Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 15 April 2018) Slot-II

done JEE Main Online Paper (Held On 15 April 2018) Slot-II

• question_answer1) A body of mass $2kg$ slides down with an acceleration of $3m/{{s}^{2}}$ on a rough inclined plane having a slope of $30{}^\circ$. The external force required to take the same body up the plane with the same acceleration will be:$(g=10m/{{s}^{2}})$ [JEE Online 15-04-2018 (II)]

A) $4N$

B) $14N$

C) $6N$

D) $20N$

• question_answer2) A plane polarized monochromatic EM wave is travelling a vacuum along z direction such that at $t={{t}_{1}}$ it is found that the electric field is zero at a spatial point ${{z}_{1}}$. The next zero that occurs in its neighbourhood is at ${{z}_{2}}$. The frequency of the electromagnetic wave is: [JEE Online 15-04-2018 (II)]

A) $\frac{3\times {{10}^{8}}}{|{{z}_{2}}-{{z}_{1}}|}$

B) $\frac{6\times {{10}^{8}}}{|{{z}_{2}}-{{z}_{1}}|}$

C) $\frac{1.5\times {{10}^{8}}}{|{{z}_{2}}-{{z}_{1}}|}$

D) $\frac{1}{{{t}_{1}}+\frac{|{{z}_{2}}-{{z}_{1}}|}{3\times {{10}^{8}}}}$

• question_answer3) A current of $1A$ is flowing on the sides of an equilateral triangle of side$4.5\times {{10}^{-2}}m$. The magnetic field at the centre of the triangle will be: [JEE Online 15-04-2018 (II)]

A) $4\times {{10}^{-5}}Wb/{{m}^{2}}$

B) Zero

C) $2\times {{10}^{-5}}Wb/{{m}^{2}}$

D) $8\times {{10}^{-5}}Wb/{{m}^{2}}$

• question_answer4) Truth table for the given circuit will be [JEE Online 15-04-2018 (II)] A)

 X Y Z 0 0 1 0 1 1 1 0 1 1 1 0

B)

 X Y Z 0 0 0 0 1 0 1 0 0 1 1 1

C)

 X Y Z 0 0 1 0 1 1 1 0 1 1 1 1

D)

 X Y Z 0 0 0 0 1 1 1 0 1 1 1 1

• question_answer5) A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be: [JEE Online 15-04-2018 (II)]

A) Increased 8 times

B) Doubled

C) Halved

D) Unchanged

• question_answer6) The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants $G,h$ and$c$. Which of the following correctly gives the Planck length? [JEE Online 15-04-2018 (II)]

A) ${{G}^{2}}hc$

B) ${{\left( \frac{Gh}{{{c}^{3}}} \right)}^{\frac{1}{2}}}$

C) ${{G}^{\frac{1}{2}}}{{h}^{2}}c$

D) $G{{h}^{2}}{{c}^{3}}$

• question_answer7) As shown in the figure, forces of ${{10}^{5}}N$ each are applied in opposite directions, on the upper and lower faces of a cube of side$10cm$, shifting the upper face parallel to itself by$0.5cm$. If the side of another cube of the same material is $20cm$, then under similar conditions as above, the displacement will be: [JEE Online 15-04-2018 (II)] A) $1.00\,\,cm$

B) $0.25\,\,cm$

C) $0.37\,\,cm$

D) $0.75\,\,cm$

• question_answer8) The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance $49\mu H$ and a capacitance of$2.5nF$. It is modulated by an audio signal of$12kHz$. The frequency range occupied by the side bands is: [JEE Online 15-04-2018 (II)]

A) $18kHz-30kHz$

B) $63kHz-75kHz$

C) $442kHz-466kHz$

D) $13482kHz-13494kHz$

• question_answer9) A copper rod of mass $m$ slides under gravity on two smooth parallel rails, with separation 1 and set at an angle of $\theta$ with the horizontal. At the bottom, rails are joined by a resistance$R$. .There is a uniform magnetic field $B$ normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is: [JEE Online 15-04-2018 (II)] A) $\frac{mgR\cos \theta }{{{B}^{2}}{{l}^{2}}}$

B) $\frac{mgR\sin \theta }{{{B}^{2}}{{l}^{2}}}$

C) $\frac{mgR\tan \theta }{{{B}^{2}}{{l}^{2}}}$

D) $\frac{mgR\cot \theta }{{{B}^{2}}{{l}^{2}}}$

• question_answer10) A think rod$MN$, free to rotate in the vertical plane about the fixed end$N$, is held horizontal. When the end $M$ is released the speed of this end, when the rod makes an angle $\alpha$ with the horizontal, will be proportional to: (see figure) [JEE Online 15-04-2018 (II)] A) $\sqrt{\cos \alpha }$

