# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 11-Jan-2019 Evening)

### done JEE Main Paper (Held On 11-Jan-2019 Evening) Total Questions - 90

• question_answer1) When 100 g of a liquid A at $100{}^\circ C$is added to 50 g of a liquid B at temperature$75{}^\circ C$, the temperature of the mixture becomes$90{}^\circ C$. The temperature of the mixture, if 100 g of liquid A at $100{}^\circ C$ is added to 50 g of liquid B at $50{}^\circ C$will b [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$70{}^\circ C$

B)
$85{}^\circ C$

C)
$60{}^\circ C$

D)
$80{}^\circ C$

• question_answer2) Two rods A and B of identical dimensions are at temperature $30{}^\circ C$. If A is heated upto $180{}^\circ C$and B upto $T{}^\circ C$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is $4:3$, then the value of T is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$200{}^\circ C$

B)
$270{}^\circ C$

C)
$230{}^\circ C$

D)
$250{}^\circ C$

• question_answer3) A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$10\text{ }rad/{{s}^{2}}$

B)
$\text{20 }rad/{{s}^{2}}$

C)
$\text{12 }rad/{{s}^{2}}$

D)
$\text{16 }rad/{{s}^{2}}$

• question_answer4) If speed (V), acceleration and force (F) are considered as fundamental units, the dimension of Young's modulus will be [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
${{V}^{-2}}{{A}^{2}}{{F}^{-2}}$

B)
${{V}^{-2}}{{A}^{2}}{{F}^{2}}$

C)
${{V}^{-4}}{{A}^{2}}F$

D)
${{V}^{-4}}{{A}^{-2}}F$

• question_answer5) A pendulum is executing simple harmonic motion and its maximum kinetic energy is ${{K}_{1}}$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case. its maximum kinetic energy is ${{K}_{2}}$. Then [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
${{K}_{2}}={{K}_{1}}$

B)
${{K}_{2}}=\frac{{{K}_{1}}}{2}$

C)
${{K}_{2}}=2{{K}_{1}}$

D)
${{K}_{2}}=\frac{{{K}_{1}}}{4}$

• question_answer6) In a double -slit experiment, green light $(\,5303\text{ }\overset{o}{\mathop{\text{A}}}\,)$ falls on a double slit having a separation of 19.44$\mu m$ and a width of 4.05$\mu m$. The number of bright fringes between the first and the second diffraction minima is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
10

B)
04

C)
05

D)
09

• question_answer7)           A particle of mass m is moving in a straight line with momentum p. Starting at time $t=0,$a force F = kt acts in the same direction on the moving particle during time interval so that its momentum changes from? to 3p. Here k is a constant. The value of T is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$2\sqrt{\frac{p}{k}}$

B)
$\sqrt{\frac{2k}{p}}$

C)
$\sqrt{\frac{2p}{k}}$

D)
$2\sqrt{\frac{k}{p}}$

• question_answer8) A particle of mass m and charge q is in an electric and magnetic field given by $\vec{E}=2\hat{i}+3\hat{j};\vec{B}=4\hat{j}+6\hat{k}.$ The charged particle is shifted from the origin to the point $P(x=1;y=1)$along a straight path. The magnitude of the total work done is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
(0.15)q

B)
(0.35)q

C)
(2.5)q

D)
5q

• question_answer9) An amplitude modulated signal is plotted below Which one of the following best describes the above signal? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$(9+\sin (2\pi \times {{10}^{4}}t))\sin (2.5\pi \times {{10}^{5}}t)V$

B)
$(9+\sin (2.5\pi \times {{10}^{5}}t))\sin (2\pi \times {{10}^{4}}t)V$

C)
$(9+\sin (4\pi \times {{10}^{4}}t))\sin (5\pi \times {{10}^{5}}t)V$

D)
$(1+9\sin (2\pi \times {{10}^{4}}t))\sin (2.5\pi \times {{10}^{5}}t)V$

• question_answer10) The region between$y=0$and$y=d$contains a magnetic field $\vec{B}=B\overset{\wedge }{\mathop{z}}\,.$ A particle of mass m and charge q enters the region with a velocity $\vec{v}=v\hat{i}.$ If $d=\frac{mv}{2qB},$ the acceleration of the charged particle at the point of its emergence at the other side is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{qvB}{m}\left( \frac{\hat{i}+\hat{j}}{\sqrt{2}} \right)$

