Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 12-Jan-2019 Morning)

done JEE Main Online Paper (Held On 12-Jan-2019 Morning)

  • question_answer1) What is the position and nature of image formed by lens combination shown in figure? (\[{{f}_{1}},{{f}_{2}}\]are focal lengths)

    A) 70 cm from point B at right; real

    B) \[\frac{20}{3}cm\]from point B at right, real

    C) 40 cm from point B at right, real

    D) 70 cm from point B at left, virtual

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  • question_answer2) A particle of mass m moves in a circular orbit in a central potential field \[U(r)=\frac{1}{2}k{{r}^{2}}.\]If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as

    A) \[{{r}_{n}}\propto {{n}^{2}},{{E}_{n}}\propto \frac{1}{{{n}^{2}}}\]            

    B) \[{{r}_{n}}\propto \sqrt{n},{{E}_{n}}\propto n\]

    C) \[{{r}_{n}}\propto \sqrt{n},{{E}_{n}}\propto \frac{1}{n}\]         

    D)   \[{{r}_{n}}\propto n,{{E}_{n}}\propto n\]

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  • question_answer3) The galvanometer deflection, when key \[{{K}_{1}}\]is closed but \[{{K}_{2}}\] is open, equals \[{{\theta }_{0}},\] (see figure). On closing \[{{K}_{2}}\]also and adjusting \[{{R}_{2}}\] to \[5\Omega ,\]the deflection in galvanometer becomes\[\frac{{{\theta }_{0}}}{5}.\] The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]

    A) \[25\Omega \]

    B) \[22\Omega \]

    C) \[5\Omega \]

    D) \[12\Omega \]

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  • question_answer4) In the figure shown, after the switch S is turned from position A to position B the energy dissipated in the circuit in terms of capacitance C and total charge Q is

    A) \[\frac{5}{8}\frac{{{Q}^{2}}}{C}\]

    B) \[\frac{1}{8}\frac{{{Q}^{2}}}{C}\]

    C) \[\frac{3}{8}\frac{{{Q}^{2}}}{C}\]

    D) \[\frac{3}{4}\frac{{{Q}^{2}}}{C}\]

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  • question_answer5) There is a uniform spherically symmetric surface charge density at a distance \[{{R}_{0}}\] from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is





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  • question_answer6) A point source of light, S is placed at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below The distance over which the man can see the image of the light source in the mirror is

    A) 3d

    B) 2d

    C) d

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

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  • question_answer7) Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre O and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is

    A) \[\frac{1}{2\pi }\sqrt{\frac{k}{m}}\]

    B) \[\frac{1}{2\pi }\sqrt{\frac{6k}{m}}\]

    C) \[\frac{1}{2\pi }\sqrt{\frac{3k}{m}}\]

    D) \[\frac{1}{2\pi }\sqrt{\frac{2k}{m}}\]

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  • question_answer8) As shown in, the figure, two infinitely long, identical wires are bent by \[90{}^\circ \] and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP=OQ=4cm, and the magnitude of the magnetic field at C) is\[{{10}^{-4}}T,\] and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}N{{A}^{-2}})\]

    A) 20 A, perpendicular into the page

    B) 40 A, perpendicular into the page

    C) 20 A, perpendicular out of the page

    D) 40 A, perpendicular out of the page.

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  • question_answer9) A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr, The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite direction is

    A) \[\frac{25}{11}\]

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

    C) \[\frac{5}{2}\]

    D) \[\frac{11}{5}\]

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  • question_answer10) The position vector of the centre of mass \[\vec{r}cm\]of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

    A) \[\vec{r}\,cm=\frac{11}{8}L\hat{x}+\frac{3}{8}L\,\hat{y}\]

    B) \[\vec{r}\,cm=\frac{13}{8}L\hat{x}+\frac{5}{8}L\,\hat{y}\]

    C) \[\vec{r}\,cm=\frac{3}{8}L\hat{x}+\frac{11}{8}L\,\hat{y}\]

    D) \[\vec{r}\,cm=\frac{5}{8}L\hat{x}+\frac{13}{8}L\,\hat{y}\]

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  • question_answer11) An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance \[5\Omega .\] The value of R, to give a potential difference of mV across 10 cm of potentiometer wire is

    A) \[490\,\Omega \]

    B) \[495\,\Omega \]

    C) \[395\,\Omega \]

    D) \[480\,\Omega \]

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  • question_answer12) Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure.

