Solved papers for JEE Main & Advanced JEE Main Solved Paper-2017

JEE Main Solved Paper-2017 Total Questions - 90

1) A particle is executing simple harmonic motion with a time period T. AT time t = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like. JEE Main Solved Paper-2017

A)

B)

C)

D)

View Answer
2) The temperature of an open room of volume \[30{{m}^{3}}\]increases from \[17{{\,}^{o}}C\]to\[27{{\,}^{o}}C\] due to sunshine. The atmospheric pressure in the room remains \[1\times {{10}^{5}}\,Pa.\] If \[{{n}_{i}}\]and \[{{n}_{f}}\] are the number of molecules in the room before and after heating, then \[{{n}_{f}}-{{n}_{i}}\]will be:- JEE Main Solved Paper-2017

A)

\[2.5\times {{10}^{25}}\]

B)

\[-2.5\times {{10}^{25}}\]

C)

\[-1.61\times {{10}^{23}}\]

D)

\[1.38\times {{10}^{23}}\]

View Answer
3) Which of the following statements is false? JEE Main Solved Paper-2017

A)

A rheostat can be used as a potential divider

B)

Kirchhoff's second law represents energy conservation

C)

Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.

D)

In a balanced wheat stone bridge if the cell and the galvanometer are exchanged, the null point is disturbed. [JEE Main 2017]

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4) The following observations were taken for determining surface tensiton T of water by capillary method : Diameter of capilary, \[D=1.25\times {{10}^{-2}}m\] rise of water, \[h=1.45\times {{10}^{-2}}m\]. Using \[g=9.80\,m/{{s}^{2}}\]and the simplified relation\[\text{T=}\frac{\text{rhg}}{\text{2}}\text{ }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{3}}}\,\text{N/m,}\] the possible error in surface tension is closest to: JEE Main Solved Paper-2017

A)

2.4%

B)

10%

C)

0.15%

D)

1.5%

View Answer
5) In amplitude modulation, sinusoidal carrier frequency used is denoted by \[{{\omega }_{c}}\]and the signal frequency is denoted by\[{{\omega }_{m}}.\]The bandwidth \[(\Delta {{\omega }_{m}})\] of the signal is such that\[\Delta {{\omega }_{m}}<<{{\omega }_{c}}.\]Which of the following frequencies is not contained in the modulated wave? JEE Main Solved Paper-2017

A)

\[{{\omega }_{m}}+{{\omega }_{c}}\]

B)

\[{{\omega }_{c}}-{{\omega }_{m}}\]

C)

\[{{\omega }_{m}}\]

D)

\[{{\omega }_{c}}\]

View Answer
6) A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is: JEE Main Solved Paper-2017

A)

real and at a distance of 40 cm from the divergent lens

B)

real and at a distance of 6 cm from the convergent lens

C)

real and at a distance of 40 cm from convergent lens

D)

virtual and at a distance of 40 cm from convergent lens. [JEE Main 2017]

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7) The moment of inertia of a uniform cylinder of length\[\ell \]and radius R about its perpendicular bisector is I. What is the ratio \[\ell /R\]such that the moment of inertia is minimum? JEE Main Solved Paper-2017

A)

1

B)

\[\frac{3}{\sqrt{2}}\]

C)

\[\sqrt{\frac{3}{\sqrt{2}}}\]

D)

\[\frac{\sqrt{3}}{2}\]

View Answer
8) An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If\[{{\lambda }_{\min }}\] is the smallest possible wavelength of X-ray in the spectrum, the variation of \[\log {{\lambda }_{\min }}\] with log V is correctly represented in:    JEE Main Solved Paper-2017

A)



B)

C)



D)

View Answer
9) A radioactive nucleus A with a half-life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by: JEE Main Solved Paper-2017

A)

\[t=T\log (1.3)\]

B)

\[t=\frac{T}{\log (1.3)}\]

C)

\[t=\frac{T\log 2}{2\log 1.3}\]

D)

\[t=T\frac{\log 1.3}{\log 2}\]

View Answer
10) An electric dipole has a fixed dipole moment\[\vec{p},\], which makes angle \[\theta \] with respect to x-axis. When subjected to an electric\[{{\vec{E}}_{1}}=E\hat{i},\] field It experiences a torque \[\vec{T}=\tau \hat{k}.\] When subjected to another electric field \[{{\vec{E}}_{2}}=\sqrt{3}{{E}_{1}}\hat{j}\] it experiences torque\[{{\vec{T}}_{2}}=-{{\vec{T}}_{1}}.\] The angle \[\theta \] is:                             [JEE Main 2017]

A)

\[{{60}^{o}}\]

B)

\[{{90}^{o}}\]

C)

\[{{30}^{o}}\]

