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

### done JEE Main Paper (Held on 10-4-2019 Morning) Total Questions - 90

• question_answer1) Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are: [JEE Main 10-4-2019 Morning]

A)
$50\mu F\text{ }and\text{ }30\mu F$

B)
$20\mu F\text{ }and\text{ }30\mu F$

C)
$60\mu F\text{ }and\text{ }40\mu F$

D)
$40\mu F\text{ }and\text{ }10\mu F$

• question_answer2) A current of 5 A passes through a copper conductor (resistivity$=1.7\times {{10}^{-8}}\Omega m$) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is $=1.1\times {{10}^{-3}}m/s.$ [JEE Main 10-4-2019 Morning]

A)
$1.3\text{ }{{m}^{2}}/Vs$

B)
$1.5\text{ }{{m}^{2}}/Vs$

C)
$1.8\text{ }{{m}^{2}}/Vs$

D)
$1.0\text{ }{{m}^{2}}/Vs$

• question_answer3) In a meter bridge experiment, the circuit diagram and the corresponding observation  table are shown in figure  SI. No. $R(\Omega )$ $l(cm)$ 1. 1000 60 2. 100 13 3. 10 1.5 4. 1 1.0
Which of the readings is inconsistent? [JEE Main 10-4-2019 Morning]

A)
4

B)
1

C)
2

D)
3

• question_answer4) One plano-convex and one plano-concave lens of same radius of curvature 'R' but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is ${{\mu }_{1}}$and that of 2 is ${{\mu }_{2}}$, then the focal length of the combination is : [JEE Main 10-4-2019 Morning]

A)
$\frac{R}{2-({{\mu }_{1}}-{{\mu }_{2}})}$

B)
$\frac{2R}{({{\mu }_{1}}-{{\mu }_{2}})}$

C)
$\frac{R}{2({{\mu }_{1}}-{{\mu }_{2}})}$

D)
$\frac{R}{{{\mu }_{1}}-{{\mu }_{2}}}$

• question_answer5) A ball is thrown upward with an initial velocity ${{V}_{0}}$from the surface of the earth. The motion of the ball is affected by a drag force equal to $m\gamma {{\upsilon }^{2}}$ (where m is mass of the ball, $\upsilon$is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is : [JEE Main 10-4-2019 Morning]

A)
$\frac{1}{\sqrt{\gamma g}}{{\sin }^{-1}}\left( \sqrt{\frac{\gamma }{g}}{{V}_{0}} \right)$

B)
$\frac{1}{\sqrt{\gamma g}}{{\tan }^{-1}}\left( \sqrt{\frac{\gamma }{g}}{{V}_{0}} \right)$

C)
$\frac{1}{\sqrt{2\gamma g}}{{\tan }^{-1}}\left( \sqrt{\frac{2\gamma }{g}}{{V}_{0}} \right)$

D)
$\frac{1}{\sqrt{\gamma g}}\ln \left( 1+\sqrt{\frac{\gamma }{g}}{{V}_{0}} \right)$

• question_answer6) A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by $20{}^\circ C$ is : [Given that $R=8.31\text{ }J\text{ }mo{{l}^{1}}\text{ }{{K}^{1}}$] [JEE Main 10-4-2019 Morning]

A)
748 J

B)
374 J

C)
350 J

D)
700 J

• question_answer7) A thin disc of mass M and radius R has mass per unit area $\sigma (r)=k{{r}^{2}}$ where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is : [JEE Main 10-4-2019 Morning]

A)
$\frac{M{{R}^{2}}}{6}$

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

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

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

• question_answer8) Two coaxial discs, having moments of inertia ${{I}_{1}}$and $\frac{{{I}_{1}}}{2},$are rotating with respective angular velocities ${{\omega }_{1}}$and $\frac{{{\omega }_{1}}}{2},$about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If ${{E}_{f}}$and${{E}_{i}}$are the final and initial total energies, then $({{E}_{f}}-{{E}_{i}})$is : [JEE Main 10-4-2019 Morning]

A)
$\frac{{{I}_{1}}\omega _{1}^{2}}{12}$

B)
$\frac{3}{8}{{I}_{1}}\omega _{1}^{2}$

C)
$\frac{{{I}_{1}}\omega _{1}^{2}}{6}$

D)
$\frac{{{I}_{1}}\omega _{1}^{2}}{24}$

• question_answer9) A particle of mass m is moving along a trajectory given by  $x={{x}_{0}}+a\cos {{\omega }_{1}}t$ $y={{y}_{0}}+b\sin {{\omega }_{2}}t$ The torque, acting on the particle about the origin, at t = 0 is :
[JEE Main 10-4-2019 Morning]

A)
$m(-{{x}_{0}}b+{{y}_{0}}a)\omega _{1}^{2}\hat{k}$

B)
$+m{{y}_{0}}a\omega _{1}^{2}\hat{k}$

C)
$-m({{x}_{0}}b\omega _{2}^{2}-{{y}_{0}}a\omega _{1}^{2})\hat{k}$

D)
Zero

• question_answer10) A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let ${{r}_{p}},{{r}_{e}}$and ${{r}_{He}}$ be their respective radii, then, [JEE Main 10-4-2019 Morning]

