# Solved papers for JEE Main & Advanced JEE Main Online Paper (Held on 09-4-2019 Morning)

### done JEE Main Online Paper (Held on 09-4-2019 Morning)

• question_answer1) In the density measurement of a cube, the mass and edge length are measured as $\left( 10.00\pm 0.10 \right)\text{ }kg$and$\left( 0.10\pm 0.01 \right)\text{ }m,$respectively. The error in the measurement of density is: [JEE Main 9-4-2019 Morning]

A) $0.10\text{ }kg/{{m}^{3}}$

B) $0.31\text{ }kg/{{m}^{3}}$

C) $0.07\text{ }kg/{{m}^{3}}$

D) $0.01\text{ }kg/{{m}^{3}}$

• question_answer2) An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $\overline{\text{v}},m$is its mass and ${{k}_{B}}$is Boltzmann constant, then its temperature will be: [JEE Main 9-4-2019 Morning]

A) $\frac{m{{\overline{\text{v}}}^{2}}}{6{{k}_{B}}}$

B) $\frac{m{{\overline{\text{v}}}^{2}}}{5{{k}_{B}}}$

C) $\frac{m{{\overline{\text{v}}}^{2}}}{3{{k}_{B}}}$

D) $\frac{m{{\overline{\text{v}}}^{2}}}{7{{k}_{B}}}$

• question_answer3) Following figure shows two processes A and B for a gas. If $\Delta {{Q}_{A}}$and $\Delta {{Q}_{B}}$are the amount of heat absorbed by the system in two cases, and $\Delta {{U}_{A}}$and $\Delta {{U}_{B}}$are changes in internal energies, respectively, then : [JEE Main 9-4-2019 Morning] A) $\Delta {{Q}_{A}}=\Delta {{Q}_{B}};\Delta {{U}_{A}}=\Delta {{U}_{B}}$

B) $\Delta {{Q}_{A}}>\Delta {{Q}_{B}};\Delta {{U}_{A}}=\Delta {{U}_{B}}$

C) $\Delta {{Q}_{A}}>\Delta {{Q}_{B}};\Delta {{U}_{A}}>\Delta {{U}_{B}}$

D) $\Delta {{Q}_{A}}<\Delta {{Q}_{B}};\Delta {{U}_{A}}<\Delta {{U}_{B}}$

• question_answer4) A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is: (E is mid-point of arm CD) [JEE Main 9-4-2019 Morning] A) $R$

B) $\frac{1}{16}R$

C) $\frac{7}{64}R$

D) $\frac{3}{4}R$

• question_answer5) The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to: [JEE Main 9-4-2019 Morning]

A) $1/{{L}^{2}}$

B) $1/L$

C) $L$

D) ${{L}^{2}}$

• question_answer6) A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac{1}{16}$th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is : [JEE Main 9-4-2019 Morning]

A) $4T\sqrt{\frac{1}{15}}$

B) $2T\sqrt{\frac{1}{10}}$

C) $4T\sqrt{\frac{1}{14}}$

D) $2T\sqrt{\frac{1}{14}}$

• question_answer7) Determine the charge on the capacitor in the following circuit : [JEE Main 9-4-2019 Morning] A) $2\mu C$

B) $60\mu C$

C) $200\mu C$

D) $10\mu C$

• question_answer8) A system of three charges are placed as shown in the figure : If $D>>d,$the potential energy of the system is best given by: [JEE Main 9-4-2019 Morning]

A) $\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ -\frac{{{q}^{2}}}{d}-\frac{qQd}{2{{D}^{2}}} \right]$

B) $\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ +\frac{{{q}^{2}}}{d}+\frac{qQd}{{{D}^{2}}} \right]$

C) $\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ -\frac{{{q}^{2}}}{d}+\frac{2qQd}{{{D}^{2}}} \right]$

D) $\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ -\frac{{{q}^{2}}}{d}-\frac{qQd}{{{D}^{2}}} \right]$

• question_answer9) The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight? [JEE Main 9-4-2019 Morning]

A) $60{}^\circ$

B) $150{}^\circ$

C) $90{}^\circ$

D) $120{}^\circ$

• question_answer10) A body of mass 2 kg makes an eleastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body? [JEE Main 9-4-2019 Morning]

A) 1.8 kg

B) 1.2 kg

C) 1.5 kg

D) 1.0 kg

• question_answer11) A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be: [JEE Main 9-4-2019 Morning]

A) $\frac{2GM}{9{{a}^{2}}}$

B) $\frac{GM}{3{{a}^{2}}}$

C) $\frac{GM}{9{{a}^{2}}}$

D) $\frac{2GM}{3{{a}^{2}}}$

• question_answer12) The pressure wave, $P=0.01$ $\sin \left[ 1000t3x \right]$$N{{m}^{2}},$corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is $0{}^\circ C$. On some other day, when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be $336m{{s}^{-1}}.$Approximate value of T is : [JEE Main 9-4-2019 Morning]

