Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 08 April 2018)

done JEE Main Online Paper (Held On 08 April 2018) Total Questions - 90

• question_answer1) It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is${{\text{P}}_{\text{d}}}$; while for its similar collision with carbon nucleus at rest, fractional loss of energy is${{\text{P}}_{\text{c}}}$. The values of ${{\text{P}}_{\text{d}}}$and ${{\text{P}}_{\text{c}}}$are respectively:  [JEE Main Online 08-04-2018]

A)
$\text{(0, 0)}$

B)
$\text{(0, 1)}$

C)
$\text{(}\cdot 89\text{, }\cdot \text{28)}$

D)
$\text{(}\cdot 28\text{, }\cdot \text{89)}$

• question_answer2) The mass of a hydrogen molecule is$3.32\times {{10}^{-27}}kg$.   If ${{10}^{23}}$ hydrogen molecules strike, per second, a fixed wall of area $\text{2 c}{{\text{m}}^{\text{2}}}$ at an angle of $\text{45 }\!\!{}^\circ\!\!\text{ }$ to the normal, and rebound elastically with a speed of $\text{1}{{\text{0}}^{\text{3}}}\text{ m/s}$, then the pressure on the wall is nearly: [JEE Main Online 08-04-2018]

A)
$\text{2}\text{.35}\times \text{1}{{\text{0}}^{2}}\,\,N/{{m}^{2}}$

B)
$4.70\times {{10}^{2}}\,\,N/{{m}^{2}}$

C)
$2.35\times {{10}^{3}}\,\,N/{{m}^{2}}$

D)
$4.70\times {{10}^{3}}\,\,N/{{m}^{2}}$

• question_answer3) A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $\left( \frac{dr}{r} \right),$is:                   [JEE Main Online 08-04-2018]

A)
$\frac{\text{mg}}{\text{3}\,\,\text{Ka}}$

B)
$\frac{mg}{Ka}$

C)
$\frac{Ka}{mg}$

D)
$\frac{Ka}{3\,\,mg}$

• question_answer4) Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of$10\,\,\Omega$. The internal resistances of the two batteries are $1\,\,\Omega$and $2\,\,\Omega$ respectively. The voltage across the load lies between: [JEE Main Online 08-04-2018]

A)
$\text{11}\text{.4 V and 11}\text{.5 V}$

B)
$\text{11}\text{.7 V and 11}\text{.8 V}$

C)
$\text{11}\text{.6 V and 11}\text{.7 V}$

D)
$\text{11}\text{.5 V and 11}\text{.6 V}$

• question_answer5) A particle is moving in a circular path of radius a under the action of an attractive potential $\text{U=-}\frac{\text{k}}{\text{2}{{\text{r}}^{\text{2}}}}$. Its total energy is:                               [JEE Main Online 08-04-2018]

A)
Zero

B)
$\text{-}\frac{\text{3}}{\text{2}}\frac{\text{k}}{{{\text{a}}^{\text{2}}}}$

C)
$\text{-}\frac{\text{k}}{\text{4 }{{\text{a}}^{\text{2}}}}$

D)
$\frac{k}{2{{a}^{2}}}$

• question_answer6) Two masses ${{m}_{1}}=5kg$ and${{m}_{2}}=10kg$, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of ${{m}_{2}}$ to stop the motion is:              [JEE Main Online 08-04-2018] A)
$\text{43}\text{.3 kg}$

B)
$\text{10}\text{.3 kg}$

C)
$\text{18}\text{.3 kg}$

D)
$\text{27}\text{.3 kg}$

• question_answer7) If the series limit frequency of the Lyman series is${{\text{v}}_{L}},$ then the series limit frequency of the Pfund series is: [JEE Main Online 08-04-2018]

A)
${{v}_{L}}/16$

B)
${{v}_{L}}/25$

C)
$25\,\,{{v}_{L}}$

D)
$16\,\,{{v}_{L}}$

• question_answer8) Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be$\frac{\text{I}}{\text{2}}$. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be$\frac{\text{I}}{8}$. The angle between polarizer A and C is: [JEE Main Online 08-04-2018]

A)
$45{}^\circ$

B)
$60{}^\circ$

C)
$0{}^\circ$

D)
$30{}^\circ$

• question_answer9) An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ${{\lambda }_{n}},\,\,{{\lambda }_{g}}$ be the de Broglie wavelength of the electron in the ${{\text{n}}^{\text{th}}}$  state and the ground state respectively. Let ${{\Lambda }_{n}}$ be the wavelength of the emitted photon in the transition from the ${{n}^{th}}$ state to the ground state. For large n, (A, B are constants)                    [JEE Main Online 08-04-2018]

A)
$\Lambda _{n}^{2}\approx A+B\lambda _{n}^{2}$

B)
$\Lambda _{n}^{2}\approx \lambda$

C)
${{\Lambda }_{n}}\approx A+\frac{B}{\lambda _{n}^{2}}$

D)
${{\Lambda }_{n}}\approx A+B{{\lambda }_{n}}$

• question_answer10) The reading of the ammeter for a silicon diode in the given circuit is:  [JEE Main Online 08-04-2018] A)
11.5 mA

B)
13.5 mA

C)
0

D)
15 mA

• question_answer11) An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii ${{r}_{e}},\,\,{{r}_{p}},\,\,{{r}_{\alpha }}$ respectively in a uniform magnetic field B. The relation between ${{r}_{e}},\,\,{{r}_{p}},\,\,{{r}_{\alpha }}$ is:                 [JEE Main Online 08-04-2018]