B) $\cos \alpha$

C) $\sin \alpha$

D) $\sqrt{\sin \alpha }$

• question_answer11) A parallel plate capacitor with area $200c{{m}^{2}}$ and separation between the plates$1.5cm$, is connected across a battery of emf V. If the force of attraction between the plates is $25\times {{10}^{-6}}N$, the value of $V$ is approximately: [JEE Online 15-04-2018 (II)] $\left( {{\in }_{0}}=8.85\times {{10}^{-12}}\frac{{{C}^{2}}}{N.{{m}^{2}}} \right)$

A) $150V$

B) $100V$

C) $250V$

D) $300V$

• question_answer12) A solid ball of radius R has a charge density $\rho$ given by $\rho ={{\rho }_{o}}\left( 1-\frac{r}{R} \right)$ for $0\le r\le R$. The electric field outside the ball is: [JEE Online 15-04-2018 (II)]

A) $\frac{{{\rho }_{0}}{{R}^{3}}}{{{\in }_{0}}{{r}^{2}}}$

B) $\frac{4{{\rho }_{0}}{{R}^{3}}}{3{{\in }_{0}}{{r}^{2}}}$

C) $\frac{3{{\rho }_{0}}{{R}^{3}}}{4{{\in }_{0}}{{r}^{2}}}$

D) $\frac{{{\rho }_{0}}{{R}^{3}}}{12{{\in }_{0}}{{r}^{2}}}$

• question_answer13) A proton of mass $m$ collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of $90{}^\circ$ with respect to each other. The mass of unknown particle is: [JEE Online 15-04-2018 (II)]

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

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

C) $2m$

D) $m$

• question_answer14) A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of 1.25cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is$(g=10m/{{s}^{2}})$ [JEE Online 15-04-2018 (II)]

A) 0.5

B) 0.7

C) 0.3

D) 0.6

• question_answer15) At the centre of a fixed large circular coil of radius $R$, a much smaller circular coil of radius $r$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current $I$. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time $t$ of its start of rotation. [JEE Online 15-04-2018 (II)]

A) $\frac{{{\mu }_{0}}I}{2R}\omega {{r}^{2}}\sin \omega t$

B) $\frac{{{\mu }_{0}}I}{4R}\omega \pi {{r}^{2}}\sin \omega t$

C) $\frac{{{\mu }_{0}}I}{2R}\omega \pi {{r}^{2}}\sin \omega t$

D) $\frac{{{\mu }_{0}}I}{4R}\omega {{r}^{2}}\sin \omega t$

• question_answer16) A capacitor ${{C}_{1}}=10\mu F$ is charged up to a voltage $V=60V$ by connecting it to battery $B$ through switch (1), Now ${{C}_{1}}$ is disconnected from battery and connected to a circuit consisting of two uncharged capacitors ${{C}_{2}}=3.0\mu F$ and $P{{C}_{3}}=6.0\mu F$ through a switch (2) as shown in the figure. The sum of final charges on ${{C}_{2}}$and ${{C}_{3}}$is: [JEE Online 15-04-2018 (II)] A) $36\mu C$

B) $20\mu C$

C) $54\mu C$

D) $40\mu C$

• question_answer17) 5 beats/ second are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either $0.95m$ or $1m$. The frequency of the fork will be: [JEE Online 15-04-2018 (II)]

A) $195Hz$

B) $251Hz$

C) $150Hz$

D) $300Hz$

• question_answer18) Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures. $x(t)=A\sin (at+\delta )$ $y(t)=B\sin (bt)$ Identify the correct match below [JEE Online 15-04-2018 (II)]

A) $\text{Parameters: A=B, a=2b;}\delta \text{=}\frac{\pi }{2};Curve:Circle$

B) $\text{Parameters: A=B, a=b;}\delta \text{=}\frac{\pi }{2};Curve:line$

C) $\text{Parameters: A}\ne \text{B, a=b; }\delta \text{=}\frac{\pi }{2};Curve:\text{Ellipse}$

D) $\text{Parameters:}A\ne B,a=b;\delta =0;\text{Curve : Parabola}$

• question_answer19) A man in a car at location $Q$ on a straight highway is moving with speed$v$. He decides to reach a point $P$ in a field at a distance $d$ from highway (point$M$) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance$RM$, so that the time taken to reach $P$ is minimum? [JEE Online 15-04-2018 (II)] A) $\frac{d}{\sqrt{3}}$

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

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

D) $d$

• question_answer20) A copper rod of cross-sectional area $A$ carries a uniform current $I$ through if. At temperature $T$, if the volume charge density of the rod is $\rho$, how long will the charges take to travel a distance $d$? [JEE Online 15-04-2018 (II)]

A) $\frac{2\rho dA}{IT}$

B) $\frac{2\rho dA}{I}$

C) $\frac{\rho dA}{I}$

D) $\frac{\rho dA}{IT}$

• question_answer21) Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at $600K$ and rejects heat to a reservoir heat to reservoir at temperature$T$. Engine$B$ receives heat rejected by engine $A$ and in turn rejects it to a reservoir at$100K$. If the efficiencies of the two engines A and B are represented by ${{\eta }_{A}}$ and ${{\eta }_{B}}$ respectively, then what is the value of $\frac{{{\eta }_{A}}}{{{\eta }_{B}}}$ [JEE Online 15-04-2018 (II)]