A)
${{r}_{e}}>{{r}_{p}}>{{r}_{He}}$

B)
${{r}_{e}}<{{r}_{p}}<{{r}_{He}}$

C)
${{r}_{e}}<{{r}_{p}}={{r}_{He}}$

D)
${{r}_{e}}>{{r}_{p}}={{r}_{He}}$

• question_answer11) The electric field of a plane electromagnetic wave is given by $\vec{E}={{E}_{0}}\hat{i}\cos (kz)cos(\omega t)$ The corresponding magnetic field $\vec{B}$is then given by: [JEE Main 10-4-2019 Morning]

A)
$\vec{B}=\frac{{{E}_{0}}}{C}\hat{j}\sin (kz)cos(\omega t)$

B)
$\vec{B}=\frac{{{E}_{0}}}{C}\hat{j}\sin (kz)sin(\omega t)$

C)
$\vec{B}=\frac{{{E}_{0}}}{C}\hat{k}\sin (kz)cos(\omega t)$

D)
$\vec{B}=\frac{{{E}_{0}}}{C}\hat{j}\sin (kz)sin(\omega t)$

• question_answer12) Two wires A & B are carrying currents ${{I}_{1}}\And {{I}_{2}}$as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are: [JEE Main 10-4-2019 Morning]

A)
$x=\left( \frac{{{I}_{1}}}{{{I}_{1}}-{{I}_{2}}} \right)d$and$x=\frac{{{I}_{2}}}{({{I}_{1}}+{{I}_{2}})}d$

B)
$x=\pm \frac{{{I}_{1}}d}{({{I}_{1}}-{{I}_{2}})}$

C)
$x=\left( \frac{{{I}_{1}}}{{{I}_{1}}+{{I}_{2}}} \right)d$and$x=\frac{{{I}_{2}}}{({{I}_{1}}-{{I}_{2}})}d$

D)
$x=\left( \frac{{{I}_{2}}}{{{I}_{1}}+{{I}_{2}}} \right)d$and$x=\left( \frac{{{I}_{2}}}{{{I}_{1}}-{{I}_{2}}} \right)d$

• question_answer13) A message signal of frequency 100 MHz and peak voltage 100 V is used to execute amplitude modulation on a carrier wave of frequency 300 GHz and peak voltage 400 V. The modulation index and difference between the two side band frequencies are : [JEE Main 10-4-2019 Morning]

A)
$4;1\times {{10}^{8}}Hz$

B)
$0.25;1\times {{10}^{8}}Hz$

C)
$4;2\times {{10}^{8}}Hz$

D)
$0.25;\,2\times {{10}^{8}}Hz$

• question_answer14) In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that : [JEE Main 10-4-2019 Morning]

A)
$R(T)=\frac{{{R}_{0}}}{{{T}^{2}}}$

B)
$R(T)={{R}_{0}}{{e}^{-{{T}^{2}}/T_{0}^{2}}}$

C)
$R(T)={{R}_{0}}{{e}^{-T_{0}^{2}/T_{{}}^{2}}}$

D)
$R(T)={{R}_{0}}{{e}^{T_{{}}^{2}/T_{0}^{2}}}$

• question_answer15) A ray of light AO in vacuum is incident on a glass slab at angle $60{}^\circ$ and refracted at angle $30{}^\circ$ along OB as shown in the figure. The optical path length of light ray from A to B is: [JEE Main 10-4-2019 Morning]

A)
$2a+2b$

B)
$2a+\frac{2b}{3}$

C)
$\frac{2\sqrt{3}}{a}+2b$

D)
$2a+\frac{2b}{\sqrt{3}}$

• question_answer16) A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10A, then the input voltage and current in the primary coil are: [JEE Main 10-4-2019 Morning]

A)
220 V and 10A

B)
440 V and 5A

C)
440 V and 20 A

D)
220 V and 20 A

• question_answer17) In a photoelectric effect experiment the threshold wavelength of the light is 380 nm. If the wavelength of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be:  Given E (in eV) $=\frac{1237}{\lambda (in\,nm)}$
[JEE Main 10-4-2019 Morning]

A)
1.5 eV

B)
4.5 eV

C)
15.1 eV

D)
3.0 eV

• question_answer18) The displacement of a damped harmonic oscillator is given by $x(t)={{e}^{-01.1t}}\cos (10\pi t+\phi ).$Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to: [JEE Main 10-4-2019 Morning]

A)
13 s

B)
7 s

C)
27 s

D)
4 s

• question_answer19) A moving coil galvanometer allows a full scale current of ${{10}^{-4}}A$. A series resistance of $2M\Omega$ is required to convert the above galvanometer into a voltmeter of range 0-5 V. Therefore the value of shunt resistance required to convert the above galvanometer into an ammeter of range 0-10 mA is : [JEE Main 10-4-2019 Morning]

A)
$200\,\Omega$

B)
$100\,\Omega$

C)
$10\,\Omega$

D)
None of these

• question_answer20) A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in $m{{s}^{-1}},$  (Given speed of sound = 300 m/s)
[JEE Main 10-4-2019 Morning]

A)
16, 14

B)
12, 18

C)
12, 16

D)
8, 18

• question_answer21) Two radioactive materials A and B have decay constants$10\lambda$and$\lambda ,$respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time : [JEE Main 10-4-2019 Morning]

A)
$\frac{11}{10\lambda }$

B)
$\frac{1}{9\lambda }$

C)
$\frac{1}{10\lambda }$

D)
$\frac{1}{11\lambda }$

• question_answer22)                    An npn transistor operates as a common emitter amplifier, with a power gain of 60 dB. The input circuit resistance is $100\Omega$and the output load resistance is $10k\Omega .$The common emitter current gain b is : [JEE Main 10-4-2019 Morning]