A)
${{r}_{e}}<{{r}_{p}}<{{r}_{\alpha }}$

B)
${{r}_{e}}<{{r}_{\alpha }}<{{r}_{p}}$

C)
${{r}_{e}}>{{r}_{p}}={{r}_{\alpha }}$

D)
${{r}_{e}}<{{r}_{p}}={{r}_{\alpha }}$

• question_answer12) A parallel plate capacitor of capacitance $\text{90 pF}$ is connected to a battery of$\text{emf 20 V}$. If a dielectric material of dielectric constant $\text{K=}\frac{5}{3}$is inserted between the plates, the magnitude of the induced charge will be:                  [JEE Main Online 08-04-2018]

A)
$\text{2}\text{.4 n C}$

B)
$\text{0}\text{.9 n C}$

C)
$\text{1}\text{.2 n C}$

D)
$\text{0}\text{.3 n C}$

• question_answer13) For an RLC circuit driven with voltage of amplitude ${{\text{v}}_{m}}$ and frequency ${{\omega }_{0}}\text{=}\frac{\text{1}}{\sqrt{\text{LC}}}$ the current exhibits resonance. The quality factor, Q is given by : [JEE Main Online 08-04-2018]

A)
$\frac{R}{({{\omega }_{o}}C)}$

B)
$\frac{CR}{{{\omega }_{o}}}$

C)
$\frac{{{\omega }_{o}}L}{R}$

D)
$\frac{{{\omega }_{o}}R}{L}$

• question_answer14) A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz? [JEE Main Online 08-04-2018]

A)
$2\times {{10}^{5}}$

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

C)
$2\times {{10}^{3}}$

D)
$2\times {{10}^{4}}$

• question_answer15) A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7\times {{10}^{3}}\text{ }kg/{{m}^{3}}$ and its Youngs modulus is$\text{9}\text{.27}\times \text{1}{{\text{0}}^{\text{10}}}\text{ Pa}$. What will be the fundamental frequency of the longitudinal vibrations?                   [JEE Main Online 08-04-2018]

A)
$10\,\,kHz$

B)
$7.5\,\,kHz$

C)
$5\,\,kHz$

D)
$2.5\,\,kHz$

• question_answer16) Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: [JEE Main Online 08-04-2018] A)
$\frac{\text{73}}{\text{2}}\text{M}{{\text{R}}^{\text{2}}}$

B)
$\frac{\text{181}}{\text{2}}\text{M}{{\text{R}}^{\text{2}}}$

C)
$\frac{\text{19}}{\text{2}}\text{M}{{\text{R}}^{\text{2}}}$

D)
$\frac{\text{55}}{\text{2}}\text{M}{{\text{R}}^{\text{2}}}$

• question_answer17) Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities$\text{+ }\sigma$, $\text{- }\sigma$ and $\text{+ }\sigma$ respectively. The potential of shell B is:            [JEE Main Online 08-04-2018]

A)
$\frac{\sigma }{{{\in }_{\text{O}}}}\left[ \frac{{{b}^{2}}-{{c}^{2}}}{b}+a \right]$

B)
$\frac{\sigma }{{{\in }_{\text{O}}}}\left[ \frac{{{b}^{2}}-{{c}^{2}}}{c}+a \right]$

C)
$\frac{\sigma }{{{\in }_{\text{O}}}}\left[ \frac{{{a}^{2}}-{{b}^{2}}}{a}+c \right]$

D)
$\frac{\sigma }{{{\in }_{\text{O}}}}\left[ \frac{{{a}^{2}}-{{b}^{2}}}{b}+c \right]$

• question_answer18) In a potentiometer experiment, it is found that no current passes that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of$\text{5 }\Omega$, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.            [JEE Main Online 08-04-2018]

A)
$\text{2 }\Omega$

B)
$\text{2}\text{.5 }\Omega$

C)
$\text{1 }\Omega$

D)
$\text{1}\text{.5 }\Omega$

• question_answer19) An EM wave from air enters a medium. The electric fields are${{\overset{\to }{\mathop{\text{E}}}\,}_{1}}={{E}_{01}}\,\,\widehat{x}\cos \left[ 2\pi v\left( \frac{z}{c}-t \right) \right]$ in air and ${{\overset{\to }{\mathop{\text{E}}}\,}_{2}}={{E}_{02}}\,\,\widehat{x}\cos [k(2z-ct)]$ in medium, where the wave number $k$ and frequency $v$ refer to their values in air. The medium is non-magnetic. If ${{\in }_{{{r}_{1}}}}$ and ${{\in }_{{{r}_{2}}}}$refer to relative permittivitys of air and medium respectively, which of the following options is correct?                    [JEE Main Online 08-04-2018]

A)
$\frac{{{\in }_{{{r}_{1}}}}}{{{\in }_{{{r}_{2}}}}}=\frac{1}{4}$

B)
$\frac{{{\in }_{{{r}_{1}}}}}{{{\in }_{{{r}_{2}}}}}=\frac{1}{2}$

C)
$\frac{{{\in }_{{{r}_{1}}}}}{{{\in }_{{{r}_{2}}}}}=4$

D)
$\frac{{{\in }_{{{r}_{1}}}}}{{{\in }_{{{r}_{2}}}}}=2$

• question_answer20) The angular width of the central maximum in a single slit diffraction pattern is $\text{60 }\!\!{}^\circ\!\!\text{ }$. The width of the slit is $\text{1}\,\,\,\mu \text{m}$. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it. Youngs fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)                 [JEE Main Online 08-04-2018]