A) $15{}^\circ C$

B) $12{}^\circ C$

C) $4{}^\circ C$

D) $11{}^\circ C$

• question_answer13) An NPN transistor is used in common emitter configuration as an amplifier with $1k\Omega$load resistance. Signal voltage of 10 mV is applied across the base-emitter. This produces a 3 mA change in the collector current and $15\mu A$ change in the base current of the amplifier. The input resistance and voltage gain are: [JEE Main 9-4-2019 Morning]

A) $0.33k\Omega ,1.5$

B) $0.67k\Omega ,200$

C) $0.33k\Omega ,300$

D) $0.67k\Omega ,300$

• question_answer14) A moving coil galvanometer has resistance $50\Omega$and it indicates full deflection at 4mA current. A voltmeter is made using this galvanometer and a $5k\Omega$resistance. The maximum voltage, that can be measured using this voltmeter, will be close to : [JEE Main 9-4-2019 Morning]

A) 10 V

B) 20 V

C) 40 V

D) 15 V

• question_answer15) The electric field of light wave is given as $\vec{E}={{10}^{-3}}\cos \left( \frac{2\pi x}{5\times {{10}^{-7}}}-2\pi \times 6\times {{10}^{14}}t \right)$$\hat{x}\frac{N}{C}.$This light falls on a metal plate of work function 2eV. The stopping potential of the photo-electrons is : Given, E (in eV) $=\frac{12375}{\lambda (in\overset{\text{o}}{\mathop{\text{A}}}\,)}$ [JEE Main 9-4-2019 Morning]

A) 0.48 V

B) 2.0 V

C) 2.48 V

D) 0.72 V

• question_answer16) A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height (p-h) diagram is : [JEE Main 9-4-2019 Morning]

A) B) C) D) • question_answer17) A capacitor with capacitance $5\mu F$is charged to $5\mu C.$If the plates are pulled apart to reduce the capacitance to $2\mu F,$how much work is done? [JEE Main 9-4-2019 Morning]

A) $3.75\times {{10}^{6}}J$

B) $2.55\times {{10}^{6}}J$

C) $2.16\times {{10}^{6}}J$

D) $6.25\times {{10}^{6}}J$

• question_answer18) A rigid square loop of side 'a' and carrying current ${{I}_{2}}$is lying on a horizontal surface near a long current ${{I}_{1}}$carrying wire in the same plane as shown in figure. The net force on the loop due to wire will be : [JEE Main 9-4-2019 Morning] A) Attractive and equal to $\frac{{{\mu }_{0}}{{I}_{1}}{{I}_{2}}}{3\pi }$

B) Repulsive and equal to $\frac{{{\mu }_{0}}{{I}_{1}}{{I}_{2}}}{4\pi }$

C) Repulsive and equal to$\frac{{{\mu }_{0}}{{I}_{1}}{{I}_{2}}}{2\pi }$

D) Zero

• question_answer19) The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index μ is put in front of one of the slits, the central maximum gest shifted by a distance equal to n fringe widths. If the wavelength of light used is $\lambda ,t$will be : [JEE Main 9-4-2019 Morning] A) $\frac{2D\lambda }{a(\mu -1)}$

B) $\frac{D\lambda }{a(\mu -1)}$

C) $\frac{2nD\lambda }{a(\mu -1)}$

D) $\frac{nD\lambda }{a(\mu -1)}$

• question_answer20) A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is $Y=0.3\sin$$(0.157x)cos$$(200\pi t)$. The length of the string is : (All quantities are in SI units.) [JEE Main 9-4-2019 Morning]

A) 20 m

B) 80 m

C) 60 m

D) 40 m

• question_answer21) The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane. : (i) a ring of radius R, (ii) a solid cylinder of radius $\frac{R}{2}$ and (iii) a solid sphere of radius $\frac{R}{4}$. If in each case, the speed of the centre of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is : [JEE Main 9-4-2019 Morning]

A) 4 : 3 : 2

B) 14 : 15 : 20

C) 10 : 15 : 7

D) 2 : 3 : 4

• question_answer22) A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $\theta ,$where $\theta$ is the angle by which it has rotated, is given as $k{{\theta }^{2}}.$If its moment of inertia is I then the angular acceleration of the disc is : [JEE Main 9-4-2019 Morning]

A) $\frac{k}{2I}\theta$

B) $\frac{k}{I}\theta$

C) $\frac{k}{4I}\theta$

D) $\frac{2k}{I}\theta$

• question_answer23) A uniform cable of mass 'M' and length 'L' is placed on a horizontal surface such that its ${{\left( \frac{1}{n} \right)}^{th}}$part is hanging below the edge of the surface. To lift the hanging part of the cable up to the surface, the work done should be : [JEE Main 9-4-2019 Morning]