B)
$\frac{qvB}{m}\left( \frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j} \right)$

C)
$\frac{qvB}{m}\left( \frac{1}{2}\hat{i}-\frac{\sqrt{3}}{2}\hat{j} \right)$

D)
$\frac{qvB}{m}\left( \frac{-\hat{j}+\hat{i}}{\sqrt{2}} \right)$

E)
None of these

• question_answer11) A   particle   moves   from   the   point $(2.0\hat{i}+4.0\hat{j})m,$at t = 0, with an initial velocity$(5.0\hat{i}+4.0\hat{j})m{{s}^{-1}}$. It is acted upon by a constant force which produces a constant acceleration $(4.0\hat{i}+4.0\hat{j})m{{s}^{-2}}.$ What is the distance of the particle from the origin at time 2s? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$20\sqrt{2}m$

B)
$5m$

C)
$15m$

D)
$10\sqrt{2}m$

• question_answer12) A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3 keeping the number of turns of the coil per unit length of the frame the same then the self-inductance of the coil [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
increases by a factor of 27

B)
decreases by a factor of $9\sqrt{3}$

C)
increases by a factor of 3

D)
decreases by a factor of 9

• question_answer13) A metal ball of mass 0.1 kg is heated upto $500{}^\circ C$ and dropped into a vessel of heat capacity$800\,\,J{{K}^{-1}}$ and containing 0.5 kg water. The initial temperature of water an d vessel is $30{}^\circ C$. What is the approximate percentage increment in the temperature of the water? [Specific heat capacities of water and metal are, respectively, 4200 $Jk{{g}^{-1}}\,{{K}^{-1}}$and 400 $J\,k{{g}^{-1}}\,{{K}^{-1}}$] [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
15%

B)
30%

C)
25%

D)
20%

• question_answer14) The circuit shown below contains two ideal diodes, each with a forward resistance of $50\Omega .$ If the battery voltage is 6 V, the current through the $100\Omega$resistance (in Amperes) is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
0.030

B)
0.027

C)
0.020

D)
0.036

• question_answer15) An electric field of 1000 V/m is applied to an electric dipole at angle of $45{}^\circ$. The value of electric dipole moment is ${{10}^{-29}}Cm.$What is the potential energy of the electric dipole? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$-10\times {{10}^{-29}}J$

B)
$-7\times {{10}^{-27}}J$

C)
$-20\times {{10}^{-18}}J$

D)
$-9\times {{10}^{-20}}J$

• question_answer16) In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is$\lambda$. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{25}{16}\lambda$

B)
$\frac{27}{20}\lambda$

C)
$\frac{16}{25}\lambda$

D)
$\frac{20}{27}\lambda$

• question_answer17) A circular disc ${{D}_{1}}$ of mass M and radius R has two identical discs ${{D}_{2}}$ and ${{D}_{3}}$of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO?, passing through the centre of ${{D}_{1}}$, as shown in the figure, will be [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$3M{{R}^{2}}$

B)
$\frac{4}{5}M{{R}^{2}}$

C)
$\frac{2}{3}M{{R}^{2}}$

D)
$M{{R}^{2}}$

• question_answer18) The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$2\sqrt{3}s$

B)
$\frac{3}{2}s$

C)
$\frac{2}{\sqrt{3}}s$

D)
$\frac{\sqrt{3}}{2}s$

• question_answer19) In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to$\left( \frac{hc}{e}=1240nm-V \right)$ [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
2.0 V

B)
0.5 V

C)
1.0 V

D)
1.5 V

• question_answer20) A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of $20\times {{10}^{-6}}J/T$ when a magnetic intensity of $60\times {{10}^{3}}A/m$is applied. Its magnetic susceptibility is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$3.3\times {{10}^{-2}}$

