Solved papers for JEE Main & Advanced JEE Main Paper (Held On 9 April 2017)

JEE Main Paper (Held On 9 April 2017) Total Questions - 90

1) If the line, \[\frac{x-3}{1}=\frac{y+2}{1}=\frac{z+\lambda }{-2}\] lies in the plane, \[2x-4y+3z=2,\] then the shortest distance between this line and the line, \[\frac{x-1}{12}=\frac{y}{9}=\frac{z}{4}\] is:      [JEE Online 09-04-2017]

A)

1

B)

2

C)

3

D)

0

View Answer
2) The coefficient of \[{{x}^{-5}}\] in the binomial expansion of \[{{\left( \frac{x+1}{{{x}^{\frac{2}{3}}}-{{x}^{\frac{1}{3}}}+1}\,-\frac{x-1}{x-{{x}^{\frac{1}{2}}}} \right)}^{10}}\] where \[x\ne 0,1\] is:     [JEE Online 09-04-2017]

A)

-1

B)

4

C)

3

D)

- 4

View Answer
3) The equation \[\operatorname{Im}\left( \frac{iz-2}{z-i} \right)\,+1=0,\,z\in C,\,z\ne i\] represents a part of a circle having radius equal to:                  [JEE Online 09-04-2017]

A)

1

B)

2

C)

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

D)

\[\frac{1}{2}\]

View Answer
4) The value of K for which the function\[f(x)=\left\{ \begin{matrix}    {{\left( \frac{4}{5} \right)}^{\frac{\tan 4x}{\tan 5x}}}, & 0<x<\frac{\pi }{2} \\    k+\frac{2}{5} & x=\frac{\pi }{2} \\ \end{matrix} \right.\] is continuous at \[x=\frac{\pi }{2},\] is        [JEE Online 09-04-2017]

A)

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

B)

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

C)

\[\frac{17}{20}\]

D)

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

View Answer
5) If \[\int\limits_{1}^{2}{\frac{dx}{{{({{x}^{2}}-2x+4)}^{\frac{3}{4}}}}\,=\frac{k}{k+5},}\] then k is equal to [JEE Online 09-04-2017]

A)

4

B)

2

C)

3

D)

1

View Answer
6) For two \[3\times 3\] matrices A and B, let \[A+B=2B'\] and \[3A+2B={{I}_{3}},\] where B' is the transpose of B and \[{{I}_{3}}\] is \[3\times 3\] identity matrix. Then: [JEE Online 09-04-2017]

A)

\[10A+5B=3{{I}_{3}}\]

B)

\[3A+6B=2{{I}_{3}}\]

C)

\[5A+10B-2{{I}_{3}}\]

D)

\[B+2A={{I}_{3}}\]

View Answer
7) If \[y=mx+c\] is the normal at a point on the parabola \[{{y}^{2}}=8x\] whose focal distance is 8 units, then |c| is equal to: [JEE Online 09-04-2017]

A)

\[8\sqrt{3}\]

B)

\[10\sqrt{3}\]

C)

\[2\sqrt{3}\]

D)

\[16\sqrt{3}\]

View Answer
8) A line drawn through the point P(4, 7) cuts the circle \[{{x}^{2}}+{{y}^{2}}=9\] at the points A and B. Then \[PA.PB\] is equal to: [JEE Online 09-04-2017]

A)

74

B)

53

C)

56

D)

65

View Answer
9) The sum of all the real values of x satisfying the equation \[{{2}^{(x-1)\,(x2+5x-50)}}=1\] is: [JEE Online 09-04-2017]

A)

16

B)

- 5

C)

- 4

D)

14

View Answer
10) The function \[f:N\to N\] defined by \[f(x)=x-5\,\left[ \frac{x}{5} \right],\] where N is the set of natural numbers and \[[x]\] denotes the greatest integer less than or equal to x, is: [JEE Online 09-04-2017]

A)

one-one but not onto

B)

one-one and onto

C)

neither one-one nor onto

D)

onto but not one-one

View Answer
11) Let f be a polynomial function such that \[f(3x)\,=f'(x)\,.f''(x),\,\] for all \[x\in R\]. Then: [JEE Online 09-04-2017]

A)

\[f(2)\,+f'(2)\,=28\]

B)

\[f''(2)\,-f'(2)=0\]

C)

\[f(2)\,-f'(2)\,+f''(2)=10\]

D)

\[f''(2)-f(2)=4\]

View Answer
12) If three positive numbers a, b and c are in A.P. such that \[abc=8,\] then the minimum possible value of b is :   [JEE Online 09-04-2017]

A)

\[{{4}^{\frac{2}{3}}}\]

B)

2

C)

\[{{4}^{\frac{1}{3}}}\]

D)

