# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 16 April 2018)

### done JEE Main Paper (Held On 16 April 2018) Total Questions - 90

• question_answer1) A charge q is spread uniformly over an insulated loop of radius. If it is rotated with an angular velocity$\omega$ with respect to normal axis then the magnetic moment of the loop is [JEE Main 16-4-2018]

A)
$A\frac{1}{2}q\omega {{r}^{2}}$

B)
$\frac{4}{3}q\omega {{r}^{2}}$

C)
$\frac{3}{2}q\omega {{r}^{2}}$

D)
$q\omega {{r}^{2}}$

• question_answer2) A heating element has a resistance of $100\Omega$at room temperature. When it is connected to a supply of 220V, a steady current of 2A passes in it and temperature is${{500}^{o}}C$more than room temperature. What is the temperature coefficient of resistance of the heating element? [JEE Main 16-4-2018]

A)
$1\times {{10}^{-4}}{{\,}^{o}}{{C}^{-1}}$

B)
$5\times {{10}^{-4}}{{\,}^{o}}{{C}^{-1}}$

C)
$2\times {{10}^{-4}}{{\,}^{o}}{{C}^{-1}}$

D)
$0.5\times {{10}^{-4}}{{\,}^{o}}{{C}^{-1}}$

• question_answer3) Let$\vec{A}=(\hat{i}+\hat{j})$and$\vec{B}=(\hat{i}-\hat{j}).$The magnitude of a coplanar vector$\vec{C}$such that$\vec{A}.\vec{C}=\vec{B}.\vec{C}=\vec{A}.\vec{B},$  is given by [JEE Main 16-4-2018]

A)
$\sqrt{\frac{5}{9}}$

B)
$\sqrt{\frac{10}{9}}$

C)
$\sqrt{\frac{20}{9}}$

D)
$\sqrt{\frac{9}{12}}$

• question_answer4) Two particles of the same mass m are moving  in circular orbits because of force, given by $F(r)=\frac{-16}{r}-{{r}^{3}}$The first particle is at a distance $r=1$and the second, at$r=4.$The best estimate for the ratio of kinetic energies of the first and the second particle is closest to [JEE Main 16-4-2018]

A)
${{10}^{-1}}$

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

C)
$6\times {{10}^{2}}$

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

• question_answer5) At some instant, a radioactive sample${{S}_{1}}$ having an activity$5\mu Ci$ has twice the number of nuclei as another sample${{S}_{2}}$which has an activity of $10\mu Ci.$The half-lives ${{S}_{1}}$of and ${{S}_{2}}$are        [JEE Main 16-4-2018]

A)
10 years and 20 years, respectively

B)
5 years and 20 years, respectively

C)
20 years and 10 years, respectively

D)
20 years and 5 years, respectively

• question_answer6) In a circuit for finding the resistance of a galvanometer by half deflection method, a 6V battery and a high resistance of$11\,k\Omega$ are used. The figure of merit of the galvanometer $60\mu A/division.$In the absence of shunt resistance, the galvanometer produces a deflection of$\theta =9$divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of $\theta /2,$ is closest to  [JEE Main 16-4-2018]

A)
$55\Omega$

B)
$110\Omega$

C)
$220\Omega$

D)
$550\Omega$

• question_answer7) A body of mass starts moving from rest along x-axis so that its velocity varies as$v=a\sqrt{s}$ where is a constant and is the distance covered by the body. The total work done by all the forces acting on the body in the first seconds after the start of the motion is [JEE Main 16-4-2018]

A)
$\frac{1}{8}m{{a}^{4}}{{t}^{2}}$

B)
$4m{{a}^{4}}{{t}^{2}}$

C)
$8m{{a}^{4}}{{t}^{2}}$

D)
$\frac{1}{4}m{{a}^{4}}{{t}^{2}}$

• question_answer8) A thin circular disk is in the$xy$ plane as shown in the figure. The ratio of its moment of inertia about z and z? axes will be [JEE Main 16-4-2018]

A)
$1:2$

B)
$1:4$

C)
$1:3$

D)
$1:5$

• question_answer9) A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let ${{P}_{2}}$be the pressure inside the inner bubble and${{P}_{0}},$the pressure outside the outer bubble. Radius of another bubble with pressure difference ${{P}_{2}}-{{P}_{0}}$ between its inside and outside would be [JEE Main 16-4-2018]

