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

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

• question_answer1) A thin uniform tube is bent into a circle of radius in the vertical plane. Equal volumes of two immiscible liquids, whose densities are and fill half the circle. The angle between the radius vector passing through the common interface and the vertical is: [JEE Online 15-04-2018]

A) $\theta ={{\tan }^{-1}}\left[ \frac{\pi }{2}\left( \frac{{{\rho }_{1}}-{{\rho }_{2}}}{{{\rho }_{1}}+{{\rho }_{2}}} \right) \right]$

B) $\theta ={{\tan }^{-1}}\frac{\pi }{2}\left( \frac{{{\rho }_{1}}-{{\rho }_{2}}}{{{\rho }_{1}}+{{\rho }_{2}}} \right)$

C) $\theta ={{\tan }^{-1}}\pi \left( \frac{{{\rho }_{1}}}{{{\rho }_{2}}} \right)$

D) None of above

• question_answer2) The relative error in the determination of the surface area of a sphere is$\alpha$. Then the relative error in the determination of its volume is: [JEE Online 15-04-2018]

A) $\frac{2}{3}\alpha$

B) $\frac{5}{2}\alpha$

C) $\frac{3}{2}\alpha$

D) $\alpha$

• question_answer3) A uniform rod AB is suspended from a point X, at a variable distance $x$ from $A$, as shown. To make the rod horizontal, a mass $m$ is suspended from its end$A$. A set of $(m,x)$ values is recorded. The appropriate variables that give a straight line, when plotted, are: [JEE Online 15-04-2018]

A) $m,\frac{l}{x}$

B) $m,\frac{l}{{{x}^{2}}}$

C) $m,x$

D) $m,{{x}^{2}}$

• question_answer4) An ideal capacitor of capacitance $0.2\mu F$ is charged to a potential difference of $10V$. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self-inductance$0.5mH$. The current at a time when the potential difference across the capacitor is $5V$, is: [JEE Online 15-04-2018]

A) 0.17 A

B) 0.15 A

C) 0.34 A

D) 0.25 A

• question_answer5) In the given circuit all resistances are of value $R$ ohm each. The equivalent resistance between $A$ and $B$ is: [JEE Online 15-04-2018]

A) $2R$

B) $\frac{5R}{2}$

C) $\frac{5R}{3}$

D) $3R$

• question_answer6) In a common emitter configuration with suitable bias, it is given than ${{R}_{L}}$ is the load resistance and ${{R}_{BE}}$ is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by: [JEE Online 15-04-2018] $\beta$ is current gain, ${{I}_{B}},{{I}_{C}},{{I}_{E}}$ are respectively base, collector and emitter currents:

A) $\beta \frac{{{R}_{L}}}{{{R}_{BE}}},\frac{\Delta {{I}_{E}}}{\Delta {{I}_{B}}},{{\beta }^{2}}\frac{{{R}_{L}}}{{{R}_{BE}}}$

B) ${{\beta }^{2}}\frac{{{R}_{L}}}{{{R}_{BE}}},\frac{\Delta {{I}_{C}}}{\Delta {{I}_{B}}},\beta \frac{{{R}_{L}}}{{{R}_{BE}}}$

C) ${{\beta }^{2}}\frac{{{R}_{L}}}{{{R}_{BE}}},\frac{\Delta {{I}_{C}}}{\Delta {{I}_{B}}},{{\beta }^{2}}\frac{{{R}_{L}}}{{{R}_{BE}}}$

D) $\beta \frac{{{R}_{L}}}{{{R}_{BE}}},\frac{\Delta {{I}_{C}}}{\Delta {{I}_{B}}},{{\beta }^{2}}\frac{{{R}_{L}}}{{{R}_{BE}}}$

• question_answer7) In a meter bridge, as shown in the figure, it is given that resistance $Y=12.5\Omega$ and that the balance is obtained at a distance $39.5cm$ from end $A$ (by jockey J). After interchanging the resistances $X$ and$Y$, a new balance point is found at a distance ${{l}_{2}}$ from end $A$. What are the values of $X$and ${{l}_{2}}$? [JEE Online 15-04-2018]

A) $\text{19}\text{.15 }\Omega$ and $\text{39}\text{.5 cm}$

B) $\text{8}\text{.16 }\Omega \text{ and 60}\text{.5 cm}$

C) $\text{19}\text{.15}\,\,\text{ }\!\!\Omega\!\!\text{ }\,\,\text{and}\,\,\text{60}\text{.5}\,\,\text{cm}$

D) $\text{8}\text{.16}\,\,\Omega \text{ and 39}\text{.5 cm}$

• question_answer8) Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are ${{\lambda }_{1}}$ and ${{\lambda }_{2}}$, their de Broglie wavelength in the frame of reference attached to their centre of mass is: JEE Online 15-04-2018]

A) ${{\lambda }_{CM}}={{\lambda }_{1}}={{\lambda }_{2}}$

B) $\frac{1}{{{\lambda }_{CM}}}=\frac{1}{{{\lambda }_{1}}}+\frac{1}{{{\lambda }_{2}}}$