4

View Answer
13) If \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{1}^{a}}+{{2}^{a}}+...{{n}^{a}}}{{{(n+1)}^{a-1}}[(na+1)\,+(na+2)+...+(na+n)]}=\frac{1}{60}\]for some positive real number a, then a is equal to                          [JEE Online 09-04-2017]

A)

\[\frac{17}{2}\]

B)

\[\frac{15}{2}\]

C)

7

D)

8

View Answer
14) If \[\left( \frac{3x-4}{3x+4} \right)\,=x+2,\,x\ne \,-\frac{4}{3},\] and \[\int_{{}}^{{}}{f(x)\,dx=A\log \,dx\,=A\log \,|1-x|+Bx+C,}\] then the ordered pair (A, B) is equal to :(where c is a constant of integration) [JEE Online 09-04-2017]

A)

\[\left( -\frac{8}{3},\,-\frac{2}{3} \right)\]

B)

\[\left( -\frac{8}{3},\,\frac{2}{3} \right)\]

C)

\[\left( \frac{8}{3},\,\frac{2}{3} \right)\]

D)

\[\left( \frac{8}{3},\,-\frac{2}{3} \right)\]

View Answer
15) A square, of each side 2, lies above the x-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle \[{{30}^{\text{o}}}\] with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is: [JEE Online 09-04-2017]

A)

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

B)

\[\sqrt{3}-2\]

C)

\[2\sqrt{3}-1\]

D)

\[\sqrt{3}-1\]

View Answer
16) A value of \[x\] satisfying the equation \[\sin \,[{{\cot }^{-1}}\,(1+x)]=cos[ta{{n}^{-1}}x],\] is: [JEE Online 09-04-2017]

A)

\[-\frac{1}{2}\]

B)

0

C)

- 1

D)

\[\frac{1}{2}\]

View Answer
17) From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one women. Then the probability for these committees to have more women than men, is: [JEE Online 09-04-2017]

A)

\[\frac{3}{11}\]

B)

\[\frac{2}{23}\]

C)

\[\frac{1}{11}\]

D)

\[\frac{21}{220}\]

View Answer
18) The function f defined by \[f(x)={{x}^{3}}-3{{x}^{2}}+5x+7,\] is: [JEE Online 09-04-2017]

A)

decreasing in R

B)

increasing in R

C)

increasing in \[(0,\,\,\infty )\] and decreasing in \[(-\infty ,\,\,0)\]

D)

decreasing in \[(0,\,\,\infty )\] and increasing in \[(-\infty ,\,\,0)\]

View Answer
19) The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, -1) and (-2, 2) is :                          [JEE Online 09-04-2017]

A)

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

B)

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

C)

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

D)

\[\frac{1}{2}\]

View Answer
20) A tangent to the curve, \[y=f(x)\] at \[P(x,\,y)\] meets x-axis at A and y-axis at B. If \[AP:BP=1:3\] and \[f(1)=1,\] then the curve also passes through the point: [JEE Online 09-04-2017]

A)

\[\left( \frac{1}{3},\,24 \right)\]

B)

\[\left( \frac{1}{2},4 \right)\]

C)

\[\left( 2,\frac{1}{8} \right)\]

D)

\[\left( 3,\,\frac{1}{28} \right)\]

View Answer
21) If \[x=a,\,\,y=b,\,\,z=c\] is solution of the system of linear equations [JEE Online 09-04-2017]                 \[x+8y+7z=0\] \[9x+2y+3z=0\] \[y+y+z=0\]        such that the point \[(a,\,b,\,c)\] lies on the plane \[x+2y+z=6,\] then \[2a+b+c\] equals:

A)

2

B)

- 1

C)

1

D)

0

View Answer
22) Let \[{{S}_{n}}=\frac{1}{{{1}^{3}}}+\frac{1+2}{{{1}^{3}}+{{2}^{3}}}+\frac{1+2+3}{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}+...+\frac{1+2+....,\,+n}{{{1}^{3}}+{{2}^{3}}+...+{{n}^{3}}}\]. If \[100\,{{S}_{n}}=n,\] then n is equal to: [JEE Online 09-04-2017]

A)

200

B)

199

C)

99

D)

19

View Answer
23) If the vector \[\vec{b}=3\hat{j}+4\hat{k}\] is written as the sum of a vector \[{{\vec{b}}_{1}},\] parallel to \[\vec{a}=\hat{i}+\hat{j}\] and a vector \[{{\vec{b}}_{2}}\] perpendicular to \[{{\vec{a}}_{1}}\] then \[{{\vec{b}}_{1}}\times {{\vec{b}}_{2}}\] is equal to [JEE Online 09-04-2017]

A)

\[6\hat{i}-6\hat{j}+\frac{9}{2}\hat{k}\]

B)

\[-3\hat{i}+3\hat{j}-9\hat{k}\]