A) $\frac{MgL}{{{n}^{2}}}$

B) $\frac{MgL}{2{{n}^{2}}}$

C) $\frac{2MgL}{{{n}^{2}}}$

D) $nMgL$

• question_answer24) If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is : [JEE Main 9-4-2019 Morning]

A) $4M$

B) $M$

C) $2M$

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

• question_answer25) Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be : [JEE Main 9-4-2019 Morning]

A) 889.2 nm

B) 642.7 nm

C) 488.9 nm

D) 388.9 nm

• question_answer26) The magnetic field of a plane electromagnetic wave is given by : $\vec{B}={{B}_{0}}\hat{i}[cos(kz-\omega t)]+{{B}_{1}}\hat{j}\cos (kz+\omega t)$ where ${{B}_{0}}=3\times {{10}^{-5}}T$ and ${{B}_{1}}=2\times {{10}^{-6}}T.$ The rms value of the force experienced by a stationary charge $Q={{10}^{-4}}C$at $z=0$is closest to : [JEE Main 9-4-2019 Morning]

A) $0.9\text{ }N$

B) $0.1\text{ }N$

C) $3\times {{10}^{2}}N$

D) $0.6N$

• question_answer27) A rectangular coil (Dimension $5cm\times 2.5cm)$ with 100 turns, carrying a current of 3 A in the clock-wise direction is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through$45{}^\circ$about Z-axis, then the torque on the coil is : [JEE Main 9-4-2019 Morning]

A) 0.55 Nm

B) 0.27 Nm

C) 0.38 Nm

D) 0.42 Nm

• question_answer28) A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is : [JEE Main 9-4-2019 Morning]

A) 1.60 m

B) 0.24 m

C) 0.16 m

D) 0.32 m

• question_answer29) A signal $A\cos \omega t$ is transmitted using ${{\text{v}}_{\text{0}}}\sin {{\omega }_{0}}t$ as carrier wave. The correct amplitude modulated (AM) signal is : [JEE Main 9-4-2019 Morning]

A) ${{\text{v}}_{\text{0}}}\sin {{\omega }_{0}}t+A\cos \omega t$

B) ${{\text{v}}_{\text{0}}}\sin {{\omega }_{0}}t+\frac{A}{2}sin({{\omega }_{0}}-\omega )t+\frac{A}{2}\sin ({{\omega }_{0}}+\omega )t$

C) $\text{(}{{\text{v}}_{\text{0}}}+A)cos\omega t\sin {{\omega }_{0}}t$

D) ${{\text{v}}_{\text{0}}}sin[{{\omega }_{0}}(1+0.01A\,sin\omega t)t]$

• question_answer30) For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at $127{}^\circ C.$ At 2 atm pressure and at$~227{}^\circ C,$the rms speed of the molecules will be : [JEE Main 9-4-2019 Morning]

A) $80\text{ }m/s$

B) 100 5 m/s

C) $80\sqrt{5}m/s$

D) $100\text{ }m/s$

• question_answer31) The correct order of the oxidation states of nitrogen in $NO,{{N}_{2}}O,N{{O}_{2}}$and ${{N}_{2}}{{O}_{3}}$is : [JEE Main 9-4-2019 Morning]

A) $N{{O}_{2}}<{{N}_{2}}{{O}_{3}}<NO<{{N}_{2}}O$

B) $N{{O}_{2}}<NO<{{N}_{2}}{{O}_{3}}<{{N}_{2}}O$

C) ${{N}_{2}}O<{{N}_{2}}{{O}_{3}}<NO<N{{O}_{2}}$

D) ${{N}_{2}}O<NO<{{N}_{2}}{{O}_{3}}<N{{O}_{2}}$

• question_answer32) The degenerate orbitals of ${{[Cr{{({{H}_{2}}O)}_{6}}]}^{3+}}$are : [JEE Main 9-4-2019 Morning]

A) ${{d}_{yz}}\,\text{and}\,\,{{d}_{{{z}^{2}}}}$

B) ${{d}_{{{z}^{2}}}}\,\text{and}\,\,{{d}_{xz}}$

C) ${{d}_{xz}}\,\text{and}\,\,{{d}_{yz}}$

D) ${{d}_{{{x}^{2}}-{{y}^{2}}}}\,\text{and}\,\,{{d}_{xy}}$

• question_answer33) The mojor product of the following reaction is : [JEE Main 9-4-2019 Morning] A) B) C) D) • question_answer34) The organic compound that gives following qualitative analysis is:

 Test Inference [a] Dil. HCl Insoluble [b] NaOH solution soluble [c] $B{{r}_{2}}$/water Decolourization
[JEE Main 9-4-2019 Morning]

A) B) C) D) • question_answer35) Which of the following statements is not true about sucrose? [JEE Main 9-4-2019 Morning]