A) $\frac{12}{7}$

B) $\frac{12}{5}$

C) $\frac{5}{12}$

D) $\frac{7}{12}$

• question_answer22) A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of$10cm$. The separation between the two lenses is$2cm$. The focal lengths of the component lenses [JEE Online 15-04-2018 (II)]

A) $18cm,20cm$

B) $10cm,12cm$

C) $12cm,14cm$

D) $16cm,18cm$

• question_answer23) A plane polarized light is incident on a polariser with its pass axis making angle $\theta$ with x-axis, as shown in the figure. At four different values of $\theta ,\theta =8{}^\circ ,38{}^\circ ,188{}^\circ$and $218{}^\circ$, the observed intensities are same. What is the angle between the direction of polarization and x-axis [JEE Online 15-04-2018 (II)] A) $203{}^\circ$

B) $45{}^\circ$

C) $98{}^\circ$

D) $128{}^\circ$

• question_answer24) An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of$8:27$. The ratio of the radii of the nuclei (assumed to be spherical ) is: [JEE Online 15-04-2018 (II)]

A) $8:27$

B) $2:3$

C) $3:2$

D) $4:9$

• question_answer25) A body takes 10 minutes to cool from $60{}^\circ C$ to$50{}^\circ C$. The temperature of surroundings is constant at$25{}^\circ C$. Then, the temperature of the body after next 10 minutes will be approximately [JEE Online 15-04-2018 (II)]

A) $43{}^\circ C$

B) $47{}^\circ C$

C) $41{}^\circ C$

D) $45{}^\circ C$

• question_answer26) A thin uniform bar of length $L$ and mass $8m$lies on a smooth horizontal table. Two point masses $m$ and $2m$ moving in the same horizontal plane from opposite sides of the bar with speeds $2v$ and $v$ respectively. The masses stick to the bar after collision at a distance $\frac{L}{3}$ and $\frac{L}{6}$ respectively from the centre of the bar. If the bar starts rotating about its centre of mass as a result of collision, the angular speed of the bar will be: [JEE Online 15-04-2018 (II)] A) $\frac{v}{6L}$

B) $\frac{6v}{5L}$

C) $\frac{3v}{5L}$

D) $\frac{v}{5L}$

• question_answer27) If the de Broglie wavelengths associated with a proton and an $\alpha -particle$are equal, then the ratio of velocities of the proton and the $\alpha -particle$ will be: [JEE Online 15-04-2018 (II)]

A) $1:4$

B) $1:2$

C) $4:1$

D) $2:1$

• question_answer28) When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes$\frac{5r}{4}$. Taking the atmospheric pressure to be equal to $10m$ height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature): [JEE Online 15-04-2018 (II)]

A) $10.5m$

B) $8.7m$

C) $11.2m$

D) $9.5m$

• question_answer29) Muon $\left( {{\mu }^{-1}} \right)$ is negatively charged $(|q|=|e|)$with a mass ${{m}_{\mu }}=200{{m}_{e}},$ where ${{m}_{e}}$ is the mass of the electron and $e$ is the electronic charge. If ${{\mu }^{-1}}$ is bound to a proton to form a hydrogen like atom, identify the correct statements [JEE Online 15-04-2018 (II)] (A) Radius of the muonic orbit is times smaller than that of the electron (B) the speed of the ${{\mu }^{-1}}$ in the nth orbit is$\frac{1}{200}$ times that of the electron in the nth orbit (C) The ionization energy of muonic atom is 200 times more than that of an hydrogen atom (D) The momentum of the muon in the nth orbit is 200 times more than that of the electron

A) (A), (B), (D)

B) (B), (D)

C) (C), (D)

D) (A), (C), (D)

• question_answer30) The value closest to the thermal velocity of a Helium atom at room temperature $(300K)$ in $m{{s}^{-1}}$ is: [JEE Online 15-04-2018 (II)] $\left[ {{k}_{B}}=1.4\times {{10}^{-23}}J/K;{{m}_{He}}=7\times {{10}^{-27}}kg \right]$

A) $1.3\times {{10}^{4}}$

B) $1.3\times {{10}^{5}}$

C) $1.3\times {{10}^{2}}$

D) $1.3\times {{10}^{3}}$

 (A) (B) (C) (D) The increasing order of diazotisation of the following compounds is? [JEE Online 15-04-2018 (II)]

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

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

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

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

• question_answer32) The total number of optically active compounds formed in the following reaction is? [JEE Online 15-04-2018 (II)] A) Zero

B) Six

C) Four

D) Two

• question_answer33) In$K{{O}_{2}}$, the nature of oxygen species and the oxidation state of oxygen atom are, respectively. [JEE Online 15-04-2018 (II)]