C)

\[-6\hat{i}+6\hat{j}-\frac{9}{2}\hat{k}\]

D)

\[3\hat{i}-3\hat{j}+9\hat{k}\]

View Answer
24) The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is \[{{60}^{\text{o}}}\] . If the area of the quadrilateral is \[4\sqrt{3},\] then the perimeter of the quadrilateral is: [JEE Online 09-04-2017]

A)

12.5

B)

13

C)

13.2

D)

12

View Answer
25) The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy \[{{B}_{1}}\] and a particular girl \[{{G}_{1}}\] never sit adjacent to each other, is: [JEE Online 09-04-2017]

A)

\[7!\]

B)

\[5\times 6!\]

C)

\[6\times 6!\]

D)

\[5\times 7!\]

View Answer
26) If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of \[\Delta ABC\] is. [JEE Online 09-04-2017]

A)

\[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}+\frac{1}{{{z}^{2}}}=1\]

B)

\[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}+\frac{1}{{{z}^{2}}}=3\]

C)

\[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}+\frac{1}{{{z}^{2}}}=9\]

D)

\[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}+\frac{1}{{{z}^{2}}}=\frac{1}{9}\]

View Answer
27) The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is: [JEE Online 09-04-2017]

A)

8.25

B)

8.50

C)

9.00

D)

8.00

View Answer
28) Let E and F be two independent events. The probability that both E and F happen is \[\frac{1}{12}\] and the probability that neither E nor F happens is \[\frac{1}{2},\] then a value of \[\frac{P(E)}{P(F)}\] is: [JEE Online 09-04-2017]

A)

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

B)

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

C)

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

D)

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

View Answer
29) If \[2x={{y}^{\frac{1}{5}}}+{{y}^{-\frac{1}{5}}}\] and \[({{x}^{2}}-1)\,\frac{{{d}^{2}}y}{d{{x}^{2}}}+\lambda x\,\frac{dy}{dx}+ky=0,\] then \[\lambda +k\] is equal to:              [JEE Online 09-04-2017]

A)

26

B)

-24

C)

-23

D)

-26

View Answer
30) Contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is: [JEE Online 09-04-2017]

A)

If the squares of two numbers are equal, then the numbers are not equal

B)

If the squares of two numbers are not equal, then the numbers are equal

C)

If the squares of two numbers are not equal, then the numbers are not equal

D)

If the squares of two numbers are equal, then the numbers are equal.

View Answer
31) The electric field component of a monochromatic radiation is given by \[\vec{E}=2{{E}_{0}}\hat{i}\,\cos kz\,\cos \omega t\] Its magnetic field \[\vec{B}\] [JEE Online 09-04-2017]

A)

\[\frac{2{{E}_{0}}}{c}\hat{j}\,\sin kz\,\sin \omega t\]

B)

\[\frac{2{{E}_{0}}}{c}\hat{j}\cos kz\,\cos \omega t\]

C)

\[\frac{2{{E}_{0}}}{c}\hat{j}\sin kz\,\cos \omega t\]

D)

\[-\frac{2{{E}_{0}}}{c}\hat{j}\sin kz\,\sin \omega t\]

View Answer
32) N moles of a diaotmic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas? [JEE Online 09-04-2017]

A)

0

B)

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

C)

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

D)

\[\frac{1}{2}\,nRT\]

View Answer
33) A circular hole of radius \[\frac{R}{4}\] is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point \[\text{O}\] and perpendicular to the plane of the disc is [JEE Online 09-04-2017]

A)

\[\frac{219{{R}^{2}}}{256}\,\]

B)

\[\frac{237M{{R}^{2}}}{512}\]

C)

\[\frac{197M{{R}^{2}}}{256}\,\]

D)

\[\frac{19M{{R}^{2}}}{512}\]

View Answer
34) A block of mass 0.1 kg is connected to an elastic spring of spring constant \[640\,\,N{{m}^{-1}}\] and oscillates in a damping medium of damping constant\[{{10}^{-2}}kg\,{{s}^{-1}}\]. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to - [JEE Online 09-04-2017]

A)

2 s

B)

5 s

C)

7 s

D)

3.5 s

View Answer
35) A steel rail of length 5 m and area of cross section \[40\,c{{m}^{2}}\] is prevented from expanding along its length while the temperature rises by\[{{10}^{\text{o}}}C\]. If coefficient of linear expansion and Young's modulus of steel are \[1.2\,\times {{10}^{-5}}\,{{K}^{-1}}\] and \[2\times {{10}^{11}}N{{m}^{-2}}\] respectively, the force developed in the rail is approximately: [JEE Online 09-04-2017]

A)

\[2\times {{10}^{7}}N\]

B)

\[2\times {{10}^{9}}N\]

C)

\[3\times {{10}^{-5}}N\]