A) On hydrolysis, it produces glucose and fructose

B) The glycosidic linkage is present between ${{C}_{1}}$of $\alpha -$glucose and ${{C}_{1}}$ of $\beta -$fructose

C) It is also named as invert sugar

D) It is a non reducing sugar

• question_answer36) Excessive release of $C{{O}_{2}}$ into the atomosphere results in : [JEE Main 9-4-2019 Morning]

A) polar vortex

B) depletion of ozone

C) formation of smog

D) global warming

• question_answer37) Among the following, the molecule expected to be stabilized by anion formation is : [JEE Main 9-4-2019 Morning] ${{C}_{2}},{{O}_{2}},NO,{{F}_{2}}$

A) $NO$

B) ${{C}_{2}}$

C) ${{F}_{2}}$

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

• question_answer38) The one that will show optical activity is : (en = ethane-1,2-diamine) [JEE Main 9-4-2019 Morning]

A) B) C) D) • question_answer39) The given plots represent the variation of the concentration of a reactant R with time for two different reactions (i) and (ii). The respective orders of the reactions are: [JEE Main 9-4-2019 Morning] A) 1, 0

B) 1, 1

C) 0, 1

D) 0, 2

• question_answer40) The aerosol is a kind of colloid in which : [JEE Main 9-4-2019 Morning]

A) gas is dispersed in solid

B) solid is dispersed in gas

C) liquid is dispersed in water

D) gas is dispersed in liquid

• question_answer41) The mojor product of the following reaction is : [JEE Main 9-4-2019 Morning] A) B) C) D) • question_answer42) For a reaction, ${{N}_{2}}(g)+3{{H}_{2}}(g)\to 2N{{H}_{3}}(g);$identify dihydrogen $({{H}_{2}})$ as a limiting reagent in the following reaction mixtures. [JEE Main 9-4-2019 Morning]

A) $\text{14g of }{{\text{N}}_{\text{2}}}\text{+4g of }{{\text{H}}_{\text{2}}}$

B) $\text{28g of }{{\text{N}}_{\text{2}}}\text{+6g of }{{\text{H}}_{\text{2}}}$

C) $\text{56g of }{{\text{N}}_{\text{2}}}\text{+10g of }{{\text{H}}_{\text{2}}}$

D) $\text{35g of }{{\text{N}}_{\text{2}}}\text{+8g of }{{\text{H}}_{\text{2}}}$

• question_answer43) The number of water molecule(s) not coordinated to copper ion directly in $CuS{{O}_{4}}.5{{H}_{2}}O,$ is : [JEE Main 9-4-2019 Morning]

A) 4

B) 3

C) 1

D) 2

• question_answer44) The correct IUPAC name of the following compound is : [JEE Main 9-4-2019 Morning] A) 5-chloro-4-methy1-1-nitrobenzene

B) 2-methyl-5-nitro-1-chlorobenzene

C) 3-chloro-4-methy1-1-nitrobenzene

D) 2-chloro-1-methy1-4-nitrobenzene

• question_answer45) ${{C}_{60}},$an allotrope of carbon contains : [JEE Main 9-4-2019 Morning]

A) 20 hexagons and 12 pentagons.

B) 12 hexagons and 20 pentagons.

C) 18 hexagons and 14 pentagons.

D) 16 hexagons and 16 pentagons.

• question_answer46) Among the following, the set of parameters that represents path function, is :

 [A] q + w [B] q [C] w [D] H-TS
[JEE Main 9-4-2019 Morning]

A) [A] and [D]

B) [B], [C] and [D]

C) [B] and [C]

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

• question_answer47) The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a solution of $0.01\,M\,BaC{{l}_{2}}$in water. Assuming complete dissociation of the given ionic compounds in water, the concentration of XY (in $mol\,{{L}^{-1}}$) in solution is : [JEE Main 9-4-2019 Morning]

A) $6\times {{10}^{-2}}$

B) $4\times {{10}^{-4}}$

C) $16\times {{10}^{-4}}$

D) $4\times {{10}^{-2}}$

• question_answer48) The standard Gibbs energy for the given cell reaction in $kJ\,mo{{l}^{-1}}$ at 298 K is :

 $Zn(s)+C{{u}^{2+}}(aq)\to Z{{n}^{2+}}(aq)+Cu(s),$ ${{E}^{o}}=2\,V\,at\,298K$ (Faraday's constant, $F=96000\,C\,mo{{l}^{-1}}$)
[JEE Main 9-4-2019 Morning]

A) -384

B) -192

C) 192

D) 384

• question_answer49) The increasing order of reactivity of the following compounds towards aromatic electrophilic substitution reaction is : [JEE Main 9-4-2019 Morning] A) $D<B<A<C$

B) $A<B<C<D$

C) $D<A<C<B$

D) $B<C<A<D$

• question_answer50) The ore that contains the metal in the form of fluoride is : [JEE Main 9-4-2019 Morning]

A) magnetite

B) sphalerite

C) malachite

D) cryolite

• question_answer51) Consider the van der Waals constants, a and b, for the following gases.