A)
$60$

B)
${{10}^{4}}$

C)
$6\times {{10}^{2}}$

D)
${{10}^{2}}$

• question_answer23) In the given circuit, an ideal voltmeter connected across the $10\Omega$resistance reads 2V. The internal resistance r, of each cell is: [JEE Main 10-4-2019 Morning]

A)
$1\Omega$

B)
$1.5\Omega$

C)
$0\Omega$

D)
$0.5\Omega$

• question_answer24) A $25\times {{10}^{-3}}{{m}^{3}}$volume cylinder is filled with 1 mol of ${{O}_{2}}$gas at room temperature (300K). The molecular diameter of ${{O}_{2}}$, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an ${{O}_{2}}$ molecule? [JEE Main 10-4-2019 Morning]

A)
$\tilde{\ }{{10}^{11}}$

B)
$\tilde{\ }{{10}^{13}}$

C)
$\tilde{\ }{{10}^{10}}$

D)
$\tilde{\ }{{10}^{12}}$

• question_answer25) n moles of an ideal gas with constant volume heat capcity ${{C}_{V}}$undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is: [JEE Main 10-4-2019 Morning]

A)
$\frac{4nR}{{{C}_{V}}-nR}$

B)
$\frac{nR}{{{C}_{V}}-nR}$

C)
$\frac{nR}{{{C}_{V}}+nR}$

D)
$\frac{4nR}{{{C}_{V}}+nR}$

• question_answer26) A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = 4a. The minimum value of u such that it crosses the origin is : [JEE Main 10-4-2019 Morning]

A)
$\sqrt{\frac{2}{m}}{{\left( \frac{1}{15}\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a} \right)}^{1/2}}$

B)
$\sqrt{\frac{2}{m}}{{\left( \frac{2}{15}\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a} \right)}^{1/2}}$

C)
$\sqrt{\frac{2}{m}}{{\left( \frac{4}{15}\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a} \right)}^{1/2}}$

D)
$\sqrt{\frac{2}{m}}{{\left( \frac{1}{5}\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a} \right)}^{1/2}}$

• question_answer27)           The value of acceleration due to gravity at Earth's surface is $9.8m{{s}^{-2}}$. The altitude above its surface at which the acceleration due to gravity decreases to $4.9\,m{{s}^{-2}}$, is close to :  (Radius of earth $=6.4\times {{10}^{6}}m$)
[JEE Main 10-4-2019 Morning]

A)
$1.6\times {{10}^{6}}m$

B)
$6.4\times {{10}^{6}}m$

C)
$9.0\times {{10}^{6}}m$

D)
$2.6\times {{10}^{6}}m$

• question_answer28) Given below in the left column are different modes of communication using the kinds of waves given the right column.  A. Optical Fibre communication P. Ultrasound B. Radar Q. Infrared Light C. Sonar R. Microwaves D. Mobile Phones S. Radio Waves
[JEE Main 10-4-2019 Morning]

A)
$A-S,\text{ }B-Q,\text{ }C-R,\text{ }D-P$

B)
$A-R,\text{ }B-P,\text{ }C-S,\text{ }D-Q$

C)
$A-Q,\text{ }B-S,\text{ }C-R,\text{ }D-P$

D)
$A-Q,\text{ }B-S,\text{ }C-P,\text{ }D-R$

• question_answer29) The radtio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to$135{}^\circ$and$0{}^\circ ,$respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius ${{r}_{1}},$ while water rises by the same amount h in a capillary tube of radius ${{r}_{2}}.$The ratio, $({{r}_{1}}/{{r}_{2}}),$is then close to: [JEE Main 10-4-2019 Morning]

A)
2/3

B)
3/5

C)
2/5

D)
4/5

• question_answer30) Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds${{\upsilon }_{1}}$and ${{\upsilon }_{2}}$, respectively. The values of ${{\upsilon }_{1}}$and ${{\upsilon }_{2}}$ are nearly: [JEE Main 10-4-2019 Morning]

A)
3.2 m/s and 6.3 m/s

B)
3.2 m/s and 12.6 m/s

C)
6.5 m/s and 6.3 m/s

D)
6.5 m/s and 3.2 m/s

• question_answer31) The major product of the following reaction is: $C{{H}_{3}}\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{2}}C{{H}_{2}}N{{H}_{2}}\xrightarrow[triethyla\min e]{ehtyl\,formate\,(lequiv.)}$ [JEE Main 10-4-2019 Morning]

A)
$C{{H}_{3}}\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{2}}C{{H}_{2}}NHCHO$

B)
$C{{H}_{3}}CH=CH-C{{H}_{2}}N{{H}_{2}}$

C)

D)
$C{{H}_{3}}-\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}\,H-CH=C{{H}_{2}}$

• question_answer32) SOLUTION A bacterial infection in an internal wound grows as $N'(t)={{N}_{0}}$ exp(t), where the time t is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as $\frac{dN}{dt}=-5{{N}^{2}}.$What will be the plot of $\frac{{{N}_{0}}}{N}$vs. t after 1 hour ? [JEE Main 10-4-2019 Morning]

A)

B)

C)

D)

• question_answer33) The correct order of catenation is : [JEE Main 10-4-2019 Morning]