A)
$75\mu m$

B)
$100\mu m$

C)
$25\mu m$

D)
$50\mu m$

• question_answer21) A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of${{10}^{12}}/\sec$. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avagadro number$\text{=6}\text{.02}\times \text{1}{{\text{0}}^{\text{23}}}\text{ gm mol}{{\text{e}}^{\text{-1}}}$).                  [JEE Main Online 08-04-2018]

A)
$2.2\,\,N/m$

B)
$5.5\,\,N/m$

C)
$6.4\,\,N/m$

D)
$7.1\,\,N/m$

• question_answer22) From a uniform circular disc of radius R and mass 9 M, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is:                     [JEE Main Online 08-04-2018] A)
$\text{10 M}{{\text{R}}^{2}}$

B)
$\frac{37}{9}\text{ M}{{\text{R}}^{2}}$

C)
$\text{4 M}{{\text{R}}^{2}}$

D)
$\frac{40}{9}\text{ M}{{\text{R}}^{2}}$

• question_answer23) In a collinear collision, a particle with an initial speed ${{v}_{o}}$ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles/after collision, is:                 [JEE Main Online 08-04-2018]

A)
$\frac{{{v}_{o}}}{2}$

B)
$\frac{{{v}_{o}}}{\sqrt{2}}$

C)
$\frac{{{v}_{o}}}{4}$

D)
$\sqrt{2}{{v}_{o}}$

• question_answer24) The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is${{B}_{1}}$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is ${{B}_{2}}.$ The ratio $\frac{{{B}_{1}}}{{{B}_{2}}}$ is: [JEE Main Online 08-04-2018]

A)
$\sqrt{2}$

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

C)
2

D)
$\sqrt{3}$

• question_answer25) The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:                   [JEE Main Online 08-04-2018]

A)
$4.5%$

B)
$6%$

C)
$2.5%$

D)
$3.5%$

• question_answer26) On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is$\text{1 k}\Omega$. How much was the resistance on the left slot before interchanging the resistances?                        [JEE Main Online 08-04-2018]

A)
$\text{550 }\Omega$

B)
$\text{910 }\Omega$

C)
$\text{990 }\Omega$

D)
$\text{505 }\Omega$

• question_answer27) In an a.c. circuit, the instantaneous e.m.f. and current are given by$\text{e=100 sin 30 t}$$\text{i=20 sin }\left( 30t-\frac{\pi }{4} \right)$. In one cycle of a.c., the average power consumed by the circuit and the wattles current are, respectively: [JEE Main Online 08-04-2018]

A)
$\frac{50}{\sqrt{2}},0$

B)
$50,\,\,0$

C)
$50,\,\,10$

D)
$\frac{1000}{\sqrt{2}},\,\,10$

• question_answer28) All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up. [JEE Main Online 08-04-2018]

A) B) C) D) • question_answer29) Two moles of an ideal monoatomic gas occupies a volume $V$ at $27{}^\circ C$. The gas expands adiabatically to a volume$\text{2 V}$. Calculate the final temperature of the gas and change in its internal energy. [JEE Main Online 08-04-2018]

A)
$\text{(A) 189 K}\text{(B) -2}\text{.7 kj}$

B)
$\text{(A) 195 K}\text{(B) 2}\text{.7 kj}$

C)
$\text{(A) 189 K}\text{(B) 2}\text{.7 kj}$

D)
$\text{(A) 195 K}\text{(B) -2}\text{.7 kj}$

• question_answer30) A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the ${{\text{n}}^{\text{th}}}$ power of R. If the period of rotation of the particle is T, then: [JEE Main Online 08-04-2018]

A)
$\text{T}\propto {{\text{R}}^{(n+1)/2}}$

B)
$\text{T}\propto {{\text{R}}^{n/2}}$

C)
$\text{T}\propto {{\text{R}}^{3/2}}$ for any $n$

D)
$T\propto {{R}^{\frac{n}{2}+1}}$

• question_answer31) If the tangent at (1, 7) to the curve ${{x}^{2}}=y-6$ touches   the   circle ${{x}^{2}}+{{y}^{2}}+16x+12y+c=0$ then the value of c is: [JEE Main Online 08-04-2018]

A)
85

B)
95

C)
195

D)
185

• question_answer32) If ${{\text{L}}_{\text{1}}}$ is the line of intersection of the planes $2x-2y+3z-2=0,\,\,x-y+z+1=0$ and ${{L}_{2}}$ is the line of intersection of the planes $x+2y-z-3=0,\text{ }3x-y+2z-1=0$, then the distance of the origin from the plane, containing the lines ${{L}_{1}}$ and ${{L}_{2}},$ is: [JEE Main Online 08-04-2018]

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

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

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

D)
$\frac{1}{3\sqrt{2}}$

• question_answer33) If $\alpha ,\,\,\beta \,\,\in \,\,C$ are the distinct roots, of the equation ${{x}^{2}}-x+1=0,$ then ${{\alpha }^{101}}+{{\beta }^{107}}$ is equal to: [JEE Main Online 08-04-2018]