D)

\[1\times {{10}^{5}}N\]

View Answer
36) In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance \[P=4\,\Omega \] and the neutral point N is at 60 cm from A. Now an unknown resistance R is connected in series to P and the new position of the neutral point is at 80 cm from A. The value of unknown resistance R is - [JEE Online 09-04-2017]

A)

\[\frac{33}{5}\Omega \]

B)

\[5\,\Omega \]

C)

\[\frac{20}{3}\Omega \]

D)

\[7\,\,\Omega \]

View Answer
37) A conical pendulum of length 1 m makes an angle \[\theta ={{45}^{\text{o}}}\] w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be - (Take \[g=10\,m{{s}^{-1}}\]) [JEE Online 09-04-2017]

A)

0.2 m/s

B)

0.4 m/s

C)

2 m/s

D)

4 m/s

View Answer
38) A signal is to be transmitted through a wave of wavelength \[\lambda ,\] using a linear antenna. The length l of the antenna and effective power radiated \[{{P}_{eff}}\] will be given respectively as - (K is a constant of proportionality) [JEE Online 09-04-2017]

A)

\[\frac{\lambda }{8},\,{{P}_{eff}}\,=K\left( \frac{l}{\lambda } \right)\]

B)

\[\frac{\lambda }{16},\,{{P}_{eff}}\,=K{{\left( \frac{1}{\lambda } \right)}^{3}}\]

C)

\[\frac{\lambda }{5},\,{{P}_{eff}}\,=K{{\left( \frac{1}{\lambda } \right)}^{\frac{1}{2}}}\]

D)

\[\lambda ,\,\,{{P}_{eff}}\,=K\,{{\left( \frac{1}{\lambda } \right)}^{2}}\]

View Answer
39) A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that \[R=5\Omega ,\,L=25\,mH\] and \[C=1000\,\mu F\]. The total impedance, and phase difference between the voltage across the source and the current will respectively be - [JEE Online 09-04-2017]

A)

\[10\,\Omega \] and \[{{\tan }^{-1}}\,\left( \frac{5}{3} \right)\]

B)

\[7\,\Omega \] and \[{{45}^{\text{o}}}\]

C)

\[7\,\Omega \] and \[{{\tan }^{-1}}\left( \frac{5}{3} \right)\]

D)

\[10\,\Omega \,\] and \[{{\tan }^{-1}}\,\left( \frac{8}{3} \right)\]

View Answer
40) A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength \[6000\overset{\text{o}}{\mathop{\text{A}}}\,\] and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is - [JEE Online 09-04-2017]

A)

9 mm

B)

3 mm

C)

4.5 mm

D)

1.5 mm

View Answer
41) In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is -    [JEE Online 09-04-2017]

A)

20.0 cm

B)

30.5 cm

C)

25.0 cm

D)

27.5 cm

View Answer
42) The mass density of a spherical body is given by \[\rho (r)\,=\frac{k}{r}\] for \[r\le R\] and \[\rho \,(r)=0\] for \[r>R,\] Where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is -        [JEE Online 09-04-2017]

A)



B)

C)



D)

View Answer
43) A uniform wire of length I and radius r has a resistance of \[100\,\Omega \]. It is recast into a wire of radius \[\frac{r}{2}\]. The resistance of new wire will be - [JEE Online 09-04-2017]

A)

\[1600\,\Omega \]

B)

\[100\,\Omega \]

C)

\[200\,\Omega \]

D)

\[400\,\Omega \]

View Answer
44) The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are \[{{P}_{1}},{{P}_{2}}\] and \[{{P}_{3}}\] respectively, then - [JEE Online 09-04-2017]

A)

\[{{P}_{2}}>{{P}_{1}}>{{P}_{3}}\]

B)

\[{{P}_{1}}>{{P}_{2}}>{{P}_{3}}\]

C)

\[{{P}_{3}}>{{P}_{2}}>{{P}_{1}}\]

D)

\[{{P}_{1}}>{{P}_{3}}>{{P}_{2}}\]

View Answer
45) A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by\[y\,(x,\,t)\,=0.5\,\sin \,\left( \frac{5\pi }{4}x \right)\,\cos \,(2\text{oo}\,\pi t)\]. What is the speed of the travelling wave moving in the positive x direction? (x and t are in meter and second, respectively.) [JEE Online 09-04-2017]

A)

120 m/s

B)

90 m/s

C)

160 m/s

D)

180 m/s

View Answer
46) In an experiment to determine the period of a simple pendulum of length 1m, it is attached to different spherical bobs of radii \[{{r}_{1}}\] and \[{{r}_{2}}\]. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be \[5\times {{10}^{-4}}s,\] the difference in radii, \[|{{r}_{1}}-{{r}_{2}}|\] is best given by - [JEE Online 09-04-2017]

