Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 09-Jan-2019 Morning)

done JEE Main Online Paper (Held On 09-Jan-2019 Morning)

  • question_answer1) A Mixture of 2 moles of helium gas\[\left( atomic\text{ }mass=4u \right)\], and 1 mole of argon gas \[\left( atomic\text{ }mass=40u \right)\] is kept at 300 K in a container. The ratio of their rms speeds \[\left[ \frac{{{V}_{rms}}\,(helium)}{{{V}_{rms}}\,(argon\,)} \right]\] , is close to:

    A) 0.32

    B) 3.16

    C) 2.24

    D) 0.45

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  • question_answer2) Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:

    A) 25 : 9

    B) 4 : 1

    C) 5 : 3

    D) 16 : 9

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  • question_answer3) A sample of radioactive material A, that has an activity of \[10\text{ }mCi(1\text{ }Ci=3.7\times {{10}^{10}}\,decays/s)\], has twice the number of nuclei as another sample of different radioactive material B which has an activity of \[20\text{ }mCi\]. The correct choices for half-lives of A and B would then be respectively:

    A) 10 days and 40 days

    B) 20 days and 10 days

    C) 5 days and 10 days

    D) 20 days and 5 days

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  • question_answer4) Temperature difference of \[120{}^\circ \,C\] is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length \[\frac{3L}{2}\], is connected across AB (See figure). In steady state, temperature difference between P and Q will be close to:

    A) \[45{}^\circ \,C\]

    B) \[75{}^\circ C\]

    C) \[35{}^\circ C\]

    D) \[60{}^\circ C\]

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  • question_answer5) A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is:

    A) 0.55 cm towards the lens

    B) 0

    C) 0.55 cm away from the lens

    D) 1.1 cm away from the lens

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  • question_answer6) For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is:

    A) \[R\sqrt{2}\]

    B) R

    C) \[\frac{R}{\sqrt{5}}\]

    D) \[\frac{R}{\sqrt{2}}\]

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  • question_answer7) Drift speed of electrons, when \[1.5\text{ }A\] of current flows in a copper wire of cross section \[5\text{ }m{{m}^{2}}\], is v. If electron density in copper is \[9\times {{10}^{28}}/{{m}^{3}}\] the value of v in mm/s is close to (Take charge of electron to be \[=\text{ }1.6\times {{10}^{-19}}C)\]

    A) 0.02

    B) 0.2

    C) 3

    D) 2

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  • question_answer8) A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, \[\overrightarrow{E}=6.3\text{ }\overrightarrow{j}\text{ }V/m\]. The corresponding magnetic field B, at that point will be

    A) \[18.9\times {{10}^{-8}}\text{ }\widehat{k}T\]

    B) \[2.1\times {{10}^{-8}}\text{ }\widehat{k}T\]

    C) \[18.9\times {{10}^{8}}\text{ }\widehat{k}T\]

    D) \[6.3\times {{10}^{-8}}\text{ }\widehat{k}T\]

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  • question_answer9) A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow into the system in path ADB is:

    A) 40 J

    B) 20 J

    C) 100 J

    D) 80 J

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  • question_answer10) A parallel plate capacitor is made of two square plates of side ?a?, separated by a distance\[d\left( d<<a \right)\]. The lower triangular; portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is:

    A) \[\frac{K{{\in }_{0}}{{a}^{2}}}{2d\,(K+1)}\]

    B) \[\frac{K{{\in }_{0}}{{a}^{2}}}{d\,(K-1)}\,\,In\,\,K\]

    C) \[\frac{K{{\in }_{0}}{{a}^{2}}}{d}\,\,In\,\,K\]

    D) \[\frac{1}{2}\,\,\,\frac{K{{\in }_{0}}{{a}^{2}}}{d}\]

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  • question_answer11) Surface of certain metal is first illuminated with light of wavelength \[{{\lambda }_{1}}=350\,nm\] nm and then, by light of wavelength \[{{\lambda }_{2}}=540nm\]. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to : (Energy of photon \[=\frac{1240}{\lambda \,(in\,\,nm)}\,e\,V)\]

    A) 5.6

    B) 2.5

    C) 1.8

    D) 1.4

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  • question_answer12) An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is \[d\left( d>>a \right)\]. If the loop applies a force F on the wire then:

    A) \[F\propto \left( \frac{{{a}^{2}}}{{{d}^{3}}} \right)\]

    B) \[F\propto \left( \frac{a}{d} \right)\]

    C) \[F\,\,=\,\,0\]

    D) \[F\propto {{\left( \frac{a}{d} \right)}^{2}}\]