A)
1

B)
2

C)
-1

D)
0

• question_answer34) Tangents are drawn to the hyperbola $4{{x}^{2}}-{{y}^{2}}=36$ at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of $\Delta \text{PTQ}$ is: [JEE Main Online 08-04-2018]

A)
$60\sqrt{3}$

B)
$36\sqrt{5}$

C)
$45\sqrt{5}$

D)
$54\sqrt{3}$

• question_answer35) If the curves ${{y}^{2}}=6x,\,\,9{{x}^{2}}+b{{y}^{2}}=16$ intersect each other at right angles, then the value of b is:                [JEE Main Online 08-04-2018]

A)
4

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

C)
6

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

• question_answer36) If the system of linear equations  $x+ky+3z=0$ $3x+ky-2z=0$ $2x+4y-3z=0$
Has a non-zero solution (x, y, z), then $\frac{xz}{{{y}^{2}}}$ is equal to:    [JEE Main Online 08-04-2018]

A)
$-30$

B)
$30$

C)
$-10$

D)
$10$

• question_answer37) Let $S=\{x\in R:x\ge 0$ and $|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0\}$. Then S: [JEE Main Online 08-04-2018]

A)
contains exactly two elements.

B)
contains exactly four elements.

C)
is an empty set.

D)
contains exactly one element.

• question_answer38) If sum of all the solutions of the equation $8\cos x\cdot \left( \cos \left( \frac{\pi }{6}+x \right)\cdot \cos \left( \frac{\pi }{6}-x \right)-\frac{1}{2} \right)=1$ in $[0,\,\,\pi ]$ is $k\pi ,$ then k is equal to: [JEE Main Online 08-04-2018]

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

B)
$\frac{20}{9}$

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

D)
$\frac{13}{9}$

• question_answer39) A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is: [JEE Main Online 08-04-2018]

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

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

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

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

• question_answer40) Let $f(x)={{x}^{2}}+\frac{1}{{{x}^{2}}}$and $g(x)=x-\frac{1}{x},$$x\in R-\{-1,0,1\}.$ If $h(x)=\frac{f(x)}{g(x)}$, then the local minimum value of $h(x)$ is: [JEE Main Online 08-04-2018]

A)
$-2\sqrt{2}$

B)
$2\sqrt{2}$

C)
3

D)
-3

• question_answer41) Two sets A and B are as under: $A=\{(a,\,\,b)\in R\times R:|a-5|<1$ and $|b-5|<1\};$ $\text{B= }\!\!\{\!\!\text{ (a,}\,\,\text{b)}\in \,\,\text{R}\times \text{R : 4(a-6}{{\text{)}}^{2}}+9{{(b-5)}^{2}}\le 36\}$.Then                  [JEE Main Online 08-04-2018]

A)
$A\cap B=\phi$ (an empty set)

B)
neither $A\subset B$ nor $B\subset A$

C)
$B\subset A$

D)
$A\subset B$

• question_answer42) The Boolean expression$\sim (p\vee q)\vee (\sim p\wedge q)$is equivalent to: [JEE Main Online 08-04-2018]

A)
q

B)
$\tilde{\ }q$

C)
$\tilde{\ }p$

D)
p

• question_answer43) Tangent and normal are drawn at $p(16,16)$on the parabola${{y}^{2}}=16x$, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and $\angle CPB=\theta$, then a value of tan $\theta$is:                        [JEE Main Online 08-04-2018]

A)
3

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

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

D)
2

• question_answer44) If $\left| \begin{matrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \\ \end{matrix} \right|=(A+Bx){{(x-A)}^{2}}$, then the ordered pair (A, B) is equal to: [JEE Main Online 08-04-2018]

A)
$(-4,5)$

B)
$(4,5)$

C)
$(-4,-5)$

D)
$(-4,3)$

• question_answer45) The sum of the co-efficient of all odd degree terms in the expansion of ${{\left( x+\sqrt{{{x}^{3}}-1} \right)}^{5}}+{{\left( x-\sqrt{{{x}^{3}}-1} \right)}^{5}},(x>1)$ is: [JEE Main Online 08-04-2018]

A)
1

B)
2

C)
-1

D)
0

• question_answer46) Let ${{a}_{1}},{{a}_{2}},{{a}_{3}},.....,{{a}_{49}}$ be in A.P. such that $\sum\limits_{k=0}^{12}{{{a}_{4k+1}}}=416$ and ${{a}_{9}}+{{a}_{43}}=66.$ If $a_{1}^{2}+a_{2}^{2}+.......+a_{17}^{2}=140m$, then $m$ is equal to: [JEE Main Online 08-04-2018]

A)
34

B)
33

C)
66

D)
68

• question_answer47) A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is: [JEE Main Online 08-04-2018]

A)
$3x+2y=xy$

B)
$3x+2y=6xy$

C)
$3x+2y=6$

D)
$2x+3y=xy$

• question_answer48) The value of $\int_{-\frac{\pi }{2}}^{\frac{\pi }{2}}{\frac{{{\sin }^{2}}x}{1+{{2}^{x}}}}dx$ is: [JEE Main Online 08-04-2018]