A) Superoxide and -1

B) Superoxide and $-1/2$

C) Peroxide and $-1/2$

D) Oxide and -2

• question_answer34) ${{\Delta }_{f}}G{}^\circ$ at 500K for substance 'S' in liquid state and gaseous state are$+100.7kcal$ $mo{{l}^{-1}}$ and $\text{+103 kcal mo}{{\text{l}}^{\text{-1}}}$, respectively. Vapour pressure of liquid 'S' at 500K is approximately equal to: $\text{(R=2cal }{{\text{K}}^{-1}}mo{{l}^{-1}})$ [JEE Online 15-04-2018 (II)]

A) 100atm

B) 1 atm

C) 10 atm

D) 0.1 atm

• question_answer35) In$Xe{{O}_{3}}{{F}_{2}}$, the number of bond pair(s), $\pi -$bond(s) and lone pair(s) on Xe atom respectively are. [JEE Online 15-04-2018 (II)]

A) $5,3,0$

B) $5,2,0$

C) $4,2,2$

D) $4,4,0$

• question_answer36) Which of the following best describes the diagram of a molecular orbital? [JEE Online 15-04-2018 (II)] A) A bonding $\pi$ orbital

B) A non-bonding orbital

C) An antibonding $\sigma$ orbital

D) An antibonding $\pi$ orbital

• question_answer37) Following four solutions are prepared by mixing different volumes of NaOH and HCl of different concentrations, pH of which one of them will be equal to 1? [JEE Online 15-04-2018 (II)]

A) $55mL\frac{M}{10}HCl+45mL\frac{M}{10}NaOH$

B) $75mL\frac{M}{5}HCl+25mL\frac{M}{5}NaOH$

C) $\text{100mL}\frac{\text{M}}{\text{10}}\text{HCl+100mL}\frac{\text{M}}{\text{10}}\text{NaOH}$

D) $\text{60mL}\frac{M}{10}HCl+40mL\frac{M}{10}NaOH$

 (i) $2F{{e}_{2}}{{O}_{3}}(s)\to 4Fe(s)+3{{O}_{2}}(g);$ ${{\Delta }_{r}}{{G}^{o}}=+1487.0kJmo{{l}^{-1}}$ (ii) $2CO(g)+{{O}_{2}}(g)\to 2C{{O}_{2}}(g);$ ${{\Delta }_{r}}G{}^\circ =-514.4kJmo{{l}^{-1}}$
Free energy change, ${{\Delta }_{r}}G{}^\circ$ $2F{{e}_{2}}{{O}_{3}}(s)+6CO(g)\to 4Fe(s)+6C{{O}_{2}}(g)$ will be. [JEE Online 15-04-2018 (II)]

A) $-112.4kJ\,\,mo{{l}^{-1}}$

B) $-56.2\text{ kJ mo}{{\text{l}}^{-1}}$

C) $-208.0\text{ kJ mo}{{\text{l}}^{-1}}$

D) $-168.2\text{ kJ mo}{{\text{l}}^{-1}}$

• question_answer39) At a certain temperature in a 5L vessel, 2moles of carbon monoxide and 3 moles of chlorine were allowed to reach equilibrium according to the reaction, $CO+C{{l}_{2}}\rightleftharpoons COC{{l}_{2}}$ At equilibrium, if one mole of CO is present then equilibrium constant $({{K}_{C}})$ for the reaction is? [JEE Online 15-04-2018 (II)]

A) $2.5$

B) $4$

C) $2$

D) $3$

• question_answer40) The correct order of spin-only magnetic moments among the following is?(Atomic number:$Mn=25,Co=27,Ni=28,Zn=30$). [JEE Online 15-04-2018 (II)]

A) ${{[ZnC{{l}_{4}}]}^{2-}}>{{[NiC{{l}_{4}}]}^{2-}}>{{[CoC{{l}_{4}}]}^{2-}}>{{[MnC{{l}_{4}}]}^{2-}}$

B) ${{[CoC{{l}_{4}}]}^{2-}}>{{[MnC{{l}_{4}}]}^{2-}}>{{[NiC{{l}_{4}}]}^{2-}}>{{[ZnC{{l}_{4}}]}^{2-}}$

C) ${{[NiC{{l}_{4}}]}^{2-}}>{{[CoC{{l}_{4}}]}^{2-}}>{{[MnC{{l}_{4}}]}^{2-}}>{{[ZnC{{l}_{4}}]}^{2-}}$

D) ${{[MnC{{l}_{4}}]}^{2-}}>{{[CoC{{l}_{4}}]}^{2-}}>{{[NiC{{l}_{4}}]}^{2-}}>{{[ZnC{{l}_{4}}]}^{2-}}$

• question_answer41) When 2-butyne is treated with ${{H}_{2}}$/Lindlar's catalyst, compound X is produced as the major product and when treated with Na/liq. $N{{H}_{3}}$ it produces Y as the major product. Which of the following statements is correct? [JEE Online 15-04-2018 (II)]

A) Y will have higher dipole moment and higher boiling point than X

B) Y will have higher dipole moment and lower boiling point than X

C) X will have lower dipole moment and lower boiling point than Y

D) X will have higher dipole moment and higher boiling point than Y

• question_answer42) For a first order reaction,$A\to P,{{t}_{1/2}}$, (half-life) is 10 days. The time required for $\frac{{{1}^{th}}}{4}$ conversion of A(in days) is: (ln $2=0.693$, ln$3=1.1$ ). [JEE Online 15-04-2018 (II)]