A)
$C>Si>Ge\approx Sn$

B)
$C>Sn>Si\approx Ge$

C)
$Ge>Sn>Si>C$

D)
$Si>Sn>C>Ge$

• question_answer34) The oxoacid of sulphur that does not contain bond between sulphur atoms is : [JEE Main 10-4-2019 Morning]

A)
${{H}_{2}}{{S}_{4}}{{O}_{6}}$

B)
${{H}_{2}}{{S}_{2}}{{O}_{7}}$

C)
${{H}_{2}}{{S}_{2}}{{O}_{3}}$

D)
${{H}_{2}}{{S}_{2}}{{O}_{4}}$

• question_answer35) Consider the statements S1 and S2 :  S1 : Conductivity always increases with decrease in the concentration of electrolyte. S2 : Molar conductivity always increases with decrease in the concentration of electrolyte.
The correct option among the following is : [JEE Main 10-4-2019 Morning]

A)
Both S1 and S2 are correct

B)
S1 is wrong and S2 is correct

C)
S1 is correct and S2 is wrong

D)
Both S1 and S2 are wrong

• question_answer36) Which of the following is a condensation polymer? [JEE Main 10-4-2019 Morning]

A)
Buna - S

B)
Nylon 6, 6

C)
Teflon

D)
Neoprene

• question_answer37) At 300 K and 1 atmospheric pressure, 10 Ml of a hydrocarbon required 55 mL of ${{O}_{2}}$ for complete combustion and 40 mL of $C{{O}_{2}}$ is formed. The formula of the hydrocarbon is : [JEE Main 10-4-2019 Morning]

A)
${{C}_{4}}{{H}_{8}}$

B)
${{C}_{4}}{{H}_{7}}Cl$

C)
${{C}_{4}}{{H}_{10}}$

D)
${{C}_{4}}{{H}_{6}}$

• question_answer38) Ethylamine $({{C}_{2}}{{H}_{5}}N{{H}_{2}})$can be obtained from N-ethylphthalimide on treatment with : [JEE Main 10-4-2019 Morning]

A)
$NaB{{H}_{4}}$

B)
$Ca{{H}_{2}}$

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

D)
$N{{H}_{2}}N{{H}_{2}}$

• question_answer39) The isoelectronic set of ions is: [JEE Main 10-4-2019 Morning]

A)
${{N}^{3-}},L{{i}^{+}},M{{g}^{2+}}$and${{O}^{2-}}$

B)
$L{{i}^{+}},N{{a}^{+}},{{O}^{2-}}$and${{F}^{-}}$

C)
${{F}^{-}},L{{i}^{+}},N{{a}^{+}}$and$M{{g}^{2+}}$

D)
${{N}^{3-}},{{O}^{2-}},{{F}^{-}}$and$N{{a}^{+}}$

• question_answer40) The species that can have a trans-isomer is :  (en = ethane 1, 2 diamine, ox = oxalate)
[JEE Main 10-4-2019 Morning]

A)
$[Pt(en)C{{l}_{2}}]$

B)
${{[Cr{{(en)}_{2}}(ox)]}^{+}}$

C)
$[Zn(en)C{{l}_{2}}]$

D)
${{[Pt{{(en)}_{2}}C{{l}_{2}}]}^{2+}}$

• question_answer41) Match the refining methods (Column I) with metals (Column II).  Column I Column II (Refining methods) (Metals) (I) Liquation [a] Zr (II) Zone Refining [b] Ni (III) Mond Process [c] Sn (IV) Van Arkel Method [d] Ga
[JEE Main 10-4-2019 Morning]

A)
$\left( I \right)\left( b \right);\left( II \right)\left( c \right);\left( III \right)\left( d \right);\left( IV \right)\left( a \right)$

B)
$\left( I \right)\left( b \right);\left( II \right)\left( d \right);\left( III \right)\left( a \right);\left( IV \right)\left( c \right)$

C)
$\left( I \right)\left( c \right);\left( II \right)\left( a \right);\left( III \right)\left( b \right);\left( IV \right)\left( d \right)$

D)
$\left( I \right)\left( c \right);\left( II \right)\left( d \right);\left( III \right)\left( b \right);\left( IV \right)\left( a \right)$

• question_answer42) Consider the following statements  [A] The pH of a mixture containing 400 mL of $0.1\,M\,{{H}_{2}}S{{O}_{4}}$and 400 mL of 0.1 M NaOH will be approximately 1.3. [B] Ionic product of water is temperature dependent. [C] A monobasic acid with ${{K}_{a}}={{10}^{-5}}$ has a pH = 5. The degree of dissociation of this acid is 50%. [D] The Le Chatelier's principle is not applicable to common-ion effect. the correct statement are :
[JEE Main 10-4-2019 Morning]

A)
[B] and [D]

B)
[A], [B] and [C]

C)
[A] and [B]

D)
[B] and [C]

• question_answer43) Major products of the following reaction are : [JEE Main 10-4-2019 Morning]

A)
$C{{H}_{3}}OH$and$HC{{O}_{2}}H$

B)

C)

D)

• question_answer44) The principle of column chromatography is : [JEE Main 10-4-2019 Morning]

A)
Capillary action.

B)
Gravitational force.

C)
Differential adsorption of the substances on the solid phase.

D)
Differential absorption of the substances on the solid phase.