A)
$4\pi$

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

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

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

• question_answer49) Let $g(x)=\cos {{x}^{2}},$ $f(x)=\sqrt{x},$ and $\alpha ,\beta (\alpha <\beta )$ be the roots of the quadratic equation $18{{x}^{2}}-9\pi x+{{\pi }^{2}}=0$. Then the area (in sq. units) bounded by the curve $y=(g\circ f)(x)$ and the lines $x=\alpha ,\,\,x=\beta$ and$y=0$, is: [JEE Main Online 08-04-2018]

A)
$\frac{1}{2}\left( \sqrt{3}-\sqrt{2} \right)$

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

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

D)
$\frac{1}{2}\left( \sqrt{3}+1 \right)$

• question_answer50) For each $t\in \mathbf{R},$ let[t] be the greatest integer less than or equal to t. Then $\underset{x\to 0+}{\mathop{\lim }}\,x\left( \left[ \frac{1}{x} \right]+\left[ \frac{2}{x} \right]+......+\left[ \frac{15}{x} \right] \right)$ [JEE Main Online 08-04-2018]

A)
is equal to 120.

B)
does not exist (in R).

C)
is equal to 0.

D)
is equal to 15.

• question_answer51) If $\sum\limits_{i=1}^{9}{({{x}_{i}}-5)=9}$ and $\sum\limits_{i=1}^{9}{{{({{x}_{i}}-5)}^{2}}=45},$then the standard deviation of the 9 items ${{x}_{1}},{{x}_{2}},.....,{{x}_{9}}$ is: [JEE Main Online 08-04-2018]

A)
2

B)
3

C)
9

D)
4

• question_answer52) The integral $\int_{{}}^{{}}{\frac{{{\sin }^{2}}x{{\cos }^{2}}x}{{{({{\sin }^{5}}x+{{\cos }^{3}}x{{\sin }^{2}}x+{{\sin }^{3}}x{{\cos }^{2}}x+{{\cos }^{5}}x)}^{2}}}dx}$is equal to: [JEE Main Online 08-04-2018]

A)
$\frac{1}{1+{{\cot }^{3}}x}+C$

B)
$\frac{-1}{1+{{\cot }^{3}}x}+C$

C)
$\frac{1}{3(1+{{\tan }^{3}}x)}+C$

D)
$\frac{-1}{3(1+{{\tan }^{3}}x)}+C$ (where C is a constant of integration)

• question_answer53) Let $S=\{t\in \mathbf{R}:f(x)=|x-\pi |\cdot ({{e}^{|x|}}-1)\sin |x|$ is not differentiable at$\text{t }\!\!\}\!\!\text{ }$. Then the set S is equal to:                         [JEE Main Online 08-04-2018]

A)
$\text{ }\!\!\{\!\!\text{ }\pi \text{ }\!\!\}\!\!\text{ }$

B)
$\text{ }\!\!\{\!\!\text{ 0, }\pi \text{ }\!\!\}\!\!\text{ }$

C)
$\phi$(an empty set)

D)
$\{0\}$

• question_answer54) Let $y=y(x)$ be the solution of the differential equation $\sin x\frac{dy}{dx}+y\cos x=4x,\,\,x\in (0,\,\,\pi ).$ If $y\left( \frac{\pi }{2} \right)=0$, then $y\left( \frac{\pi }{6} \right)$ is equal to: [JEE Main Online 08-04-2018]

A)
$-\frac{8}{9}{{\pi }^{2}}$

B)
$-\frac{4}{9}{{\pi }^{2}}$

C)
$-\frac{4}{9\sqrt{3}}{{\pi }^{2}}$

D)
$\frac{-8}{9\sqrt{3}}{{\pi }^{2}}$

• question_answer55) Let $\overset{\to }{\mathop{u}}\,$ be a vector coplanar with the vectors $\overset{\to }{\mathop{a}}\,=2\widehat{i}+3\widehat{j}-\widehat{k}$ and $\overset{\to }{\mathop{b}}\,=\widehat{j}+\widehat{k}.$ If $\overset{\to }{\mathop{u}}\,$ is perpendicular to $\overset{\to }{\mathop{a}}\,$ and $\overset{\to }{\mathop{u}}\,\cdot \overset{\to }{\mathop{b}}\,=24$, then ${{\left| \overset{\to }{\mathop{u}}\, \right|}^{2}}$ is equal to:   [JEE Main Online 08-04-2018]

A)
256

B)
84

C)
336

D)
315

• question_answer56) The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, $x+y+z=7$ is:                                                         [JEE Main Online 08-04-2018]

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

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

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

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

• question_answer57) PQR is a triangular park with PQ=PR=200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R-are respectively $\text{45 }\!\!{}^\circ\!\!\text{ }$ , $\text{30 }\!\!{}^\circ\!\!\text{ }$ and $\text{30 }\!\!{}^\circ\!\!\text{ }$, then the height of the tower (in m) is:                    [JEE Main Online 08-04-2018]

A)
$\text{100}\sqrt{3}$

B)
$50\sqrt{2}$

C)
100

D)
50

• question_answer58) From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is: [JEE Main Online 08-04-2018]

A)
at least 500 but less than 750

B)
at least 750 but less than 1000

C)
at least 1000

D)
less than 500

• question_answer59) Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series${{1}^{2}}+2\cdot {{2}^{2}}+{{3}^{2}}+2\cdot {{4}^{2}}+{{5}^{2}}+2\cdot {{6}^{2}}+......$. If$B-2A=100\lambda$, then $\lambda$ is equal to:                                            [JEE Main Online 08-04-2018]