A) $3.2$

B) $2.5$

C) $4.1$

D) $5$

• question_answer43) The major product formed in the following reaction is? [JEE Online 15-04-2018 (II)] A) B) C) D) • question_answer44) The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is? [JEE Online 15-04-2018 (II)]

A) $\text{4 }\!\!\times\!\!\text{ 0}\text{.529}\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $\text{2 }\!\!\pi\!\!\text{ }\!\!\times\!\!\text{ 0}\text{.529}\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $\frac{\text{0}\text{.529}}{\text{2 }\!\!\pi\!\!\text{ }}\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $\text{0}\text{.529}\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer45) Lithium aluminium hydride reacts with silicon tetrachloride to form. [JEE Online 15-04-2018 (II)]

A) $LiCl,Al{{H}_{3}}$ and$Si{{H}_{4}}$

B) $LiCl,AlC{{l}_{3}}$ and $Si{{H}_{4}}$

C) $LiH,AlC{{l}_{3}}$ and $SiC{{l}_{2}}$

D) $LiH,Al{{H}_{3}}$ and$Si{{H}_{4}}$

• question_answer46) The correct order of electron affinity is? [JEE Online 15-04-2018 (II)]

A) $O>F>Cl$

B) $F>O>Cl$

C) $F>Cl>O$

D) $Cl>F>O$

• question_answer47) Two 5 molal solutions are prepared by dissolving a non-electrolyte non-volatile solute separately in the solvents X and Y. The molecular weights of the solvents are ${{M}_{X}}$ and ${{M}_{Y}}$, respectively where ${{M}_{X}}=\frac{3}{4}{{M}_{Y}}$. The relative lowering of vapour pressure of the solution in X is "m" times that of the solution in Y. Given that the number of moles of solute is very small in comparison to that of solvent, the value of "m" is? [JEE Online 15-04-2018 (II)]

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

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

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

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

• question_answer48) On the treatment of the following compound with a strong acid, the most susceptible site for bond cleavage is? [JEE Online 15-04-2018 (II)] A) $O2-C3$

B) $O5-C6$

C) $C4-O5$

D) $C1-O2$

• question_answer49) All of the following share the same crystal structure except. [JEE Online 15-04-2018 (II)]

A) RbCl

B) NaCl

C) CsCl

D) LiCl

• question_answer50) The total number of possible isomers for square-planar${{[Pt(Cl)(N{{O}_{2}})(N{{O}_{3}})(SCN)]}^{2-}}$is? [JEE Online 15-04-2018 (II)]

A) 16

B) 12

C) 8

D) 24

• question_answer51) Two compounds I and II are eluted by column chromatography (adsorption of I II). Which one of the following is a correct statement? [JEE Online 15-04-2018 (II)]

A) II moves slower and has higher ${{R}_{f}}$value than I

B) II moves faster and has higher ${{R}_{f}}$ value than I

C) I moves faster and has higher ${{R}_{f}}$ value than II

D) I moves slower and has higher ${{R}_{f}}$ value than II

• question_answer52) The number of P - O bonds is ${{P}_{4}}{{O}_{6}}$ is? [JEE Online 15-04-2018 (II)]

A) 9

B) 6

C) 12

D) 18

• question_answer53) The major product formed in the following reaction is? [JEE Online 15-04-2018 (II)] A) B) C) D) • question_answer54) For per gram of reactant, the maximum quantity of ${{N}_{2}}$ gas is produced in which of the following thermal decomposition reactions? (Given: Atomic wt.$-Cr=52u,Ba=137u$). [JEE Online 15-04-2018 (II)]

A) $Ba{{({{N}_{3}})}_{2}}(s)\to Ba(C)+3{{N}_{2}}(g)$

B) ${{(N{{H}_{4}})}_{2}}C{{r}_{2}}{{O}_{7}}(s)\to {{N}_{2}}(g)+4{{H}_{2}}O(g)+C{{r}_{2}}{{O}_{3}}(s)$

C) $2N{{H}_{3}}(g)\to {{N}_{2}}(g)+3{{H}_{2}}(g)$

D) $2N{{H}_{4}}N{{O}_{3}}(s)\to 2{{N}_{2}}(g)+4{{H}_{2}}O(g)+{{O}_{2}}(g)$

• question_answer55) If x gram of gas is adsorbed by m gram of adsorbent at pressure P, the plot of log $\frac{x}{m}$versus log P is linear. The slope of the plot is? (n and k are constants and n > l) [JEE Online 15-04-2018 (II)]

A) $\log k$

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

C) $2k$

D) $n$

• question_answer56) Biochemical Oxygen Demand (BOD) value can be a measure of water pollution caused by the organic matter. Which of the following statements is correct? [JEE Online 15-04-2018 (II)]