A)

0.01 cm

B)

0.1 cm

C)

0.5 cm

D)

1 cm

View Answer
47) Two particles A and B of equal mass M are moving with the same speed \[\upsilon \] as shown in the figure. They collide completely in elastically and move as a single particle C. The angle \[\theta \] that the path of C makes with the X-axis is given by - [JEE Online 09-04-2017]

A)

\[\tan \theta \,=\frac{\sqrt{3}-\sqrt{2}}{1-\sqrt{2}}\]

B)

\[\tan \theta \,=\frac{1-\sqrt{2}}{\sqrt{2}(1+\sqrt{3})}\]

C)

\[\tan \theta \,\frac{1-\sqrt{3}}{1+\sqrt{2}}\]

D)

\[\tan \theta \,=\frac{\sqrt{3}+\sqrt{2}}{1-\sqrt{2}}\]

View Answer
48) A laser light of wavelength 660 nm is used to weld Retina detachment. If a laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are -            [JEE Online 09-04-2017] [Take Planck's constant \[h=6.62\,\times {{10}^{-34}}Js\]]

A)

\[{{10}^{22}}\]

B)

\[{{10}^{19}}\]

C)

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

D)

\[{{10}^{18}}\]

View Answer
49) The current gain of a common emitter amplifier is 69. If the emitter current is 7.0 mA, collector current is - [JEE Online 09-04-2017]

A)

69 mA

B)

0.69 mA

C)

6.9 mA

D)

9.6 mA

View Answer
50) Four closed surfaces and corresponding charge distributions are shown below - Let the respective electric fluxes through the surfaces be \[{{\Phi }_{1}},\,{{\Phi }_{2}},\,{{\Phi }_{3}}\] and\[{{\Phi }_{4}}\]. Then - [JEE Online 09-04-2017]

A)

\[{{\Phi }_{1}}>{{\Phi }_{2}}>{{\Phi }_{3}}>{{\Phi }_{4}}\]

B)

\[{{\Phi }_{1}}<{{\Phi }_{2}}={{\Phi }_{3}}>{{\Phi }_{4}}\]

C)

\[{{\Phi }_{1}}>{{\Phi }_{3}};\,\,{{\Phi }_{2}}>{{\Phi }_{4}}\]

D)

\[{{\Phi }_{1}}={{\Phi }_{2}}={{\Phi }_{3}}={{\Phi }_{4}}\]

View Answer
51) A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is - [JEE Online 09-04-2017]

A)

away from the wire

B)

towards the wire

C)

parallel to the wire along the current

D)

parallel to the wire opposite to the current

View Answer
52) A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop \[(abcd)\] of sides \[10\,cm\,\times 5\,cm\] carries a current \[I\] of 12 A. Out of the following different orientations which one corresponds to stable equilibrium? [JEE Online 09-04-2017]

A)

B)

C)

D)

View Answer
53) The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is - [JEE Online 09-04-2017]

A)

\[\frac{{{h}^{2}}}{4\pi {{m}^{2}}{{r}^{3}}}\]

B)

\[\frac{{{h}^{2}}}{{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\]

C)

\[\frac{{{h}^{2}}}{8{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\]

D)

\[\frac{{{h}^{2}}}{4{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\]

View Answer
54) Two tubes of radii \[{{r}_{1}}\] and \[{{r}_{2}},\] and lengths \[{{I}_{1}}\] and \[{{I}_{2}},\] respectively, are connected in series and a liquid flows through each of them in stream line conditions. \[{{P}_{1}}\] and \[{{P}_{2}}\] are pressure differences across the two tubes. If \[{{P}_{2}}\] is \[4{{P}_{1}}\] and \[{{I}_{2}}\] is \[\frac{{{I}_{1}}}{4},\] then the radius \[{{r}_{2}}\] will be equal to -                        [JEE Online 09-04-2017]

A)

\[4{{r}_{1}}\]

B)

\[{{r}_{1}}\]

C)

\[2{{r}_{1}}\]

D)

\[\frac{{{r}_{1}}}{2}\]

View Answer
55) A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration \[2\,m/{{s}^{2}}\] and the car has acceleration \[4\,m/{{s}^{2}}\]. The car will catch up with the bus after at time of -           [JEE Online 09-04-2017]

A)

\[\sqrt{120}\,s\]

B)

\[15\,s\]

C)

\[\sqrt{110}\,s\]

D)

\[10\sqrt{2}\,s\]

View Answer
56) The machine as shown has 2 rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. [JEE Online 09-04-2017] If the roller is moving towards right at a constant speed, the weight moves up with a -

A)

speed which is \[\frac{3}{4}th\] of that of the roller when the weight is 0.4 m above the ground