B)
$4.3\times {{10}^{-2}}$

C)
$3.3\times {{10}^{-4}}$

D)
$2.3\times {{10}^{-2}}$

• question_answer21) In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process, the temperature of the gas is increased by $\Delta T$. The amount of heat absorbed by gas is (R is gas constant) [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{2K}{3}\Delta T$

B)
$\frac{1}{2}R\Delta T$

C)
$\frac{3}{2}R\Delta T$

D)
$\frac{1}{2}KR\Delta T$

• question_answer22) In the circuit shown, the potential difference between A and B is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
6V

B)
3 V

C)
2 V

D)
1 V

• question_answer23) A thermometer graduated according to a linear scale reads a value ${{x}_{0}}$ when in. contact with boiling water, and ${{x}_{0}}/3$ when in contact with ice. What is the temperature of an object in${}^\circ C$, if this thermometer in the contact with the object reads${{x}_{0}}/2$ ? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
35

B)
25

C)
66

D)
40

• question_answer24) In the experimental set up of metre bridgre shown in the figure, the null point is obtained at a distance of 40 cm from A. If a $10\Omega$resistor is connected in series with ${{R}_{1}},$ the null point shifts by 10 cm. The resistance that should be connected in parallel with $({{R}_{1}}+10)\Omega$ such that the null point shifts back to its initial position is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$40\,\Omega$

B)
$20\,\Omega$

C)
$60\,\Omega$

D)
$30\,\Omega$

• question_answer25) A galvanometer having a resistance of $20\,\Omega$and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$80\,\Omega$

B)
$125\,\Omega$

C)
$120\,\Omega$

D)
$100\,\Omega$

• question_answer26) The magnitude of torque on a particle of mass 1 kg is 2.5 N m about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians) [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{\pi }{3}$

B)
$\frac{\pi }{8}$

C)
$\frac{\pi }{4}$

D)
$\frac{\pi }{6}$

• question_answer27) Seven capacitors, each of capacitance $2\mu F,$are to be connected in a configuration to obtain an effective capacitance of $\left( \frac{6}{13} \right)\mu F,$Which of the combinations, shown in figures below, will achieve the desired value? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)

B)

C)

D)

• question_answer28) A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is $\sqrt{3},$then the angle of incidence is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$60{}^\circ$

B)
$45{}^\circ$

C)
$90{}^\circ$

D)
$30{}^\circ$

• question_answer29) A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of ${{10}^{-2}}$m. The relative change in the angular frequency of the pendulum is best given by [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
${{10}^{-5}}rad/s$

B)
${{10}^{-1}}rad/s$

C)
$1rad/s$

D)
${{10}^{-3}}rad/s$

• question_answer30) A 27 mW laser beam has a cross-sectional area of$10\text{ }m{{m}^{2}}$. The magnitude of the maximum electric field in this electromagnetic wave is given by [Given permittivity of space${{\varepsilon }_{0}}=9\times {{10}^{-12}}$ SI units, speed of light $c=3\times {{10}^{8}}m/s$] [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
2 kV/m

B)
0.7 kV/m

C)
1 kV/m

D)
1.4 kV/m

• question_answer31) The number of bridging CO ligand(s) and Co-Co bond(s) in ${{C}_{{{O}_{2}}}}{{(CO)}_{8}},$respectively are [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
0 and 2

B)
4 and 0

C)
2 and 0

D)
2 and 1

• question_answer32) The higher concentration of which gas in air can cause stiffness of flower buds?