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  • question_answer13) A heavy ball the mass M is suspended from the ceiling of a car by a right string of mass m \[\left( m<<M \right)\]. When the car is at rest, the speed of transverse waves in the string is\[60\text{ }m{{s}^{-1}}\]. When the car has acceleration a, the wave-speed increases to\[60.5\text{ }m{{s}^{-1}}\]. The value of a, in terms of gravitational acceleration g, is closest to:

    A) \[\frac{g}{20}\]

    B) \[\frac{g}{5}\]

    C) \[\frac{g}{10}\]

    D) \[\frac{g}{30}\]

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  • question_answer14) When the switch S, in circuit shown, is closed, then the value of current i will be:

    A) 4 A

    B) 5 A

    C) 3 A

    D) 2 A

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  • question_answer15) A current loop, having two circular arcs joined by two radial lines y shown in the figure. It carries a current of 10 A. The magnetic field at point 0 will be close to:

    A) \[~1.5\,\,\times \,\,\text{1}{{0}^{-5}}\,T\]

    B) \[1.0\times {{10}^{-\,5}}\,T\]

    C) \[1.5\,\,\times \,\,{{10}^{-7}}\,T~\]

    D) \[1.0\times \text{1}{{0}^{-7}}\,T\]

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  • question_answer16) Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is \[{{10}^{19}}{{m}^{-3}}\] and their mobility is \[1.6\text{ }{{m}^{2}}/\left( V.s \right)\] then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close to:

    A) \[0.4\text{ }\Omega \,m\]

    B) \[2\text{ }\Omega \,m\]

    C) \[4\,\,\Omega \,m\]

    D) \[0.2\,\,\Omega \,m\]

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  • question_answer17) Consider a tank made of glass (refractive index 1.5) with s. thick bottom. It is filled with a liquid of refractive index \[\mu \]. A student finds that, irrespective of what the incident angle I (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of \[\mu \] is:

    A) \[\sqrt{\frac{5}{3}}\]

    B) \[\frac{4}{3}\]

    C) \[\frac{5}{\sqrt{3}}\]

    D) \[\frac{3}{\sqrt{5}}\]

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  • question_answer18) If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is:

    A) \[\frac{L}{m}\]

    B) \[\frac{L}{2m}\]

    C) \[\frac{4L}{m}\]

    D) \[\frac{2L}{m}\]

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  • question_answer19) A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward?

    A) 32 N

    B) 25 N

    C) 23 N

    D) 18 N

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  • question_answer20) A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion \[a/{}^\circ C\]. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by \[\Delta \] TK. Young?s modulus, Y, for this metal is:

    A) \[\frac{F}{A\alpha \Delta T}\]

    B) \[\frac{F}{2A\alpha \Delta T}\]

    C) \[\frac{2\,F}{A\alpha \Delta T}\]

    D) \[\frac{\,F}{A\alpha (\Delta T-273)}\]

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  • question_answer21) A particle is moving with a velocity \[\overrightarrow{v}=K\left( y\,\,\overrightarrow{i}+x\,\,\overrightarrow{j} \right)\], where K is a constant. The general equation for its path is:

    A) \[y={{x}^{2}}+constant\]

    B) \[{{y}^{2}}=\text{ }{{x}^{2}}+constant\]

    C) \[{{y}^{2}}=\,\,x+constant\]

    D) \[xy\text{ }=\text{ }constant\]

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  • question_answer22) A conducting circular loop made of a thin wire, has area \[3.5\,\,\times \,\,{{10}^{-3}}\,{{m}^{2}}\] and resistance 100. It is placed perpendicular to a time dependent magnetic field\[B\left( t \right)=\left( 0.4T \right)sin\left( 50\pi t \right)\]. The field is uniform in space. Then the net charge flowing through the loop during \[t\,\,=\,\,0\] s and \[t\,\,=\,\,0\] ms is close to:

    A) 6 mC

    B) 14 mC

    C) 7 mC

    D) 21 mC

    E) None of These

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  • question_answer23) An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If \[\,AB=BC\], and the angle made by AB with downward vertical is \[\theta \], then:

    A) \[\tan \,\theta \,\,=\,\,\frac{1}{3}\]

    B) \[\tan \,\theta \,\,=\,\,\frac{1}{2}\]

    C) \[\tan \,\theta \,\,=\,\,\frac{2}{\sqrt{3}}\]

    D) \[\tan \,\theta \,\,=\,\,\frac{1}{2\sqrt{3}}\]

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  • question_answer24) A copper wire is stretcher! to make it \[0.5\,%\] longer. The percentage change m in its electrical resistance if its volume remain unchanged is:

    A) \[0.5\text{ }%\]

    B) \[2.5\text{ }%\]

    C) \[2.0\text{ }%\]

    D) \[1.0\text{ }%\]

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  • question_answer25) Three charges +Q, q, +Q are placed respectively, at distance, 0, \[d/2\] and d from the origin, on the x-axis. If the net force experienced \[by+Q\], placed at \[x=0\], is zero then value of q is:

    A) +Q/2

    B) -Q/4

    C) +Q/4

    D) -Q/2

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  • question_answer26) A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is:

    A) 2600 A/m

    B) 1200 A/m

    C) 520 A/m

    D) 285 A/m

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  • question_answer27) A resistance is shown in the figure. Its value and tolerance are given respectively by:

    A) \[270\text{ }\Omega ,\text{ }10\text{ }%\]

    B) \[270\text{ }\Omega ,\text{ }5\text{ }%\]

    C) \[27\text{ }k\Omega ,\text{ }10\,%\]

    D) \[27\text{ }k\Omega ,\text{ }20\,%\]

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  • question_answer28) A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initally at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is

    A) \[\frac{2F}{\sqrt{mk}}\]

    B) \[\frac{\pi \,F}{\sqrt{mk}}\]

    C) \[\frac{F}{\pi \,\sqrt{mk}}\]

    D) \[\frac{F}{\sqrt{mk}}\]

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  • question_answer29) Two masses m and \[\frac{m}{2}\] are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system (see figure). Because of torsional constant k, the restoring torque is \[\tau \,\,=\,\,k\theta \] for angular displacement \[\theta \]. If the rod is rotated by \[{{\theta }_{0}}\] and released, the tension in it when it passes through its mean position will be:

    A) \[\frac{2\,k\,{{\theta }_{0}}^{2}}{l}\]

    B) \[\frac{k\,{{\theta }_{0}}^{2}}{l}\]

    C) \[\frac{3k\,{{\theta }_{0}}^{2}}{l}\]

    D) \[\frac{k\,{{\theta }_{0}}^{2}}{2\,l}\]

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  • question_answer30) Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an initial speed v towards B due to which it collides with B perfectly inelastically \[\frac{5}{6}th\] of the initial kinetic energy is lost in whole process. What is value of M/m?

    A) 2

    B) 3

    C) 5

    D) 4

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  • question_answer31) In general the properties that decrease and increase down a group in the periodic table, respectively, are-

    A) electronegativity, and atomic radius.

    B) electronegativity and electron gain enthalpy.

    C) atomic radius and electronegativity.

    D) electron gain enthalpy and electronegativity.

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  • question_answer32) The major product of following reaction is: \[R-C\equiv N\,\,\xrightarrow[(2)\,\,{{H}_{2}}O]{(1)\,\,AlH\,{{(i-Bu)}_{2}}}\,\,?\]

    A) RCHO

    B) RCOOH

    C) \[RCON{{H}_{2}}\]

    D) \[RC{{H}_{2}}N{{H}_{2}}\]

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  • question_answer33) Which amongst the following is the strongest acid?

    A) \[CHB{{r}_{3}}~\]

    B) \[CHC{{l}_{3}}\]

    C) \[CH{{\left( CN \right)}_{3}}\]

    D) \[CH{{I}_{3}}\]

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  • question_answer34) Arrange the following amines in the decreasing order of basicity:

    A) \[I>III>II\]

    B) \[III>I>II\]

    C) \[I>II>III\]

    D) \[III>II>I\]

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  • question_answer35) The ore that contains both iron and copper is -

    A) dolomite

    B) malachite

    C) copper pyrites

    D) azurite

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  • question_answer36) The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of \[PbS{{O}_{4}}\] electrolyzed in g during the process is: (Molar mass of \[PbS{{O}_{4}}-=303\text{ }g\text{ }mo{{l}^{-1}}\])

    A) 15.2

    B) 7.6

    C) 11.4

    D) 22.8

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  • question_answer37) Correct statements among a to d regarding silicones are - (a) They are polymers with hydrophobic character. (b) They are biocompatible. (c) In general, they have high thermal stability and low dielectric strength. (d) Usually, they are resistant to oxidation and used as greases.

    A) (a), (b) and (d) only

    B) (a), (b) and (c) only

    C) (a), (b), (c) and (d)

    D) (a) and (b) only

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  • question_answer38) The following results were obtained during kinetic studies of the reaction: \[2A\,\,+\,\,B\,\,\to \] Products

    Experi-ment in \[\mathbf{mol}\text{ }{{\mathbf{L}}^{-\mathbf{1}}}\] (in \[\mathbf{mol}\text{ }{{\mathbf{L}}^{-\mathbf{1}}}\] Initial Rate of reaction (in \[\mathbf{mol}\text{ }{{\mathbf{L}}^{-\mathbf{1}}}\] \[\mathbf{mi}{{\mathbf{n}}^{\mathbf{-1}}}\])
    I 0.10 0.20 \[6.93\,\,\times \,\,{{10}^{-3}}\]
    II 0.10 0.25 \[6.93\,\,\times \,\,{{10}^{-3}}\]
    III 0.20 0.30 \[1.386\,\,\times \,\,{{10}^{-2}}\]
    The time (in minutes) required to consume half of A is -