    A) \[2ql\,\hat{j}\]

    B) \[(ql)\,\frac{\hat{i}+\,\hat{j}}{\sqrt{2}}\]

    C) \[\sqrt{3}ql\,\frac{\,\hat{j}-\hat{i}}{\sqrt{2}}\]

    D) \[-\sqrt{3}ql\,\hat{j}\]

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  • question_answer13) A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely in elastically. The speeds of the satellite and meteorite are the same, just before the collision. The subsequent motion of the combined body will be

    A) in an elliptical orbit

    B) in the same circular orbit of radius R

    C) in a circular orbit of a different radius

    D) such that it escapes to infinity.

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  • question_answer14) A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is \[{{K}_{1}}\]and that of the outer cylinder is\[{{K}_{2}}\]. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is

    A) \[\frac{2{{K}_{1}}+3{{K}_{2}}}{5}\]

    B) \[\frac{{{K}_{1}}+{{K}_{2}}}{2}\]

    C) \[{{K}_{1}}+{{K}_{2}}\]

    D) \[\frac{{{K}_{1}}+3{{K}_{2}}}{4}\]

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  • question_answer15) A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is \[30V\,{{m}^{-1}},\]then the amplitude of the electric field for the wave propagating in the glass medium will be

    A) \[24V\,{{m}^{-1}}\]

    B) \[10V\,{{m}^{-1}}\]

    C) \[30V\,{{m}^{-1}}\]

    D) \[6V\,{{m}^{-1}}\]

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  • question_answer16) A travelling harmonic wave is represented by the equation \[y(x,t)={{10}^{-3}}\sin (50t+2x),\]where x and t are in meter and t is in seconds. Which of the following is a correct statement about the wave?

    A) The wave is propagating along the positive x-axis with speed \[25\,m\,{{s}^{-1}}\].

    B) The wave is propagating along the positive x-axis with speed \[100\,m\,{{s}^{-1}}\].

    C) The wave is propagating along the negative x-axis with speed \[25\,m\,{{s}^{-1}}\].

    D) The wave is propagating along the negative x-axis with speed \[100\,m\,{{s}^{-1}}\].

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  • question_answer17) A simple pendulum, made of a string of length I and a bob of mass m, is released from a small angle \[{{\theta }_{0}}.\]It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle \[{{\theta }_{1}}.\]Then M is given by

    A) \[\frac{m}{2}\left( \frac{{{\theta }_{0}}-{{\theta }_{1}}}{{{\theta }_{0}}+{{\theta }_{1}}} \right)\]

    B) \[m\left( \frac{{{\theta }_{0}}+{{\theta }_{1}}}{{{\theta }_{0}}-{{\theta }_{1}}} \right)\]

    C) \[\frac{m}{2}\left( \frac{{{\theta }_{0}}+{{\theta }_{1}}}{{{\theta }_{0}}-{{\theta }_{1}}} \right)\]

    D) \[m\left( \frac{{{\theta }_{0}}-{{\theta }_{1}}}{{{\theta }_{0}}+{{\theta }_{1}}} \right)\]

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  • question_answer18) For the given cyclic process CAB as shown for a gas, the work done is

    A) 10 J

    B) 1 J

    C) 5 J

    D) 30 J

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  • question_answer19) In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that the variation \[\frac{dR}{dl}\]of its resistance R with length l is \[\frac{dR}{dl}\propto \frac{1}{\sqrt{l}}.\] Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP?