D)

\[{{45}^{o}}\]

View Answer
11) In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be: JEE Main Solved Paper-2017

A)

\[{{135}^{o}}\]

B)

\[{{180}^{o}}\]

C)

\[{{45}^{o}}\]

D)

\[{{90}^{o}}\]

View Answer
12) \[{{C}_{p}}\]and\[{{C}_{v}}\]are specific heats at constant pressure and constant volume respectively. It is observed that \[{{C}_{p}}-{{C}_{v}}=a\]for hydrogen gas \[{{C}_{p}}-{{C}_{v}}=b\]for nitrogen gas The correct relation between a and b is:    JEE Main Solved Paper-2017

A)

\[a=14\,b\]

B)

\[a=28\,b\]

C)

\[a=\frac{1}{14}b\]

D)

\[a=b\]

View Answer
13) A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be \[75{{\,}^{o}}C.\] T is given by: (Given : room temperature\[=30{{\,}^{o}}C,\]specific heat of copper\[\text{=}\,\text{0}\text{.1}\,\text{cal/gm}{{\,}^{\text{o}}}\text{C}\] JEE Main Solved Paper-2017

A)

\[\text{1250}{{\,}^{o}}\text{C}\]

B)

\[825{{\,}^{o}}\text{C}\]

C)

\[800{{\,}^{o}}\text{C}\]

D)

\[885{{\,}^{o}}\text{C}\]

View Answer
14) A body of mass \[m={{10}^{-2}}kg\]is moving in a medium and experiences a frictional force \[m={{10}^{-2}}kg\]Its intial speed is \[{{v}_{0}}=10m{{s}^{-1}}.\]If, after 10 s, its energy is\[\frac{1}{8}mv_{0}^{2},\] JEE Main Solved Paper-2017

A)

\[{{10}^{-4}}kg\,{{m}^{-1}}\]

B)

\[{{10}^{-1}}kg\,{{m}^{-1}}{{S}^{-1}}\]

C)

\[{{10}^{-3}}kg\,{{m}^{-1}}\]

D)

\[{{10}^{-3}}kg\,{{s}^{-1}}\]

View Answer
15) When a current of 5 mA is passed through a galvanometer having a coil of resistance \[15\,\Omega ,\] it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into to voltmeter of range 0 - 10 V is:    JEE Main Solved Paper-2017

A)

\[2.535\times {{10}^{3}}\Omega \]

B)

\[4.005\times {{10}^{3}}\Omega \]

C)

\[1.985\times {{10}^{3}}\Omega \]

D)

\[2.045\times {{10}^{3}}\Omega \]

View Answer
16) A slender uniform rod of mass M and length \[\ell \] is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle\[\theta \] with the vertical   JEE Main Solved Paper-2017

A)

\[\frac{3g}{2\ell }\cos \theta \]

B)

\[\frac{2g}{3\ell }\cos \theta \]

C)

\[\frac{3g}{2\ell }\sin \theta \]

D)

\[\frac{2g}{3\ell }\sin \theta \]

View Answer
17) Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths \[r={{\lambda }_{1}}/{{\lambda }_{2}},\]is given by: JEE Main Solved Paper-2017

A)

\[r=\frac{3}{4}\]

B)

\[r=\frac{1}{3}\]

C)

\[r=\frac{4}{3}\]

D)

\[r=\frac{2}{3}\]

View Answer
18) A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of : JEE Main Solved Paper-2017

A)

81

B)

\[\frac{1}{81}\]

C)

9

D)

\[\frac{1}{9}\]

View Answer
19) In a coil of resistance \[100\,\Omega ,\] a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:   JEE Main Solved Paper-2017

A)

250 Wb

B)

275 Wb

C)

200 Wb

D)

225 Wb

View Answer
20) In a Young's double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is: JEE Main Solved Paper-2017

A)

9.75 mm

B)

15.6 mm

C)

1.56 mm

D)

7.8 mm

View Answer
21) A magnetic needle of magnetic moment \[6.7\times {{10}^{-2}}\,A{{m}^{2}}\]and moment of inertia \[7.5\times {{10}^{-6}}\,kg\,{{m}^{2}}\]is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is: JEE Main Solved Paper-2017

A)

6.98 s

B)

8.76 s

C)

6.65 s

D)

8.89 s

View Answer
22) The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius): JEE Main Solved Paper-2017

A)

B)

C)

D)

View Answer
23) In the above circuit the current in each resistance is:    JEE Main Solved Paper-2017

A)

0.5

B)

0 A

C)

1 A

D)

0.25 A

View Answer
24) A particle A of mass m and initial velocity v collides with a particle B of mass\[\frac{m}{2}\]which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths \[{{\lambda }_{A}}\]to \[{{\lambda }_{B}}\] after the collision is: JEE Main Solved Paper-2017