B)

constant speed

C)

decreasing speed

D)

increasing speed

View Answer
57) A physical quantity P is described by the relation\[P={{a}^{1/2}}\,{{b}^{2}}{{c}^{3}}{{d}^{-4}}\]. If the relative errors in the measurement of \[a,\,b,\,c\] and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be - [JEE Online 09-04-2017]

A)

12%

B)

8%

C)

25%

D)

32%

View Answer
58) Imagine that a reactor converts all given mass into energy and that it operates at a power level of \[{{10}^{9}}\] watt. The mass of the fuel consumed per hour in the reactor will be: (velocity of light, c is \[3\times {{10}^{8}}\,m/s\]) [JEE Online 09-04-2017]

A)

\[6.6\,\times {{10}^{-5}}\,gm\]

B)

\[0.96\,gm\]

C)

\[4\times {{10}^{-2}}\,gm\]

D)

\[0.8\,gm\]

View Answer
59) A combination of parallel plate capacitors is maintained at a certain potential difference. When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab.                                 [JEE Online 09-04-2017]

A)

6

B)

4

C)

3

D)

5

View Answer
60) For the P-V diagram given for an ideal gas, out of the following which one correctly represents the T-P diagram? [JEE Online 09-04-2017]

A)

B)

C)

D)

View Answer
61) A compound of molecular formula \[{{C}_{8}}{{H}_{8}}{{O}_{2}}\] reacts with acetophenone to form a single cross-aldol product in the presence of base. The same compound on reaction with conc. \[NaOH\] forms bezyl alcohol as one of the products. The structure of the compound is: [JEE Online 09-04-2017]

A)

B)

C)

D)

View Answer
62) Which of the following ions does not liberate hydrogen gas on reaction with dilute acids? [JEE Online 09-04-2017]

A)

\[{{V}^{2+}}\]

B)

\[T{{i}^{2+}}\]

C)

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

D)

\[C{{r}^{2+}}\]

View Answer
63) The rate of a reaction quadruples when the temperature changes from 300 to 310 K. The activation energy of this reaction is: (Assume activation energy and pre-exponential factor are independent of temperature; [JEE Online 09-04-2017]\[\ln \,2=\,0.693;\,\,R=8.314\,J\,\,mo{{l}^{-1}}\,{{K}^{-1}}\])

A)

\[53.6\,kJ\,mo{{l}^{-1}}\]

B)

\[214.4\,\,kJ\,mo{{l}^{-1}}\]

C)

\[107.2\,kJ\,mo{{l}^{-1}}\]

D)

\[26.8\,kJ\,mo{{l}^{-1}}\]

View Answer
64) The group having triangular planar structure is: [JEE Online 09-04-2017]

A)

\[B{{F}_{3}},\,N{{F}_{3}},\,CO_{3}^{2-}\]

B)

\[CO_{3}^{2-},\,NO_{3}^{2-},\,S{{O}_{3}}\]

C)

\[N{{H}_{3}},\,S{{O}_{3}},\,CO_{3}^{2-}\]

D)

\[NC{{l}_{3}},\,BC{{l}_{3}},\,S{{O}_{3}}\]

View Answer
65) The electronic configuration with the highest ionization enthalpy is: [JEE Online 09-04-2017]

A)

\[[Ar]\,3{{d}^{10}}4{{s}^{2}}4{{p}^{3}}\]

B)

\[[Ne]\,3{{s}^{2}}3{{p}^{1}}\]

C)

\[[Ne]\,3{{s}^{2}}\,3{{p}^{3}}\]

D)

\[[Ne]\,3{{s}^{2}}\,3{{p}^{2}}\]

View Answer
66) The electron in the hydrogen atom undergoes transition from higher orbitals to orbital of radius 211.6 pm. This transition is associated with:                       [JEE Online 09-04-2017]

A)

Lyman series

B)

Balmer series

C)

Brackett series

D)

Paschen series

View Answer
67) Which one of the following is an oxide? [JEE Online 09-04-2017]

A)

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

B)

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

C)

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

D)

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

View Answer
68) 50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M \[HCl\]. If \[p{{K}_{b}}\] of ammonia solution is 4.75, the pH of the mixture will be: [JEE Online 09-04-2017]

A)

8.25

B)

9.25

C)

3.75

D)

4.75

View Answer
69) Which of the following compounds is most reactive to an aqueous solution of sodium carbonate?            [JEE Online 09-04-2017]

A)



B)

C)



D)

View Answer
70) The number of P-OH bonds and the oxidation state of phosphorus atom in pyrophosphoric acid \[({{H}_{4}}{{P}_{2}}{{O}_{7}})\] respectively are: [JEE Online 09-04-2017]