A)
6 cm

B)
12 cm

C)
4.8 cm

D)
2.4 cm

• question_answer10) The de-Broglie wavelength$({{\lambda }_{B}})$associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state$({{\lambda }_{G}})$by [JEE Main 16-4-2018]

A)
${{\lambda }_{B}}={{\lambda }_{G/3}}$

B)
${{\lambda }_{B}}={{\lambda }_{G/2}}$

C)
${{\lambda }_{B}}=2{{\lambda }_{G}}$

D)
${{\lambda }_{B}}=3{{\lambda }_{G}}$

• question_answer11) A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity$\omega ,$the maximum e.m.f. induced in the coil will be [JEE Main 16-4-2018]

A)
$nBA\omega$

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

C)
$3nBA\omega$

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

• question_answer12) Unpolarized light of intensity I is incident on a system of two polarizes, A followed by B. The intensity of emergent light is$I/2.$ If a third polarizer C is placed between A and B, the intensity of emergent light is reduced to I/3. The angle between the polarizers A and C is $\theta .$Then          [JEE Main 16-4-2018]

A)
$\cos \theta ={{\left( \frac{2}{3} \right)}^{1/4}}$

B)
$\cos \theta ={{\left( \frac{1}{3} \right)}^{1/4}}$

C)
$\cos \theta ={{\left( \frac{1}{3} \right)}^{1/2}}$

D)
$\cos \theta ={{\left( \frac{2}{3} \right)}^{1/2}}$

• question_answer13) A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns, giving the output power at 230 V. If the current in the primary of the transformer is 5A, and its efficiency is 90%, the output current would be:      [JEE Main 16-4-2018]

A)
20 A

B)
45 A

C)
45 A

D)
25 A

• question_answer14) The percentage errors in quantities P, Q, R and S are $0.5%,1%,3%$and$1.5%$ respectively in the measurement of a physical quantity.$A=\frac{{{P}^{3}}{{Q}^{2}}}{\sqrt{RS}}.$ The maximum percentage error in the value of will be [JEE Main 16-4-2018]

A)
$8.5%$

B)
$6.0%$

C)
$7.5%$

D)
$6.5%$

• question_answer15) An oscillator of mass M is at rest in its equilibrium position in a potential $V=\frac{1}{2}k{{(x-X)}^{2}}.$A particle of mass comes from right with speed u and collides completely in elastically with and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after collisions is:$(M=10,m=5,u=1,k=1).$[JEE Main 16-4-2018]

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

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

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

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

• question_answer16) Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths${{\lambda }_{N}},{{\lambda }_{A}}$respectively. The ratio $\frac{\lambda N}{\lambda A}$ is closest to [JEE Main 16-4-2018]

A)
${{10}^{-6}}$

B)
10

C)
${{10}^{-1}}$

D)
${{10}^{-10}}$

• question_answer17) The end correction of a resonance column is $1\,cm$If the shortest length resonating with the tuning fork is$10\,cm,$the next resonating length should be          [JEE Main 16-4-2018]

A)
32 cm

B)
40 cm

C)
28 cm

D)
36 cm

• question_answer18)  In the following circuit, the switch S is closed at$t=0$.The charge on the capacitor${{C}_{1}}$as a function of time will be given by $\left( {{C}_{eq}}=\frac{{{C}_{1}}{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}} \right).$  [JEE Main 16-4-2018]

A)
${{C}_{eq}}E[1-\exp (-t/R{{C}_{eq}})]$

B)
${{C}_{1}}E[1-\exp (-tR/{{C}_{1}})]$

C)
${{C}_{2}}E[1-\exp (-t/R{{C}_{2}})]$

D)
${{C}_{eq}}E\exp (-t/R{{C}_{eq}})$

• question_answer19) The relative uncertainty in the period of a satellite orbiting around the earth is ${{10}^{-2}}.$ If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is [JEE Main 16-4-2018]

A)
$3\times {{10}^{-2}}$

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

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

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

• question_answer20) Two moles of helium are mixed with moles of hydrogen. If$\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{3}{2}$ for the mixture, then the value of n is [JEE Main 16-4-2018]

A)
3/2

B)
2

C)
1

D)
3

• question_answer21) A particle executes simple harmonic motion and is located at$x=a,b$and c at times${{t}_{0}},2{{t}_{0}}$ and$3{{t}_{0}}$respectively. The frequency of the oscillation is      [JEE Main 16-4-2018]