    A) 5

    B) 1

    C) 100

    D) 10

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  • question_answer39) The major product of the following reaction is:

    A)

    B)

    C)

    D)

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  • question_answer40) The one that is extensively used as a piezoelectric material is -

    A) mica

    B) quartz

    C) amorphous silica

    D) tridymite

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  • question_answer41) 0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume \[10\text{ }{{m}^{3}}\] at 1000 K. Given R is the gas constant in \[J{{K}^{-1}}\,\,mo{{l}^{-1}}\], x is -

    A) \[\frac{2R}{4-R}\]

    B) \[\frac{4+R}{2R}\]

    C) \[\frac{4-R}{2R}\]

    D) \[\frac{2R}{4+R}\]

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  • question_answer42) For emission line of atomic hydrogen from \[{{n}_{1}}=8\] to \[{{n}_{f}}=n\], the plot of wave number \[\left( \overline{v} \right)\] against \[\left( \frac{1}{{{n}^{2}}} \right)\] will be (The Rydberg constant, \[{{R}_{H}}\] is wave number unit)

    A) Linear with slope - \[{{R}_{H}}\]

    B) Linear with slope -\[{{R}_{H}}\]

    C) Non linear

    D) Linear with intercept - \[{{R}_{H}}\]

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  • question_answer43) Major product of the following reaction is:

    A)

    B)

    C)

    D)

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  • question_answer44) The correct decreasing order for acid strength is:

    A) \[N{{O}_{2}}C{{H}_{2}}COOH\text{ }>\text{ }FC{{H}_{2}}COOH\text{ }>CNC{{H}_{2}}COOH\text{ }>\text{ }ClC{{H}_{2}}COOH\]

    B) \[CNC{{H}_{2}}COOH>{{O}_{2}}NC{{H}_{2}}COOH\text{ }>FC{{H}_{2}}COOH\text{ }>\text{ }ClC{{H}_{2}}COOH\]

    C) \[FC{{H}_{2}}COOH>ClC{{H}_{2}}COOH>N{{O}_{2}}C{{H}_{2}}COOH\text{ }>\text{ }ClC{{H}_{2}}COOH\]

    D) \[N{{O}_{2}}C{{H}_{2}}COOH>NCC{{H}_{2}}COOH>FC{{H}_{2}}COOH>ClC{{H}_{2}}COOH\]

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  • question_answer45) 20 mL of 0.1 M \[{{H}_{2}}S{{O}_{4}}\] solution is added to 30 mL of 0.2 M \[N{{H}_{4}}OH\] solution. The pH of the resultant mixture is: \[[p{{K}_{b}}\text{ }of\text{ }N{{H}_{4}}OH\,\,=\,\,4.7]\].

    A) 5.2

    B) 9.4

    C) 9.0

    D) 5.0

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  • question_answer46) The alkaline earth metal nitrate that does not crystallize with water molecules, is -

    A) \[Ba{{\left( N{{O}_{3}} \right)}_{2}}\]

    B) \[Mg{{\left( N{{O}_{3}} \right)}_{2}}\]

    C) \[Ca{{\left( N{{O}_{3}} \right)}_{2}}\]

    D) \[Sr{{\left( N{{O}_{3}} \right)}_{2}}\]

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  • question_answer47) Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures T1 and \[{{T}_{2}}\left( {{T}_{1}}<\text{ }{{T}_{2}} \right)\]. The correct graphical depiction of the dependence of work done (W) on the final volume (V) is -

    A)

    B)

    C)

    D)

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  • question_answer48) Adsorption of a gas follows Freundlich adsorption isotherm. IN the given plot, x is the mass of the gas adsorbed on mass m of the adsorbent at pressure P. \[\frac{x}{m}\] is proportional to:

    A) P

    B) \[{{P}^{1/2}}\]

    C) \[{{P}^{2}}\]

    D) \[{{P}^{1/4}}\]

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  • question_answer49) The increasing order of pKa of the following ammo acids in aqueous solution is: Gly Asp Lys Arg

    A) \[Asp<Gly<Lys<Arg\]

    B) \[Arg<Lys<Gly<Asp\]

    C) \[Gly<Asp<Arg<Lys\]

    D) \[Asp<Gly<Arg<Lys\]

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  • question_answer50) According to molecular orbital theory, which of the following is true with respect to\[{{L}_{i2}}+and\text{ }{{L}_{i2}}-\]?