A)

\[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{2}{3}\]

B)

\[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}\]

C)

\[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}\]

D)

\[\frac{{{\lambda }_{A}}}{{{\lambda }_{_{B}}}}=2\]

View Answer
25) An external pressure P is applied on a cube at \[0{{\,}^{o}}C\]so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and\[\alpha \]is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:    JEE Main Solved Paper-2017

A)

\[\frac{3\alpha }{PK}\]

B)

\[3PK\alpha \]

C)

\[\frac{P}{3\alpha K}\]

D)

\[\frac{P}{\alpha K}\]

View Answer
26) A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:    JEE Main Solved Paper-2017

A)

9 J

B)

18 J

C)

4.5 J

D)

22 J

View Answer
27) An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light\[=3\times {{10}^{8}}\,m{{s}^{-1}}\]) JEE Main Solved Paper-2017

A)

17.3 GHz

B)

15.3 GHz

C)

10.1 GHz

D)

12.1 GHz

View Answer
28) In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be: JEE Main Solved Paper-2017

A)

\[CE\frac{{{r}_{2}}}{(r+{{r}_{2}})}\]

B)

\[CE\frac{{{r}_{1}}}{({{r}_{1}}+r)}\]

C)

CE

D)

\[CE\frac{{{r}_{1}}}{({{r}_{2}}+r)}\]

View Answer
29) A capacitance of \[2\mu F\]is required in an electrical circuit across a potential difference of 1.0 kV. A large number of\[1\mu F\]capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is:   JEE Main Solved Paper-2017

A)

24

B)

32

C)

2

D)

16

View Answer
30) A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? JEE Main Solved Paper-2017

A)

B)

C)

D)

View Answer
31) Let k be an integer such that triangle with vertices \[(k,-3k),(5,k)\] and (-k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point:   JEE Main Solved Paper-2017

A)

\[\left( 2,\frac{1}{2} \right)\]

B)

\[\left( 2,-\frac{1}{2} \right)\]

C)

\[\left( 1,\frac{3}{4} \right)\]

D)

\[\left( 1,-\frac{3}{4} \right)\]

View Answer
32) If, for a positive integer n, the quadratic equation, \[x(x+1)+(x+1)(x+2)+.....\] \[+(x+\overline{n-1})(x+n)=10n\] has two consecutive integral solutions, then n is equal to: JEE Main Solved Paper-2017

A)

11

B)

12

C)

9

D)

10

View Answer
33) The function \[f:R\to \left[ -\frac{1}{2},\frac{1}{2} \right]\]defined as \[f(x)=\frac{x}{1+{{x}^{2}}},\]is: JEE Main Solved Paper-2017

A)

neither injective nor surjective.

B)

invertible.

C)

injective but not surjective.

D)

surjective but not injective

View Answer
34) The following statement \[(p\to q)\to [(\tilde{\ }p\to q)\to q]\]is: JEE Main Solved Paper-2017

A)

a fallacy

B)

a tautology

C)

equivalent to \[\tilde{\ }p\to q\]

D)

equivalent to \[p\to -q\]

View Answer
35) If S is the set of distinct values of 'b' for which the following system of linear equations \[x+y+z=1\] \[x+ay+z=1\] \[ax+by+z=0\] has no solution, then S is : JEE Main Solved Paper-2017

A)

a singleton

B)

an empty set

C)

an infinite set

D)

a finite set containing two or more elements

View Answer
36) The area (in sq. units) of the region \[\{(x,y)\}:x\ge 0,x+y\le 3,{{x}^{2}}\le 4y\]and \[y\le 1+\sqrt{x}\}\]is:    JEE Main Solved Paper-2017

A)

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

B)

\[\frac{59}{12}\]

C)

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

D)

\[\frac{7}{3}\]

View Answer
37) For any three positive real numbers a, b and c, \[9(25{{a}^{2}}+{{b}^{2}})+25({{c}^{2}}-3ac)=15b(3a+c).\] Then: JEE Main Solved Paper-2017

A)

a, b and c are in G.P.

B)

b, c and a are in G.P.

C)

b, c and a are in A.P.

D)

a, b and c are in A.P.