A)
$\frac{1}{2\pi {{t}_{0}}}{{\cos }^{-1}}\left( \frac{a+b}{2c} \right)$

B)
$\frac{1}{2\pi {{t}_{0}}}{{\cos }^{-1}}\left( \frac{a+b}{3c} \right)$

C)
$\frac{1}{2\pi {{t}_{0}}}{{\cos }^{-1}}\left( \frac{2a+3c}{b} \right)$

D)
$\frac{1}{2\pi {{t}_{0}}}{{\cos }^{-1}}\left( \frac{a+c}{2b} \right)$

• question_answer22) A galvanometer with its coil resistance $25\Omega$requires a current of 1mA for its full deflection. In order to construct an ammeter to read up to a current of 2A, the approximate value of the shunt resistance should be            [JEE Main 16-4-2018]

A)
$2.5\times {{10}^{-2}}\Omega$

B)
$1.25\times {{10}^{-3}}\Omega$

C)
$2.5\times {{10}^{-3}}\Omega$

D)
$1.25\times {{10}^{-2}}\Omega$

• question_answer23) Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats and frequency $5\,Hz.$ The tension of the string B is slightly increased and the beat frequency is found to decrease by$3\,Hz.$If the frequency of is , the original frequency of A is 425 Hz, the original frequency of B is [JEE Main 16-4-2018]

A)
430 Hz

B)
428 Hz

C)
422 Hz

D)
420 Hz

• question_answer24) Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence. [JEE Main 16-4-2018]

A)
There will be no change in weight anywhere on the earth

B)
Weight of the object, everywhere on the earth, will decrease

C)
Weight of the object, everywhere on the earth, will increase

D)
Except at poles, weight of the object on the earth will decrease

• question_answer25)  In the given circuit, the current through zener diode is:            [JEE Main 16-4-2018]

A)
2.5 mA

B)
3.3 mA

C)
5.5 mA

D)
6.7 mA

• question_answer26) Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameter, and the force between them is F. A third identical conducting sphere C is uncharged. Sphere C is first touched to A then to B, and the removed. As a result, the force between A and B would be equal to [JEE Main 16-4-2018]

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

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

C)
F

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

• question_answer27) A ray of light is incident at an angle of ${{60}^{o}}$on one face of a prism of angle${{30}^{o}}.$The emergent ray of light makes an angle of with incident ray. The angle made by the emergent ray with second face of prism will be:               [JEE Main 16-4-2018]

A)
${{30}^{o}}$

B)
${{90}^{o}}$

C)
${{0}^{o}}$

D)
${{45}^{o}}$

• question_answer28)  One mole of an ideal monoatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by            [JEE Main 16-4-2018]

A)
$\frac{25}{8}\frac{{{P}_{0}}{{V}_{0}}}{R}$

B)
$\frac{25}{4}\frac{{{P}_{0}}{{V}_{0}}}{R}$

C)
$\frac{25}{16}\frac{{{P}_{0}}{{V}_{0}}}{R}$

D)
$\frac{5}{8}\frac{{{P}_{0}}{{V}_{0}}}{R}$

• question_answer29) A carrier wave of peak voltage 14 V is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of 80% will be: [JEE Main 16-4-2018]

A)
11.2 V

B)
7 V

C)
22.4 V

D)
28 V

• question_answer30) A plane electromagnetic wave of wavelength$\lambda$ has an intensity $I.$ It is propagating along the positive$Y-direction.$ The allowed expressions for the electric and magnetic fields are given by [JEE Main 16-4-2018]

A)
$\vec{E}=\sqrt{\frac{I}{{{\varepsilon }_{0}}C}}\cos \left[ \frac{2\pi }{\lambda }(y-ct) \right]\hat{i};\vec{B}=\frac{1}{c}E\hat{k}$

B)
$\vec{E}=\sqrt{\frac{I}{{{\varepsilon }_{0}}C}}\cos \left[ \frac{2\pi }{\lambda }(y-ct) \right]\hat{k};\vec{B}=-\frac{1}{c}E\hat{i}$

C)
$\vec{E}=\sqrt{\frac{2I}{{{\varepsilon }_{0}}C}}\cos \left[ \frac{2\pi }{\lambda }(y-ct) \right]\hat{k};\vec{B}=+\frac{1}{c}E\hat{i}$

