afternoon]

A)

\[\left( -\frac{5}{3},0 \right)\]

B)

\[(5,0)\]

C)

\[(-5,0)\]

D)

\[\left( \frac{5}{3},0 \right)\]

View Answer
69) The sum \[1+\frac{{{1}^{3}}+{{2}^{3}}}{1+2}+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}{1+2+3}+....\] \[+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+....+{{15}^{3}}}{1+2+3+....+15}-\frac{1}{2}(1+2+3+....+15)]\] [JEE Main 10-4-2019 Afternoon]

A)

1240

B)

1860

C)

660

D)

620

View Answer
70) If the line \[ax+y=c,\]touches both the curves \[{{x}^{2}}+{{y}^{2}}=1\] and \[{{y}^{2}}=4\sqrt{2}\text{ }x,\]then \[|c|\]is equal to : [JEE Main 10-4-2019 Afternoon]

A)

\[1/2\]

B)

\[2\]

C)

\[\sqrt{2}\]

D)

\[\frac{1}{\sqrt{2}}\]

View Answer
71) If \[{{\cos }^{-1}}x-{{\cos }^{-1}}\frac{y}{2}=\alpha ,\] where \[-1\le x\le 1,\]\[-2\le y\le 2,x\le \frac{y}{2},\]then for all x, y, \[4{{x}^{2}}-4xy\cos \alpha +{{y}^{2}}\]is equal to [JEE Main 10-4-2019 Afternoon]

A)

\[4{{\sin }^{2}}\alpha -2{{x}^{2}}{{y}^{2}}\]

B)

\[4{{\cos }^{2}}\alpha +2{{x}^{2}}{{y}^{2}}\]

C)

\[4{{\sin }^{2}}\alpha \]

D)

\[2{{\sin }^{2}}\alpha \]

View Answer
72) If \[\int_{{}}^{{}}{{{x}^{5}}{{e}^{-{{x}^{2}}}}dx}=g(x){{e}^{-{{x}^{2}}}}+c,\]where c is a constant of integration, then g(-1) is equal to: [JEE Main 10-4-2019 Afternoon]

A)

\[-\frac{5}{2}\]

B)

\[1\]

C)

\[-\frac{1}{2}\]

D)

\[-1\]

View Answer
73) The locus of the centres of the circles, which touch the circle, \[{{x}^{2}}+{{y}^{2}}=1\]externally, also touch the y-axis and lie in the first quadrant, is : [JEE Main 10-4-2019 Afternoon]

A)

\[y=\sqrt{1+4x},x\ge 0\]

B)

\[x=\sqrt{1+4y},y\ge 0\]

C)

\[x=\sqrt{1+2y},y\ge 0\]

D)

\[y=\sqrt{1+2x},x\ge 0\]

View Answer
74) Lines are drawn parallel to the line \[4x3y+2=0,\]at a distance \[\frac{3}{5}\]from the origin. Then which one of the following points lies on any of these lines? [JEE Main 10-4-2019 Afternoon]

A)

\[\left( -\frac{1}{4},\frac{2}{3} \right)\]

B)

\[\left( \frac{1}{4},\frac{1}{3} \right)\]

C)

\[\left( -\frac{1}{4},-\frac{2}{3} \right)\]

D)

\[\left( \frac{1}{4},-\frac{1}{3} \right)\]

View Answer
75) The area (in sq. units) of the region bounded by the curves \[y={{2}^{x}}\]and \[y=\left| x+1 \right|,\] in the first quadrant is : [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{3}{2}-\frac{1}{{{\log }_{e}}2}\]

B)

\[\frac{1}{2}\]

C)

\[{{\log }_{e}}2+\frac{3}{2}\]

D)

\[\frac{3}{2}\]

View Answer
76) If the plane \[2xy+2z+3=0\]has the distances \[\frac{1}{3}\]and\[\frac{2}{3}\]units from the planes \[4x2y+4z+\lambda =0\]and\[2xy+2z+\mu =0,\]respectively, then the maximum value of \[\lambda +\mu \] is equal to : [JEE Main 10-4-2019 Afternoon]

A)

15

B)

5

C)

13

D)

9

View Answer
77) If z and w are two complex numbers such that \[\left| zw \right|=1\]and \[arg\left( z \right)arg\left( \text{w} \right)=\frac{\pi }{2},\]then : [JEE Main 10-4-2019 Afternoon]

A)

\[\overline{z}\,\text{w}=i\]

B)

\[\overline{z}\,\text{w}=-i\]

C)

\[\,z\,\overline{\text{w}}=\frac{1-i}{\sqrt{2}}\]

D)

\[\,z\,\overline{\text{w}}=\frac{-1+i}{\sqrt{2}}\]

View Answer
78) Let a, b and c be in G. P. with common ratio where\[a\ne 0\]and \[0<r\le \frac{1}{2}.\] If 3a, 7b and 15c are the first three terms of an A. P., then the 4th term of this A. P. is: [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{7}{3}a\]

B)

\[a\]

C)

\[\frac{2}{3}a\]

D)

\[5a\]

View Answer
79) The integral\[\int\limits_{\pi /6}^{\pi /3}{{{\sec }^{2/3}}}x\cos e{{c}^{4/3}}xdx\]equal to : [JEE Main 10-4-2019 Afternoon]