    A) 0.35 m

    B) 0.2 m

    C) 0.25 m

    D) 0.3 m

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  • question_answer20) The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure \[5\mu m\]diameter of a wire is

    A) 50

    B) 100

    C) 200

    D) 500

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  • question_answer21) A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle \[60{}^\circ \] with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is

    A) v

    B) \[\frac{\sqrt{3}}{2}v\]

    C) \[\frac{2v}{\sqrt{3}}\]

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

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  • question_answer22) Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers \[{{P}_{1}}\]and \[{{P}_{2}}\]respectively, then

    A) \[{{P}_{1}}=9W,{{P}_{2}}=16W\]

    B) \[{{P}_{1}}=16\,W,{{P}_{2}}=4W\]

    C) \[{{P}_{1}}=4\,W,{{P}_{2}}=16W\]

    D) \[{{P}_{1}}=16\,W,{{P}_{2}}=9W\]

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  • question_answer23) The output of the given logic circuit is

    A) \[\bar{A}B\]

    B) \[A\bar{B}\]

    C) \[AB+\overline{AB}\]

    D) \[A\overline{B}+\overline{A}B\]

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  • question_answer24) A proton and an \[\alpha -\]particle (with their masses in the ratio 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform, magnetic field is set up perpendicular to their' velocities, the ratio of the radii \[{{r}_{p}}:{{r}_{\alpha }}\]of the circular paths described by them will be

    A) \[1:3\]

    B) \[1:\sqrt{2}\]

    C) \[1:2\]

    D) \[1:\sqrt{3}\]

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  • question_answer25) An ideal gas occupies a volume of \[2{{m}^{3}}\] at a pressure of\[3\times {{10}^{6}}Pa\]. The energy of the gas is

    A) \[9\times {{10}^{6}}J\]

    B) \[3\times {{10}^{2}}J\]

    C) \[6\times {{10}^{4}}J\]

    D) \[{{10}^{8}}J\]

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  • question_answer26) A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?

    A) 0.4

    B) 0.5

    C) 0.6

    D) 0.3

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  • question_answer27) A straight rod of length L extends from x=a to \[x=L+a.\] The gravitational force it exerts on a point mass m at x=0, if the mass per unit length of the rod is \[A+B{{x}^{2}},\], is given by

    A) \[Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)-BL \right]\]

    B) \[Gm\left[ A\left( \frac{1}{a+L}-\frac{1}{a} \right)-BL \right]\]

    C) \[Gm\left[ A\left( \frac{1}{a+L}-\frac{1}{a} \right)+BL \right]\]

    D) \[Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)+BL \right]\]

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  • question_answer28) In the figure shown, a circuit contains two identical resistors with resistance \[R=5\Omega \] and an inductance with L=2mH. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is closed?

    A) 3 A

    B) 5.5 A

    C) 7.5 A

    D) 6 A

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  • question_answer29) Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also J, is

    A) 14 cm

    B) 16 cm

    C) 12 cm

    D) 18 cm

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  • question_answer30) A particle A of mass m and charge q is accelerated by a potential difference of 50 V. Another particle B of mass 4 m and charge q is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths\[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}\] is close to

    A) 14.14

    B) 0.07

    C) 4.47

    D) 10.00

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  • question_answer31) In the Hall-Heroult process, aluminium is formed at the cathode. The cathode is made out of

    A) platinum

    B) pure aluminium

    C) copper

    D) carbon.

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  • question_answer32) What is the work function of the metal if the light of wavelength \[4000\text{ }\overset{o}{\mathop{\text{A}}}\,\] generates photoelectrons of velocity \[6\times {{10}^{5}}m\,{{s}^{-1}}\]from it?

    (Mass of electron \[=9\times {{10}^{-31}}kg,\]
    Velocity of light\[=3\times {{10}^{8}}m\,{{s}^{-1}},\]
    Planck?s constant \[=6.626\times {{10}^{-34}}Js,\]
    Charge of electron\[=1.6\times {{10}^{-19}}Je{{V}^{-1}}\])

    A) 4.0 eV

    B) 2.1 Ev

    C) 0.9 eV

    D) 3.1 eV

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  • question_answer33) A metal on combustion in excess air forms X. X upon hydrolysis with water yields \[{{H}_{2}}{{O}_{2}}\]and \[{{O}_{2}}\] along with another product. The metal is

    A) Li

    B) Rb

    C) Mg

    D) Na

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  • question_answer34) Two solids dissociate as follows

    The total pressure when both the solids dissociate simultaneously is

    A) \[\sqrt{x+y}atm\]

    B) \[{{x}^{2}}+{{y}^{2}}atm\]