D)
$\vec{E}=\sqrt{\frac{2I}{{{\varepsilon }_{0}}C}}\cos \left[ \frac{2\pi }{\lambda }(y+ct) \right]\hat{k};\vec{B}=\frac{1}{c}E\hat{i}$

• question_answer31)  Products A and B formed in the following reactions are respectively: [JEE Main 16-4-2018]

A)

B)

C)

D)

• question_answer32) Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is: (Atomic wt. of$Cl=35.5u$) [JEE Main 16-4-2018]

A)
16.4

B)
1.46

C)
0.64

D)
0.46

• question_answer33) In Wilkinson's catalyst, the hybridization of central metal ion and its shape are respectively are [JEE Main 16-4-2018]

A)
$s{{p}^{3}}d$A trigonal bipyramidal

B)
${{d}^{2}}s{{p}^{3}},$octahedral

C)
$ds{{p}^{2}},$square planar

D)
$s{{p}^{3}},$tetrahedral

• question_answer34) The major product of the following reaction is:                        [JEE Main 16-4-2018]

A)

B)

C)

D)

• question_answer35) At 320K, a gas${{A}_{2}}$ is 20% dissociated to$A(g).$The standard free energy change at 320K and  1 atm in $J\,mo{{l}^{-1}}$approximately:  $(R=8.314\,J{{K}^{-1}}\,mo{{l}^{-1}};\ln \,2=0.693;\,\ln \,3=1.098)$[JEE Main 16-4-2018]

A)
4763

B)
2068

C)
4281

D)
1844

• question_answer36)                                                   An unknown chlorohydrocarbon has 3.55 % of chlorine. If each molecule of the hydrocarbon has one chlorine atom only; chlorine atoms present in 1g of chlorohydrocarbon are: (Atomic wt. of$Cl=35.5u$); Avogadro constant$=6.023\times {{10}^{23}}mo{{l}^{-1}}$)[JEE Main 16-4-2018]

A)
$6.023\times {{10}^{23}}$

B)
$6.023\times {{10}^{21}}$

C)
$6.023\times {{10}^{9}}$

D)
$6.023\times {{10}^{20}}$

• question_answer37) When$X{{O}_{2}}$is fused with an alkali metal hydroxide in presence of an oxidizing agent such as$KN{{O}_{3}};$ a dark green product is formed which disproportionaltes= in acidic solution to afford a dark purple solution X is: [JEE Main 16-4-2018]

A)
Cr

B)
V

C)
Ti

D)
Mn

• question_answer38) Which of the following compounds will most readily be dehydrated to give alkene under acidic condition? [JEE Main 16-4-2018]

A)
2-Hydroxycyclopentanone

B)
1-Pentanol

C)
3-Hydroxypentan-2-one

D)
4-Hydroxypentan-2-one

• question_answer39) In a complexpmetric tritration of metal ion with ligand$M(Metal\,ion)+L(Ligand)\to C(Complex)$end point is estimated spectrophoto-metrically (through light absorption). If 'M' and 'C' do not absorb light and only 'L' absorbs, then the titration plot between absorbed light  versus volume of ligand ' L' (V would like: [JEE Main 16-4-2018]

A)

B)

C)

D)

• question_answer40) Among the following, the incorrect statement is:                      [JEE Main 16-4-2018]

A)
Cellulose and amylose has 1,4-glycosidic linkage

B)
Maltose and lactose has 1,4-glycosidic linkage

C)
Lactose contains $\beta -D-$galactose and -$\beta -D-$ glocose

D)
D Sucrose and amylose has 1,2-glycosidic linkages

• question_answer41) Among the oxides of nitrogen: ${{N}_{2}}{{O}_{3}},{{N}_{2}}{{O}_{4}}$and ${{N}_{2}}{{O}_{5}};$the molecule(s) having nitrogen-nitrogen bond is/are: [JEE Main 16-4-2018]

A)
Only ${{N}_{2}}{{O}_{5}}$

B)
${{N}_{2}}{{O}_{3}}$and${{N}_{2}}{{O}_{4}}$

C)
${{N}_{2}}{{O}_{3}}$and${{N}_{2}}{{O}_{5}}$

D)
${{N}_{2}}{{O}_{4}}$and${{N}_{2}}{{O}_{5}}$

• question_answer42) Which of the following complexes will show geometrical isomerism?