A)
$S{{O}_{2}}$

B)
$CO$

C)
$N{{O}_{2}}$

D)
$C{{O}_{2}}$

• question_answer33) The relative stability of +1 oxidation state of group 13 elements follows the order [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$Tl<In<Ga<Al$

B)
$Al<Ga<In<Tl$

C)
$Ga<Al<In<Tl$

D)
$Al<Ga<Tl<In$

• question_answer34) The reaction that does not define calcination is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$2C{{u}_{2}}S+3{{O}_{2}}\xrightarrow[{}]{\Delta }2C{{u}_{2}}O+2S{{O}_{2}}$

B)
$F{{e}_{2}}{{O}_{3}}.x{{H}_{2}}O\xrightarrow[{}]{\Delta }F{{e}_{2}}{{O}_{3}}+x{{H}_{2}}O$

C)
$ZnC{{O}_{3}}\xrightarrow[{}]{\Delta }ZnO+C{{O}_{2}}$

D)
$CaC{{O}_{3}}.MgC{{O}_{3}}\xrightarrow[{}]{\Delta }CaO+MgO+2C{{O}_{2}}$

• question_answer35) The hydride that is not electron deficient is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
${{B}_{2}}{{H}_{6}}$

B)
$Al{{H}_{3}}$

C)
$Si{{H}_{4}}$

D)
$Ga{{H}_{3}}$

• question_answer36) The major product of the following reaction is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)

B)

C)

D)

• question_answer37) A compound X on treatment with $B{{r}_{2}}/NaOH,$provided ${{C}_{3}}{{H}_{9}}N,$which gives positive carbylamine test. Compound X is

A)
$C{{H}_{3}}CON{{(C{{H}_{3}})}_{2}}$

B)
$C{{H}_{3}}COC{{H}_{2}}NHC{{H}_{3}}$

C)
$C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CON{{H}_{2}}$

D)
$C{{H}_{3}}C{{H}_{2}}COC{{H}_{2}}N{{H}_{2}}$

• question_answer38) ${{K}_{2}}Hg{{I}_{4}}$is 40% ionised in aqueous solution. The value of its van't Hoff factor (i) is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
1.8

B)
2.2

C)
1.6

D)
2.0

• question_answer39) The coordination number of Th in${{K}_{4}}[Th{{({{C}_{2}}{{O}_{4}})}_{4}}{{(O{{H}_{2}})}_{2}}]$is                      $({{C}_{2}}O_{4}^{2-}=oxalato)$ [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
8

B)
10

C)
14

D)
6

• question_answer40) Match the following items in column-I with the corresponding items in column-II.  Column-I Column-II (i) $N{{a}_{2}}C{{O}_{3}}.10{{H}_{2}}O$ A. Portland cement ingredient (ii) $Mg{{(HC{{O}_{3}})}_{2}}$ B. Castner- Kellner process (iii) $NaOH$ C. Solvay process (iv) $C{{a}_{3}}A{{l}_{2}}{{O}_{6}}$ D. Temporary hardness
[JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$(i)\to B,(ii)\to C,(iii)\to A,(iv)\to D$

B)
$(i)\to C,(ii)\to B,(iii)\to D,(iv)\to A$

C)
$(i)\to C,(ii)\to D,(iii)\to B,(iv)\to A$

D)
$(i)\to D,(ii)\to A,(iii)\to B,(iv)\to C$

• question_answer41) The reaction $2X\to B$is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life is 6 h. When the initial concentration of X is 0.5 M the time required to reach its final concentration of 0.2 M will be [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
12.0 h

B)
9.0 h

C)
7.2h

D)
18.0 h

• question_answer42) Which of the following compounds will produce a precipitate with $AgN{{O}_{3}}$? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)

B)

C)

D)

• question_answer43) The correct option with respect to the Pauling electronegativity values of the elements is

A)
$Si<Al$

B)
$Ga<Ge$

C)
$Te>Se$

D)
$P>S$

• question_answer44) The standard reaction Gibbs energy for a chemical reaction at an absolute temperature T is given by ${{\Delta }_{r}}{{G}^{o}}=A-BT,$where A and B are non-zero constants. Which of the following is true about this reaction? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
Exothermic if $A>0$and $B<0$

B)
Endothermic if $A<0$ and $B>0$

C)
Endothermic if $A>0$

D)
Exothermic if $B<0$

• question_answer45) In the following compound, the favourable site/s for protonation is/are [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
(i)