View Answer
38) A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :    JEE Main Solved Paper-2017

A)

484

B)

485

C)

468

D)

469

View Answer
39) The normal to the curve\[y(x-2)(x-3)=x+6\] at the point where the curve intersects the y-axis passes through the point:    JEE Main Solved Paper-2017

A)

\[\left( \frac{1}{2},\frac{1}{3} \right)\]

B)

\[\left( -\frac{1}{2},\frac{1}{2} \right)\]

C)

\[\left( \frac{1}{2},\frac{1}{2} \right)\]

D)

\[\left( \frac{1}{2},-\frac{1}{3} \right)\]

View Answer
40) A hyperbola passes through the point \[\text{P(}\sqrt{\text{2}}\text{,}\sqrt{\text{3}}\text{)}\]and has foci at \[(\pm \,2,0).\]Then the tangent to this hyperbola at P is also passes through the point: JEE Main Solved Paper-2017

A)

\[\left( -\sqrt{2},-\sqrt{3} \right)\]

B)

\[\left( 3\sqrt{2},2\sqrt{3} \right)\]

C)

\[\left( 2\sqrt{2},3\sqrt{3} \right)\]

D)

\[\left( \sqrt{3},\sqrt{2} \right)\]

View Answer
41) Let \[a,b,c\in R.\]If \[f(x)=a{{x}^{2}}+bx+c\]is such that \[a+b+c=3\]and \[f(x+y)=f(x)+f(y)+xy,\forall x,y\in R,\]then \[\sum\limits_{n=1}^{10}{f(n)}\]is equal to: JEE Main Solved Paper-2017

A)

225

B)

330

C)

165

D)

190

View Answer
42) Let \[\vec{a}=2\hat{i}+\hat{j}-2\hat{k}\]and \[\vec{b}=\hat{i}+\hat{j}.\]Let \[\vec{c}\]be a vector such that\[|\vec{c}-\vec{a}|=3,\left| (\vec{a}\times \vec{b})\times \vec{c} \right|=3\]and the angle between \[\vec{c}\]and \[\vec{a}\times \vec{b}\] be \[{{30}^{o}}.\] Then \[\vec{a}.\vec{c}\] is equal to: JEE Main Solved Paper-2017

A)

\[\frac{1}{8}\]

B)

\[\frac{25}{8}\]

C)

2

D)

5

View Answer
43) Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If \[\angle BPC=\beta ,\] then \[\text{tan}\,\beta \] is equal to :- JEE Main Solved Paper-2017

A)

\[\frac{4}{9}\]

B)

\[\frac{6}{7}\]

C)

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

D)

\[\frac{2}{9}\]

View Answer
44) Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower -bed, is :-   JEE Main Solved Paper-2017

A)

30

B)

12.5

C)

10

D)

25

View Answer
45) The integral\[\int\limits_{\frac{\pi }{4}}^{\frac{3\pi }{4}}{\frac{dx}{1+cos\,x}}\]is equal to:- JEE Main Solved Paper-2017

A)

-1

B)

-2

C)

2

D)

4

View Answer
46) If \[(2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0\]and \[y(0)=1,\]then \[y\left( \frac{\pi }{2} \right)\]is equal to:- JEE Main Solved Paper-2017

A)

\[\frac{4}{3}\]

B)

\[\frac{1}{3}\]

C)

\[-\frac{2}{3}\]

D)

\[-\frac{1}{3}\]

View Answer
47) Let\[{{I}_{n}}=\int_{{}}^{{}}{{{\tan }^{n}}xdx,(n>1).{{I}_{4}}+{{I}_{6}}}\]\[=a{{\tan }^{5}}x+b{{x}^{5}}+C,\]where C is a constant of integration, then ordered pair (a, b) is equal to:-                                      JEE Main Solved Paper-2017 ]

A)

\[\left( -\frac{1}{5},0 \right)\]

B)

\[\left( -\frac{1}{5},1 \right)\]

C)

\[\left( \frac{1}{5},0 \right)\]

D)

\[\left( \frac{1}{5},-1 \right)\]

View Answer
48) Let \[\omega \]be a complex number such that \[2\omega +1=z\]where \[z=\sqrt{-3}.\]If \[\left| \begin{matrix}    1 & 1 & 1 \\    1 & -{{\omega }^{2}}-1 & {{\omega }^{2}} \\    1 & {{\omega }^{2}} & {{\omega }^{7}} \\ \end{matrix} \right|=3k,\] then k is equal to:-   JEE Main Solved Paper-2017

A)

1

B)

\[-z\]

C)

z

D)

-1

View Answer
49) The value of \[({{\,}^{21}}{{C}_{1}}-{{\,}^{10}}{{C}_{1}})+({{\,}^{21}}{{C}_{2}}-{{\,}^{10}}{{C}_{2}})+\] \[({{\,}^{21}}{{C}_{3}}-{{\,}^{10}}{{C}_{3}})+({{\,}^{21}}{{C}_{4}}-{{\,}^{10}}{{C}_{4}})+....+\] \[({{\,}^{21}}{{C}_{10}}-{{\,}^{10}}{{C}_{10}})\]is:- JEE Main Solved Paper-2017

A)

\[{{2}^{20}}-{{2}^{10}}\]