A)
potassium amminetrichloroplatinate (II)

B)
potassium tris(oxalato) chormate (III)

C)
aquachlorobis (ethylenediamine) cobalt (II) chloride

D)
pentaquachlorochromium (III) chloride

• question_answer43)   The major product B formed in the following reaction sequence is:  [JEE Main 16-4-2018]

A)

B)

C)

D)

• question_answer44) The incorrect geometry is represented by _________. [JEE Main 16-4-2018]

A)
$N{{F}_{3}}-$ trigonal planar

B)
${{H}_{2}}O-$ bent

C)
$As{{F}_{5}}-$trigonal bipyramidal

D)
$B{{F}_{3}}-$ trigonal planar

• question_answer45) The correct match between items of List- I and List- II is:                    [JEE Main 16-4-2018]  List I List 11 [A] Ptienelrine (P) Pyrimldine [B] Cnlorwylenol (Q) Furan [C] Uracll (R) Hydrazlne [D] Rantltidlne (S) Phenol

A)
- (S);  - (R) ;  - (P); -(Q)

B)
- (R);  - (S); - (P); -(Q)

C)
C  - (R) ;  - (S) ;  - (Q); -(P)

D)
- (S);  - (R); - (Q); -(P)

• question_answer46) A group 13 element X reacts with chlorine gas to produce a compound$XC{{l}_{3}}.XC{{l}_{3}}$is electron deficient and easily reacts with$N{{H}_{3}}$ to form$C{{l}_{3}}X\to N{{H}_{3}}$adduct; however, $XC{{l}_{3}}$does not dimerize. X is: [JEE Main 16-4-2018]

A)
B

B)
Al

C)
Ga

D)
In

• question_answer47) The major product of the given reaction is: [JEE Main 16-4-2018]

A)

B)

C)

D)

• question_answer48) Which one of the following is not a property of physical adsorption?

A)
Lower the temperature, more the adsorption

B)
Greater the surface area, more the adsorption

C)
Higher the pressure, more the adsorption

D)

• question_answer49) Which of the following conversions involves change in both shape and hybridisation? [JEE Main 16-4-2018]

A)
$C{{H}_{4}}\to {{C}_{2}}{{H}_{6}}$

B)
$N{{H}_{3}}\to NH_{4}^{+}$

C)
${{H}_{2}}O\to {{H}_{3}}{{O}^{+}}$

D)
$B{{F}_{3}}\to BF_{4}^{-}$

• question_answer50) If 50 % of a reaction occurs in 100 second and 75% of the reaction occurs in 200 second, the order of this reaction is: [JEE Main 16-4-2018]

A)
1

B)
Zero

C)
2

D)
3

• question_answer51) When 9.65 ampere current was passed for 1.0 hour into nitrobenzene in acidic medium, the amount of p-aminophenol produced is _______.    [JEE Main 16-4-2018]

A)
$10.9g$

B)
$109.0g$

C)
$9.81g$

D)
98.1 g

• question_answer52) The incorrect statement out of the following is ______________.

A)
A Ferric ion gives blood red colour with potassium thirocyanate

B)
$c{{u}^{2+}}$salts give red coloured borax bead test in reducing flame.

C)
$c{{u}^{2+}}$ion gives chocolate coloured precipitate with potassium ferrocyanide solution

D)
$C{{u}^{2+}}$and$N{{i}^{2+}}$ ions give black precipitate with in presence of solution

• question_answer53) The gas phase reaction $2N{{O}_{2}}(g)\to {{N}_{2}}{{O}_{4}}(g)$is an exothermic reaction. The decomposition of${{N}_{2}}{{O}_{4}},$ in equilibrium mixture of $N{{O}_{2}}(g)$and ${{N}_{2}}{{O}_{4}}(g),$can be increased by: [JEE Main 16-4-2018]

A)
A increasing the pressure

B)
addition of an inert gas at constant pressure

C)
lowering the temperature

D)
addition of an inert gas at constant volume

• question_answer54) The most polar compound among the following is:      [JEE Main 16-4-2018]

A)

B)

C)

D)

• question_answer55) The major product of the following reaction is:                        [JEE Main 16-4-2018]

A)

B)

C)

D)