B)
(ii),(iii) and (iv)

C)
(i) and (iv)

D)
(i) and (v)

• question_answer46) The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is (edge length is represented by a) [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
0.027 a

B)
0.134 a

C)
0.047 a

D)
0.067 a

• question_answer47) 25 mL of the given HCl solution requires 30 mL of 0. 1 M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2 M aqueous NaOH solution? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
50 mL

B)
75 mL

C)
12.5 mL

D)
25 mL

• question_answer48) The correct match between item-I and item-II is  Item-I Item-II A. Ester test P. Tyr B. Carbylamine test Q. Asp C. Phthaleindye test R. Ser S. Lys
[JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$A\to R,B\to Q,C\to P$

B)
$A\to R,B\to S,C\to Q$

C)
$A\to Q,B\to S,C\to R$

D)
$A\to Q,B\to S,C\to P$

• question_answer49) Among the colloids, cheese , milk (M) and smoke (S), the correct combination of the dispersed phase and dispersion medium, respectively is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
C : solid in liquid, M : liquid in liquid, S : gas in solid

B)
C : solid in liquid, M : solid in liquid, S : solid in gas

C)
C : liquid in solid, M : liquid in solid, S: solid in gas

D)
C : liquid in solid, M : liquid in liquid, S : solid in gas

• question_answer50) The homo polymer formed from 4-hydroxy- butanoic acid is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)

B)

C)

D)

• question_answer51) The major product obtained in the following reaction is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)

B)

C)

D)

• question_answer52) Which of the following compounds reacts with ethylmagnesium bromide and also decolourizes bromine water solution? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)

B)

C)

D)

• question_answer53) The de Broglie wavelength $(\lambda )$associated with a photoelectron varies with the frequency $(\upsilon )$of the incident radiation as, [${{\upsilon }_{0}}$ is threshold frequency] [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\lambda \propto \frac{1}{(\upsilon -{{\upsilon }_{0}})}$

B)
$\lambda \propto \frac{1}{{{(\upsilon -{{\upsilon }_{0}})}^{1/2}}}$

C)
$\lambda \propto \frac{1}{{{(\upsilon -{{\upsilon }_{0}})}^{3/2}}}$

D)
$\lambda \propto \frac{1}{{{(\upsilon -{{\upsilon }_{0}})}^{1/4}}}$

• question_answer54) The major product obtained in the following reaction is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)

B)

C)

D)

• question_answer55)                         The reaction,$Mg{{O}_{(s)}}+{{C}_{(s)}}\to M{{g}_{s}}+C{{O}_{g}},$for which ${{\Delta }_{r}}{{H}^{o}}=+491.1kJ\,mo{{l}^{-1}}$ and${{\Delta }_{r}}{{S}^{o}}=198.0J\,{{K}^{-1}}mo{{l}^{-1}},$is not feasible at 298 K. Temperature above which reaction will be feasible is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
2040.5 K

B)
1890.0 K

C)
2480.3 K

D)
2380.5 K

• question_answer56) For the equilibrium,$2{{H}_{2}}O{{H}_{3}}{{O}^{+}}+O{{H}^{-}},$the value of $\Delta {{G}^{o}}$at 298 K is approximately [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$-80kJ\,mo{{l}^{-1}}$

B)
$100kJ\,mo{{l}^{-1}}$

C)
$-100kJ\,mo{{l}^{-1}}$

D)
$80kJ\,mo{{l}^{-1}}$

• question_answer57) Given the equilibrium constant ${{K}_{c}}$of the reaction: $C{{u}_{(s)}}+2A{{g}^{+}}_{(aq)}\to C{{u}^{2+}}_{(aq)}+2A{{g}_{(s)}}$is $10\times {{10}^{15}},$calculate the $E_{cell}^{o}$of this reaction at 298 K. $\left[ 2.303\frac{RT}{F}at\,298\,K=0.059V \right]$ [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
0.04736 V

B)
0.4736 V

C)
0.4736 mV

D)
0.04736 mV

• question_answer58) Taj Mahal is being slowly disfigured and discoloured. This is primarily due to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
acid rain

B)
soil pollution

C)
water pollution

D)
global warming.