C) ${{\lambda }_{CM}}=\frac{2{{\lambda }_{1}}{{\lambda }_{2}}}{\sqrt{{{\lambda }_{1}}^{2}+{{\lambda }_{2}}^{2}}}$

D) ${{\lambda }_{CM}}=\left( \frac{{{\lambda }_{1}}+{{\lambda }_{2}}}{2} \right)$

• question_answer9) A tuning fork vibrates with frequency $256Hz$and gives one best per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (Speed of sound of air is $340m{{s}^{-1}}$) [JEE Online 15-04-2018]

A) $190cm$

B) $180cm$

C) $220cm$

D) $200cm$

• question_answer10) The number of amplitude modulated broadcast stations that can be accommodated in a $300kHz$ band width for the highest modulating frequency $15kHz$ will be: [JEE Online 15-04-2018]

A) 20

B) 10

C) 8

D) 15

• question_answer11) A body of mass $m$ is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$, and the other mass, in a circular orbit of radius $\frac{3R}{2}$. The difference between the final initial total energies is: [JEE Online 15-04-2018]

A) $-\frac{GMm}{2R}$

B) $+\frac{GMm}{6R}$

C) $-\frac{GMm}{6R}$

D) $\frac{GMm}{2R}$

• question_answer12) Light wavelength $550nm$ falls normally on a slit of width$22.0\times {{10}^{-5}}cm$. The angular position of the second minima from the central maximum will be (in radians) [JEE Online 15-04-2018]

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

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

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

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

• question_answer13) A force of $40N$acts on a point $B$ at the end of an L-shaped object, as shown in the figure. The angle $0$ that will produce maximum moment of the force about point $A$ is given by: [JEE Online 15-04-2018]

A) $\tan \theta =\frac{1}{4}$

B) $\tan \theta =2$

C) $\tan \theta =\frac{1}{2}$

D) $\tan \theta =4$

• question_answer14) A given object takes $n$ times more time to slide down a $45{}^\circ$ rough inclined plane as it takes to slide down a perfectly smooth $45{}^\circ$ incline. The coefficient of kinetic friction between the object and the incline is : [JEE Online 15-04-2018]

A) $\sqrt{1-\frac{1}{{{n}^{2}}}}$

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

C) $\frac{1}{2-{{n}^{2}}}$

D) $\sqrt{\frac{1}{1-{{n}^{2}}}}$

• question_answer15) The equivalent capacitance between A and B in the circuit given below is: [JEE Online 15-04-2018]

A) $4.9\mu F$

B) $3.6\mu F$

C) $5.4\mu F$

D) $2.4\mu F$

• question_answer16) A Carnot's engine works as a refrigerator between $250K$ and $300K$. It receives $500cal$ heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is: [JEE Online 15-04-2018]

A) $420J$

B) $2100J$

C) $772J$

D) $2520J$

• question_answer17) One mode of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, $27{}^\circ C$. The work done on the gas will be: [JEE Online 15-04-2018]

A) $300R\,\,In\,\,6$

B) $300R$

C) $300R\,\,In\,\,7$

D) $300R\,\,In\,\,2$

• question_answer18) An automobile, travelling at $40km/h$, can be stopped at a distance of $40m$by applying brakes. If the same automobile is travelling at $80km/h$, the minimum stopping distance, in metres, is (assume no skidding) [JEE Online 15-04-2018]

A) $75m$

B) $160m$

C) $100m$

D) $150m$

• question_answer19) Take the mean distance of the moon and the sun from the earth to be $0.4\times {{10}^{6}}km$and $150\times {{10}^{6}}km$ respectively. Their masses are $8\times {{10}^{22}}kg$and $2\times {{10}^{30}}kg$ respectively. The radius of the earth is$6400km$. Let $\Delta {{F}_{1}}$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $\Delta {{F}_{2}}$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $\frac{\Delta {{F}_{1}}}{\Delta {{F}_{2}}}$ is: [JEE Online 15-04-2018]

A) 2

B) 6

C) ${{10}^{-2}}$

D) 0.6

• question_answer20) The B-H curve for a Ferro magnet is shown in the figure. The Ferro magnet is placed inside a ling solenoid with 1000 turns/cm. The current that should be passed in the solenoid to demagnetise the Ferro magnet completely is: [JEE Online 15-04-2018]

A) $2mA$

B) $1mA$

C) $40\mu A$

D) $20\mu A$

• question_answer21) A plan convex lens becomes an optical system of $28cm$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A. If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length$10cm$. The refractive index of the material of lens if: [JEE Online 15-04-2018]

A) $1.50$

B) $1.55$

C) $1.75$

D) $1.51$

• question_answer22) A body of mass $M$ and charge $q$ is connected to a spring of spring constant$k$. It is oscillating along x-direction about its equilibrium position, taken to be at $x=0$, with an amplitude $A$. An electric field $E$ is applied along the x-direction. Which of the following statements is correct? [JEE Online 15-04-2018]

A) The total energy of the system is $\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}+\frac{1}{2}\frac{{{q}^{2}}{{E}^{2}}}{k}$

B) The new equilibrium position is at a distance: $\frac{2qE}{k}$ from $x=0$

C) The new equilibrium position is at a distance:$\frac{qE}{2k}$ from $x=0$

D) The total energy of the system is$\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}-\frac{1}{2}\frac{{{q}^{2}}{{E}^{2}}}{k}$