    A) Both are unstable

    B) Both are stable

    C) \[{{L}_{i2}}+\] is stable and \[{{L}_{i2}}-\] is unstable

    D) \[{{L}_{i{{2}^{+}}}}\]is unstable and \[{{L}_{i2}}-\] is stable

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  • question_answer51) A water sample has ppm level \[Fe=0.2\]; \[Mn=5.0\] ; \[Cu=3.0\] ; \[Zn=5.0\] The metal that makes the water sample unsuitable for drinking is:

    A) Zn

    B) Fe

    C) Cu

    D) Mn

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  • question_answer52) Two complexes \[\left[ Cr{{\left( {{H}_{2}}0 \right)}_{6}} \right]C{{l}_{3}}\] and \[\left[ Cr{{\left( N{{H}_{3}} \right)}_{6}} \right]C{{l}_{3}}\] are violet and yellow coloured, respectively. The incorrect statement regarding, them is-

    A) \[{{\Delta }_{0}}\] value for is less than that of (B).

    B) both absorb energies corresponding to their complementary colors.

    C) \[{{\Delta }_{0}}\] values of and are calculated. From the energies of violet and yellow light, respectively.

    D) both are paramagnetic with three unpaired electrons.

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  • question_answer53) The major product of the following reaction is:

    A)

    B)

    C)

    D)

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  • question_answer54) Which one of the following statements regarding Henery's law is not correct?

    A) Different gases have different \[{{K}_{H}}\] (Henry's law constant) values at the same temperature.

    B) The partial pressure of the gas in vapour phase is proportional to the mole fraction of the gas in the solution.

    C) The value of \[{{K}_{H}}\] increases with increase of temperature and \[{{K}_{H}}\] is function of the nature of the gas.

    D) Higher the value of \[{{K}_{H}}\] at a given pressure, higher is the solubility of the gas in the liquids.

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  • question_answer55) The compound A and B in the following reaction are respectively:

    A) A = Benzyl alcohol, B = Benzyl cyanide

    B) A = Benzyl chloride, B = Benzyl cyanide

    C) A = Benzyl alcohol, B = Benzyl isocyanide

    D) A = Benzyl chloride, B = Benzyl isocyanide

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  • question_answer56) The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is-

    A) 6.93

    B) 5.92

    C) 4.90

    D) 3.87

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  • question_answer57) A solution of sodium sulfate contains \[92\text{ }g\text{ }of\text{ }N{{a}^{+}}\] ions per kilogram of water. The molality of \[N{{a}^{+}}\] ions in that solution in \[mol\text{ }k{{g}^{-1}}\] is:

    A) 8

    B) 4

    C) 12

    D) 16

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  • question_answer58) The correct match between Item-I am Item-II is:

    Item-I (drug) Item-II (test)
    (A) Chlorozylenol (P) Carbolamine test
    (B) Norethindrone (Q) Sodium hydrogen carbonate test
    (C) Sulphapyridine (R) Ferric chlorine test
    (D) Penicillin (S) Bayer's test
     

    A) \[A\to R;\,\,\,B\to S;\,\,\,C\to P;\,\,\,D\to Q\]

    B) \[A\to Q;\,\,\,B\to P;\,\,\,C\to S;\,\,\,D\to R\]

    C) \[A\to Q;\,\,\,B\to S;\,\,\,C\to P;\,\,\,D\to R\]

    D) \[A\to R;\,\,\,B\to P;\,\,\,C\to S;\,\,\,D\to Q\]

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  • question_answer59) The isotopes of hydrogen are:

    A) Protium and deuterium only

    B) Protium, deuterium and tritium

    C) Deuterium and tritium only

    D) Tritium and protium only

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  • question_answer60) Aluminium is usually found in +3 oxidation state. In contrast, thallium exists in +1 and + 3 oxidation states. This is due to -

    A) diagonal relationship

    B) lanthanoid contraction

    C) inert pair effect

    D) lattice effect

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  • question_answer61) \[\underset{y\to 0}{\mathop{\lim }}\,\frac{\sqrt{1+\sqrt{1+{{y}^{4}}}}-\sqrt{2}}{{{y}^{4}}}\]

    A) exists and equals \[\frac{1}{2\sqrt{2}}\]

    B) exists and equals \[\frac{1}{4\sqrt{2}}\]

    C) exists and equals \[\frac{1}{2\sqrt{2}(\sqrt{2}+1)}\]

    D) does not exist

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  • question_answer62) If a, b and c be three distinct real numbers in G.P. and \[a+b+c=xb\], then x cannot be:

    A) -2

    B) 2

    C) -3

    D) 4

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  • question_answer63) The maximum volume (in cu. m) of the right circular cone having slant height 3 m is:

    A) \[6\pi \]

    B) \[\frac{4}{3}\pi \]

    C) \[2\sqrt{3}\,\pi \]

    D) \[3\sqrt{3}\,\pi \]

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  • question_answer64)