 $\begin{matrix} Gas & Ar & Ne & Kr & Xe \\ a/(atm\,d{{m}^{6}}\,mo{{l}^{-2}}) & 1.3 & 0.2 & 5.1 & 4.1 \\ b/({{10}^{-2}}\,d{{m}^{3}}\,mo{{l}^{-1}}) & 3.2 & 1.7 & 1.0 & 5.0 \\ \end{matrix}$
Which gas is expected to have the highest critical temperature? [JEE Main 9-4-2019 Morning]

A) Kr

B) Ne

C) Ar

D) Xe

• question_answer52) The major product of the following reaction is : [JEE Main 9-4-2019 Morning]

A) B) C) D) • question_answer53) The major product of the following reaction is : $C{{H}_{3}}CH=CHC{{O}_{2}}C{{H}_{3}}\xrightarrow[{}]{LiAl{{H}_{4}}}$ [JEE Main 9-4-2019 Morning]

A) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CHO$

B) $C{{H}_{3}}CH=CHC{{H}_{2}}OH$

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

D) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}OH$

• question_answer54) Magnisium powder burns in air to give: [JEE Main 9-4-2019 Morning]

A) $MgO$ only

B) $MgO$and $Mg{{(N{{O}_{3}})}_{2}}$

C) $MgO$and $M{{g}_{3}}{{N}_{2}}$

D) $Mg{{(N{{O}_{3}})}_{2}}$and $M{{g}_{3}}{{N}_{2}}$

• question_answer55) Liquid 'M' and liquid 'N' form an ideal solution. The vapour pressures of pure liquids 'M' and 'N' are 450 and 700 mmHg, respectively, at the same temperature. Then correct statement is:

 (${{x}_{M}}$ = Mole fraction of 'M' in solution ; ${{x}_{N}}$ = Mole fraction of 'N' in solution ; ${{y}_{M}}$ = Mole fraction of 'M' in vapour phase ; ${{y}_{N}}$ = Mole fraction of 'N' in vapour phase)
[JEE Main 9-4-2019 Morning]

A) $({{x}_{M}}-{{y}_{M}})<({{x}_{N}}-{{y}_{N}})$

B) $\frac{{{x}_{M}}}{{{x}_{N}}}<\frac{{{y}_{M}}}{{{y}_{N}}}$

C) $\frac{{{x}_{M}}}{{{x}_{N}}}>\frac{{{y}_{M}}}{{{y}_{N}}}$

D) $\frac{{{x}_{M}}}{{{x}_{N}}}=\frac{{{y}_{M}}}{{{y}_{N}}}$

• question_answer56) Aniline dissolved in dilute HCl is reacted with sodium nitrite at $0{}^\text{o}C$. This solution was added drop wise to a solution containing equimolar mixture of aniline and phenol in dil. HCl. The structure of the major product is : [JEE Main 9-4-2019 Morning]

A) B) C) D) • question_answer57) The element having greatest difference between its first and second ionization energies, is : [JEE Main 9-4-2019 Morning]

A) Ca

B) K

C) Ba

D) Sc

• question_answer58) For any given series of spectral lines of atomic hydrogen, let $\Delta \text{\bar{v}=}{{\text{\bar{v}}}_{\max }}-{{\text{\bar{v}}}_{\min }}$ be the difference in maximum and minimum frequencies in $c{{m}^{-1}}.$The ratio $\Delta {{\text{\bar{v}}}_{Lyman}}/\Delta {{\text{\bar{v}}}_{Balmer}}$is : [JEE Main 9-4-2019 Morning]

A) 27 : 5

B) 4 : 1

C) 5 : 4

D) 9 : 4

• question_answer59) The mojor product of the following reaction is : [JEE Main 9-4-2019 Morning]

A) $C{{H}_{3}}CD(Cl)CHD(I)$

B) $C{{H}_{3}}C{{D}_{2}}CH(Cl)(I)$

C) $C{{H}_{3}}CD(I)CHD(Cl)$

D) $C{{H}_{3}}C(I)(Cl)CH{{D}_{2}}$

• question_answer60) Match the catalysts (Column I) with products (Column II).