• question_answer23) In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is: [JEE Online 15-04-2018]

A) $0.0430cm$

B) $0.3150cm$

C) $0.4300cm$

D) $0.2150cm$

• question_answer24) A solution containing active cobalt $_{27}^{60}Co$having activity of $0.8\mu Ci$ and decay constant $\lambda$ is injected in an animal's body. If $1c{{m}^{3}}$ of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body? ($1Ci=3.7\times {{10}^{10}}$decay per second and at $t=10hrs$${{e}^{-\lambda t}}=0.84$) [JEE Online 15-04-2018]

A) litres

B) litres

C) litres

D) litres

• question_answer25) A charge $Q$ is placed at a distance $a/2$ above the centre of the square surface of edge $a$ as shown in the figure. The electric flux through the square surface is: [JEE Online 15-04-2018]

A) $\frac{Q}{3{{\in }_{0}}}$

B) $\frac{Q}{6{{\in }_{0}}}$

C) $\frac{Q}{2{{\in }_{0}}}$

D) $\frac{Q}{{{\in }_{0}}}$

• question_answer26) The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is: [JEE Online 15-04-2018]

A) $20eV$

B) $79eV$

C) $109eV$

D) $34eV$

• question_answer27) A monochromatic beam of light has a frequency $v=\frac{3}{2\pi }\times {{10}^{12}}Hz$ and is propagating along the direction$\frac{\widehat{i}+\widehat{j}}{\sqrt{2}}$. It is polarized along $\widehat{k}$ the direction. The acceptable form for the magnetic field is: [JEE Online 15-04-2018]

A) $k\frac{{{E}_{0}}}{C}\left( \frac{\widehat{i}-\widehat{j}}{\sqrt{2}} \right)\cos \left[ {{10}^{4}}\left( \frac{\widehat{i}-\widehat{j}}{\sqrt{2}} \right).\overrightarrow{r}-(3\times {{10}^{12}})t \right]$

B) $\frac{{{E}_{0}}}{C}\left( \frac{\widehat{i}-\widehat{j}}{\sqrt{2}} \right)\cos \left[ {{10}^{4}}\left( \frac{\widehat{i}+\widehat{j}}{\sqrt{2}} \right).\overrightarrow{r}-(3\times {{10}^{12}})t \right]$

C) $\frac{{{E}_{0}}}{C}\widehat{k}\cos \left[ {{10}^{4}}\left( \frac{\widehat{i}+\widehat{j}}{\sqrt{2}} \right).\overrightarrow{r}+(3\times {{10}^{12}})t \right]$

D) $\frac{{{E}_{0}}}{C}\frac{\left( \widehat{i}+\widehat{j}+\widehat{k} \right)}{\sqrt{3}}\cos \left[ {{10}^{4}}\left( \frac{\widehat{i}+\widehat{j}}{\sqrt{2}} \right).\overrightarrow{r}+(3\times {{10}^{12}})t \right]$

• question_answer28) The velocity-time graphs of a car and a scooter are shown in the figure. (i) the difference between the distance travelled by the car and the scooter in 15s and (ii) the time at which the car will catch up with the scooter are, respectively [JEE Online 15-04-2018]

A) $337.5m\,\,\,and\,\,25s$

B) $225.5m\,\,and\,\,10s$

C) $112.5m\,\,and\,\,22.5s$

D) $11.2.5m\,\,and\,\,15s$

• question_answer29) A Helmholtz coil has pair of loops, each with $N$ turns and radius$R$. They are placed coaxially at distance $R$ and the same current $I$ flows through the loops in the same direction. The magnitude of magnetic field at $P$, midway between the centres $A$and $C$, is given by (Refer to figure): [JEE Online 15-04-2018]

A) $\frac{4N{{\mu }_{0}}I}{{{5}^{3/2}}R}$

B) $\frac{8N{{\mu }_{0}}I}{{{5}^{3/2}}R}$

C) $\frac{4N{{\mu }_{0}}I}{{{5}^{1/2}}R}$

D) $\frac{8N{{\mu }_{0}}I}{{{5}^{1/2}}R}$

• question_answer30) A particle is oscillating on the X-axis with an amplitude $2cm$ about the point ${{x}_{0}}=10cm$ with a frequency$\omega$. A concave mirror of focal length $5cm$ is placed at the origin (see figure) Identify the correct statements: [JEE Online 15-04-2018]

 (A) The image executes periodic motion (B) The image executes no n-periodic motion (C) The turning points of the image are asymmetric w.r.t the image of the point at $x=10cm$ (D) The distance between the turning points of the oscillation of the image is$\frac{100}{21}$

A) (B), (D)

B) (B), (C)

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

D) (A), (D)

• question_answer31) The increasing order of nitration of the following compounds is? [JEE Online 15-04-2018]

A) $(b)<(a)<(c)<(d)$

B) $(b)<(a)<(d)<(c)$

C) $(a)<(b)<(c)<(d)$

D) $(a)<(b)<(d)<(c)$

• question_answer32) In graphite and diamond, the percentage of p-characters of the hybrid orbitals in hybridisation are respectively _________. [JEE Online 15-04-2018]