B)

\[{{2}^{21}}-{{2}^{11}}\]

C)

\[{{2}^{21}}-{{2}^{10}}\]

D)

\[{{2}^{20}}-{{2}^{9}}\]

View Answer
50) \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\cot x-\cos x}{{{(\pi -2x)}^{3}}}\]               JEE Main Solved Paper-2017

A)

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

B)

\[\frac{1}{24}\]

C)

\[\frac{1}{16}\]

D)

\[\frac{1}{8}\]

View Answer
51) \[5({{\tan }^{2}}x-{{\cos }^{2}}x)=2\cos 2x+9,\]then the value of \[\cos 4x\]is :- JEE Main Solved Paper-2017

A)

\[-\frac{7}{9}\]

B)

\[-\frac{3}{5}\]

C)

\[\frac{1}{3}\]

D)

\[\frac{2}{9}\]

View Answer
52) If the image of the point P(1,-2,3) in the plane, \[2x+3y-4z+22=0\]measured parallel to line, \[\frac{x}{1}=\frac{y}{4}=\frac{z}{5}\]is Q, then PQ is equal to:- JEE Main Solved Paper-2017

A)

\[6\sqrt{5}\]

B)

\[3\sqrt{5}\]

C)

\[2\sqrt{42}\]

D)

\[\sqrt{42}\]

View Answer
53) The distance of the point (1, 3, -7) from the plane passing through the point (1, -1, -1), having normal perpendicular to both the lines \[\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}\]and \[\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1},\]is:-    JEE Main Solved Paper-2017

A)

\[\frac{10}{\sqrt{74}}\]

B)

\[\frac{20}{\sqrt{74}}\]

C)

\[\frac{10}{\sqrt{83}}\]

D)

\[\frac{5}{\sqrt{83}}\]

View Answer
54) If for \[x\in \left( 0,\frac{1}{4} \right),\]the derivative of \[{{\tan }^{-1}}\left( \frac{6x\sqrt{x}}{1-9{{x}^{3}}} \right)\]is \[\sqrt{x}.g(x),\]then \[g(x)\]equals:-   JEE Main Solved Paper-2017

A)

\[\frac{3}{1+9{{x}^{3}}}\]

B)

\[\frac{9}{1+9{{x}^{3}}}\]

C)

\[\frac{3x\sqrt{x}}{1-9{{x}^{3}}}\]

D)

\[\frac{3x}{1-9{{x}^{3}}}\]

View Answer
55) The radius of a circle, having minimum area, which touches the curve \[y=4{{x}^{2}}\]and the lines,\[y=\,|x|\]:-               JEE Main Solved Paper-2017

A)

\[4\left( \sqrt{2}+1 \right)\]

B)

\[2\left( \sqrt{2}+1 \right)\]

C)

\[2\left( \sqrt{2}-1 \right)\]

D)

\[4\left( \sqrt{2}-1 \right)\]

View Answer
56) A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :- JEE Main Solved Paper-2017

A)

\[\frac{6}{25}\]

B)

\[\frac{12}{5}\]

C)

6

D)

4

View Answer
57) The eccentricity of an ellipse whose centre is at the origin is \[\frac{1}{2}.\]If one of its directices is \[x=-4,\]then the equation of the normal to it at \[\left( 1,\frac{3}{2} \right)\]is:-                  JEE Main Solved Paper-2017

A)

\[x+2y=4\]

B)

\[2y-x=2\]

C)

\[4x-2y=1\]

D)

\[4x+2y=7\]

View Answer
58) If two different numbers are taken from the set {0, 1, 2, 3, ......., 10), then the probability that their sum as well as absolute difference are both multiple of 4, is :- JEE Main Solved Paper-2017

A)

\[\frac{7}{55}\]

B)

\[\frac{6}{55}\]

C)

\[\frac{12}{55}\]

D)

\[\frac{14}{45}\]

View Answer
59) For three events A, B and C, P(Exactly one of A or B occurs)= P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) \[=\frac{1}{4}\]and P(All the three events occur simultaneously) \[=\frac{1}{16}.\] Then the probability that at least one of the events occurs, is :-   JEE Main Solved Paper-2017

A)

\[\frac{3}{16}\]

B)

\[\frac{7}{32}\]

C)

\[\frac{7}{16}\]

D)

\[\frac{7}{64}\]

View Answer
60) If \[A\left[ \begin{matrix}    2 & -3 \\    -4 & 1 \\ \end{matrix} \right],\]then adj \[(3{{A}^{2}}+12A)\]is equal to:-                                              JEE Main Solved Paper-2017

A)

\[\left[ \begin{matrix}    72 & -63 \\    -84 & 51 \\ \end{matrix} \right]\]