    C) \[2\left( \sqrt{x+y} \right)atm\]

    D) \[(x+y)atm\]

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  • question_answer35) \[C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ Ph \end{smallmatrix}}{\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\] cannot be prepared by

    A) \[PhCOC{{H}_{3}}+C{{H}_{3}}C{{H}_{2}}MgX\]

    B) \[HCHO+PhCH(C{{H}_{3}})C{{H}_{2}}MgX\]

    C) \[PhCOC{{H}_{2}}C{{H}_{3}}+C{{H}_{3}}MgX\]

    D) \[C{{H}_{3}}C{{H}_{2}}COC{{H}_{3}}+PhMgX\]

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  • question_answer36) Water samples with BOD values of 4 ppm and 18 ppm, respectively, are

    A) clean and highly polluted

    B) highly polluted and highly polluted

    C) highly polluted and clean

    D) clean and clean.

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  • question_answer37) The element with Z = 120 (not yet discovered) will be an/a

    A) inner-transition metal

    B) alkaline earth metal

    C) alkali metal

    D) transition metal.

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  • question_answer38) Given

    Gas \[{{H}_{2}}\] \[C{{H}_{4}}\] \[C{{O}_{2}}\] \[S{{O}_{2}}\]
    Critical 33 190 304 630
    On the basis of data given above, predict which of the following gases shows least adsorption on a definite amount of charcoal?

    A) \[{{H}_{2}}\]                                       

    B) \[C{{H}_{4}}\]

    C) \[C{{O}_{2}}\]                        

    D)   \[S{{O}_{2}}\]

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  • question_answer39) The main product of the following reaction is





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  • question_answer40) In a chemical reaction, \[A+2B2C+D,\]the initial concentration of B was 1.5 times of the concentration of A, but the equilibrium concentrations of A and B were found to be equal. The equilibrium constant (K) for the aforesaid chemical reaction is

    A) 1

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

    C) 4

    D) 16

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  • question_answer41) Among the following four aromatic compounds, which one will have the lowest melting point?





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  • question_answer42) The standard electrode potential \[E{}^\circ \]and its temperature coefficient \[\left( \frac{d{{E}^{o}}}{dT} \right)\]for a cell are 2 V and \[-5\times {{10}^{-4}}V\,{{K}^{-1}}\]at 300 K respectively.

    The cell reaction is
    The standard reaction enthalpy \[({{\Delta }_{r}}{{H}^{o}})\]at 300 K in \[kJ\,mo{{l}^{-1}}\]is, [Use \[R=8\,J\,{{K}^{-1}}mo{{l}^{-1}}\]and \[F=96,000\,C\,mo{{l}^{-1}}\]]

    A) \[-412.8\]

    B) 192.0

    C) \[-384.0\]

    D) 206.4

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  • question_answer43) The hardness of a water sample (in terms of equivalents of \[CaC{{O}_{3}}\]) containing \[{{10}^{-3}}M\,CaS{{O}_{4}}\]is (molar mass of \[\,CaS{{O}_{4}}=136g\,mo{{l}^{-1}}\])

    A) 10 ppm

    B) 100 ppm

    C) 50 ppm

    D) 90 ppm

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  • question_answer44) Decomposition of X exhibits a rate constant of\[0.05\,\,\mu g/year\]. How many years are required for the decomposition of \[5\mu g\]of X into\[2.5\mu g\]?

    A) 25

    B) 50

    C) 20

    D) 40

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  • question_answer45) The increasing order of reactivity of the following compounds towards reaction with alkyl halides directly is


    A) \[(B)<(A)<(D)<(C)\]

    B) \[(A)<(C)<(D)<(B)\]

    C) \[(B)<(A)<(C)<(D)\]

    D) \[(A)<(B)<(C)<(D)\]

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  • question_answer46) Iodine reacts with concentrated \[HN{{O}_{3}}\]to yield Y along with other products. The oxidation state of iodine in Y, is

    A) 5

    B) 1

    C) 7

    D) 3

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  • question_answer47) For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?