 Column I Column II [A]${{V}_{2}}{{O}_{5}}$ (i) Polyethylene [B]$TiC{{l}_{4}}/Al{{(Me)}_{3}}$ (ii) ethanol [C]$PdC{{l}_{2}}$ (iii)${{H}_{2}}S{{O}_{4}}$ [D] Iron Oxide (iv)$N{{H}_{3}}$
[JEE Main 9-4-2019 Morning]

A) $(A)\text{-}\left( \text{ii} \right)\text{; }\left( \text{B} \right)\text{-}\left( \text{iii} \right)\text{; }\left( \text{C} \right)\text{-}\left( \text{i} \right)\text{; }\left( \text{D} \right)\text{-}\left( \text{iv} \right)$

B) $\left( \text{A} \right)\text{-}\left( \text{iii} \right)\text{; }\left( \text{B} \right)\text{-}\left( \text{i} \right)\text{; }\left( \text{C} \right)\text{-}\left( \text{ii} \right)\text{; }\left( \text{D} \right)\text{-}\left( \text{iv} \right)$

C) $\left( \text{A} \right)\text{-}\left( \text{iii} \right)\text{; }\left( \text{B} \right)\text{-}\left( \text{iv} \right)\text{; }\left( \text{C} \right)\text{-}\left( \text{i} \right)\text{; }\left( \text{D} \right)\text{-}\left( \text{ii} \right)$

D) $\left( \text{A} \right)\text{-}\left( \text{iv} \right)\text{; }\left( \text{B} \right)\text{-}\left( \text{iii} \right)\text{; }\left( \text{C} \right)\text{-}\left( \text{ii} \right)\text{; }\left( \text{D} \right)\text{-}\left( \text{i} \right)$

• question_answer61) Let $\vec{\alpha }=3\hat{i}+\hat{j}$and$\vec{\beta }=2\hat{i}-\hat{j}+3\hat{k}.$If$\vec{\beta }={{\vec{\beta }}_{1}}-{{\vec{\beta }}_{2}},$where ${{\vec{\beta }}_{1}}$ is parallel to $\vec{\alpha }$ and ${{\vec{\beta }}_{2}}$ is perpendicular to $\vec{\alpha },$then ${{\vec{\beta }}_{1}}\times {{\vec{\beta }}_{2}}$is equal to:- [JEE Main 9-4-2019 Morning]

A) $-3\hat{i}+9\hat{j}+5\hat{k}$

B) $3\hat{i}-9\hat{j}-5\hat{k}$

C) $\frac{1}{2}\left( -3\hat{i}+9\hat{j}+5\hat{k} \right)$

D) $\frac{1}{2}\left( 3\hat{i}-9\hat{j}+5\hat{k} \right)$

• question_answer62) For any two statements p and q, the negation of the expression $p\vee (\tilde{\ }p\wedge q)$is [JEE Main 9-4-2019 Morning]

A) $p\wedge q$

B) $p\leftrightarrow q$

C) $\tilde{\ }p\vee q\tilde{\ }q$

D) $\tilde{\ }p\wedge \tilde{\ }q$

• question_answer63) The value of$\int\limits_{0}^{\pi /2}{\frac{{{\sin }^{3}}x}{\sin x+\cos x}}dx$is [JEE Main 9-4-2019 Morning]

A) $\frac{\pi -2}{4}$

B) $\frac{\pi -2}{8}$

C) $\frac{\pi -1}{4}$

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

• question_answer64) If $\left( x \right)$is a non-zero polynomial of degree four, having local extreme points at $x=1,0,1;$then the set $S=$$\{x\in R:\left( x \right)=\left( 0 \right)\}$ Contains exactly : [JEE Main 9-4-2019 Morning]

A) four irrational numbers.

B) two irrational and one rational number.

C) four rational numbers.

D) two irrational and two rational numbers.

• question_answer65) If the standard deviation of the numbers -1, 0, 1, k is $\sqrt{5}$where $k>0,$then k is equal to [JEE Main 9-4-2019 Morning]

A) $2\sqrt{\frac{10}{3}}$

B) $2\sqrt{6}$

C) $4\sqrt{\frac{5}{3}}$

D) $\sqrt{6}$

• question_answer66) All the points in the set $S=\left\{ \frac{\alpha +i}{\alpha -i}:\alpha \in R \right\}\left( i=\sqrt{-1} \right)lie$on [JEE Main 9-4-2019 Morning]

A) circle whose radius is 1.

B) straight line whose slope is 1.

C) straight line whose slope is -1

D) circle whose radius is $\sqrt{2}$.