B)

\[\left[ \begin{matrix}    72 & -84 \\    -63 & 51 \\ \end{matrix} \right]\]

C)

\[\left[ \begin{matrix}    51 & 63 \\    84 & 72 \\ \end{matrix} \right]\]

D)

\[\left[ \begin{matrix}    51 & 84 \\    63 & 72 \\ \end{matrix} \right]\]

View Answer
61) Which of the following compounds will significant amont of meta product during mono-nitration reaction?   JEE Main Solved Paper-2017

A)



B)

C)



D)

View Answer
62) \[\text{ }\!\!\Delta\!\!\text{ U}\]is equal to JEE Main Solved Paper-2017

A)

Isochoric work

B)

Isobaric work

C)

Adiabatic work

D)

Isothermal work

View Answer
63) The increasing order of the reactivity of the following halides for the \[{{\text{S}}_{\text{N}}}\text{1}\]reaction is [JEE Main 2017] \[\text{C}{{\text{H}}_{\text{3}}}\underset{\text{Cl}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{HC}{{\text{H}}_{\text{2}}}\text{C}{{\text{H}}_{\text{3}}}\]                \[\text{C}{{\text{H}}_{\text{3}}}\text{C}{{\text{H}}_{\text{2}}}\text{C}{{\text{H}}_{\text{2}}}\text{Cl}\] \[p-{{H}_{3}}CO-{{C}_{6}}{{H}_{4}}-C{{H}_{2}}Cl\] JEE Main Solved Paper-2017

A)

(III) < (II) < (I)

B)

(II) < (I) < (III)

C)

< (III) < (II)

D)

(II) < (III) < (I)

View Answer
64) The radius of the second Bohr orbit for hydrogen atom is: (Plank's const. \[\text{h}\,\text{=}\,\text{6}\text{.6262}\times \text{1}{{\text{0}}^{-34}}\,Js;\]mass of electron\[=9.1091\times {{10}^{-31}}\,kg;\]charge of electron \[e=1.60210\times {{10}^{-19}}C;\]permittivity of vaccum\[{{\in }_{0}}=8.854185\times {{10}^{-12}}\,k{{g}^{-1}}{{m}^{-3}}{{A}^{2}})\]                                              JEE Main Solved Paper-2017

A)

\[1.65\overset{\text{o}}{\mathop{\text{A}}}\,\]

B)

\[4.76\overset{\text{o}}{\mathop{\text{A}}}\,\]

C)

\[0.529\overset{\text{o}}{\mathop{\text{A}}}\,\]

D)

\[212\overset{\text{o}}{\mathop{\text{A}}}\,\]

View Answer
65) \[\text{p}{{\text{K}}_{\text{a}}}\]of a weak acid (HA) and \[\text{p}{{\text{K}}_{\text{b}}}\]of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is JEE Main Solved Paper-2017

A)

7.2

B)

6.9

C)

7.0

D)

1.0

View Answer
66) The formation of which of the following polymers involves hydrolysis reaction? JEE Main Solved Paper-2017

A)

Nylon 6

B)

Bakelite

C)

Nylon 6, 6

D)

Terylene

View Answer
67) The most abundant elements by mass in the body of a healthy human adult are: Oxygen (61.4%); Carbon (22.9%), Hydrogen (10.0%); and Nitrogen (2.6%). The weight which a 75 kg person would gain if all 1H atoms are replaced by\[{{\,}^{\text{2}}}\text{H}\] atoms is JEE Main Solved Paper-2017

A)

15 kg

B)

37.5 kg

C)

7.5 kg

D)

10 kg

View Answer
68) Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to decolourize the colour of bromine? JEE Main Solved Paper-2017

A)

B)

C)

D)

View Answer
69) In the following reactions, ZnO is respectively acting as a/an :       ] \[ZnO+N{{a}_{2}}O\to N{{a}_{2}}Zn{{O}_{2}}\] \[ZnO+C{{O}_{2}}\to ZnC{{O}_{3}}\] JEE Main Solved Paper-2017

A)

base and acid

B)

base and base

C)

acid and acid

D)

acid and base

View Answer
70) Both lithium and magnesium display several similar properties due to the diagonal relationship ; however, the one which is incorrect is: JEE Main Solved Paper-2017

A)

Both form basic carbonates

B)

Both form soluble bicarbonates

C)

Both form nitrides

D)

Nitrates of both Li and Mg yield\[\text{N}{{\text{O}}_{\text{2}}}\] and \[{{\text{O}}_{\text{2}}}\]on heating

View Answer
71) 3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is :- JEE Main Solved Paper-2017

A)

Six

B)

Zero

C)

Two

D)

Four

View Answer
72) A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is 'a', the closest approach between two atoms in metallic crystal will be :- JEE Main Solved Paper-2017