    The system of linear equations
    \[x+y+z=2\]
    \[2x+3y+2z=\text{ }5\]
    \[2x+3y+\left( {{a}^{2}}-1 \right)z\text{ }=\text{ }a+1\]

    A) has infinitely many solutions for \[a=4\]

    B) has a unique solution for I a I \[=\,\,\sqrt{3}\]

    C) is inconsistent when I a I = \[=\,\,\sqrt{3}\]

    D) is inconsistent when \[a=4\]

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  • question_answer65) Let \[f:\,\,R\to R\] be a function defined as Then, f is

    A) continuous if \[a=0\] and \[b=5\]

    B) continuous if \[a=-5\] and \[b=10\]

    C) continuous if \[a=5\] and \[b=5\]

    D) not continuous for any values of a and b

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  • question_answer66) Axis of a parabola lies along x-axis. If its vertex and focus are at distance 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

    A) \[\left( 8,\text{ }6 \right)\]

    B) \[\left( 4,\,-4 \right)\]

    C) \[(6,\,\,4\sqrt{2})\]

    D) \[(5,\,\,2\sqrt{6})\]

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  • question_answer67) Let \[\alpha \text{ }and\text{ }\beta \] be two roots of the equation \[{{x}^{2}}+2x+2=0\], then \[{{\alpha }^{15}}+{{\beta }^{15}}\] is equal to:

    A) -256

    B) 512

    C) -512

    D) 256

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  • question_answer68) If the Boolean express. \[(p\oplus q)\,\,\wedge (\sim p\,\odot q)\] is equivalent to \[p\wedge q\], where \[\oplus ,\,\,\odot \,\,\in \{\wedge ,\,\,\vee \},\]then the ordered pair \[(\oplus ,\,\,\odot )\] is

    A) \[(\vee ,\,\,\,\vee )\]

    B) \[(\wedge ,\,\,\,\wedge )\]

    C) \[(\wedge ,\,\,\,\vee )\]

    D) \[(\vee ,\,\,\,\wedge )\]

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  • question_answer69) Let \[\overrightarrow{a}=\widehat{i}-\widehat{\text{j}}\,,\,\,\,\overrightarrow{b}=\widehat{i}+\widehat{j}+\widehat{k}\,\,\,and\,\,\overrightarrow{c}\,\] and be a vector such that \[\overrightarrow{a}\,\,\times \,\,\overrightarrow{c}\,\,+\,\,\overrightarrow{b}\,\,=\,\,\overrightarrow{0}\] and \[\overrightarrow{a}\text{ }.\text{ }\overrightarrow{c}\text{ }=4\], then \[{{\overrightarrow{\left| \,c\, \right|}}^{2}}\] is equal to:

    A) \[\frac{19}{2}\]

    B) 8

    C) \[\frac{17}{2}\]

    D) 9

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  • question_answer70) 5 students of a class have an average height 150 cm and variance \[18\text{ }c{{m}^{2}}\]. A new student, whose height is 156 cm, joined them. The variance (in \[c{{m}^{2}}\]) of the height of these six students is:

    A) 20

    B) 18

    C) 16

    D) 22

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  • question_answer71) For \[x\in R\text{ }-\left\{ 0,\text{ }1 \right\},\text{ }let\text{ }{{f}_{1}}\left( x \right)\,\,=\,\,\frac{1}{x}\,\,,\text{ }{{f}_{2}}\left( x \right)=1-x\] and \[{{f}_{3}}\left( x \right)=\frac{1}{1-x}\] be three given functions. If a function, J(x) satisfies \[\left( fz\circ \text{ }J\circ \,\,{{f}_{1}} \right)\left( x \right)=\text{ }{{f}_{3}}\text{ }\left( x \right)\] then J(x) is equal to:

    A) \[\frac{1}{x}{{f}_{3}}\,(x)\]

    B) \[{{f}_{2}}\,(x)\]

    C) \[{{f}_{3}}\,(x)\]

    D) \[{{f}_{1}}\,(x)\]

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  • question_answer72) Let A= \[\left\{ \theta \in \left( -\frac{\pi }{2},\,\pi \right):\,\frac{3+2i\,\,\sin \theta }{1-2i\,\,\sin \,\theta }\,is\,\,purely\,\,imaginary \right\}.\] Then the sum of the elements in A is:

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

    B) \[\frac{3\pi }{4}\]

    C) \[\frac{2\pi }{3}\]

    D) \[\pi \]

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  • question_answer73) Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:

    A) 300

    B) 500

    C) 200

    D) 350

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  • question_answer74) For any \[\theta \,\,\,\,\in \,\,\,\,\left( \frac{\pi }{4},\,\,\frac{\pi }{2} \right)\], the expression \[3{{\left( sin\,\theta -cos\,\theta \right)}^{4}}+6{{\left( sin\,\theta +cos\,\theta \right)}^{2}}+4\,si{{n}^{6}}\theta \]equals:

    A) \[13-4\,co{{s}^{4}}\theta +2\,si{{n}^{2}}\theta \,co{{s}^{2}}\theta \]

    B) \[13-4\,co{{s}^{2}}\theta +6\,si{{n}^{2}}\theta \,co{{s}^{2}}\theta \]

    C) \[13-4\text{ }cos{{\,}^{2}}\,\theta +6\,\,co{{s}^{4}}\,\theta \]

    D) \[13-4\text{ }cos{{\,}^{6}}\,\theta \]

    View Answer play_arrow
  • question_answer75) Equation of a common tangent to the circle \[{{x}^{2}}+{{y}^{2}}-6x=0\] and the parabola, \[{{y}^{2}}=4x\], is:

    A) \[\sqrt{3}y=x+3\]

    B) \[\sqrt{3}y=3x+3\]

    C) \[2\sqrt{3}y=\,\,-x-12\]

    D) \[2\sqrt{3}\,y=12x+1\]

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  • question_answer76) Let \[{{a}_{1}},\text{ }{{a}_{2}},\text{ }.......,\text{ }{{a}_{30}}\] be an A.P., \[S=\sum\limits_{i\,=\,1}^{30}{{{a}_{i}}}\,\,and\,\,T\,\,=\,\,\sum\limits_{i\,=\,1}^{15}{{{a}_{(2i-1)}}}\]If \[{{a}_{5}}=27\] and \[S-2T=75\], then \[{{a}_{10}}\] is equal to:

    A) 47

    B) 42

    C) 52

    D) 57

    View Answer play_arrow
  • question_answer77) For \[{{x}^{2}}\ne n\pi \,+\,1,\,\,n\in N\] (the set of natural numbers), the integral \[\int{x\,\,\frac{2\,\sin \,({{x}^{2}}-1)\,\,-\,\sin 2\,({{x}^{2}}-1)}{2\,\sin \,({{x}^{2}}-1)+sin\,2({{x}^{2}}-1)}}\,dx\] is equal to: (where c is a constant of integration)

    A) \[{{\log }_{e}}\,\left| \sec \,\left( \frac{{{x}^{2}}-1}{2} \right) \right|\,\,+c\]

    B) \[{{\log }_{e}}\,\left| \frac{1}{2}{{\sec }^{2}}\,({{x}^{2}}-1) \right|\,\,+c\]

    C) \[\frac{1}{2}\,{{\log }_{e}}\,\left| {{\sec }^{2}}\,\left( \frac{{{x}^{2}}-1}{2} \right) \right|\,\,+c\]

    D) \[\frac{1}{2}\,{{\log }_{e}}\,\left| \sec ({{x}^{2}}-1) \right|\,\,+\,\,c\]

    View Answer play_arrow
  • question_answer78) Three circles of radii a, b, c (a < b < c) touch each other externally. If they have x-axis as a common tangent, then:

    A) \[\frac{1}{\sqrt{b}}\,\,=\,\,\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{c}}\,\]

    B) a, b, c are in A. P.

    C) \[\sqrt{a},\,\,\sqrt{b},\,\,\sqrt{c}\,\,are\,\,in\,\,A.P.\]

    D) \[\frac{1}{\sqrt{a}}=\frac{1}{\sqrt{b}}+\frac{1}{\sqrt{c}}\]

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  • question_answer79) If \[A\,\,=\,\,\left[ \begin{align} & \cos \,\theta \,\,\,\,\,\,-\sin \theta \\ & \sin \,\theta \,\,\,\,\,\,\,\,\,\,\,\cos \,\theta \\ \end{align} \right]\] then matrix \[{{A}^{-50}}\] when \[\theta =\frac{\pi }{12}\], is equal to:

    A) \[\left| \begin{align} & \frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{\sqrt{3}}{2} \\ & -\frac{\sqrt{3}}{2}\,\,\,\,\,\,\,\,\frac{1}{2} \\ \end{align} \right|\]

    B) \[\left| \begin{align} & \frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,-\,\frac{\sqrt{3}}{2} \\ & \frac{\sqrt{3}}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{2} \\ \end{align} \right|\]

    C) \[\left| \begin{align} & \frac{\sqrt{3}}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{2}\,\,\, \\ & -\frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{\sqrt{3}}{2} \\ \end{align} \right|\]

    D) \[\left| \begin{align} & \frac{\sqrt{3}}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\frac{1}{2}\,\,\, \\ & \frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{\sqrt{3}}{2} \\ \end{align} \right|\]

    View Answer play_arrow
  • question_answer80) If \[\cos {{\,}^{-1}}\,\left( \frac{2}{3x} \right)\,\,+\,\,\cos {{\,}^{-1}}\,\left( \frac{3}{4x} \right)\,=\,\frac{\pi }{2}\,\,\left( x>\frac{3}{4} \right)\,\] then x is equal to