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  • question_answer48) \[M{{n}_{2}}{{(CO)}_{10}}\]is an organometallic compound due to the presence of

    A) \[C-O\text{ }bond\]

    B) \[Mn-O\text{ }bond\]

    C) \[Mn-C\text{ }bond\]

    D) \[Mn-Mn\text{ }bond\]

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  • question_answer49) The main product of the following reaction is





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  • question_answer50) The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressures of the gases for equal number of moles are

    A) \[2{{P}_{A}}=3{{P}_{B}}\]

    B) \[3{{P}_{A}}=2{{P}_{B}}\]

    C) \[{{P}_{A}}=2{{P}_{B}}\]

    D) \[{{P}_{A}}=3{{P}_{B}}\]

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  • question_answer51) Among the following compounds most basic amino acid is

    A) histidine

    B) serine

    C) asparagine

    D) lysine.

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  • question_answer52) The correct order for acid strength of compounds \[CH\equiv CH,C{{H}_{3}}-C\equiv CH\] and \[C{{H}_{2}}=C{{H}_{2}}\]is as follows

    A) \[C{{H}_{3}}-C\equiv CH>CH\equiv CH>C{{H}_{2}}=C{{H}_{2}}\]

    B) \[C{{H}_{3}}-C\equiv CH>C{{H}_{2}}=C{{H}_{2}}>HC\equiv CH\]

    C) \[HC\equiv CH>C{{H}_{3}}-C\equiv CH>C{{H}_{2}}=C{{H}_{2}}\]

    D) \[CH\equiv CH>C{{H}_{2}}=C{{H}_{2}}>C{{H}_{3}}-C\equiv CH\]

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  • question_answer53) Poly-\[\beta \]-hydroxybutyrate- co-\[\beta \]-hydroxyvalerate (PHBV) is a copolymer of

    A) 2-hydroxybutanoic acid and 3-hydroxypentanoic acid

    B) 3-hydroxybutanoic acid and 3-hydroxypentanoic acid

    C) 3-hydroxybutanoic acid and 2-hydroxypentanoic acid

    D) 3-hydroxybutanoic acid and 4-hydroxypentanoic acid.

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  • question_answer54) A and B in the following reactions is





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  • question_answer55) The metal d- orbital that are directly facing the ligands in \[{{K}_{3}}[Co{{(CN)}_{6}}]\]are

    A) \[{{d}_{xy}}and\,{{d}_{{{x}^{2}}-{{y}^{2}}}}\]

    B) \[{{d}_{xy'}}{{d}_{xz}}\,and\,{{d}_{yz}}\]

    C) \[{{d}_{{{x}^{2}}-{{y}^{2}}}}\,and\,{{d}_{{{z}^{2}}}}\]

    D) \[{{d}_{xy'}}{{d}_{yz}}\,and\,{{d}_{{{z}^{2.}}}}\]

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  • question_answer56) The pair of metal ions that can give a spin- only magnetic moment of 3.9 B.M. for the complex \[[M{{({{H}_{2}}O)}_{6}}]C{{l}_{2}}\] is

    A) \[C{{r}^{2+}}and\,M{{n}^{2+}}\]

    B) \[{{V}^{2+}}and\,C{{o}^{2+}}\]

    C) \[{{V}^{2+}}and\,F{{e}^{2+}}\]

    D) \[C{{o}^{2+}}and\,F{{e}^{2+}}\]

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  • question_answer57) 50 mL of 0.5 M oxalic acid is needed to neutralise 25 mL of sodium hydroxide solution. The amount of NaOH in 50 mL of the given sodium hydroxide solution is

    A) 10 g

    B) 80 g

    C) 40 g

    D) 20 g

    E) None of these

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  • question_answer58) The molecule that has minimum/no role in the formation of photochemical smog, is

    A) \[C{{H}_{2}}=O\]

    B) \[{{N}_{2}}\]

    C) \[{{O}_{3}}\]

    D) NO

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  • question_answer59) In the following reaction

    Aldehyde + Alcohol \[\xrightarrow[{}]{HCl}\]Acetal
    Aldehyde Alcohol
    \[HClO\] \[t-BuOH\]
    \[C{{H}_{3}}CHO\] \[MeOH\]
    The best combination is

    A) \[HCHO\,and\,t-BuOH\]