• question_answer56) In the extraction of copper from its sulphide ore, metal is finally obtained by the oxidation of cuprous sulphide with: [JEE Main 16-4-2018]

A)
$S{{O}_{2}}$

B)
$F{{e}_{2}}S{{O}_{3}}$

C)
$C{{u}_{2}}O$

D)
CO

• question_answer57) Which of the following statements is false? [JEE Main 16-4-2018]

A)
A Photon has momentum as well as wavelength

B)
Frequency of emitted radiation from a lower wavelength to higher wavelength as the temperature increases

C)
Rydberg constant has unit of energy

D)
Splitting of spectral lines an electrical field is called Stark effect

• question_answer58) The mass of non-volatile, non-elctrolyte solute (molar mass$50gmo{{l}^{-1}}$) needed to be dissolved in114g octane to reduce its vapour pressure to 75%, is ___________. [JEE Main 16-4-2018]

A)
150g

B)
75g

C)
37.5g

D)
50g

• question_answer59) For which of the following processes,$\Delta S$is negative?      [JEE Main 16-4-2018]

A)
${{N}_{2}}(g,273K)\to {{N}_{2}}(g,300K)$

B)
${{N}_{2}}(g,1atm)\to {{N}_{2}}(g,5atm)$

C)
$C(diamond)\to C(graphite)$

D)
${{H}_{2}}(g)\to 2H(g)$

• question_answer60) For standardizing NaOH solution, which of the following is used as a primary standard? [JEE Main 16-4-2018]

A)
Ferrous Ammonium Sulfate

B)
Oxalic acid

C)
Sodium tetraborate

D)
dil. HCl

• question_answer61) Let $A=\left[ \begin{matrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \\ \end{matrix} \right]$and $B={{A}^{20}}.$Then the sum of the elements of the first column of B is? [JEE Main 16-4-2018]

A)
211

B)
210

C)
231

D)
251

• question_answer62) A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min, for the angle of depression of the car to change from ${{30}^{o}}$to${{45}^{o}};$  then after this, the time taken (in min) by the car to reach the foot of the tower, is? [JEE Main 16-4-2018]

A)
$9(1+\sqrt{3})$

B)
$\frac{9}{2}(1\sqrt{3}-1)$

C)
$18(1+\sqrt{3})$

D)
$18(\sqrt{3}-1)$

• question_answer63) Let$\frac{1}{{{x}_{1}}},\frac{1}{{{x}_{2}}},....,\frac{1}{{{x}_{n}}}({{x}_{i}}\ne 0for\,i=1,2,...,n)$be in A.P. such that${{x}_{1}}=4$and${{x}_{21}}=20.$If n is the least positive integer for which,${{x}_{n}}>50,$ then $\sum\limits_{i=1}^{n}{\left( \frac{1}{{{x}_{i}}} \right)}$is equal to. [JEE Main 16-4-2018]

A)
3

B)
$\frac{13}{8}$

C)
$\frac{13}{4}$

D)
$\frac{1}{8}$

• question_answer64) The locus of the point of intersection of the lines,$\sqrt{2x}-y+4\sqrt{2k}=0$and $\sqrt{2}kx+ky-4\sqrt{2}=0$(k is any non-zero real parameter), is?     [JEE Main 16-4-2018]

A)
A hyperbola with length of its transeverse axis$8\sqrt{2}$

B)
An ellipse with length of its major axis $8\sqrt{2}$

C)
An ellipse whose eccentricity is $\frac{1}{\sqrt{3}}$

D)
A hyperbola whose eccentricity is $\sqrt{3}$

• question_answer65) The number of numbers between 2,000 and 5,000 that can be formed with the digits (repetition of digits 0, 1, 2, 3, 4 is not allowed) and are multiple of 3 is? [JEE Main 16-4-2018]

A)
30

B)
48

C)
24

D)
36

• question_answer66) Let p, q, and r be real numbers $(p\ne q,r\ne 0),$ such that the roots of the equation$\frac{1}{x+p}+\frac{1}{x+q}=\frac{1}{r}$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to. [JEE Main 16-4-2018]

A)
${{p}^{2}}+{{q}^{2}}+{{r}^{2}}$

B)
${{p}^{2}}+{{q}^{2}}$

C)
$2({{p}^{2}}+{{q}^{2}})$

D)
$\frac{{{p}^{2}}+{{q}^{2}}}{2}$

• question_answer67) $p\to (\tilde{\ }pV\tilde{\ }q)$is false, then the truth values of p and q are respectively. [JEE Main 16-4-2018]