A) $\text{50}\,\,\text{and}\,\,\text{75}$

B) $\text{67}\,\,\text{and }\,\,\text{75}$

C) $\text{33}\,\,\text{and 25}$

D) $\text{33}\,\,\text{and}\,\,\text{75}$

• question_answer33) Identify the pair in which the geometry of the species is T-shape and square pyramidal, respectively are __________. [JEE Online 15-04-2018]

A) $Cl{{F}_{3}}$and $IO_{4}^{-}$

B) $lCl_{2}^{-}$ and $lC{{l}_{5}}$

C) $lO_{3}^{-}$ and $l{{O}_{2}}F_{2}^{-}$

D) $XeO{{F}_{2}}$and $XeO{{F}_{4}}$

• question_answer34) ${{N}_{2}}{{O}_{5}}$ Decomposes to $N{{O}_{2}}$ and ${{O}_{2}}$ and follows first order kinetics. After 50 minutes, the pressure inside the vessel increases from $50mm$ Hg of $87.5mm$Hg. The pressure of the gaseous mixture after 100 minute at constant temperature will be __________. [JEE Online 15-04-2018]

A) $116.25\text{ mmHg}$

B) $106.25\text{ mmHg}$

C) $136.25\text{ mmHg}$

D) $175.0\text{ mmHg}$

• question_answer35) Which of the following statements about colloids is False? [JEE Online 15-04-2018]

A) Colloidal particles can pass through ordinary filter paper

B) Freezing point of colloidal solution is lower than true solution at same concentration of a solute

C) When silver nitrate solution is added to potassium iodide solution, a negatively charged colloidal solution is formed

D) When excess of electrolyte is added to colloidal solution, colloidal particle will be precipitated

• question_answer36) The major product of the following reaction is? [JEE Online 15-04-2018]

A)

B)

C)

D)

• question_answer37) An ideal gas undergoes a cyclic process as shown in Figure. [JEE Online 15-04-2018] $\Delta {{\text{U}}_{BC}}=-5mJ\,\,mo{{l}^{-1}},\,\,{{q}_{AB}}=2kJ\,\,mo{{l}^{-1}}$ ${{W}_{AB}}=-5\,\,kJ\,\,mo{{l}^{-1}},\,\,{{W}_{CA}}=3\,\,kJ\,\,mo{{l}^{-1}}$ Heat absorbed by the system during process CA is:

A) $18kJ\,\,mo{{l}^{-1}}$

B) $-18kJ\,\,mo{{l}^{-1}}$

C) $-5\,\,kJ\,\,mo{{l}^{-1}}$

D) $+5\,\,kJ\,\,mo{{l}^{-1}}$

• question_answer38) Which of the following will most readily give the dehydrohalogenation product? [JEE Online 15-04-2018]

A)

B)

C)

D)

• question_answer39) The minimum volume of water required to dissolve 0.1g lead(II) chloride to get a saturated solution (${{K}_{sp}}$ of $PbC{{l}_{2}}=3.2\times {{10}^{-8}}$; atomic mass of $Pb=207u$) is? [JEE Online 15-04-2018]

A) 0.18 L

B) 17.98 L

C) 1.798 L

D) 0.36 L

• question_answer40) The decreasing order of bond angles in $B{{F}_{3}},N{{H}_{3}},P{{F}_{3}}$ and $I_{3}^{-}$ is? [JEE Online 15-04-2018]

A) $B{{F}_{3}}>I_{3}^{-}>P{{F}_{3}}>N{{H}_{3}}$

B) $I_{3}^{-}>N{{H}_{3}}>P{{F}_{3}}>B{{F}_{3}}$

C) $B{{F}_{3}}>N{{H}_{3}}>P{{F}_{3}}>I_{3}^{-}$

D) $I_{3}^{-}>B{{F}_{3}}>N{{H}_{3}}>P{{F}_{3}}$

• question_answer41) In the molecular orbital diagram for the molecular ion, $N_{2}^{+}$, the number of electrons in the ${{\sigma }_{2p}}$ molecular orbital is? [JEE Online 15-04-2018]

A) 1

B) 2

C) 3

D) 4

• question_answer42) The correct combination is? [JEE Online 15-04-2018]

A) ${{[Ni{{(CN)}_{4}}]}^{2-}}$-tetrahedral;$[Ni{{(CO)}_{4}}]$-Paramagnetic

B) ${{[NiC{{l}_{4}}]}^{2-}}$ -paramagnetic; $[Ni{{(CO)}_{4}}]$-tetrahedral

C) ${{[NiC{{l}_{4}}]}^{2-}}$ -diamagnetic; $[Ni{{(CO)}_{4}}]$ -square-planar

D) ${{[NiC{{l}_{4}}]}^{2-}}$ -Square-planar; ${{[Ni{{(CN)}_{4}}]}^{2-}}$ -paramagnetic

• question_answer43) Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by applying 0.5V when the radiation of 250nm is used. The work function of the metal is? [JEE Online 15-04-2018]

A) $5.5\,\,eV$

B) $4\,\,eV$

C) $5\,\,eV$

D) $4.5\,\,eV$

• question_answer44) Which of the following is the correct structure of Adenosine? [JEE Online 15-04-2018]