A)
464

B)
496

C)
232

D)
248

• question_answer60) Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter,  is:   [JEE Main Online 08-04-2018]

A)
$3\sqrt{\frac{5}{2}}$

B)
$\frac{3\sqrt{5}}{2}$

C)
$\sqrt{10}$

D)
$2\sqrt{10}$

• question_answer61) Total number of line pair of electrons in $I_{3}^{-}ion$ is:              [JEE Main Online 08-04-2018]

A)
9

B)
12

C)
3

D)
6

• question_answer62) Which of the following salts is the most basic in aqueous solution?     [JEE Main Online 08-04-2018]

A)
$\text{FeC}{{\text{l}}_{\text{3}}}$

B)
$\text{Pb(C}{{\text{H}}_{\text{3}}}\text{COO}{{\text{)}}_{\text{2}}}$

C)
$\text{Al(CN}{{\text{)}}_{3}}$

D)
$\text{C}{{\text{H}}_{\text{3}}}\text{COOK}$

• question_answer63) Phenol reacts with methyl chloroformate in the presence of NaOH to form product A. A reacts with $\text{B}{{\text{r}}_{2}}$ to form product B. A and B are respectively:[JEE Main Online 08-04-2018]

A) B) C) D) • question_answer64) The increasing order of basicity of a following compounds is:             [JEE Main Online 08-04-2018]  (a) (b) (c) (d) A)
(b)<(a)<(d)<(c)

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

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

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

• question_answer65) An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correct combination?                        [JEE Main Online 08-04-2018]

A)
 Base Acid End point Weak Strong Yellow to pinkish red

B)
 Base Acid End point Strong Strong Pink to colourless

C)
 Base Acid End point Weak Strong Colourless to pink

D)
 Base Acid End point Strong Strong Pinkish red to yellow

• question_answer66) The trans-alkenes are reduction of alkynes with:          [JEE Main Online 08-04-2018]

A)
$Na/liq.N{{H}_{3}}$

B)
$Sn-HCl$

C)
${{H}_{2}}-Pd/C,\,\,BaS{{O}_{4}}$

D)
$NaB{{H}_{4}}$

• question_answer67) The ratio of mass percent of C and H of an organic compound $({{C}_{X}}{{H}_{Y}}{{O}_{Z}})$ is 6 : 1. If one molecule of the above compound $({{C}_{X}}{{H}_{Y}}{{O}_{Z}})$ contains half as much oxygen as required to burn one molecule of compound ${{C}_{X}}{{H}_{Y}}$completely to $C{{O}_{2}}$ and ${{H}_{2}}O$. The empirical formula of compound ${{C}_{X}}{{H}_{Y}}{{O}_{Z}}$ is: [JEE Main Online 08-04-2018]

A)
${{C}_{3}}{{H}_{4}}{{O}_{2}}$

B)
${{C}_{2}}{{H}_{4}}{{O}_{3}}$

C)
${{C}_{3}}{{H}_{6}}{{O}_{3}}$

D)
${{C}_{2}}{{H}_{4}}O$

• question_answer68) Hydrogen peroxide oxidises ${{[Fe{{(CN)}_{6}}]}^{4-}}$ to ${{[Fe{{(CN)}_{6}}]}^{3-}}$  in acidic medium but reduces ${{[Fe{{(CN)}_{6}}]}^{3-}}$ to ${{[Fe{{(CN)}_{6}}]}^{4-}}$ in alkaline medium. The other products formed are, respectively: [JEE Main Online 08-04-2018]

A)
${{\text{H}}_{\text{2}}}\text{O}$ and $\text{(}{{\text{H}}_{2}}O+{{O}_{2}})$

B)
${{\text{H}}_{\text{2}}}\text{O}$ and $\text{(}{{\text{H}}_{\text{2}}}\text{O+O}{{\text{H}}^{\text{-}}}\text{)}$

C)
$\text{(}{{\text{H}}_{\text{2}}}\text{O+}{{\text{O}}_{2}}\text{)}$ and ${{\text{H}}_{\text{2}}}\text{O}$

D)
$\text{(}{{\text{H}}_{\text{2}}}\text{O+}{{\text{O}}_{\text{2}}}\text{)}$ and $\text{(}{{\text{H}}_{\text{2}}}\text{O+O}{{\text{H}}^{\text{-}}}\text{)}$

• question_answer69) The major product formed in the following reaction is:                        [JEE Main Online 08-04-2018] A) B) C) D) • question_answer70) How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66 g of diborane? (Atomic weight of B=10.8 u) [JEE Main Online 08-04-2018]

A)
$\text{3}\text{.2 hours}$

B)
$\text{1}\text{.6 hours}$

C)
$\text{6}\text{.4 hours}$

D)
$\text{0}\text{.8 hours}$

• question_answer71) Which of the following lines correctly show the temperature dependence of equilibrium constant, K, for an exothermic reaction?               [JEE Main Online 08-04-2018] A)
C and D

B)
A and D

C)
A and B

D)
B and C

• question_answer72) At$\text{518 }\!\!{}^\circ\!\!\text{ C}$, die rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 Torr, was 1.00 Torr ${{\text{s}}^{-1}}$ when 5% had reacted and, 0.5 Torr ${{\text{s}}^{-1}}$ when 33% had reacted. The order of me reaction is:   [JEE Main Online 08-04-2018]