A)
T, F

B)
F, F

C)
F, T

D)
T, T

• question_answer68) If an angle A of a $\Delta ABC$ satisfies, then the roots of the quadratic$9{{x}^{2}}+27x+20=0$ equation, are. [JEE Main 16-4-2018]

A)
$\sin A,\sec A$

B)
$\sec A,\tan A$

C)
$\tan A,\cos A$

D)
$\operatorname{secA},cotA$

• question_answer69) If $x=\sqrt{{{2}^{\cos e{{c}^{-1}}t}}}$and $y=\sqrt{{{2}^{{{\sec }^{-1t}}}}(|t|\ge 1)},$then $\frac{dy}{dx}$is equal to.    [JEE Main 16-4-2018]

A)
$\frac{y}{x}$

B)
$-\frac{y}{x}$

C)
$-\frac{x}{y}$

D)
$\frac{x}{y}$

• question_answer70) The coefficient of${{x}^{2}}$ in the expansion of the product$(2-{{x}^{2}}).({{(1+2x+3{{x}^{2}})}^{6}}+{{(1-4{{x}^{2}})}^{6}})$ is? [JEE Main 16-4-2018]

A)
106

B)
107

C)
155

D)
108

• question_answer71) The sum of the intercepts on the coordinate axes of the plane passing through the points$(-2,-2,2)$ and containing the line joining the points and is? The differential equation representing the family of ellipse having foci either on the x-axis or on the y-axis, centre at the origin and passing through the points$(1,-1,2)$ and $(1,1,1)$is? [JEE Main 16-4-2018]

A)
12

B)
-8

C)
-4

D)
4

• question_answer72) The differential equation representing the family of ellipse having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point $(0,3)$is?

A)
$xyy'+{{y}^{2}}-9=0$

B)
$x+y{{y}^{''}}=0$

C)
$xyy''+x{{(y')}^{2}}-yy'=0$

D)
$xyy'-{{y}^{2}}+9=0$

• question_answer73) Let A, B and C be three events, which are pair-wise independence and$\bar{E}$denotes the complement of an event E.$P(A\cap B\cap C)=0$and $P(C)>0,$then $P[(\bar{A}\cap \bar{B}|C)]$is equal to [JEE Main 16-4-2018]

A)
$P(A+P(\bar{B})$

B)
$P(\bar{A})-P(\bar{B})$

C)
$P(\bar{A})-P(B)$

D)
$P(\bar{A})+P(\bar{B})$

• question_answer74) The number of values of k for which the system of linear equations, $(k+2)x+10y=k,kx+(k+3)y=k-1$has no solution, is?      [JEE Main 16-4-2018]

A)
Infinitely many

B)
3

C)
1

D)
2

• question_answer75) If the angle between the lines,$\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$and $\frac{5-x}{-2}=\frac{7y-14}{P}=\frac{z-3}{4}$is${{\cos }^{-1}}\left( \frac{2}{3} \right)$, then p is equal to? [JEE Main 16-4-2018]

A)
$-\frac{7}{4}$

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

C)
$-\frac{4}{7}$

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

• question_answer76) Let $\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{c}=\hat{j}-\hat{k}$and a vector $\vec{b}$be such that $\vec{a}\times \vec{b}=\vec{c}$and $\vec{a}.\vec{b}=3.$Then $|\vec{b}|$equals?

A)
$\sqrt{\frac{11}{3}}$

B)
$\sqrt{\frac{11}{3}}$

C)
$\frac{11}{\sqrt{3}}$

D)
$\frac{11}{3}$

• question_answer77) The least positive integer n for which ${{\left( \frac{1+i\sqrt{3}}{1-i\sqrt{3}} \right)}^{n}}=1,$is?  [JEE Main 16-4-2018]

A)
2

B)
6

C)
5

D)
3

• question_answer78)                            $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{(27+x)}^{\frac{1}{3}}}-3}{9-{{(27+x)}^{^{\frac{2}{3}}}}}$equals.   [JEE Main 16-4-2018]

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

B)
$\frac{1}{6}$

C)
$-\frac{1}{6}$

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

• question_answer79) If $f(x)=\int_{0}^{x}{t(\sin x-\sin t)}dt$then? [JEE Main 16-4-2018]