A)

five and four

B)

four and five

C)

five and five

D)

four and four

View Answer
71) The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal: \[F{{e}_{2}}{{O}_{3}}(s)+3CO(g)\,3Fe(\ell )\,+3C{{O}_{2}}(g)\]. Using the Le Chatelier?s principle, predict which one of the following will not disturb the equilibrium?    [JEE Online 09-04-2017]

A)

Addition of \[C{{O}_{2}}\]

B)

Removal of \[C{{O}_{2}}\]

C)

Addition of \[F{{e}_{2}}{{O}_{3}}\]

D)

Removal of \[CO\]

View Answer
72) A solution is prepared by mixing 8.5 g of \[C{{H}_{2}}C{{l}_{2}}\] and 11.95 g of \[CHC{{l}_{3}}\]. If vapour pressure of \[C{{H}_{2}}C{{l}_{2}}\] and \[CHC{{l}_{3}}\] at 298 K are 415 and 200 mm Hg respectively, the mole fraction of CHCl3 in vapour form is : (Molar mass of \[Cl=35.5\,g\,mo{{l}^{-1}}\]) [JEE Online 09-04-2017]

A)

0.162

B)

0.675

C)

0.325

D)

0.486

View Answer
73) The increasing order of the boiling points for the following compounds is: [JEE Online 09-04-2017] (I) \[{{C}_{2}}{{H}_{5}}OH\]                         (II) \[{{C}_{2}}{{H}_{5}}Cl\] (III) \[{{C}_{2}}{{H}_{5}}C{{H}_{3}}\]                        \[{{C}_{2}}{{H}_{5}}OC{{H}_{3}}\]

A)

(IV) < (III) < (I) < (II)

B)

(III) < (II) < (I) < (IV)

C)

(III) < (IV) < (II) < (I)

D)

(II) < (III) < (IV) < (I)

View Answer
74) An ideal gas undergoes isothermal expansion at constant pressure. During the process: [JEE Online 09-04-2017]

A)

enthalpy remains constant but entropy increases.

B)

enthalpy decreases but entropy increases.

C)

enthalpy increases but entropy decreases.

D)

Both enthalpy and entropy remain constant.

View Answer
75) \[[C{{O}_{2}}{{(CO)}_{8}}]\] displays: [JEE Online 09-04-2017]

A)

no Co-Co bond, six terminal CO and two bridging CO

B)

no Co-Co bond, four terminal CO and four bridging CO

C)

one Co-Co bond, six terminal CO and two bridging CO

D)

one Co-Co bond, four terminal CO and four bridging CO

View Answer
76) The correct sequence of decreasing number of \[\pi \]-bonds in the structure of \[{{H}_{2}}S{{O}_{3}},\,{{H}_{2}}S{{O}_{4}}\] and \[{{H}_{2}}{{S}_{2}}{{O}_{7}}\] is: [JEE Online 09-04-2017]

A)

\[{{H}_{2}}{{S}_{2}}{{O}_{7}}>{{H}_{2}}S{{O}_{3}}>{{H}_{2}}S{{O}_{4}}\]

B)

\[{{H}_{2}}{{S}_{2}}{{O}_{7}}>{{H}_{2}}S{{O}_{4}}>{{H}_{2}}S{{O}_{3}}\]

C)

\[{{H}_{2}}S{{O}_{4}}>{{H}_{2}}{{S}_{2}}{{O}_{7}}>{{H}_{2}}S{{O}_{3}}\]

D)

\[{{H}_{2}}S{{O}_{3}}>{{H}_{2}}S{{O}_{4}}>{{H}_{2}}{{S}_{2}}{{O}_{7}}\]

View Answer
77) At 300 K, the density of a certain gaseous molecule at 2 bar is double to that of dinitrogen \[({{N}_{2}})\] at 4 bar. The molar mass of gaseous molecule is: [JEE Online 09-04-2017]

A)

\[224\,g\,mo{{l}^{-1}}\]

B)

\[112\,g\,mo{{l}^{-1}}\]

C)

\[56\,g\,mo{{l}^{-1}}\]

D)

\[28\,g\,mo{{l}^{-1}}\]

View Answer
78) A gas undergoes change from state A to state B. In this process, the heat absorbed and work done by the gas is 5 J and 8 J, respectively. Now gas is brought back to A by another process during which 3 J of heat is evolved. In this reverse process of B to A: [JEE Online 09-04-2017]

A)

6 J of the work will be done by the gas

B)

6 J of the work will be done by the surrounding on gas.

C)

10 J of the work will be done by the surrounding on gas.

D)

10 J of the work will be done by the gas

View Answer
79) Which of the following is a biodegradable polymer?        [JEE Online 09-04-2017]

A)



B)

C)



D)



View Answer
80) \[Xe{{F}_{6}}\] on partial hydrolysis with water produces a compound ?X?. The same compound ?X? is formed when \[Xe{{F}_{6}}\] reacts with silica. The compound ?X? is: [JEE Online 09-04-2017]