    B) \[C{{H}_{3}}CHO\,\,and\,\,t-BuOH\]

    C) \[C{{H}_{3}}CHO\,and\,MeOH\]

    D) \[HCHO\,\,and\,\,MeOH\]

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  • question_answer60) Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A, then molecular weight of Y is

    A) 2A

    B) 3A

    C) A

    D) 4A

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  • question_answer61) The sum of the distinct real values of \[\mu \], for which the vectors, \[\mu \hat{i}+\hat{j}+\hat{k},\hat{i}+\mu \hat{j}+\hat{k},\hat{i}+\hat{j}+\mu \,\hat{k}\]are co-planar, is

    A) 2

    B) 0

    C) -1

    D) 1

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  • question_answer62) The area (in sq. units) of the region bounded by the parabola, \[y={{x}^{2}}+2\] and the lines, \[y=x+1,x=0\]and \[x=3,\] is

    A) 15/2

    B) 17/4

    C) 21/2

    D) 15/4

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  • question_answer63) Let \[{{C}_{1}}\]and \[{{C}_{2}}\]be the centres of the circles \[{{x}^{2}}+{{y}^{2}}-2x-2y-2=0\]and \[{{x}^{2}}+{{y}^{2}}-6x-6y+14=0\]respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the Quadrilateral \[P{{C}_{1}}Q{{C}_{2}}\] is

    A) 8

    B) 4

    C) 6

    D) 9

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  • question_answer64) Consider three boxes, each containing 10 balls labelled 1, 2, ..... 10. Suppose one ball is randomly drawn from each of the boxes. Denote by \[{{n}_{i}},\]the label of the ball drawn from the \[{{i}^{th}}\] box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that \[{{n}_{1}}<{{n}_{2}}<{{n}_{3}}\] is

    A) 120

    B) 164

    C) 240

    D) 82

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  • question_answer65) Considering only the principal values of inverse functions, the set

    \[A=\left\{ x\ge 0:{{\tan }^{-1}}(2x)+ta{{n}^{-1}}(3x)=\frac{\pi }{4} \right\}\]

    A) contains two elements

    B) contains more than two elements

    C) is an empty set

    D) is a singleton

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  • question_answer66) The perpendicular distance from the origin to the plane containing the two lines,\[\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}\]and\[\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7},\]is

    A) 11

    B) \[6\sqrt{11}\]

    C) \[\frac{11}{\sqrt{6}}\]

    D) \[11\sqrt{6}\]

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  • question_answer67) If \[\frac{z-\alpha }{z+\alpha }(\alpha \in R)\]is a purely imaginary number and \[|z|=2,\] then a value of \[\alpha \] is

    A) 1

    B) \[\sqrt{2}\]

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

    D) 2

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  • question_answer68) If the straight line, \[2x-3y+17=0\] is perpendicular to the line passing through the points (7, 17) and \[(15,\beta ),\] then \[\beta \]equals

    A) 5

    B) \[\frac{35}{3}\]

    C) \[-\frac{35}{3}\]

    D) \[-5\]

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  • question_answer69) The Boolean expression \[((p\wedge q)\vee (p\vee \tilde{\ }q))\]\[\wedge (\tilde{\ }p\wedge \tilde{\ }q)\]is equivalent to

    A) \[(\tilde{\ }p)\wedge (\tilde{\ }q)\]

    B) \[p\wedge (\tilde{\ }q)\]

    C) \[p\wedge q\]

    D) \[p\vee (\tilde{\ }q)\]

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  • question_answer70) Let\[{{S}_{k}}=\frac{1+2+3+...+k}{k}.\]If \[S_{1}^{2}+S_{2}^{2}+...+S_{10}^{2}\]\[=\frac{5}{12}A,\] then A is equal to

    A) 303

    B) 283

    C) 301

    D) 156

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  • question_answer71) An ordered pair \[(\alpha ,\beta )\]for which the system of linear equations \[(1+\alpha )x+\beta y+z=2,\]\[\alpha x+(1+\beta )y+z=3,\]\[\alpha x+\beta y+2z=2\] has a unique solution, is

    A) \[(-3,\text{ }1)\]

    B) \[(2,\text{ 4})\]