    A) \[\frac{\sqrt{145}}{10}\]

    B) \[\frac{\sqrt{145}}{11}\]

    C) \[\frac{\sqrt{145}}{12}\]

    D) \[\frac{\sqrt{146}}{12}\]

    View Answer play_arrow
  • question_answer81) If the fractional part of the number \[\frac{{{2}^{\,403}}}{15}\] is \[\frac{k}{15}\], then k is equal to:

    A) 8

    B) 14

    C) 6

    D) 4

    View Answer play_arrow
  • question_answer82) Consider the set of all lines \[px+qy+r=0\] such that \[3p+2q+4r=0\]. Which one of the following statements is true?

    A) The lines are not concurrent

    B) The lines are concurrent at the point\[\left( \frac{3}{4},\,\,\frac{1}{2} \right)\]

    C) The lines are all parallel

    D) Each line passes through the origin

    View Answer play_arrow
  • question_answer83) Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then \[P\left( X=1 \right)+P\left( X=2 \right)\] equals:

    A) 25/169

    B) 24/169

    C) 49/169

    D) 52/169

    View Answer play_arrow
  • question_answer84) The equation of the line passing through \[\left( -4,\text{ }3,\text{ }1 \right)\], parallel to the plane \[x+2y-z-5=0\] and intersecting the line\[\frac{x+1}{-3}\,\,\,=\,\,\,\frac{y-3}{2}\,\,=\,\,\frac{z-2}{-1}\]

    A) \[\frac{x+4}{3}\,\,\,=\,\,\,\frac{y-3}{-1}\,\,=\,\,\frac{z-1}{1}\]

    B) \[\frac{x+4}{1}\,\,\,=\,\,\,\frac{y-3}{1}\,\,=\,\,\frac{z-1}{3}\]

    C) \[\frac{x+4}{-1}\,\,\,=\,\,\,\frac{y-3}{1}\,\,=\,\,\frac{z-1}{1}\]

    D) \[\frac{x-4}{2}\,\,\,=\,\,\,\frac{y-3}{1}\,\,=\,\,\frac{z+1}{4}\]

    View Answer play_arrow
  • question_answer85) The plane through the intersection of the planes \[x+y+z=1\text{ }and\text{ }2x+3y-z+4=0\] and parallel to y-axis also passes through the point:

    A) (- 3, 1, 1)

    B) (-3, 0, -1)

    C) (3, 3, -1)

    D) (3, 2, 1)

    View Answer play_arrow
  • question_answer86) If \[\theta \] denotes the acute angle between the curves, \[y=10-{{x}^{2}}\] and \[y=2+{{x}^{2}}\] at a point of their intersection, then \[\left| \tan \,\,\theta \right|\] is equal to:

    A) \[\frac{4}{9}\]

    B) \[\frac{7}{17}\]

    C) \[\frac{8}{17}\]

    D) \[\frac{8}{15}\]

    View Answer play_arrow
  • question_answer87) The value of \[\int\limits_{0}^{\pi }{{{\left| \cos \,\,x \right|}^{3}}\,\,dx}\] is:

    A) \[-\frac{4}{3}\]

    B) 0

    C) \[\frac{4}{3}\]

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

    View Answer play_arrow
  • question_answer88) The area (in sq. units) bounded by the parabola \[y={{x}^{2}}-1\], the tangent at the point (2, 3) to it and the y-axis is:

    A) \[\frac{56}{3}\]

    B) \[\frac{32}{3}\]

    C) \[\frac{8}{3}\]

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

    View Answer play_arrow
  • question_answer89) If \[y=y\left( x \right)\] is the solution of the differential equation, \[x\frac{dy}{dx}\,\,+\,\,2y\,\,=\,\,{{x}^{2}}\] satisfying \[y\left( 1 \right)=1\], then \[y\left( \frac{1}{2} \right)\] is equal to:

    A) \[\frac{7}{64}\]

    B) \[\frac{49}{16}\]

    C) \[\frac{1}{4}\]

    D) \[\frac{13}{16}\]

    View Answer play_arrow
  • question_answer90) Let \[0<\theta <\frac{\pi }{2}\]. If the eccentricity of the hyperbola \[\frac{{{x}^{2}}}{{{\cos }^{2}}\theta }-\frac{{{y}^{2}}}{{{\sin }^{2}}\,\theta }\,\,=\,\,1\] is greater than 2, then the length of its latus rectum lies in the interval:

    A) \[\left( 3,\text{ }\infty \right)\]

    B) (1, 3/2]

    C) (3/2, 2]

    D) (2, 3]

    View Answer play_arrow

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JEE Main Online Paper (Held On 09-Jan-2019 Morning)
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