• question_answer67) Let S be the set of all values of x for which the tangent to the curve $y=f(x)={{x}^{3}}-{{x}^{2}}-2x$at $\left( x,y \right)$is parallel to the line segment joining the points $\left( 1,\left( 1 \right) \right)$and $\left( 1,\left( 1 \right) \right),$then S is equal to : [JEE Main 9-4-2019 Morning]

A) $\left\{ -\frac{1}{3},-1 \right\}$

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

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

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

• question_answer68) Let $f(x)=15-\left| x-10 \right|;x\in R.$Then the set of all values of x, at which the function, $g\left( x \right)=\left( \left( x \right) \right)$ is not differentiable, is : [JEE Main 9-4-2019 Morning]

A) {5, 10, 15, 20}

B) {10, 15}

C) {5, 10, 15}

D) {10}

• question_answer69) Let $p,q\in R.$If $2-\sqrt{3}$ is a root of the quadratic equation, ${{x}^{2}}+px+q=0,$ then : [JEE Main 9-4-2019 Morning]

A) ${{q}^{2}}+4p+14=0$

B) ${{p}^{2}}4q12=0$

C) ${{q}^{2}}4p16=0$

D) ${{p}^{2}}4q+12=0$

• question_answer70) Slope of a line passing through $P(2,3)$and intersecting the line, $x+y=7$at a distance of 4 units from P, is [JEE Main 9-4-2019 Morning]

A) $\frac{\sqrt{5}-1}{\sqrt{5}+1}$

B) $\frac{1-\sqrt{5}}{1+\sqrt{5}}$

C) $\frac{1-\sqrt{7}}{1+\sqrt{7}}$

D) $\frac{\sqrt{7}-1}{\sqrt{7}+1}$

• question_answer71) A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then : [JEE Main 9-4-2019 Morning]

A) $m=n=78$

B) $n=m8$

C) $m+n=68$

D) $m=n=68$

• question_answer72) If the fourth term in the binomial expansion of${{\left( \frac{2}{x}+{{x}^{{{\log }_{8}}x}} \right)}^{6}}(x>0)$is $20\times {{8}^{7}},$then a value of x is : [JEE Main 9-4-2019 Morning]

A) $8$

B) ${{8}^{2}}$

C) ${{8}^{-2}}$

D) ${{8}^{3}}$

• question_answer73) The solution of the differential equation $x\frac{dy}{dx}+2y={{x}^{2}}$$(x\ne 0)$with y(1) = 1, is [JEE Main 9-4-2019 Morning]

A) $y=\frac{{{x}^{3}}}{5}+\frac{1}{5{{x}^{2}}}$

B) $y=\frac{4}{5}{{x}^{3}}+\frac{1}{5{{x}^{2}}}$

C) $y=\frac{3}{4}{{x}^{2}}+\frac{1}{4{{x}^{2}}}$

D) $y=\frac{{{x}^{2}}}{4}+\frac{3}{4{{x}^{2}}}$

• question_answer74) A plane passing through the points (0, -1, 0) and (0, 0, 1) and making an angle $\frac{\pi }{4}$with the plane $yz+5=0,$also passes through the point [JEE Main 9-4-2019 Morning]

A) $\left( -\sqrt{2},1,-4 \right)$

B) $\left( \sqrt{2},1,4 \right)$

C) $\left( \sqrt{2},-1,4 \right)$

D) $\left( -\sqrt{2},-1,-4 \right)$

• question_answer75) The integral $\int_{{}}^{{}}{{{\sec }^{2/3}}}x\,\cos \,e{{c}^{4/3}}x\,dx$is equal to (Hence C is a constant of integration) [JEE Main 9-4-2019 Morning]

A) $3{{\tan }^{-1/3}}x+C$

B) $-\frac{3}{4}{{\tan }^{-4/3}}x+C$

C) $-3{{\cot }^{-1/3}}x+C$

D) $-3{{\tan }^{-1/3}}x+C$

• question_answer76) Let the sum of the first n terms of a non constant $A.P.,{{a}_{1}},{{a}_{2}},{{a}_{3}},$..... be $50n+\frac{n(n-7)}{2}A,$ where A is a constant. If d is the common difference of this A.P., then the ordered pair $(d,{{a}_{50}})$ is equal to [JEE Main 9-4-2019 Morning]

A) $\left( A,50+46A \right)$

B) $\left( A,50+45A \right)$

C) $\left( 50,50+46A \right)$

D) $\left( 50,50+45A \right)$

• question_answer77) The area (in sq. units) of the region $A=\{(x,y):{{x}^{2}}\le y\le x+2\}$ is [JEE Main 9-4-2019 Morning]

A) $\frac{10}{3}$

B) $\frac{9}{2}$

C) $\frac{31}{6}$

D) $\frac{13}{6}$

• question_answer78) If the line,$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{4}$meets the plane, $x+2y+3z=15$at a point P, then the distance of P from the origin is [JEE Main 9-4-2019 Morning]

A) $\frac{9}{2}$

B) $2\sqrt{5}$

C) $\frac{\sqrt{5}}{2}$

D) $\frac{7}{2}$

• question_answer79) Let$\sum\limits_{k=1}^{10}{f(a+k)=16}\left( {{2}^{10}}-1 \right),$ where the function ? satisfies $\left( x+y \right)=\left( x \right)\left( y \right)$for all natural numbers x, y and ?(1) = 2. then the natural number 'a' is [JEE Main 9-4-2019 Morning]