A)

2a

B)

\[2\sqrt{2}a\]

C)

\[\sqrt{2}a\]

D)

\[\frac{a}{\sqrt{2}}\]

View Answer
73) Two reactions\[{{R}_{1}}\]and\[{{R}_{2}}\]have identical preexponential factors. Activation energy of \[{{R}_{1}}\]exceeds that of \[{{R}_{2}}\]by \[10\,kJ\,mo{{l}^{-1}}.\] If \[{{k}_{1}}\]and \[{{k}_{2}}\]are rate constants for reactions \[{{R}_{1}}\]and \[{{R}_{2}}\]respectively at 300 K, then ln \[({{k}_{2}}/{{k}_{1}})\] is equal to:- \[(R=8.314\,J\,mo{{l}^{-1}}{{K}^{-1}})\ JEE Main Solved Paper-2017

A)

8

B)

12

C)

6

D)

4

View Answer
74) The correct sequence of reagents for the following conversion will be:- JEE Main Solved Paper-2017

A)

\[{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}O{{H}^{-}},{{H}^{+}}/C{{H}_{3}}OH,C{{H}_{3}}MgBr\]

B)

\[C{{H}_{3}}MgBr,{{H}^{+}}/C{{H}_{3}}OH,{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}O{{H}^{-}}\]

C)

\[C{{H}_{3}}MgBr,{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}O{{H}^{-}},{{H}^{+}},C{{H}_{3}}OH\]

D)

\[{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}O{{H}^{-}},C{{H}_{3}}C{{H}_{3}}MgBr,{{H}^{+}}/C{{H}_{3}}OH\]

View Answer
75) The Tyndall effect is observed only when following conditions are satisfied :- [JEE Main 2017] [a] The diameter of the dispersed particles is much smaller than the wavelength of the ligh used. [b] The diameter of the dispersed particle is not much smaller than the wavelength of the light used. [c] The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude. [d] The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude. JEE Main Solved Paper-2017

A)

[a] and [d]

B)

[b] and [d]

C)

[a] and [c]

D)

[b] and [c]

View Answer
76) Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution?              JEE Main Solved Paper-2017

A)



B)

C)



D)

View Answer
77) Given \[{{C}_{(grahite)}}+{{O}_{2}}(g)\to C{{O}_{2}}(g);\] \[{{\Delta }_{r}}{{H}^{o}}=-393.5\,kJ\,mo{{l}^{-1}}\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\to {{H}_{2}}O(l);\] \[{{\Delta }_{r}}{{H}^{o}}=-285.8\,kJ\,mo{{l}^{-1}}\] \[C{{O}_{2}}(g)+2{{H}_{2}}O(l)\to C{{H}_{4}}(g)+2{{O}_{2}}(g);\] \[{{\Delta }_{r}}{{H}^{o}}=+890.3\,kJ\,mo{{l}^{-1}}\] Based on the above thermochemical equations, the value of \[{{\Delta }_{r}}{{H}^{o}}\]at 298 K for the reaction\[{{C}_{(grahite)}}+2{{H}_{2}}(g)\to C{{H}_{4}}(g)\]will be:- JEE Main Solved Paper-2017

A)

\[+\,74.8\,kJ\,mo{{l}^{-1}}\]

B)

\[+\,144.0\,\,kJ\,mo{{l}^{-1}}\]

C)

\[-74.8\,\,kJ\,mo{{l}^{-1}}\]

D)

\[-144.0\,kJ\,mo{{l}^{-1}}\]

View Answer
78) Which of the following reactions is an example of a redox reaction? JEE Main Solved Paper-2017

A)

\[Xe{{F}_{4}}+{{O}_{2}}{{F}_{2}}\to Xe{{F}_{6}}+{{O}_{2}}\]

B)

\[Xe{{F}_{2}}+P{{F}_{5}}\to {{[XeF]}^{+}}P{{F}_{6}}^{-}\]

C)

\[Xe{{F}_{6}}+{{H}_{2}}O\to XeO{{F}_{4}}+2HF\]

D)

\[Xe{{F}_{6}}+2{{H}_{2}}O\to Xe{{O}_{2}}{{F}_{2}}+4HF\]

View Answer
79) The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are:- JEE Main Solved Paper-2017

A)

\[Cl{{O}^{-}}\]and \[ClO_{3}^{-}\]

B)

\[ClO_{2}^{-}\]and \[ClO_{3}^{-}\]

C)

\[C{{l}^{-}}\]and \[Cl{{O}^{-}}\]

D)

\[C{{l}^{-}}\]and \[ClO_{2}^{-}\]

View Answer
80) The major product obtained in the following reaction is :- JEE Main Solved Paper-2017