• question_answer59) $A\xrightarrow[{}]{4KOH,{{O}_{2}}}\underset{(green)}{\mathop{2B}}\,+2{{H}_{2}}O$ $3B\xrightarrow[{}]{4HCl}\underset{(purple)}{\mathop{2C}}\,+Mn{{O}_{2}}+2{{H}_{2}}O$ $2C\xrightarrow[{}]{{{H}_{2}}O,KI}2A+2KOH+D$ In the above sequence of reactions, A and D, respectively are [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$KI$and$KMn{{O}_{4}}$

B)
$KI{{O}_{3}}$and$Mn{{O}_{2}}$

C)
$KI$and${{K}_{2}}Mn{{O}_{4}}$

D)
$Mn{{O}_{2}}$and$KI{{O}_{3}}$

• question_answer60) The correct match between item-I and item-II is  Item-I Item-II A. Allosteric effect P. Molecule binding to the active site of enzyme B. Competitive inhibitor Q. Molecule crucial for communication in the body C. Receptor R. Molecule binding to a site other than the active site of enzyme D. Posion S. Molecule binding to the enzyme covalently
[JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$A\to P,B\to R,C\to Q,D\to S$

B)
$A\to R,B\to P,C\to Q,D\to S$

C)
$A\to P,B\to R,C\to S,D\to Q$

D)
$A\to R,B\to P,C\to S,D\to Q$

• question_answer61) All x satisfying the inequality${{(co{{t}^{-1}}x)}^{2}}-7(co{{t}^{-1}}x)+10>0,$ lie in the interval [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$(-\infty ,\cot 5)\cup (cot4,cot2)$

B)
$(\cot 5,cot4)$

C)
$(-\infty ,\cot 5)\cup (cot2,\infty )$

D)
$(cot2,\infty )$

• question_answer62) Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression $\frac{{{x}^{m}}{{y}^{n}}}{(1+{{x}^{2m}})(1+{{y}^{2n}})}$is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{m+n}{6mn}$

B)
1

C)
1/2

D)
¼

• question_answer63) Contrapositive of the statement "If two numbers are not equal, then their squares are not equal." is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
If the squares of two numbers are not equal, then the numbers are equal.

B)
If the squares of two numbers are not equal, then the numbers are not equal.

C)
If the squares of two numbers are equal, then the numbers are equal.

D)
If the squares of two numbers are equal, then the numbers are not equal.

• question_answer64) Let $\sqrt{3}\hat{i}+\hat{j},\hat{i}+\sqrt{3}\hat{j}$and $\beta \hat{i}+(1-\beta )\hat{j}$respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is $\frac{3}{\sqrt{2}},$then the sum of all possible values of $\beta$ is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
1

B)
4

C)
3

D)
2

• question_answer65) Two lines $\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}$and$\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4}$intersect at the point R. The reflection of R in the xy-plane has coordinates [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$(2,-4,-7)$

B)
$(2,4,7)$

C)
$(2,-4,7)$

D)
$(-2,4,7)$

• question_answer66) In a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5) then the equation of the diagonal AD is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$5x-3y+1=0$

B)
$3x-5y+7=0$

C)
$5x+3y-11=0$

D)
$3x+5y-13=0$

• question_answer67) A circle cuts a chord of length 4a on the x- axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
a parabola

B)
a straight line

C)
an ellipse

D)
a hyperbola

• question_answer68) If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
13/12

B)
2

C)
13/6

D)
13/8

• question_answer69) Set ${{S}_{n}}=1+q+{{q}^{2}}+...+{{q}^{n}}$and ${{T}_{n}}=1+\left( \frac{q+1}{2} \right)+{{\left( \frac{q+1}{2} \right)}^{2}}+...+{{\left( \frac{q+1}{2} \right)}^{n}}$where q is a real number and $q\ne 1.$ It $^{101}{{C}_{1}}{{+}^{101}}{{C}_{2}}{{S}_{1}}+...{{+}^{101}}{{C}_{101}}{{S}_{100}}=\alpha {{T}_{100}},$then $\alpha$ is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
${{2}^{100}}$