A)

B)

C)

D)

• question_answer45) When an electric current is passes through acidified water, 112mL of hydrogen gas at N.T.P. was collected at the cathode in 965 seconds. The current passed, in ampere, is _______. [JEE Online 15-04-2018]

A) 0.1

B) 2.0

C) 1.0

D) 0.5

• question_answer46) A sample of $NaCl{{O}_{3}}$ is converted by heat to $NaCl$ with a loss of 0.16g of oxygen. The residue is dissolved in water and precipitated as $AgCl$. The mass of $AgCl$ (in g) obtained will be: (Given: Molar mass of $\text{AgCl=143}\text{.5g}\,\,\text{mo}{{\text{l}}^{\text{-1}}}$) [JEE Online 15-04-2018]

A) 0.41

B) 0.35

C) 0.48

D) 0.54

• question_answer47) The IUPAC name of the following compound is? [JEE Online 15-04-2018]

A) 3-ethyl-4-methylhex-4-ene

B) 4, 4-diethyl-3-methylbut-2-ene

C) 4-ethyl-3-methylhex-2-ene

D) 4-methyl-3-ethylhex-4-ene

• question_answer48) For which of the following reactions, $\Delta H$ is equal to$\Delta U$? [JEE Online 15-04-2018]

A) $2HI(g)\to {{H}_{2}}(g)+{{I}_{2}}(g)$

B) $2S{{O}_{2}}(g)+{{O}_{2}}(g)\to 2S{{O}_{3}}(g)$

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

D) $2NH{{O}_{2}}(g)\to {{N}_{2}}{{O}_{4}}(g)$

• question_answer49) \begin{align} & \text{ }\left( \text{I} \right)\text{ }\left( \text{II} \right) \\ & \text{H - N - - -N - - -N} \\ \end{align} In hydrogen azide, the bond orders of bonds (I) and (II) are _________. [JEE Online 15-04-2018]

A) $\text{(i)-2, (ii)-2}$

B) $(i)->2,\,\,(ii)->2$

C) $(i)->2,\,\,(ii)-<2$

D) $(i)-<2,\,\,(ii)<2$

• question_answer50) Xenon hexafluoride on partial hydrolysis produces compounds 'X' and 'Y'. Compounds 'X' and 'Y' and the oxidation state of Xe are respectively _______. [JEE Online 15-04-2018]

A) $XeO{{F}_{4}}(+6)$and $Xe{{O}_{2}}{{F}_{2}}(+6)$

B) $XeO{{F}_{4}}(+6)$ and $Xe{{O}_{3}}(+6)$

C) $Xe{{O}_{2}}{{F}_{2}}(+6)$ and $Xe{{O}_{2}}(+4)$

D) $Xe{{O}_{2}}(+4)$ and $Xe{{O}_{3}}(+6)$

• question_answer51) A white sodium salt dissolves readily in water to give a solution which is neutral to litmus. When silver nitrate solution is added to the aforementioned solution, a white precipitate is obtained which does not dissolve in dil. nitric acid. The anion is __________. [JEE Online 15-04-2018]

A) $CO_{3}^{2-}$

B) ${{S}^{2-}}$

C) $SO_{4}^{2-}$

D) $C{{l}^{-}}$

• question_answer52) The copolymer formed by addition polymerization of styrene and acrylonitrile in the presence of peroxide is? [JEE Online 15-04-2018]

A)

B)

C)

D)

• question_answer53) For $N{{a}^{+}},M{{g}^{2+}},{{F}^{-}}$ and ${{O}^{2-}}$; the correct order of increasing ionic radii is? [JEE Online 15-04-2018]

A) ${{O}^{2-}}<{{F}^{-}}<N{{a}^{+}}<M{{g}^{2+}}$

B) $M{{g}^{2+}}<N{{a}^{+}}<{{F}^{-}}<{{O}^{2-}}$

C) $M{{g}^{2+}}<{{O}^{2-}}<N{{a}^{+}}<{{F}^{-}}$

D) $N{{a}^{+}}<M{{g}^{2+}}<{{F}^{-}}<{{O}^{2-}}$

• question_answer54) In which of the following reactions, an increase in the volume of the container will favour the formation of products? [JEE Online 15-04-2018]

A) $4N{{H}_{3}}(g)+5{{O}_{2}}(g)4NO(g)+6{{H}_{2}}O(l)$

B) $2N{{O}_{2}}(g)2NO(g)+{{O}_{2}}(g)$

C) ${{H}_{2}}(g)+{{I}_{2}}(g)2Hl(g)$

D) $3{{O}_{2}}(g)2{{O}_{3}}(g)$

• question_answer55) Which of the following will not exist in zwitter ionic form at $\text{pH=7}$? [JEE Online 15-04-2018]

A)

B)

C)

D)

• question_answer56) The reagent(s) required for the following conversion are __________. [JEE Online 15-04-2018]

A) (i) $\text{NaB}{{\text{H}}_{4}}$, (ii) Raney$Ni/{{H}_{2}}$ (iii) ${{H}_{3}}{{O}^{+}}$