A) Polluted water has BOD value higher than 10 ppm

B) Aerobic bacteria decrease the BOD value

C) Anaerobic bacteria increase the BOD value

D) Clean water has BOD value higher than 10 ppm

• question_answer57) In the leaching method, bauxite ore is digested with a concentrated solution of NaOH that produces 'X'. When $C{{O}_{2}}$ gas is passed through the aqueous solution of 'X', a hydrated compound 'Y' is precipitated. 'X' and 'Y' respectively are. [JEE Online 15-04-2018 (II)]

A) $Na[Al{{(OH)}_{4}}]andA{{l}_{2}}{{(C{{O}_{3}})}_{3}}\cdot x{{H}_{2}}O$

B) $Al{{(OH)}_{3}}andA{{l}_{2}}{{O}_{3}}\cdot x{{H}_{2}}O$

C) $NaAl{{O}_{2}}and\,\,A{{l}_{2}}{{(C{{O}_{3}})}_{3}}\cdot x{{H}_{2}}O$

D) $Na[Al{{(OH)}_{4}}]and\,\,A{{l}_{2}}{{O}_{3}}\cdot x{{H}_{2}}O$

• question_answer58) Which of the following statements is not true? [JEE Online 15-04-2018 (II)]

A) Chain growth polymerisation involves homopolymerisation only

B) Chain growth polymerisation includes both homopolymerisation and copolymerisation

C) Nylon 6 is an example of step-growth polymerisation

D) Step growth polymerisation requires a bifunctional monomer

• question_answer59) The dipeptide, Gln-Gly, on treatment with $C{{H}_{3}}COCl$ followed by aqueous work up gives. [JEE Online 15-04-2018 (II)]

A) B) C) D) • question_answer60) The increasing order of the acidity of the following carboxylic acids is? [JEE Online 15-04-2018 (II)] A) $III<II<IV<I$

B) $I<III<II<IV$

C) $IV<II<III<I$

D) $II<IV<III<I$

• question_answer61) Let $\int_{{}}^{{}}{:A\to }B$ be a function defined as $\int_{{}}^{{}}{(x)}=\frac{x-1}{x-2}$, where$A=R-\{2\}$ and $B=R\{1\}$. Then $\int_{{}}^{{}}{{}}$ is [JEE Online 15-04-2018 (II)]

A) Invertible and ${{f}^{-1}}(y)=\frac{2y+1}{y-1}$

B) Invertible and ${{f}^{-1}}(y)=\frac{3y+1}{y-1}$

C) No invertible

D) Invertible and ${{f}^{-1}}(y)=\frac{2y-1}{y-1}$

• question_answer62) The coefficient of ${{x}^{10}}$ in the expansion of ${{(1+x)}^{2}}{{(1+{{x}^{2}})}^{3}}{{(1+{{x}^{3}})}^{4}}$ is equal to [JEE Online 15-04-2018 (II)]

A) 52

B) 44

C) 50

D) 56

• question_answer63) If the system of linear equations $x+ay+z=3$ $x+2y+2z=6$ $x+5y+3z=b$ has no solution, then [JEE Online 15-04-2018 (II)]

A) $a=1,b\ne 9$

B) $a\ne -1,b=9$

C) $a=-1,b=9$

D) $a=-1,b\ne 9$

• question_answer64) If $f(x)$ is a quadratic expression such that $f(1)+f(2)=0$, and $-1$ is a root of $f(x)=0$, then the other root of $f(x)=0$ is [JEE Online 15-04-2018 (II)]

A) $-\frac{5}{8}$

B) $-\frac{8}{5}$

C) $\frac{5}{8}$

D) $\frac{8}{5}$

• question_answer65) The number of four letter words that can be formed using the letters of the word BARRACK is [JEE Online 15-04-2018 (II)]

A) 144

B) 120

C) 264

D) 270

• question_answer66) The number of solutions of $\sin 3x=\cos 2x$, in the interval $\left( \frac{\pi }{2},\pi \right)$is [JEE Online 15-04-2018 (II)]

A) 3

B) 4

C) 2

D) 1

• question_answer67) The curve satisfying the differential equation, $({{x}^{2}}-{{y}^{2}})dx+2xydy=0$and passing through the point $(1,1)$is [JEE Online 15-04-2018 (II)]

A) A circle of radius two

B) A circle of radius one

C) A hyperbola

D) An ellipse

• question_answer68) A player$X$ has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of ?p? is [JEE Online 15-04-2018 (II)]

A) $\frac{1}{3}$

B) $\frac{1}{5}$

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

D) $\frac{2}{5}$

• question_answer69) Consider the following two statements:

 Statement p: The value of $\sin 120{}^\circ$ can be divided by taking $\theta =240{}^\circ$in the equation$2\sin \frac{\theta }{2}=\sqrt{1+\sin \theta }-\sqrt{1-2\theta }$. Statement q: The angles A, B, C and D of any quadrilateral ABCD satisfy the equation $\cos \left( \frac{1}{2}(A+C) \right)+\cos \left( \frac{1}{2}(B+D) \right)=0$. Then the truth values of p and q are respectively.
[JEE Online 15-04-2018 (II)]