    C) \[(1,\text{ }-3)\]

    D) \[(-4,\text{ 2})\]

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  • question_answer72) The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, \[y=12-{{x}^{2}}\]such that the rectangle lies inside the parabola, is

    A) 36

    B) \[18\sqrt{3}\]

    C) \[20\sqrt{2}\]

    D) 32

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  • question_answer73) Let S = {1, 2, 3, ..., 100}. The number of non- empty subsets A of S such that the product of elements in A is even is

    A) \[{{2}^{50}}({{2}^{50}}-1)\]

    B) \[{{2}^{50}}-1\]

    C) \[{{2}^{50}}+1\]

    D) \[{{2}^{100}}-1\]

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  • question_answer74) Let f and g be continuous functions on [0, a] such that \[f(x)=f(a-x)\]and \[g(x)=g(a-x)=4,\]then \[\int\limits_{0}^{a}{f(x)g(x)dx}\]is equal to

    A) \[2\int\limits_{0}^{a}{f(x)dx}\]

    B) \[4\int\limits_{0}^{a}{f(x)dx}\]

    C) \[-3\int\limits_{0}^{a}{f(x)dx}\]

    D) \[\int\limits_{0}^{a}{f(x)dx}\]

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  • question_answer75) If\[x>1\]for\[{{(2x)}^{2y}}=4{{e}^{2x-2y}},\]then\[{{(1+lo{{g}_{e}}2x)}^{2}}\frac{dy}{dx}\]equals

    A) \[\frac{x\,{{\log }_{e}}2x-{{\log }_{e}}2}{x}\]

    B) \[{{\log }_{e}}2x\]

    C) \[\frac{x\,{{\log }_{e}}2x+{{\log }_{e}}2}{x}\]

    D) \[x\,{{\log }_{e}}2x\]

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  • question_answer76) If a variable line, \[3x+4y-\lambda =0\]is such that the two circles \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\]and\[{{x}^{2}}+{{y}^{2}}-18x\]\[-2y+78=0\]are on its opposite sides, then the set of all values of \[\lambda \] is the interval

    A) (23, 31)

    B) (2, 17)

    C) [13, 23]

    D) [12, 21]

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  • question_answer77) If X be the ratio of the roots of the quadratic equation in \[x,3{{m}^{2}}{{x}^{2}}+m(m-4)x+2=0,\]then the least value of m for which \[\lambda +\frac{1}{\lambda }=1,\]is

    A) \[-2+\sqrt{2}\]

    B) \[4-3\sqrt{2}\]

    C) \[4-2\sqrt{3}\]

    D) \[2-\sqrt{3}\]

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  • question_answer78) In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

    A) \[\frac{150}{{{6}^{5}}}\]

    B) \[\frac{225}{{{6}^{5}}}\]

    C) \[\frac{175}{{{6}^{5}}}\]

    D) \[\frac{200}{{{6}^{5}}}\]

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  • question_answer79) The maximum value of the expression \[3\cos \theta +5\sin \left( \theta -\frac{\pi }{6} \right)\]for any real value of \[\theta \]is

    A) \[\frac{\sqrt{79}}{2}\]

    B) \[\sqrt{31}\]

    C) \[\sqrt{34}\]

    D) \[\sqrt{19}\]

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  • question_answer80) If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is

    A) 30

    B) 51

    C) 31

    D) 50

    View Answer play_arrow
  • question_answer81) Let \[y=y(x)\]be the solution of the differential equation, \[x\frac{dy}{dx}+y=x{{\log }_{e}}x,\]\[(x>1)\]. If \[2y(2)=lo{{g}_{e}}4-1,\]then\[y(e)\]is equal to

    A) \[\frac{{{e}^{2}}}{4}\]

    B) \[-\frac{{{e}^{2}}}{2}\]

    C) \[-\frac{e}{2}\]

    D) \[\frac{e}{4}\]

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  • question_answer82) If the vertices of a hyperbola be at \[(-2,\text{ }0)\,\,\,and\,\,\,(2,\text{ }0)\]and one of its foci be at\[(-3,\text{ }0)\], then which one of the following points does not lie on this hyperbola?