B) (i) ${{B}_{2}}{{H}_{6}}$ (ii) $SnC{{l}_{2}}/HCl$ (iii)${{H}_{3}}{{O}^{+}}$

C) (i) $LiAl{{H}_{4}}$ (ii) ${{H}_{3}}{{O}^{+}}$

D) (i) ${{B}_{2}}{{H}_{6}}$ (ii) $\text{DIBAL-H}$ (iii)${{\text{H}}_{3}}{{O}^{+}}$

• question_answer57) The correct match between items of List-I and List-II is? [JEE Online 15-04-2018]

 List-I List-II (A) Coloured impurity (P) Steam distillation (B) Mixture of O-nitrophenol and p-nitrophenol (Q) Fractical distillation (C) Crude Naphtha (R) Charcoal treatment (D) Mixture of glycerol and sugars (S) Distillation under reduced pressure.

A) (A)-(R), (B)-(S), (C)-(P), (D)-(Q)

B) (A)-(R), (B)-(P), (C)-(S), (D)-(Q)

C) (A)-(P), (B)-(S), (C)-(R), (D)-(Q)

D) (A)-(R), (B)-(P), (C)-(Q), (D)-(S)

• question_answer58) Which of the following is a Lewis acid? [JEE Online 15-04-2018]

A) $B{{(C{{H}_{3}})}_{3}}$

B) $NaH$

C) $N{{F}_{3}}$

D) $P{{H}_{3}}$

• question_answer59) The main reduction product of the following compound with $NaB{{H}_{4}}$ in methanol is? [JEE Online 15-04-2018]

A)

B)

C)

D)

• question_answer60) Which of the following arrangements shows the schematic alignment of magnetic moments of antiferromagnetic substance? [JEE Online 15-04-2018]

A) $\uparrow \bigcirc \uparrow \bigcirc \uparrow \bigcirc \uparrow \bigcirc \uparrow \bigcirc \uparrow \bigcirc$

B) $\uparrow \bigcirc \uparrow \bigcirc \downarrow \bigcirc \uparrow \bigcirc \uparrow \bigcirc \downarrow \bigcirc$

C) $\uparrow \bigcirc \downarrow \bigcirc \downarrow \bigcirc \downarrow \bigcirc \downarrow \bigcirc \uparrow \bigcirc$

D) $\uparrow \bigcirc \downarrow \bigcirc \uparrow \bigcirc \downarrow \bigcirc \uparrow \bigcirc \downarrow \bigcirc$

• question_answer61) In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are $x+y=5$and$x=4$ respectively, Then area of $\Delta ABC$ (in sq. units) is [JEE Online 15-04-2018]

A) 5

B) 9

C) 12

D) 4

• question_answer62) If $b$ is the first term of an infinite G.P. whose sum is five, then $b$ lies in the interval. [JEE Online 15-04-2018]

A) $(-\infty ,-10]$

B) $(10,\infty )$

C) $(0,10)$

D) $(-10,0)$

• question_answer63) A variable plane passes through a fixed point $(3,2,1)$ and meets $x,y$ and $z$ axes at A, B and C respectively. A plane is drawn parallel to $yz-plane$ through $A$, a second plane is drawn parallel $zx-plane$ through $B$ and a third plane is drawn parallel to $xy-plane$ through C. Then the locus of the point of intersection of these three planes, is [JEE Online 15-04-2018]

A) $x+y+z=6$

B) $\frac{x}{3}+\frac{y}{2}+\frac{z}{1}=1$

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

D) $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{11}{6}$

• question_answer64) If $f\left( \frac{x-4}{x+2} \right)=2x+1,(x\in R=\{1,-2\})$, $\int_{{}}^{{}}{f(x)dx}$ is equal to (where C is a constant of integration) [JEE Online 15-04-2018]

A) $12{{\log }_{e}}|1-x|-3x+c$

B) $-12{{\log }_{e}}|1-x|-3x+c$

C) $-12{{\log }_{e}}|1-x|+3x+c$

D) $12{{\log }_{e}}|1-x|+3x+c$

• question_answer65) If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation, ${{x}^{2}}+(2-\lambda )x+(10-\lambda )=0$ is minimum, then the magnitude of the difference of the roots of this equation is [JEE Online 15-04-2018]

A) $20$

B) $2\sqrt{5}$

C) $2\sqrt{7}$

D) $4\sqrt{2}$

• question_answer66) Consider the following two binary relations on the set $\text{A=}\left\{ \text{a,b,c} \right\}\text{:}{{\text{R}}_{\text{1}}}\text{=}\left\{ \left( \text{c,a} \right)\text{,}\left( \text{b,b} \right)\text{,}\left( \text{a,c} \right)\text{,}\left( \text{c,c} \right)\text{,}\left( \text{b,c} \right)\text{,}\left( \text{a,a} \right) \right\}$ and $R2=\left\{ \left( a,b \right),\left( b,a \right),\left( c,c \right),\left( c,a \right),\left( a,a \right),\left( b,b \right),\left( a,c \right) \right\}$ Then [JEE Online 15-04-2018]