A) F, T

B) T, T

C) F, F

D) T, F

• question_answer70) $\int_{{}}^{{}}{\frac{2x+5}{\sqrt{7-6x-{{x}^{2}}}}dx=A\sqrt{7-6x-{{x}^{2}}}+B{{\sin }^{-1}}\left( \frac{x+3}{4} \right)+C}$ (where $C$ is a constant of integration), then the ordered pair $(A,B)$ is equal to [JEE Online 15-04-2018 (II)]

A) $(-2,-1)$

B) $(2,-1)$

C) $(-2,1)$

D) $(2,1)$

• question_answer71) A plane bisects the line segment joining the points (1,2,3) and (-3,4,5) at right angles. Then this plane also passes through the point. [JEE Online 15-04-2018 (II)]

A) $(-3,2,1)$

B) $(3,2,1)$

C) $(1,2,-3)$

D) $(-1,2,3)$

• question_answer72) If $|z-3+2i|\le 4$ then the difference between the greatest value and the least value of $|z|$ is [JEE Online 15-04-2018 (II)]

A) $\sqrt{13}$

B) $2\sqrt{13}$

C) $8$

D) $4+\sqrt{13}$

• question_answer73) If the position vectors of the vertices A, B and C of a $\Delta ABC$ are respectively $4\widehat{i}+7\widehat{j}+8\widehat{k},2\widehat{i}+3\widehat{j}+4\widehat{k}$ and $2\widehat{i}+5\widehat{j}+7\widehat{k}$, then the position vector of the point, where the bisector of $\angle A$ meets BC is [JEE Online 15-04-2018 (II)]

A) $\frac{1}{2}(4\widehat{i}+8\widehat{j}+11\widehat{k})$

B) $\frac{1}{3}(6\widehat{i}+13\widehat{j}+18\widehat{k})$

C) $\frac{1}{4}(8\widehat{i}+14\widehat{j}+9\widehat{k})$

D) $\frac{1}{3}(6\widehat{i}+11\widehat{j}+15\widehat{k})$

• question_answer74) The foot of the perpendicular drawn from the origin, on the line, $3x+y=\lambda (\lambda \ne 0)$ is $P$. If the line meets x-axis at $A$ and y-axis at $B$, then the ratio $BP:PA$ is [JEE Online 15-04-2018 (II)]

A) 9:1

B) 1:3

C) 1:9

D) 3:1

• question_answer75) If $f(x)={{\sin }^{-1}}\left( \frac{2\times {{3}^{x}}}{1+{{9}^{x}}} \right)$, then $f'\left( -\frac{1}{2} \right)$ equals. [JEE Online 15-04-2018 (II)]

A) $\sqrt{3}{{\log }_{e}}\sqrt{3}$

B) $-\sqrt{3}{{\log }_{e}}\sqrt{3}$

C) $-\sqrt{3}{{\log }_{e}}3$

D) $-\sqrt{3}{{\log }_{e}}3$

• question_answer76) Let ${{A}_{n}}=\left( \frac{3}{4} \right)-{{\left( \frac{3}{4} \right)}^{2}}+{{\left( \frac{3}{4} \right)}^{3}}-........+{{(-1)}^{n-1}}{{\left( \frac{3}{4} \right)}^{n}}$ and ${{B}_{n}}=1-{{A}_{n}}.$ Then, the least odd natural number $p$, so that ${{B}_{n}}>{{A}_{n}}$, for all $n\ge p$ is [JEE Online 15-04-2018 (II)]

A) 5

B) 7

C) 11

D) 9

• question_answer77) A normal to the hyperbola,$4{{x}^{2}}-9{{y}^{2}}=36$ meets the co-ordinate axes $x$ and $y$ at A and B, respectively. If the parallelogram $OABP$(O being the origin) is formed, then the locus of $P$ is [JEE Online 15-04-2018 (II)]

A) $4{{x}^{2}}-9{{y}^{2}}=121$

B) $4{{x}^{2}}+9{{y}^{2}}=121$

C) $9{{x}^{2}}-4{{y}^{2}}=169$

D) $9{{x}^{2}}+4{{y}^{2}}=169$

• question_answer78) Let $f(x)$ be a polynomial of degree 4 having extreme values at $x=1$ and $x=2$. If $\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{f(x)}{{{x}^{2}}}+1 \right)=3$ then $f(-1)$ is equal to [JEE Online 15-04-2018 (II)]

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

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

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

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

• question_answer79) If the mean of the data:$7,8,9,7,8,7,\lambda ,8$is$8,$ then the variance of this data is [JEE Online 15-04-2018 (II)]

A) $\frac{9}{8}$

B) $2$

C) $\frac{7}{8}$

D) $1$

• question_answer80) An angle between the lines whose direction cosines are given by the equations, $l+3m+5n=0$ and $5lm-2mn+6nl=0$, is [JEE Online 15-04-2018 (II)]