• question_answer45) The major product of the following reaction is : [JEE Main 10-4-2019 Morning]

A)

B)

C)

D)

• question_answer46) Amylopectin is composed of : [JEE Main 10-4-2019 Morning]

A)
$\alpha \text{-D-glucose, }{{\text{C}}_{\text{1}}}\text{--}{{\text{C}}_{\text{4}}}$ and ${{\text{C}}_{\text{1}}}\text{--}{{\text{C}}_{\text{6}}}\text{ linkages}$

B)
$\alpha \text{-D-glucose, }{{\text{C}}_{\text{1}}}\text{--}{{\text{C}}_{\text{4}}}$ and ${{\text{C}}_{2}}\text{--}{{\text{C}}_{\text{6}}}\text{ linkages}$

C)
$\beta \text{-D-glucose, }{{\text{C}}_{\text{1}}}\text{--}{{\text{C}}_{\text{4}}}$and ${{\text{C}}_{2}}\text{--}{{\text{C}}_{\text{6}}}\text{ linkages}$

D)
$\beta \text{-D-glucose, }{{\text{C}}_{\text{1}}}\text{--}{{\text{C}}_{\text{4}}}$and ${{\text{C}}_{1}}\text{--}{{\text{C}}_{\text{6}}}\text{ linkages}$

• question_answer47) Consider the hydrates ions of $T{{i}^{2+}},{{V}^{2+}},T{{i}^{3+}}$and $S{{c}^{3+}}.$The correct order of their spin-only magnetic moments is : [JEE Main 10-4-2019 Morning]

A)
$S{{c}^{3+}}<T{{i}^{3+}}<T{{i}^{2+}}<{{V}^{2+}}$

B)
$T{{i}^{3+}}<T{{i}^{2+}}<S{{c}^{3+}}<{{V}^{2+}}$

C)
$S{{c}^{3+}}<T{{i}^{3+}}<{{V}^{2+}}<T{{i}^{2+}}$

D)
${{V}^{2+}}<T{{i}^{2+}}<T{{i}^{3+}}<S{{c}^{3+}}$

• question_answer48) A gas undergoes physical adsorption on a surface and follows the given Freundlich adsorption isotherm equation$\frac{x}{m}=k{{p}^{0.5}}$ Adsorption of the gas increases with : [JEE Main 10-4-2019 Morning]

A)
Decrease in p and decrease in T

B)
Increase in p and increase in T

C)
Increase in p and decrease in T

D)
Decrease in p and increase in T

• question_answer49) Three complexes,  ${{[CoCl{{(N{{H}_{3}})}_{5}}]}^{2+}}(I),$ ${{[Co{{(N{{H}_{3}})}_{5}}{{H}_{2}}O]}^{3+}}(II)$and ${{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}(III)$ absorb light in the visible region. The correct order of the wavelength of light absorbed by them is :
[JEE Main 10-4-2019 Morning]

A)
$\left( III \right)>\left( I \right)>\left( II \right)$

B)
$\left( I \right)>\left( II \right)>\left( III \right)$

C)
$(II)>\left( I \right)>\left( III \right)$

D)
$\left( III \right)>\left( II \right)>\left( I \right)$

• question_answer50) During the change of ${{O}_{2}}$to $O_{2}^{-},$the incoming electron goes to the orbital : [JEE Main 10-4-2019 Morning]

A)
$\sigma {{*}^{2}}{{P}_{z}}$

B)
${{\pi }^{2}}{{P}_{y}}$

C)
$\pi *\,{{\,}^{2}}{{P}_{x}}$

D)
$\pi {{\,}^{2}}{{P}_{x}}$

• question_answer51) Increasing rate of ${{S}_{N}}1$ reaction in the following compounds is:  [A] [B] [C] [D]
[JEE Main 10-4-2019 Morning]

A)
$(A)<(B)<(C)<(D)$

B)
$(B)<(A)<(D)<(C)$

C)
$(B)<(A)<(C)<(D)$

D)
$(A)<(B)<(D)<(C)$

• question_answer52) Consider the following table :  Gas $a/(k\,Pa\,d{{m}^{6}}\,mo{{l}^{-1}})$ $b/(\,d{{m}^{3}}\,mo{{l}^{-1}})$ A 642.32 0.05196 B 155.21 0.04136 C 431.91 0.05196 D 155.21 0.4382
 a and b are vander waals constant. The correct statement about the gases is:
[JEE Main 10-4-2019 Morning]

A)
Gas C will occupy lesser volume than gas A; gas B will be lesser compressible than gas D

B)
Gas C will occupy more volume than gas A; gas B will be lesser compressible than gas D

C)
Gas C will occupy more volume than gas A; gas B will be more compressible than gas D

D)
Gas C will occupy lesser volume than gas A; gas B will be more compressible than gas D

• question_answer53) The increasing order of the reactivity of the following compounds towards electrophilic aromatic substitution reactions is :- [JEE Main 10-4-2019 Morning]

A)
$I<III<II$

B)
$II<I<III$

C)
$III<I<II$

D)
$III<II<I$

• question_answer54) The graph between $|\psi {{|}^{2}}$and r(radial distance) is shown below. This represents :- [JEE Main 10-4-2019 Morning]

A)
3s orbital

B)
1s orbital

C)
2p orbital

D)
2s orbital

• question_answer55) At room temperature, a dilute soluton of urea is prepared by dissolving 0.60 g of urea in 360 g of water. If the vapour pressure of pure water at this temperature is 35 mmHg, lowering of vapour pressure will be (molar mass of urea $=60g\,mo{{l}^{-1}}$):- [JEE Main 10-4-2019 Morning]