B)
${{2}^{99}}$

C)
202

D)
200

• question_answer70) Let $f(x)=\frac{x}{\sqrt{{{a}^{2}}+{{x}^{2}}}}-\frac{d-x}{\sqrt{{{b}^{2}}+{{(d-x)}^{2}}}},x\in R$where a, b and d are non-zero real constants. Then [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
f' is not a continuous function of x

B)
f is neither increasing nor decreasing function of x

C)
f is an increasing function of x

D)
f is a decreasing function of x

• question_answer71) Given:$\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$for a $\Delta ABC$with usual notation. It $\frac{\cos A}{\alpha }=\frac{\operatorname{cosB}}{\beta }=\frac{\operatorname{cosC}}{\gamma },$then the ordered triad $(\alpha ,\beta ,\gamma )$has a value [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
(19, 7, 25)

B)
(5, 12, 13)

C)
(7, 19, 25)

D)
(3, 4, 5)

• question_answer72) $\underset{x\to 0}{\mathop{\lim }}\,\frac{x\cot (4x)}{{{\sin }^{2}}x{{\cot }^{2}}(2x)}$is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
0

B)
2

C)
4

D)
1

• question_answer73) If ${{19}^{th}}$ term of a non-zero A.P. is zero, then it $({{49}^{th}}\,\,term):({{29}^{th}}\,\,term)$is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
1 : 3

B)
2 : 1

C)
3 : 1

D)
4 : 1

• question_answer74) If the area  of the  triangle  whose one vertex is at the vertex of the parabola, ${{y}^{2}}+4(x-{{a}^{2}})=0$ and the other two vertices are the points of intersection of the parabola and y-axis. is 250 sq. units, then a value of a is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$5\sqrt{5}$

B)
${{(10)}^{2/3}}$

C)
$5{{(2)}^{1/3}}$

D)
5

• question_answer75) Let ${{(x+10)}^{50}}+{{(x-10)}^{50}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+$$...+{{a}_{50}}{{x}^{50}},$ for all$x\in R;$then $\frac{{{a}_{2}}}{{{a}_{0}}}$is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
12.00

B)
12.75

C)
12.25

D)
12.50

• question_answer76) The area (in sq. units) in the first quadrant bounded by the parabola$y={{x}^{2}}+1,$ the tangent to it at the point (2, 5) and the coordinate axes is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
8/3

B)
187/24

C)
14/3

D)
37/24

• question_answer77) Let a function$f:(0,\infty )\to (0,\infty )$be defined by$f(x)=\left| 1-\frac{1}{x} \right|.$Then f is

A)
injective only

B)
both injective as well as surjective

C)
not injective but it is surjective

D)
neither injective nor surjective

E)
None of these

• question_answer78) Let A and B be two invertible matrices of order $3\times 3.$If $\det (AB{{A}^{T}})=8$and $\det (A{{B}^{-1}})=8,$then $\det (B{{A}^{-1}}{{B}^{T}})$is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
1

B)
16

C)
1/16

D)
¼

• question_answer79) Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it? [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$(4\sqrt{2},2\sqrt{3})$

B)
$(4\sqrt{3},2\sqrt{3})$

C)
$(4\sqrt{2},2\sqrt{2})$

D)
$(4\sqrt{3},2\sqrt{2})$

• question_answer80) A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $\left( \frac{Mean\,of\,X}{S\tan dard\,Deviation\,of\,X} \right)$ is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$4\sqrt{3}$

B)
$\frac{4\sqrt{3}}{3}$

C)
$3\sqrt{2}$

D)
4

• question_answer81) If $\left| \begin{matrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \\ \end{matrix} \right|$$=(a+b+c){{(x+a+b+c)}^{2}},x\ne 0$and$a+b+c\ne 0$then x is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$abc$