A) ${{R}_{2}}$ is symmetric but it is not transitive

B) Both ${{R}_{1}}$ and ${{R}_{2}}$ are transitive

C) Both ${{R}_{1}}$ and ${{R}_{2}}$ are not symmetric

D) ${{R}_{1}}$ is not symmetric but it is transitive

• question_answer67) If ${{x}^{2}}+{{y}^{2}}+\sin y=4$, then the value of $\frac{{{d}^{2}}y}{d{{x}^{2}}}$ at the point $(-2,0)$ is [JEE Online 15-04-2018]

A) $-34$

B) $-32$

C) $-2$

D) $4$

• question_answer68) A circle passes through the points $(2,3)$ and $(4,5)$. If its centre lies on the line, $y-4x+3=0$, then its radius is equal to [JEE Online 15-04-2018]

A) $\sqrt{5}$

B) $1$

C) $\sqrt{2}$

D) $2$

• question_answer69) If the tangents drawn to the hyperbola $4{{y}^{2}}={{x}^{2}}+1$ intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid-point of AB is [JEE Online 15-04-2018]

A) ${{x}^{2}}-4{{y}^{2}}+16{{x}^{2}}{{y}^{2}}=0$

B) $4{{x}^{2}}-{{y}^{2}}+16{{x}^{2}}{{y}^{2}}=0$

C) $4{{x}^{2}}-{{y}^{2}}-16{{x}^{2}}{{y}^{2}}=0$

D) ${{x}^{2}}-4{{y}^{2}}-16{{x}^{2}}{{y}^{2}}=0$

• question_answer70) Let A be a matrix such that $A.\left[ \begin{matrix} 1 & 2 \\ 0 & 3 \\ \end{matrix} \right]$is a scalar matrix and $|3A|=108$. Then ${{A}^{2}}$ equals. [JEE Online 15-04-2018]

A) $\left[ \begin{matrix} 4 & -32 \\ 0 & 36 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 4 & 0 \\ -32 & 36 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 36 & 0 \\ -32 & 4 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 36 & -32 \\ 0 & 4 \\ \end{matrix} \right]$

• question_answer71) If $f(x)=\left| \begin{matrix} \cos x & x & 1 \\ 2\sin x & {{x}^{2}} & 2x \\ \tan x & x & 1 \\ \end{matrix} \right|,then\underset{x\to 0}{\mathop{\lim }}\,\frac{f'(x)}{x}$, [JEE Online 15-04-2018]

A) Exists and is equal to -2

B) Does not exist

C) Exist and is equal to 0

D) Exists and is equal to 2

• question_answer72) If ${{x}_{1}},{{x}_{2}},......,{{x}_{n}}$ and $\frac{1}{{{h}_{1}}},\frac{1}{{{h}_{2}}},.....,\frac{1}{{{h}_{n}}}$ are two A.P.s such that ${{x}_{3}}={{h}_{2}}=8$ and ${{x}_{8}}={{h}_{7}}=20$, then ${{x}_{5}}\cdot {{h}_{10}}$ equals. [JEE Online 15-04-2018]

A) 2560

B) 2650

C) 3200

D) 1600

• question_answer73) The mean of a set of 30 observations is 75. If each other observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by 25, their mean remains the same. The $\lambda$ is equal to [JEE Online 15-04-2018]

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

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

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

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

• question_answer74) If $n$ is the degree of the polynomial, ${{\left[ \frac{1}{\sqrt{5{{x}^{3}}+1}-\sqrt{5{{x}^{3}}-1}} \right]}^{8}}+{{\left[ \frac{1}{\sqrt{5{{x}^{3}}+1}+\sqrt{5{{x}^{3}}-1}} \right]}^{8}}$and $m$ is the coefficient of ${{x}^{n}}$ in it, then the ordered pair $(n,m)$ is equal to [JEE Online 15-04-2018]

A) $(12,{{(20)}^{4}})$

B) $(8,5{{(10)}^{4}})$

C) $(24,{{(10)}^{8}})$

D) $(12,8{{(10)}^{4}})$

• question_answer75) Let $S$ be the set of all real values of $k$ for which the system of linear equations $x+y+z=2$ $2x+y-z=3$ $3x+2y+kz=4$ has a unique solution. Then S is [JEE Online 15-04-2018]

A) An empty set

B) Equal to $R-\{0\}$

C) Equal to $\{0\}$

D) Equal to $R$

• question_answer76) The value of the integral $\int_{-\frac{\pi }{2}}^{\frac{x}{2}}{{{\sin }^{4}}\left( 1+\log \left( \frac{2+\sin x}{2-\sin x} \right) \right)dx}$is [JEE Online 15-04-2018]

A) $\frac{3}{16}\pi$

B) 0

C) $\frac{3}{8}\pi$

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

• question_answer77) An angle between the plane, $x+y+z=5$ and the line of intersection of the planes, $3x+4y+z-1=0$ and $5x+8y+2z+14=0$, is [JEE Online 15-04-2018]

A) ${{\cos }^{-1}}\left( \frac{3}{\sqrt{17}} \right)$

B) ${{\cos }^{-1}}\left( \sqrt{\frac{3}{17}} \right)$

C) ${{\sin }^{-1}}\left( \frac{3}{\sqrt{17}} \right)$

D) ${{\sin }^{-1}}\left( \sqrt{\frac{3}{17}} \right)$

• question_answer78) If a right circular cone, having maximum volume, is inscribed in a sphere of radius $3cm$, then the curved surface area $(in\,\,c{{m}^{2}})$of this cone is [JEE Online 15-04-2018]