A)
$f'''(x)+f'(x)=\cos x-2x\sin x$

B)
$f'''(x)+f''(x)-f'(x)=\cos x$

C)
$f'''(x)-f''(x)=\cos x-2x\sin x$

D)
$f'''(x)+f''(x)=\sin x$

• question_answer80) Let M and m be respectively the absolute maximum and the absolute minimum values of the function,$f(x)=2{{x}^{3}}-9{{x}^{2}}+12x+5$in the interval $[0,3]$. Then$M-m$ is equal to. [JEE Main 16-4-2018]

A)
1

B)
5

C)
4

D)
9

• question_answer81) If a circle C, whose radius is 3, touches externally the circle, ${{x}^{2}}+{{y}^{2}}+2x-4y-4=0$at the point$(2,2)$, then the length of the intercept cut by this circle C, on the x-axis is equal to.     [JEE Main 16-4-2018]

A)
$\sqrt{5}$

B)
$2\sqrt{3}$

C)
$3\sqrt{2}$

D)
$2\sqrt{5}$

• question_answer82) If the area of the region bounded by the curves, $y={{x}^{2}},y=\frac{1}{x}$and the lines$y=0$ and$x=t(t>1)$ is sq. unit, then t is equal to? [JEE Main 16-4-2018]

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

B)
${{e}^{2/3}}$

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

D)
${{e}^{3/2}}$

• question_answer83) Let P be a point on the parabola$,$${{x}^{2}}=4y$.If the distance of P from the centre of the circle, ${{x}^{2}}+{{y}^{2}}+6x+8=0$is minimum, then the equation of the tangent to the parabola at P, is? [JEE Main 16-4-2018]

A)
$x+4y-2=0$

B)
$x+2y=0$

C)
$x+y+1=0$

D)
$x-y+3=0$

• question_answer84) If the function$f$defined as$f(x)=\frac{1}{x}-\frac{k-1}{{{e}^{2x}}-1},$$x\ne 0,$is continuous at $x=0,$then the ordered pair$(k,f(0))$is equal to?                  [JEE Main 16-4-2018]

A)
(3, 1)

B)
(3, 2)

C)
$\left( \frac{1}{3},2 \right)$

D)
(2, 1)

• question_answer85) The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes10, then their s.d. is?        [JEE Main 16-4-2018]

A)
0

B)
4

C)
2

D)
1

• question_answer86) Let N denote the set of all natural numbers. Define two binary relations on N as${{R}_{1}}=\{(x,y)\in N\times N:2x+y=10\}$and${{R}_{2}}=\{(x,y)\in N\times N:x+2y=10\}.$Then. [JEE Main 16-4-2018]

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

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

C)
Range of${{R}_{2}}$ is$\{1,2,3,4\}$

D)
Range of${{R}_{1}}$ is$\{2,4,8\}$

• question_answer87) The sum of the first 20 terms of the series $1+\frac{3}{7}+\frac{7}{4}+\frac{15}{8}+\frac{31}{16}+....$is? [JEE Main 16-4-2018]

A)
$39+\frac{1}{{{2}^{20}}}$

B)
$39+\frac{1}{{{2}^{19}}}$

C)
$39+\frac{1}{{{2}^{20}}}$

D)
$38+\frac{1}{{{2}^{19}}}$

• question_answer88) . If the length of the latus rectum of an ellipse is units and the distance between a focus and its nearest vertex on the major axis is$\frac{3}{2}$ units, then its eccentricity is? [JEE Main 16-4-2018]

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

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

C)
$\frac{1}{9}$

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

• question_answer89) Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is$\frac{1}{12},$ then the number of children in each family is? [JEE Main 16-4-2018]

A)
4

B)
6

C)
3

D)
5

• question_answer90) If $\int_{{}}^{{}}{\frac{\tan x}{1+\tan x+{{\tan }^{2}}x}}dx=x-\frac{K}{\sqrt{A}}{{\tan }^{-1}}\left( \frac{K\tan x+1}{\sqrt{A}} \right)+C,$ (C is a constant of integration), then the ordered pair (K, A) is equal to. [JEE Main 16-4-2018]

A)
(2, 3)

B)
(2, 1)

C)
$(-2,1)$

D)
$(-2,3)$