A)
0.027 mmHg

B)
0.028 mmHg

C)
0.017 mmHg

D)
0.031 mmHg

• question_answer56) The synonym for water gas when used in the production of methanol is :- [JEE Main 10-4-2019 Morning]

A)
natural gas

B)
laughing gas

C)
syn gas

D)
fuel gas

• question_answer57) A process will be spontaneous at all temperatures if :- [JEE Main 10-4-2019 Morning]

A)
$\Delta H>0$ and $\Delta S<0$

B)
$\Delta H<0$ and $\Delta S>0$

C)
$\Delta H>0$ and $\Delta S>0$

D)
$\Delta H<0$ and $\Delta S<0$

• question_answer58) The major product of the following reaction is :- [JEE Main 10-4-2019 Morning]

A)

B)

C)

D)

• question_answer59) The regions of the atmosphere, where clouds form and where we line respectively, are :- [JEE Main 10-4-2019 Morning]

A)
Stratosphere and Troposphere

B)
Troposphere and Stratosphere

C)
Troposphere and Troposphere

D)
Stratosphere and Stratosphere

• question_answer60) The alloy used in the construction of aircrafts is :- [JEE Main 10-4-2019 Morning]

A)
$MgSn$

B)
$MgMn$

C)
$MgAl$

D)
$MgZn$

• question_answer61) If for some $x\in R,$the frequency distribution of the marks obtained by 20 students in a test is:  Marks 2 3 5 7 Frequency ${{(x+1)}^{2}}$ $2x-5$ ${{x}^{2}}-3x$ $x$
 then the mean of the marks is :
[JEE Main 10-4-2019 Morning]

A)
2.8

B)
3.2

C)
3.0

D)
2.5

• question_answer62) If${{\Delta }_{1}}=\left| \begin{matrix} x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & l & x \\ \end{matrix} \right|$and ${{\Delta }_{2}}=\left| \begin{matrix} x & \sin 2\theta & \cos 2\theta \\ -\sin 2\theta & -x & 1 \\ \cos 2\theta & \text{l} & x \\ \end{matrix} \right|,x\ne 0;$then for all$\theta \in \left( 0,\frac{\pi }{2} \right):$ [JEE Main 10-4-2019 Morning]

A)
${{\Delta }_{1}}-{{\Delta }_{2}}=x(cos2\theta -cos4\theta )$

B)
${{\Delta }_{1}}+{{\Delta }_{2}}=-2{{x}^{3}}$

C)
${{\Delta }_{1}}-{{\Delta }_{2}}=-2{{x}^{3}}$

D)
${{\Delta }_{1}}+{{\Delta }_{2}}=-2({{x}^{3}}+x-1)$

• question_answer63) If$\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{4}}-1}{x-1}=\underset{x\to k}{\mathop{\lim }}\,\frac{{{x}^{3}}-{{k}^{3}}}{{{x}^{2}}-{{k}^{2}}},$then k is: [JEE Main 10-4-2019 Morning]

A)
$\frac{3}{8}$

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

C)
$\frac{4}{3}$

D)
$\frac{8}{3}$

• question_answer64) If the system of linear equations  $x+y+z=5$ $x+2y+2z=6$ $x+3y+\lambda z=\mu ,$$(\lambda ,\mu \in R),$has infinitely many solutions, then the value of $\lambda +\mu$ is :
[JEE Main 10-4-2019 Morning]

A)
12

B)
10

C)
9

D)
7

• question_answer65) If the circles ${{x}^{2}}+{{y}^{2}}+5Kx+2y+K=0$and $2\left( {{x}^{2}}+{{y}^{2}} \right)+2Kx+3y1=0,(K\in R),$ intersect at the points P and Q, then the line $4x+5yK=0$ passes through P and Q for : [JEE Main 10-4-2019 Morning]

A)
exactly two values of K

B)
exactly one value of K

C)
no value of K.

D)
infinitely many values of K

• question_answer66) Le $f(x)={{x}^{2}},x\in R.$For any $A\subseteq R,$define$g(A)=\{x\in R,f(x)\in A\}$If $S=\left[ 0,4 \right],$ then which one of the following statements is not true? [JEE Main 10-4-2019 Morning]

A)
$f(g(S))\ne f(S)$

B)
$f(g(S))=S$

C)
$g(f(S))=g(S)$

D)
$g(f(S))\ne (S)$

• question_answer67) Let$f(x)={{e}^{x}}-x$ and $g(x){{x}^{2}}-x,\forall x\in R.$  Then the set of all $x\in R,$where the function $h(x)=(fog)(x)$is increasing is :
[JEE Main 10-4-2019 Morning]

A)
$\left[ -1,\frac{-1}{2} \right]\cup \left[ \frac{1}{2},\infty \right)$

B)
$\left[ 0,\frac{1}{2} \right]\cup \left[ 1,\infty \right)$

C)
$\left[ \frac{-1}{2},0 \right]\cup \left[ 1,\infty \right)$

D)
$\left[ 0,\infty \right)$

• question_answer68) Which one of the following Boolean expressions is a tautology? [JEE Main 10-4-2019 Morning]