A) $8\sqrt{3}\pi$

B) $6\sqrt{2}\pi$

C) $6\sqrt{3}\pi$

D) $8\sqrt{2}\pi$

• question_answer79) If $\tan A$ and $\tan B$ are the roots of the quadratic equation, $3{{x}^{2}}-10x-25=0$ then the value of $3{{\sin }^{2}}(A+B)-10\sin (A+B).\cos (A+B)-25{{\cos }^{2}}(A+B)$ is [JEE Online 15-04-2018]

A) 25

B) -25

C) -10

D) 10

• question_answer80) Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is? [JEE Online 15-04-2018]

A) $3(x+y)+4=0$

B) $8(2x+y)+3=0$

C) $4(x+y)+3=0$

D) $x+2y+3=0$

• question_answer81) Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}+2y=f(x)$, where $f(x)=\left\{ \begin{matrix} 1, & x\in [0,1] \\ 0, & otherwise \\ \end{matrix} \right.$ If $\text{y(0)=0,then}\,\,\,\text{y}\,\,\left( \frac{\text{3}}{\text{2}} \right)\text{is}$ [JEE Online 15-04-2018]

A) $\frac{{{e}^{2}}-1}{2{{e}^{3}}}$

B) $\frac{{{e}^{2}}-1}{{{e}^{3}}}$

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

D) $\frac{{{e}^{2}}+1}{2{{e}^{4}}}$

• question_answer82) The area (in sq. units) of the region $\left\{ x\in R:x\ge 0,y\ge 0,y\ge x-2\,\,\,and\,\,\,y\le \sqrt{x} \right\}$, is [JEE Online 15-04-2018]

A) $\frac{13}{3}$

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

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

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

• question_answer83) If $\beta$ is one of the angles between the normal to the ellipse, ${{x}^{2}}+3{{y}^{2}}=9$ at the points $(3\cos \theta ,\sqrt{3}\sin \theta )$ and $(-3\sin \theta ,\sqrt{3}\cos \theta );\theta \in \left( 0,\frac{\pi }{2} \right);$ then $\frac{2\cot \beta }{\sin 2\theta }$is equal to [JEE Online 15-04-2018]

A) $\sqrt{2}$

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

C) $\frac{1}{\sqrt{3}}$

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

• question_answer84) If $(p\wedge \tilde{\ }q)\wedge (p\wedge r)\to \tilde{\ }p\vee q$ is false, m then the truth values of $p,q$ and $r$ are, respectively. [JEE Online 15-04-2018]

A) F, T, F

B) T, F, T

C) F, F, F

D) T, T, T

• question_answer85) The set of all $\alpha \in R$, for which $w=\frac{1+(1-8\alpha )z}{1-z}$ is a purely imaginary number, for all $z\in C$ satisfying $|z|=1$ and $\operatorname{Re}z\ne 1$, is [JEE Online 15-04-2018]

A) $\{0\}$

B) an empty set

C) $\left\{ 0,\frac{1}{4},-\frac{1}{4} \right\}$

D) equal to R

• question_answer86) If $\overrightarrow{a},\overrightarrow{b}$, and $\overrightarrow{c}$ are unit vectors such that $\overrightarrow{a}+2\overrightarrow{b}+2\overrightarrow{c}=\overrightarrow{0}$, the $|\overrightarrow{a}\times \overrightarrow{c}|$ is equal to [JEE Online 15-04-2018]

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

B) $\frac{\sqrt{15}}{4}$

C) $\frac{15}{16}$

D) $\frac{\sqrt{15}}{16}$

• question_answer87) An aeroplane flying at a constant speed, parallel to the horizontal ground, $\sqrt{3}km$ above it, is observed at an elevation of $60{}^\circ$ from a point on the ground. If, after five seconds, its elevation from the same point, is $30{}^\circ$ , then the speed (in km/ hr) of the aeroplane, is [JEE Online 15-04-2018]

A) 1500

B) 750

C) 720

D) 1440

• question_answer88) Let $S=\{(\lambda ,\mu )\in R\times R:f(t)=(|\lambda |{{e}^{|t|}}-\mu ).\sin (2|t|),t\in R$ Is a differentiable function}. Then is a subset of? [JEE Online 15-04-2018]

A) $R\times [0,\infty )$

B) $(-\infty ,0)\times R$

C) $[0,\infty )\times R$

D) $R\times (-\infty ,0)$

• question_answer89) $n-digit$ numbers are formed using only three digits 2, 5 and 7. The smallest value of $n$ for which $900$ such distinct numbers can be formed, is [JEE Online 15-04-2018]

A) 6

B) 8

C) 9

D) 7

• question_answer90) A box $'A'$ contains 2 white, 3 red and 2 black balls. Another box $'B'$ contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ?B? is [JEE Online 15-04-2018]

A) $\frac{7}{16}$

B) $\frac{9}{32}$

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

D) $\frac{9}{16}$