A)

\[{{3}^{7/6}}-{{3}^{5/6}}\]

B)

\[{{3}^{5/3}}-{{3}^{1/3}}\]

C)

\[{{3}^{4/3}}-{{3}^{1/3}}\]

D)

\[{{3}^{5/6}}-{{3}^{2/3}}\]

View Answer
80) Let \[y=y\left( x \right)\] be the solution of the differential equation, \[\frac{dy}{dx}+y\tan x=2x+{{x}^{2}}\tan x,\] \[x\in \left( -\frac{\pi }{2},\frac{\pi }{2} \right),\]such that \[y(0)=1.\]Then : [JEE Main 10-4-2019 Afternoon]

A)

\[y'\left( \frac{\pi }{4} \right)+y'\left( \frac{-\pi }{4} \right)=-\sqrt{2}\]

B)

\[y'\left( \frac{\pi }{4} \right)-y'\left( \frac{-\pi }{4} \right)=\pi -\sqrt{2}\]

C)

\[y\left( \frac{\pi }{4} \right)-y\left( -\frac{\pi }{4} \right)=\sqrt{2}\]

D)

\[y\left( \frac{\pi }{4} \right)+y\left( -\frac{\pi }{4} \right)=\frac{{{\pi }^{2}}}{2}+2\]

View Answer
81) Let \[{{a}_{1}},{{a}_{2}},{{a}_{3}},\]......be an A. P. with \[{{a}_{6}}=2.\]Then the common difference of this A. P., which maximizes the produce \[{{a}_{1}}{{a}_{4}}{{a}_{5}},\]is : [JEE Main 10-4-2019 Afternoon]

A)

\[\frac{6}{5}\]

B)

\[\frac{8}{5}\]

C)

\[\frac{2}{3}\]

D)

\[\frac{3}{2}\]

View Answer
82)             The angles A, B and C of a triangle ABC are in A.P. and\[a:b=1:\sqrt{3}.\] If \[c=4\text{ }cm,\] then the area (in sq. cm) of this triangle is: [JEE Main 10-4-2019 Afternoon]

A)

\[4\sqrt{3}\]

B)

\[\frac{2}{\sqrt{3}}\]

C)

\[2\sqrt{3}\]

D)

\[\frac{4}{\sqrt{3}}\]

View Answer
83) Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is : [JEE Main 10-4-2019 Afternoon]

A)

5

B)

6

C)

7

D)

8

View Answer
84) Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number beams is : [JEE Main 10-4-2019 Afternoon]

A)

210

B)

190

C)

170

D)

180

View Answer
85) The sum of the real roots of the equatuion\[\left| \begin{matrix} x & -6 & -1 \\ 2 & -3x & x-3 \\ -3 & 2x & x+2 \\ \end{matrix} \right|=0,\]is equal to: [JEE Main 10-4-2019 Afternoon]

A)

6

B)

1

C)

0

D)

-4

View Answer
86) Let \[f(x)\,\,\,=\,\,\,lo{{g}_{e}}(sin\,x),\,\,\,\,\,\,(0<x<\pi )\] and \[g(x)={{\sin }^{-1}}({{e}^{-\,x}}),(x\ge 0).\]If \[\alpha \]is a positive real number such that \[a=(fog)'(\alpha )\] and \[b=(fog)(\alpha ),\]then : [JEE Main 10-4-2019 Afternoon]

A)

\[a{{\alpha }^{2}}-b\alpha -a=0\]

B)

\[a{{\alpha }^{2}}+b\alpha -a=-2{{\alpha }^{2}}\]

C)

\[a{{\alpha }^{2}}+b\alpha +a=0\]

D)

\[a{{\alpha }^{2}}-b\alpha -a=1\]

View Answer
87) If the tangent to the curve \[y=\frac{x}{{{x}^{2}}-3},x\in R,\]\[\left( x\ne \pm \sqrt{3} \right),\]at a point \[(\alpha ,\beta )\ne (0,0)\] on it is parallel to the line \[2x+6y11=0,\]then : [JEE Main 10-4-2019 Afternoon]

A)

\[|6\alpha +2\beta |=19\]

B)

\[|2\alpha +6\beta |=11\]

C)

\[|6\alpha +2\beta |=9\]

D)

\[|2\alpha +6\beta |=19\]

View Answer
88)             The number of real roots of the equation \[5+|{{2}^{x}}-1|={{2}^{x}}({{2}^{x}}-2)\]is : [JEE Main 10-4-2019 Afternoon]

A)

2

B)

3

C)

4

D)

                         1

View Answer
89) If \[\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{2}}-ax+b}{x-1}=5,\] then\[a+b\]is equal to:- [JEE Main 10-4-2019 Afternoon]

A)

-7

B)

-4

C)

5

D)

1

View Answer
90) The negation of the boolean expression \[\tilde{\ }s\vee (\tilde{\ }r\wedge s)\]is equivalent to : [JEE Main 10-4-2019 Afternoon]

A)

\[r\]

B)

\[s\wedge r\]

C)

\[s\vee r\]

D)

\[\tilde{\ }s\wedge \tilde{\ }r\]

View Answer