A) ${{\cos }^{-1}}\left( \frac{1}{8} \right)$

B) ${{\cos }^{-1}}\left( \frac{1}{6} \right)$

C) ${{\cos }^{-1}}\left( \frac{1}{3} \right)$

D) ${{\cos }^{-1}}\left( \frac{1}{4} \right)$

• question_answer81) The tangent to the circle ${{C}_{1}}:{{x}^{2}}+{{y}^{2}}-2x-1=0$ at the point $(2,1)$ cuts off a chord of length 4 from a circle ${{C}_{2}}$ whose centre is $(3,-2)$. The radius of ${{C}_{2}}$ is [JEE Online 15-04-2018 (II)]

A) $\sqrt{6}$

B) $2$

C) $\sqrt{2}$

D) $3$

• question_answer82) Suppose $A$ is any $3\times 3$ non-singular matrix and $(A-3I)(A-5I)=O$, where $I={{I}_{3}}$ and $O={{O}_{3}}$. If $\alpha A+\beta {{A}^{-1}}=4I$, then $\alpha +\beta$ is equal to [JEE Online 15-04-2018 (II)]

A) 8

B) 12

C) 13

D) 7

• question_answer83) The value of integral $\int_{\frac{\pi }{4}}^{\frac{3\pi }{4}}{\frac{x}{1+\sin x}dx}$ is [JEE Online 15-04-2018 (II)]

A) $\frac{\pi }{2}\left( \sqrt{2}+1 \right)$

B) $\pi \left( \sqrt{2}-1 \right)$

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

D) $\pi \sqrt{2}$

• question_answer84) A tower ${{T}_{1}}$ of height $60m$ is located exactly opposite to a tower ${{T}_{2}}$ of height $80m$ on a straight road. From the top of ${{T}_{1}}$, if the angle of depression of the foot of ${{T}_{2}}$ is twice the angle of elevation of the top of${{T}_{2}}$ , then the width (in m) of the road between the feet of the towers ${{T}_{1}}$ and ${{T}_{2}}$ is [JEE Online 15-04-2018 (II)]

A) $20\sqrt{2}$

B) $10\sqrt{2}$

C) $10\sqrt{3}$

D) $20\sqrt{3}$

• question_answer85) If ${{I}_{1}}=\int_{0}^{1}{{{e}^{-x}}{{\cos }^{2}}xdx;}\,\,\,\,{{I}_{2}}=\int_{0}^{1}{{{e}^{-{{x}^{2}}}}{{\cos }^{2}}xdx}\,\,\,and\,\,\,{{I}_{3}}=\int_{0}^{1}{{{e}^{-{{x}^{2}}}}dx;}$then [JEE Online 15-04-2018 (II)]

A) ${{I}_{2}}>{{I}_{3}}>{{I}_{1}}$

B) ${{I}_{3}}>{{I}_{1}}>{{I}_{2}}$

C) ${{I}_{2}}>{{I}_{1}}>{{I}_{3}}$

D) ${{I}_{3}}>{{I}_{2}}>{{I}_{1}}$

• question_answer86) The sides of a rhombus $ABCD$ are parallel to the lines, $x-y+2=0$ and $7x-y+3=0$. If the diagonals of the rhombus intersect at $P(1,2)$ and the vertex $A$ (different from the origin) is on the y-axis, then the ordinate of is [JEE Online 15-04-2018 (II)]

A) 2

B) $\frac{7}{4}$

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

D) $\frac{5}{2}$

• question_answer87) $\underset{x\to 0}{\mathop{\lim }}\,\frac{x\tan 2x-2x\tan x}{{{(1-\cos 2x)}^{2}}}$ equals. [JEE Online 15-04-2018 (II)]

A) 1

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

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

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

• question_answer88) Let f(x)=\left\{ \begin{align} & {{(x-1)}^{\frac{1}{2-x}}},x>1,x\ne 2k, \\ & x=2 \\ \end{align} \right. The value of $k$ for which $f$ is continuous at $x=2$ is [JEE Online 15-04-2018 (II)]

A) ${{e}^{-2}}$

B) $e$

C) ${{e}^{-1}}$

D) $1$

• question_answer89) If $a,b,c$are in A.P. and ${{a}^{2}},{{b}^{2}},{{c}^{2}}$ are in G.P. such that $a<b<c$ and $a+b+c=\frac{3}{4}$, then the value of $a$ is [JEE Online 15-04-2018 (II)]

A) $\frac{1}{4}-\frac{1}{3\sqrt{2}}$

B) $\frac{1}{4}-\frac{1}{4\sqrt{2}}$

C) $\frac{1}{4}-\frac{1}{\sqrt{2}}$

D) $\frac{1}{4}-\frac{1}{2\sqrt{2}}$

• question_answer90) Tangents drawn from the point $(-8,0)$ to the parabola ${{y}^{2}}=8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola, then the area of the triangle $PFQ$ (in sq. units) is equal to [JEE Online 15-04-2018 (II)]

A) 48

B) 32

C) 24

D) 64

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