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

    B) \[(-6,2\sqrt{10})\]

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

    D) \[(4,\sqrt{15})\]

    View Answer play_arrow
  • question_answer83) Let \[P=\left[ \begin{matrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \\ \end{matrix} \right]\]and \[Q=[{{q}_{ij}}]\]be two \[3\times 3\]matrices such that \[Q-{{P}^{5}}={{I}_{3}}.\]Then \[\frac{{{q}_{21}}+{{q}_{31}}}{{{q}_{32}}}\]is equal to

    A) 10

    B) 135

    C) 9

    D) 15

    View Answer play_arrow
  • question_answer84) Integral \[\int_{{}}^{{}}{\cos (lo{{g}_{e}}x)}dx\]equals (where C is the constant of integration)

    A) \[\frac{x}{2}[sin(lo{{g}_{e}}x)-cos(lo{{g}_{e}}x)]+C\]

    B) \[x[cos(lo{{g}_{e}}x)-\sin (lo{{g}_{e}}x)]+C\]

    C) \[\frac{x}{2}[cos(lo{{g}_{e}}x)+\sin (lo{{g}_{e}}x)]+C\]

    D) \[x[cos(lo{{g}_{e}}x)+\sin (lo{{g}_{e}}x)]+C\]

    View Answer play_arrow
  • question_answer85) Let \[P(4,-4)\]and \[Q(9,6)\]be two points on the parabola, \[{{y}^{2}}=4x\] and let X be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of APXQ is maximum. Then this maximum area (in sq. units) is

    A) \[\frac{125}{2}\]

    B) \[\frac{125}{4}\]

    C) \[\frac{625}{4}\]

    D) \[\frac{75}{2}\]

    View Answer play_arrow
  • question_answer86) The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is

    A) 36

    B) 24

    C) 28

    D) 32

    View Answer play_arrow
  • question_answer87) \[\underset{x\to \pi /4}{\mathop{\lim }}\,\frac{{{\cot }^{3}}x-\tan x}{\cos \left( x+\frac{\pi }{4} \right)}\] is

    A) \[4\sqrt{2}\]

    B) \[8\sqrt{2}\]

    C) 4

    D) 8

    View Answer play_arrow
  • question_answer88) A ratio of the \[{{5}^{th}}\] term from the beginning to the \[{{5}^{th}}\] term from the end in the binomial is expansion of \[{{\left( {{2}^{1/3}}+\frac{1}{2{{(3)}^{1/3}}} \right)}^{10}}\] is

    A) \[4{{(36)}^{1/3}}:1\]

    B) \[1:2{{(6)}^{1/3}}\]

    C) \[2{{(36)}^{1/3}}:1\]

    D) \[1:4{{(16)}^{1/3}}\]

    View Answer play_arrow
  • question_answer89) Let 5 be the set of all points in \[(-\pi ,\pi )\]at which the function, \[f(x)=\min \{\sin x,\cos x\}\]is not differentiable. Then S is a subset of which of the following?

    A) \[\left\{ -\frac{\pi }{4},0,\frac{\pi }{4} \right\}\]

    B) \[\left\{ -\frac{3\pi }{4},-\frac{\pi }{4},\frac{3\pi }{4},\frac{\pi }{4} \right\}\]

    C) \[\left\{ -\frac{3\pi }{4},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{4} \right\}\]

    D) \[\left\{ -\frac{\pi }{2},-\frac{\pi }{4},\frac{\pi }{4},\frac{\pi }{2} \right\}\]

    View Answer play_arrow
  • question_answer90) A tetrahedron has vertices \[P(1,2,1),Q(2,1,3),\]\[R(-1,1,2)\]and \[O(0,0,0).\]The angle between the faces OPQ and PQR is

    A) \[{{\cos }^{-1}}\left( \frac{7}{31} \right)\]

    B) \[{{\cos }^{-1}}\left( \frac{17}{31} \right)\]

    C) \[{{\cos }^{-1}}\left( \frac{19}{35} \right)\]

    D) \[{{\cos }^{-1}}\left( \frac{9}{35} \right)\]

    View Answer play_arrow

Study Package

JEE Main Online Paper (Held On 12-Jan-2019 Morning)
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