B)
$-(a+b+c)$

C)
$-2(a+b+c)$

D)
$2(a+b+c)$

• question_answer82) Let $\alpha$and $\beta$be the roots of the quadratic equation ${{x}^{2}}\sin \theta -x(sin\theta cos\theta +1)$$+(cos\theta =0({{0}^{o}}<\theta <{{45}^{o}})$and $\alpha <\beta .$Then $\sum\limits_{n=0}^{\infty }{\left( {{\alpha }^{n}}\frac{{{(-1)}^{n}}}{{{\beta }^{n}}} \right)}$is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{1}{1-\cos \theta }+\frac{1}{1+\sin \theta }$

B)
$\frac{1}{1+\cos \theta }-\frac{1}{1-\sin \theta }$

C)
$\frac{1}{1+\cos \theta }+\frac{1}{1-\sin \theta }$

D)
$\frac{1}{1-\cos \theta }-\frac{1}{1+\sin \theta }$

• question_answer83) If$\int_{{}}^{{}}{\frac{x+1}{\sqrt{2x-1}}}dx=f(x)\sqrt{2x-1}+C,$where C is a constant of integration, then f(x) is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{1}{3}(x+1)$

B)
$\frac{1}{3}(x+4)$

C)
$\frac{2}{3}(x+2)$

D)
$\frac{2}{3}(x-4)$

• question_answer84) The number of functions f from {1, 2, 3,...., 20} onto {1, 2, 3,..., 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4 is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
${{6}^{5}}\times (15)!$

B)
$(15)!\times 6!$

C)
${{5}^{6}}\times 15$

D)
$5!\times 6!$

• question_answer85) The  integral $\int\limits_{\pi /6}^{\pi /4}{\frac{dx}{\sin 2x(ta{{n}^{5}}x+co{{t}^{5}}x)}}$ [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{1}{10}\left( \frac{\pi }{4}-{{\tan }^{-1}}\left( \frac{1}{9\sqrt{3}} \right) \right)$

B)
$\frac{1}{20}{{\tan }^{-1}}\left( \frac{1}{9\sqrt{3}} \right)$

C)
$\frac{1}{5}\left( \frac{\pi }{4}-{{\tan }^{-1}}\left( \frac{1}{3\sqrt{3}} \right) \right)$

D)
$\frac{\pi }{40}$

• question_answer86) The solution of the differential equation,$\frac{dy}{dx}={{(x-y)}^{2}},$when$y(1)=1$is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$-{{\log }_{e}}\left| \frac{1+x-y}{1-x+y} \right|=x+y-2$

B)
${{\log }_{e}}\left| \frac{2-x}{2-y} \right|=x-y$

C)
$-{{\log }_{e}}\left| \frac{1-x+y}{1+x-y} \right|=2(x-1)$

D)
${{\log }_{e}}\left| \frac{2-y}{x-x} \right|=2(y-1)$

• question_answer87) Let K be the set of all real values of x where the function$f(x)=\sin |x|-|x|+2(x-\pi )$is not differentiable. Then the set K is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\{\pi \}$

B)
$\left\{ 0 \right\}$

C)
$\phi$(an empty set)

D)
$\{0,\pi \}$

• question_answer88) Let z be a complex number such that $|z|+z=3+i$(where $i=\sqrt{-1})$). Then |z| is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{\sqrt{34}}{3}$

B)
$\frac{5}{4}$

C)
$\frac{\sqrt{41}}{4}$

D)
$\frac{5}{3}$

• question_answer89) If the point $(2,\alpha ,\beta )$lies on the plane which passes through the points (3,4, 2) and (7,0,6) and is perpendicular to the plane $2x-5y=15,$then $2\alpha -3\beta$is equal to [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
5

B)
7

C)
17

D)
12

• question_answer90) Let S = {1, 2, .... 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is "nice" is [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A)
$\frac{5}{{{2}^{20}}}$

B)
$\frac{7}{{{2}^{20}}}$

C)
$\frac{4}{{{2}^{20}}}$

D)
$\frac{6}{{{2}^{20}}}$