A)
1

B)
0

C)
2

D)
3

• question_answer73) Glucose on prolonged heating with HI gives:               [JEE Main Online 08-04-2018]

A)
Hexanoic acid

B)
6-iodohexanal

C)
$n-Hexane$

D)
$1-Hexene$

• question_answer74) Consider the following reaction and statements:                      [JEE Main Online 08-04-2018]  ${{[Co{{(N{{H}_{3}})}_{4}}B{{r}_{2}}]}^{+}}+B{{r}^{-}}\to [Co{{(N{{H}_{3}})}_{3}}B{{r}_{3}}]+N{{H}_{3}}$ (I) Two isomers are produced if the reactant complex ion is a cis-isomer. (II) Two isomers are produced if the reactant complex ion is a trans-isomer. (III) Only one isomer is produced if the reactant complex ion is a trans-isomer. (IV) Only one isomer is produced if the reactant complex ion is a cis-isomer.
The correct statements are:

A)
(III) and (IV)

B)
(II) and (IV)

C)
(I) and (II)

D)
(I) and (III)

• question_answer75) The major product of the following reaction is:                        [JEE Main Online 08-04-2018] A) B) C) D) • question_answer76) Phenol on treatment with $C{{O}_{2}}$ in the presence of $NaOH$ followed by acidification produces compound X as the major product. X on treatment with ${{(C{{H}_{3}}CO)}_{2}}O$ in the presence of catalytic amount of ${{H}_{2}}S{{O}_{4}}$ produces:                            [JEE Main Online 08-04-2018]

A) B) C) D) • question_answer77) An aqueous solution contains an unknown concentration of $\text{B}{{\text{a}}^{\text{2+}}}$. When 50 mL of a 1 M solution of $\text{N}{{\text{a}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$ is added, $\text{BaS}{{\text{O}}_{4}}$ just begins to precipitate. The final volume is 500 mL. The solubility product of $\text{BaS}{{\text{O}}_{4}}$ is$1\times {{10}^{-10}}$.  What is the original concentration of $B{{a}^{2+}}?$    [JEE Main Online 08-04-2018]

A)
$1.1\times {{10}^{-9}}\,\,M$

B)
$1.0\times {{10}^{-10}}\,\,M$

C)
$5\times {{10}^{-9}}\,\,M$

D)
$2\times {{10}^{-9}}\,\,M$

• question_answer78) Which of the following compounds will be suitable for Kjeldahls method for nitrogen estimation? [JEE Main Online 08-04-2018]

A) B) C) D) • question_answer79) When metal M is treated with NaOH, a white gelatinous precipitate X is obtained, which is soluble in excess of $\text{NaOH}$ Compound X when heated strongly gives an oxide which is used in chromatography as an adsorbent. The metal M is:                   [JEE Main Online 08-04-2018]

A)
Al

B)
Fe

C)
Zn

D)
Ca

• question_answer80) An aqueous solution contains 0.10 M ${{\text{H}}_{\text{2}}}\text{S}$ and 0.20 M $\text{HCl}$. If the equilibrium constants for the formation of $\text{H}{{\text{S}}^{-}}$ from ${{\text{H}}_{\text{2}}}\text{S}$ is $\text{1}\text{.0}\times \text{1}{{\text{0}}^{-7}}$ and that of ${{S}^{2-}}$ from  $\text{H}{{\text{S}}^{\text{-}}}$ions is $\text{1}\text{.2}\times \text{1}{{\text{0}}^{-13}}$ then the concentration of ${{S}^{2-}}$ions in aqueous solution is:                       [JEE Main Online 08-04-2018]

A)
$6\times {{10}^{-21}}$

B)
$5\times {{10}^{-19}}$

C)
$5\times {{10}^{-8}}$

D)
$3\times {{10}^{-20}}$

• question_answer81) The recommended concentration of fluoride ion in drinking water is up to 1 ppm as fluoride ion is required to make teeth enamel harder by converting $[3C{{a}_{3}}{{(P{{O}_{4}})}_{2}}\cdot Ca{{(OH)}_{2}}]$ to:  [JEE Main Online 08-04-2018]

A)
$[3C{{a}_{3}}{{(P{{O}_{4}})}_{2}}\cdot Ca{{F}_{2}}]$

B)
$[3\{Ca{{(OH)}_{2}}\}\cdot Ca{{F}_{2}}]$

C)
$[Ca{{F}_{2}}]$

D)
$[3(Ca{{F}_{2}})\cdot Ca{{(OH)}_{2}}]$

• question_answer82) The compound that does not produce nitrogen gas by the thermal decomposition is: [JEE Main Online 08-04-2018]

A)
$\text{N}{{\text{H}}_{\text{4}}}\text{N}{{\text{O}}_{\text{2}}}$

B)
${{\text{(N}{{\text{H}}_{\text{4}}}\text{)}}_{2}}\text{S}{{\text{O}}_{4}}$

C)
$\text{Ba(}{{\text{N}}_{\text{3}}}{{\text{)}}_{\text{2}}}$

D)
${{\text{(N}{{\text{H}}_{\text{4}}}\text{)}}_{\text{2}}}\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}$

• question_answer83) The predominant form of histamine present in human blood is $\text{(p}{{\text{K}}_{a}},\,\,Histidine=6.0)$                         [JEE Main Online 08-04-2018]