A)

\[Xe{{F}_{4}}\]

B)

\[Xe{{F}_{2}}\]

C)

\[Xe{{O}_{3}}\]

D)

\[XeO{{F}_{4}}\]

View Answer
81) In the following structure, the double bonds are marked as I, II, III and IV. Geometrical isomerism is not possible at site (s): [JEE Online 09-04-2017]

A)

I and III

B)

III

C)

I

D)

III and IV

View Answer
82) Adsorption of a gas on a surface follows Freundlich adsorption isotherm. Plot of \[\frac{x}{m}\] versus log p gives a straight line with slope equal to 0.5, then : (\[\frac{x}{m}\] is the mass of the gas adsorbed per gram of adsorbent) [JEE Online 09-04-2017]

A)

Adsorption is proportional to the square root of pressure.

B)

Adsorption is proportional to the square of pressure.

C)

Adsorption is proportional to the pressure.

D)

Adsorption is independent of pressure.

View Answer
83) The incorrect statement among the following is: [JEE Online 09-04-2017]

A)

\[\alpha \]-D-glucose and \[\beta \]-D-glucose are enantiomers.

B)

The penta acetate of glucose does not react with hydroxyl amine.

C)

\[\alpha \]-D-glucose and \[\beta \]-D-glucose are anomers.

D)

Cellulose is a straight chain polysaccharide made up of only \[\beta \]-D-glucose units.

View Answer
84) In the following reaction sequence : \[\underset{({{C}_{3}}{{H}_{6}}C{{l}_{2}})}{\mathop{I}}\,\,\xrightarrow{KOH\,(aq)}\,II\,\xrightarrow[(II)\,{{H}_{2}}O/{{H}^{+}}]{(I)\,C{{H}_{3}}MgBr}\,III\,\xrightarrow{Anhy.\,ZnC{{l}_{2}}+Conc.\,HCl}\]\[\,gives\,turbidity\,immediately\] The compound I is: [JEE Online 09-04-2017]

A)

\[C{{H}_{3}}-\underset{\begin{smallmatrix} \,\,\,| \\ Cl \end{smallmatrix}}{\overset{\begin{smallmatrix} Cl \\ \,\,| \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]

B)

\[Cl-\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}C{{H}_{3}}\]

C)

\[\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,-\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{3}}\]

D)

\[\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\]

View Answer
85) The major product of the following reaction is: [JEE Online 09-04-2017]

A)

B)

C)

D)

View Answer
86) Among the following compounds, the increasing order of their basic strength is: [JEE Online 09-04-2017] (I)              (II) (III)           (IV)

A)

(II) < (I) < (III) < (IV)

B)

(II) < (I) < (IV) < (III)

C)

(I) < (II) < (IV) < (III)

D)

(I) < (II) < (III) < (IV)

View Answer
87) What quantity (in mL) of a 45% acid solution of a mono-protic strong acid must be mixed with a 20% solution of the same acid to produce 800 mL of a 29.875% acid solution? [JEE Online 09-04-2017]

A)

316

B)

320

C)

325

D)

330

View Answer
88) To find the standard potential of \[{{M}^{3+}}/M\] electrode, the following cell is constituted: \[Pt/M/{{M}^{3+}}\]                [JEE Online 09-04-2017]\[(0.\,001\,\,mol\,{{L}^{-1}})\,/A{{g}^{+}}\,(0.01\,\,mol\,{{L}^{-1}}\,)/Ag\]. The emf of the cell is found to be 0.421 volt at 298 K. The standard potential of half reaction \[{{M}^{3+}}\] \[+3{{e}^{-}}\to M\] at 298 K will be : (Given \[{{E}^{\odot -}}_{A{{g}^{+}}/Ag}\] at 298 K = 0.80 volt)

A)

0.38 volt

B)

1.28 volt

C)

0.32 volt

D)

0.66 volt

View Answer
89) Which of the following is a set of greenhouse gases?      [JEE Online 09-04-2017]

A)

\[{{O}_{3}},\,N{{O}_{2}},\,S{{O}_{2}},\,C{{l}_{2}}\]

B)

\[C{{H}_{4}},\,{{O}_{3}},\,{{N}_{2}},\,S{{O}_{2}}\]

C)

\[C{{O}_{2}},\,C{{H}_{4}},\,{{N}_{2}}O,\,{{O}_{3}}\]

D)

\[{{O}_{3}},\,{{N}_{2}},\,C{{O}_{2}},\,N{{O}_{2}}\]

View Answer
90) Which of the following compounds will show highest dipole moment? [JEE Online 09-04-2017] (I)                    (II) (III)             (IV)

A)

(II)

B)

(IV)

C)

(III)

D)

(I)

View Answer