A) 4

B) 3

C) 16

D) 2

• question_answer80) Let$\alpha$and $\beta$be the roots of the equation ${{x}^{2}}+x+1=0.$ Then for $y\ne 0$in R, $\left| \begin{matrix} y+1 & \alpha & \beta \\ \alpha & y+\beta & 1 \\ \beta & 1 & y+\alpha \\ \end{matrix} \right|$is equal to [JEE Main 9-4-2019 Morning]

A) ${{y}^{3}}$

B) ${{y}^{3}}-1$

C) $y({{y}^{2}}-1)$

D) $y({{y}^{2}}-3)$

• question_answer81) If the tangent to the curve, $y={{x}^{3}}+axb$ at the point (1, -5) is perpendicular to the line, $x+y+4=0,$then which one of the following points lies on the curve? [JEE Main 9-4-2019 Morning]

A) (-2, 2)

B) (2, -2)

C) (2, -1)

D) (-2, 1)

• question_answer82) Four persons can hit a target correctly with Probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac{1}{8}$ respectively. if all hit at the target independently, then the probability that the target would be hit, is [JEE Main 9-4-2019 Morning]

A) $\frac{25}{192}$

B) $\frac{1}{192}$

C) $\frac{25}{32}$

D) $\frac{7}{32}$

• question_answer83) If the line $y=mx+7\sqrt{3}$is normal to the hyperbola $\frac{{{x}^{2}}}{24}-\frac{{{y}^{2}}}{18}=1,$then a value of m is [JEE Main 9-4-2019 Morning]

A) $\frac{\sqrt{5}}{2}$

B) $\frac{3}{\sqrt{5}}$

C) $\frac{2}{\sqrt{5}}$

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

• question_answer84) Let $S=\{\theta \in [-2\pi ,2\pi ]:2co{{s}^{2}}\theta +3sin\theta =0\}.$ Then the sum of the elements of S is [JEE Main 9-4-2019 Morning]

A) $\frac{13\pi }{6}$

B) $\pi$

C) $2\pi$

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

• question_answer85) The value of $co{{s}^{2}}10{}^\circ cos10{}^\circ cos50{}^\circ +co{{s}^{2}}50{}^\circ$is [JEE Main 9-4-2019 Morning]

A) $\frac{3}{2}(1+cos20{}^\circ )$

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

C) $\frac{3}{4}+\cos {{20}^{o}}$

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

• question_answer86) If a tangent to the circle${{x}^{2}}+{{y}^{2}}=1$intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is [JEE Main 9-4-2019 Morning]

A) ${{x}^{2}}+{{y}^{2}}2xy=0$

B) ${{x}^{2}}+{{y}^{2}}16{{x}^{2}}{{y}^{2}}=0$

C) ${{x}^{2}}+{{y}^{2}}4{{x}^{2}}{{y}^{2}}=0$

D) ${{x}^{2}}+{{y}^{2}}2{{x}^{2}}{{y}^{2}}=0$

• question_answer87) If the function ? defined on$\left( \frac{\pi }{6},\frac{\pi }{3} \right)$by$f(x)=\left\{ \begin{matrix} \frac{\sqrt{2}\cos x-1}{\cot x-1}, & x\ne \frac{\pi }{4} \\ k, & x=\frac{\pi }{4} \\ \end{matrix} \right.$ is continuous, then k is equal to [JEE Main 9-4-2019 Morning]

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

B) $1$

C) $\frac{1}{\sqrt{2}}$

D) $2$

• question_answer88) If$\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right].\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \\ \end{matrix} \right].\left[ \begin{matrix} 1 & 3 \\ 0 & 1 \\ \end{matrix} \right]......\left[ \begin{matrix} 1 & n-1 \\ 0 & 1 \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 78 \\ 0 & 1 \\ \end{matrix} \right],$then the inverse of$\left[ \begin{matrix} 1 & n \\ 0 & 1 \\ \end{matrix} \right]$is [JEE Main 9-4-2019 Morning]

A) $\left[ \begin{matrix} 1 & -13 \\ 0 & 1 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 1 & 0 \\ 12 & 1 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 1 & -12 \\ 0 & 1 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 1 & 0 \\ 13 & 1 \\ \end{matrix} \right]$

• question_answer89) If one end of a focal chord of the parabola, ${{y}^{2}}=16x$ is at (1, 4), then the length of this focal chord is [JEE Main 9-4-2019 Morning]

A) 25

B) 24

C) 20

D) 22

• question_answer90) If the function $f:R-\{1,-1\}\to A$defined by $f(x)=\frac{{{x}^{2}}}{1-{{x}^{2}}},$is subjective, then A is equal to [JEE Main 9-4-2019 Morning]

A) $R-[-1,0)$

B) $R-(-1,0)$

C) $R-\{-1\}$

D) $[0,\infty )$

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