A)
$\left( P\vee q \right)\wedge (\tilde{\ }p\vee \tilde{\ }q)$

B)
$\left( P\wedge q \right)\vee (p\wedge \tilde{\ }q)$

C)
$\left( P\vee q \right)\wedge (p\vee \tilde{\ }q)$

D)
$\left( P\vee q \right)\vee (p\vee \tilde{\ }q)$

• question_answer69) All the pairs (x, y) that satisfy the inequality $2\sqrt{{{\sin }^{2}}x-2\sin x+5}.$$\frac{1}{{{4}^{{{\sin }^{2}}y}}}\le 1$also satisfy the equation. [JEE Main 10-4-2019 Morning]

A)
$\sin x=|\sin y|$

B)
$\sin x=2\sin y$

C)
$2|\sin x|=3\sin y$

D)
$2\sin x=\sin y$

• question_answer70) The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is : [JEE Main 10-4-2019 Morning]

A)
36

B)
60

C)
48

D)
72

• question_answer71) Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is : [JEE Main 10-4-2019 Morning]

A)
$\frac{1}{11}$

B)
$\frac{1}{17}$

C)
$\frac{1}{10}$

D)
$\frac{1}{12}$

• question_answer72) The sum $=\frac{3\times {{1}^{3}}}{{{1}^{2}}}+\frac{5\times \left( {{1}^{3}}+{{2}^{3}} \right)}{{{1}^{2}}+{{2}^{2}}}+\frac{7\times \left( {{1}^{3}}+{{2}^{3}}+{{3}^{3}} \right)}{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}+......$ [JEE Main 10-4-2019 Morning]

A)
660

B)
620

C)
680

D)
600

• question_answer73) If a directrix of a hyperbola centred at the origin and passing through the point $\left( 4,-2\sqrt{3} \right)$is $5x=4\sqrt{5}$and its eccentricity is e, then : [JEE Main 10-4-2019 Morning]

A)
$4{{e}^{4}}-24{{e}^{2}}+35=0$

B)
$4{{e}^{4}}+8{{e}^{2}}-35=0$

C)
$4{{e}^{4}}-12{{e}^{2}}-27=0$

D)
$4{{e}^{4}}-24{{e}^{2}}+27=0$

• question_answer74) Iff(x)=\left\{ \begin{align} & \frac{\sin (p+1)+sin\,x}{x}\,\,\,\,,\,\,\,\,x<0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,q\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,x=0 \\ & \frac{\sqrt{x+{{x}^{2}}}-\sqrt{x}}{{{x}^{{}^{3}/{}_{2}}}}\,\,\,\,\,\,\,\,,\,\,\,\,x>0 \\ \end{align} \right. is continuous at x = 0, then the ordered pair (p,q) is equal to :                         [JEE Main 10-4-2019 Morning]

A)
$\left( \frac{5}{2},\frac{1}{2} \right)$

B)
$\left( -\frac{3}{2},-\frac{1}{2} \right)$

C)
$\left( -\frac{1}{2},\frac{3}{2} \right)$

D)
$\left( -\frac{3}{2},\frac{1}{2} \right)$

• question_answer75) If $y=y\left( x \right)$is the solution of the differential equation $\frac{dy}{dx}=(tanx-y)se{{c}^{2}}x,x\in \left( -\frac{\pi }{2},\frac{\pi }{2} \right),$such that$y(0)=0,$then $y\left( -\frac{\pi }{4} \right)$is equal to : [JEE Main 10-4-2019 Morning]

A)
$2+\frac{1}{e}$

B)
$\frac{1}{2}-e$

C)
$e-2$

D)
$\frac{1}{2}-e$

• question_answer76) If the line $x2y=12$is tangent to the ellipse $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$at the point $\left( 3,\frac{-9}{2} \right),$then the length of the latus recturm of the ellipse is : [JEE Main 10-4-2019 Morning]

A)
$9$

B)
$8\sqrt{3}$

C)
$12\sqrt{2}$

D)
$5$

• question_answer77) The value of $\int\limits_{0}^{2\pi }{\left[ \sin 2x(1+cos3x) \right]}dx,$where [t] denotes the greatest integer function, is : [JEE Main 10-4-2019 Morning]

A)
$-2\pi$

B)
$\pi$

C)
$-\pi$

D)
$2\pi$

• question_answer78) The region represented by $|x-y|\le 2$and $|x+y|\,\le 2$is bounded by a : [JEE Main 10-4-2019 Morning]

A)
square of side length $2\sqrt{2}$units

B)
rhombus of side length 2 units

C)
square of area 16 sq, units

D)
rhombus of area $8\sqrt{2}$ sq. units

• question_answer79) The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, -3), then its radius is : [JEE Main 10-4-2019 Morning]

A)
$3\sqrt{2}$

B)
$3$

C)
$2\sqrt{2}$

D)
$2$

• question_answer80) Let $A\left( 3,0,1 \right),B\left( 2,10,6 \right)$and $C\left( 1,2,1 \right)$be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the ratio, 2 : 1, then $\cos \left( \angle GOA \right)$(O being the origin) is equal to: [JEE Main 10-4-2019 Morning]

A)
$\frac{1}{\sqrt{30}}$

B)
$\frac{1}{6\sqrt{10}}$

C)
$\frac{1}{\sqrt{15}}$

D)
$\frac{1}{2\sqrt{15}}$

• question_answer81) Let $f:R\to R$be differentiable at $c\in R$and $f(c)=0$. If $g(x)=|f(x)|,$then at $x=c,g$is : [JEE Main 10-4-2019 Morning]