A)

\[(\pm )\,{{C}_{6}}{{H}_{5}}CH({{O}^{t}}Bu)C{{H}_{2}}C{{H}_{6}}{{H}_{5}}\]

B)

\[{{C}_{6}}{{H}_{5}}CH=CH{{C}_{6}}{{H}_{5}}\]

C)

\[(+){{C}_{6}}{{H}_{5}}CH({{O}^{t}}Bu)C{{H}_{2}}{{H}_{5}}\]

D)

\[(-){{C}_{6}}{{H}_{5}}CH({{O}^{t}}Bu)C{{H}_{2}}{{C}_{6}}{{H}_{5}}\]

View Answer
81) Sodium salt of an organic acid 'X' produces effervescence with conc. \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{.}\]'X' reacts with the acidified aqueous \[\text{CaC}{{\text{l}}_{\text{2}}}\] solution to give a white precipitate which decolourises acidic solution of \[\text{KMn}{{\text{O}}_{4}}.\] 'X' is :- JEE Main Solved Paper-2017

A)

\[{{C}_{6}}{{H}_{5}}COONa\]

B)

\[HCOONa\]

C)

\[CH3COONa\]

D)

\[N{{a}_{2}}{{C}_{2}}{{O}_{4}}\]

View Answer
82) Which of the following species is not paramagnetic :-                 JEE Main Solved Paper-2017

A)

NO

B)

CO

C)

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

D)

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

View Answer
83) The freezing point of benzene decreases by \[0.45{{\,}^{o}}C\]when 0.2 g of acetic acid is added to 20 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be :- (\[{{K}_{f}}\]for benzene \[=5.12\,K\,kg\,mo{{l}^{-1}}\]) JEE Main Solved Paper-2017

A)

64.6%

B)

80.4%

C)

74.6%

D)

94.6%

View Answer
84) Which of the following molecules is least resonance stabilized? JEE Main Solved Paper-2017

A)

B)

C)

D)

View Answer
85) On treatment of 100 mL of 0.1 M solution of \[CoC{{l}_{3}}.6{{H}_{2}}O\]with excess \[AgN{{O}_{3}};1.2\times {{10}^{22}}\]ions are precipitated. The complex is :- JEE Main Solved Paper-2017

A)

\[AgN{{O}_{3}};1.2\times {{10}^{22}}\]

B)

\[[Co{{({{H}_{2}}O)}_{3}}C{{l}_{3}}].3{{H}_{2}}O\]

C)

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

D)

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

View Answer
86) The major product obtained in the following reaction is :-                            JEE Main Solved Paper-2017

A)



B)



C)



D)

View Answer
87) A water sample has ppm level concentration of following anions \[{{F}^{-}}=10;\,SO_{4}^{2-}=100;\,NO_{3}^{-}=50\] the anion/anions that make / makes the water sample unsuitable for drinking is / are : JEE Main Solved Paper-2017

A)

only\[NO_{3}^{-}\]

B)

both \[SO_{4}^{2-}\]and \[NO_{3}^{-}\]

C)

only\[F-\]

D)

only \[SO_{4}^{2-}\]

View Answer
88) 1 gram of a carbonate \[({{M}_{2}}C{{O}_{3}})\] on treatment with excess HCl produces 0.01186 mole of \[C{{O}_{2}}.\]the molar mass of \[{{\text{M}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]in \[\text{g}\,\text{mo}{{\text{l}}^{-1}}\]is:-                           JEE Main Solved Paper-2017

A)

1186

B)

84.3

C)

118.6

D)

11.86

View Answer
89) Given \[E_{Cl{{ }_{2}}/C{{l}^{-}}}^{0}=13.6,E_{C{{r}^{3+}}/Cr}^{0}=-0.74\,V\] \[E_{C{{r}_{2}}O_{7}^{2-}/C{{r}^{3+}}}^{0}=1.33V,E_{MnO_{4}^{-}/M{{n}^{2+}}}^{0}=1.51\,V.\] Among the following, the strongest reducing agent is                           JEE Main Solved Paper-2017

A)

Cr

B)

\[M{{n}^{2+}}\]

C)

\[C{{r}^{3+}}\]

D)

\[C{{l}^{-}}\]

View Answer
90) The group having isoelectronic species is :- JEE Main Solved Paper-2017

A)

\[{{\text{O}}^{2-}},{{F}^{-}},N{{a}^{+}},M{{g}^{2+}}\]

B)

\[{{O}^{-}},{{F}^{-}},Na,M{{g}^{+}}\]

C)

\[{{O}^{2-}},{{F}^{-}},Na,M{{g}^{2+}}\]

D)

\[{{O}^{-}},{{F}^{-}},N{{a}^{+}},M{{g}^{2+}}\]

View Answer