A) B) C) D) • question_answer84) The oxidation states of $\text{Cr}$ in $\text{ }\!\![\!\!\text{ Cr(}{{\text{H}}_{\text{2}}}\text{O}{{\text{)}}_{\text{6}}}\text{ }\!\!]\!\!\text{ C}{{\text{l}}_{\text{3}}}$, $\text{ }\!\![\!\!\text{ Cr(}{{\text{C}}_{6}}{{\text{H}}_{6}}{{\text{)}}_{2}}\text{ }\!\!]\!\!\text{ }$, and ${{\text{K}}_{\text{2}}}\text{ }\!\![\!\!\text{ Cr(CN}{{\text{)}}_{\text{2}}}{{\text{(O)}}_{\text{2}}}\text{(}{{\text{O}}_{\text{2}}}\text{)(N}{{\text{H}}_{\text{3}}}\text{) }\!\!]\!\!\text{ }$ Respectively are:                         [JEE Main Online 08-04-2018]

A)
$\text{+3, 0, and +6}$

B)
$\text{+3, 0, and +4}$

C)
$\text{+3, +4 and +6}$

D)
$\text{+3, +2 and +4}$

• question_answer85) Which type of defect has the presence of cations in the interstitial sites? [JEE Main Online 08-04-2018]

A)
Frenkel defect

B)
Metal deficiency defect

C)
Schottky defect

D)
Vacancy defect

• question_answer86) The combustion of benzene (l) gives $\text{C}{{\text{O}}_{2}}(g)$ and${{\text{H}}_{\text{2}}}\text{O(l)}$. Given that heat of combustion of benzene at constant volume is $\text{-3263}\text{.9 kJ mo}{{\text{l}}^{\text{-1}}}$ at $\text{25 }\!\!{}^\circ\!\!\text{ C}$; heat of combustion (in$\text{kJ mo}{{\text{l}}^{\text{-1}}}$) of benzene at constant pressure will be:                       [JEE Main Online 08-04-2018] $\text{(R=8}\text{.314 J}{{\text{K}}^{\text{-1}}}\text{ mo}{{\text{l}}^{\text{-1}}}\text{)}$

A)
3260

B)
-3267.6

C)
4152.6

D)
-452.46

• question_answer87) Which of the following are Lewis acids?                      [JEE Main Online 08-04-2018]

A)
$\text{P}{{\text{H}}_{\text{3 }}}\text{and SiC}{{\text{l}}_{\text{4}}}$

B)
$\text{BC}{{\text{l}}_{3}}$ and $\text{AlC}{{\text{l}}_{\text{3}}}$

C)
$\text{P}{{\text{H}}_{3}}$ and $\text{BC}{{\text{l}}_{\text{3}}}$

D)
$\text{AlC}{{\text{l}}_{3}}$ and $\text{SiC}{{\text{l}}_{\text{4}}}$

• question_answer88) Which of the following compounds contain(s) no/covalent bond(s)? [JEE Main Online 08-04-2018] $\text{KCl, P}{{\text{H}}_{\text{3}}}\text{,}{{\text{O}}_{\text{2}}}\text{,}{{\text{B}}_{\text{2}}}{{\text{H}}_{\text{6}}}\text{,}{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$

A)
KCl

B)
$\text{KCl, }{{\text{B}}_{\text{2}}}{{\text{H}}_{\text{6}}}$

C)
$\text{KCl, }{{\text{B}}_{\text{2}}}{{\text{H}}_{\text{6}}}\text{,}\,\,\text{P}{{\text{H}}_{\text{3}}}$

D)
$\text{KCl, }{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$

• question_answer89) For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point? [JEE Main Online 08-04-2018]

A)
$\text{ }\!\![\!\!\text{ Co(}{{\text{H}}_{\text{2}}}\text{O}{{\text{)}}_{\text{4}}}\text{C}{{\text{l}}_{\text{2}}}\text{ }\!\!]\!\!\text{ Cl}\text{.2}{{\text{H}}_{\text{2}}}\text{O}$

B)
$\text{ }\!\![\!\!\text{ Co(}{{\text{H}}_{\text{2}}}\text{O}{{\text{)}}_{\text{3}}}\text{C}{{\text{l}}_{\text{3}}}\text{ }\!\!]\!\!\text{ }\cdot \text{3}{{\text{H}}_{\text{2}}}\text{O}$

C)
$\text{ }\!\![\!\!\text{ Co(}{{\text{H}}_{\text{2}}}\text{O}{{\text{)}}_{\text{6}}}\text{ }\!\!]\!\!\text{ C}{{\text{l}}_{\text{3}}}$

D)
$\text{ }\!\![\!\!\text{ Co(}{{\text{H}}_{\text{2}}}\text{O}{{\text{)}}_{\text{5}}}\text{Cl }\!\!]\!\!\text{ C}{{\text{l}}_{\text{2}}}\text{.}{{\text{H}}_{\text{2}}}\text{O}$

• question_answer90) According to molecular orbital theory, which of the following will not be a viable molecule? [JEE Main Online 08-04-2018]

A)
$\text{H}_{2}^{-}$

B)
$\text{H}_{2}^{2-}$

C)
$\text{He}_{2}^{2+}$

D)
$\text{He}_{2}^{+}$

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