A)
differentiable if$f'(c)=0$

B)
not differentiable

C)
differentiable if $f'(c)\ne 0$

D)
not differentiable if $f'(c)=0$

• question_answer82) If $\alpha$ and $\beta$ are the roots of the quadratic equation, ${{x}^{2}}+x\sin \theta -2\sin \theta =0,\theta \in \left( 0,\frac{\pi }{2} \right),$ then $\frac{{{\alpha }^{12}}+{{\beta }^{12}}}{\left( {{\alpha }^{-12}}+{{\beta }^{-12}} \right){{\left( \alpha -\beta \right)}^{24}}}$is equal to : [JEE Main 10-4-2019 Morning]

A)
$\frac{{{2}^{6}}}{{{\left( \sin \theta +8 \right)}^{12}}}$

B)
$\frac{{{2}^{12}}}{{{\left( \sin \theta -8 \right)}^{6}}}$

C)
$\frac{{{2}^{12}}}{{{\left( \sin \theta -4 \right)}^{12}}}$

D)
$\frac{{{2}^{12}}}{{{\left( \sin \theta +8 \right)}^{12}}}$

• question_answer83) If the length of the perpendicular from the point $(\beta ,0,\beta )(\beta \ne 0)$ to the line,$\frac{x}{1}=\frac{y-1}{0}=\frac{z+1}{-1}$ is $\sqrt{\frac{3}{2}},$then $\beta$is equal to : [JEE Main 10-4-2019 Morning]

A)
-1

B)
2

C)
-2

D)
1

• question_answer84) If $\int_{{}}^{{}}{\frac{dx}{{{\left( {{x}^{2}}-2x+10 \right)}^{2}}}}$$=A\left( {{\tan }^{-1}}\left( \frac{x-1}{3} \right)+\frac{f(x)}{{{x}^{2}}-2x+10} \right)+C$ where C is a constant of integration, then : [JEE Main 10-4-2019 Morning]

A)
$A=\frac{1}{27}\text{and}\,f(x)=9(x-1)$

B)
$A=\frac{1}{81}\text{and}\,f(x)=3(x-1)$

C)
$A=\frac{1}{54}\text{and}\,f(x)=9{{(x-1)}^{2}}$

D)
$A=\frac{1}{54}\text{and}\,f(x)=3(x-1)$

• question_answer85) ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are ${{\cot }^{-1}}\left( 3\sqrt{2} \right)$ and $\cos e{{c}^{-1}}\left( 2\sqrt{2} \right)$ respectively,  then the height of the tower (in metres) is : [JEE Main 10-4-2019 Morning]

A)
$10\sqrt{5}$

B)
$\frac{100}{3\sqrt{3}}$

C)
$20$

D)
$25$

• question_answer86) If ${{a}_{1}},{{a}_{2}},{{a}_{3}},$........., ${{a}_{n}}$are in A.P. and ${{a}_{1}}+{{a}_{4}}+{{a}_{7}}+$......... $+{{a}_{16}}=114,$then ${{a}_{1}}+{{a}_{6}}+{{a}_{11}}+{{a}_{16}}$is equal to : [JEE Main 10-4-2019 Morning]

A)
38

B)
98

C)
76

D)
64

• question_answer87) $\underset{n\to \infty }{\mathop{\lim }}\,\left( \frac{{{(n+1)}^{{}^{1}/{}_{3}}}}{{{n}^{{}^{4}/{}_{3}}}}+\frac{{{(n+2)}^{{}^{1}/{}_{3}}}}{{{n}^{{}^{4}/{}_{3}}}}+......+\frac{{{(2n)}^{{}^{1}/{}_{3}}}}{{{n}^{{}^{4}/{}_{3}}}} \right)$ is equal to: [JEE Main 10-4-2019 Morning]

A)
$\frac{4}{3}{{(2)}^{{}^{4}/{}_{3}}}$

B)
$\frac{3}{4}{{(2)}^{{}^{4}/{}_{3}}}-\frac{4}{3}$

C)
$\frac{3}{4}{{(2)}^{{}^{4}/{}_{3}}}-\frac{3}{4}$

D)
$\frac{4}{3}{{(2)}^{{}^{3}/{}_{4}}}$

• question_answer88) If $Q\left( 0,1,3 \right)$is the image of the point P in the plane $3xy+4z=2$and R is the point (3, -1, -2), then the area (in sq. units) of $\Delta PQR$is: [JEE Main 10-4-2019 Morning]

A)
$\frac{\sqrt{65}}{2}$

B)
$\frac{\sqrt{91}}{4}$

C)
$2\sqrt{13}$

D)
$\frac{\sqrt{91}}{2}$

• question_answer89) If the coefficients of ${{x}^{2}}$and ${{x}^{3}}$are both zero, in the expansion of the expression $(1+ax+b{{x}^{2}})$${{(1-3x)}^{15}}$in powers of x, then the ordered pair (a, b) is equal to: [JEE Main 10-4-2019 Morning]

A)
(28, 315)

B)
(-54, 315)

C)
(-21, 714)

D)
(24, 861)

• question_answer90) If $a>0$and $z=\frac{{{\left( 1+i \right)}^{2}}}{a-i},$has magnitude$\sqrt{\frac{2}{5},}$then $\overline{z}$is equal to : [JEE Main 10-4-2019 Morning]

A)
$-\frac{3}{5}-\frac{1}{5}i$

B)
$-\frac{1}{5}+\frac{3}{5}i$

C)
$-\frac{1}{5}-\frac{3}{5}i$

D)
$\frac{1}{5}-\frac{3}{5}i$