Solved papers for JEE Main & Advanced JEE Main Paper (Held On 10 April 2016)

JEE Main Paper (Held On 10 April 2016) Total Questions - 90

1) A bottle has an opening of radius a and length b. A cork of length b and radius \[\left( a+\Delta a \right)\] where \[\left( \Delta a<        JEE Main Online Paper (Held On 10 April 2016)

A)

\[\left( 2\pi g\mu B\,\,b \right)\Delta a\]

B)

\[\left( \pi \mu B\,\,b \right)\Delta a\]

C)

\[\left( \pi \mu \,B\,\,b \right)a\]

D)

\[\left( 4\pi \mu \,B\,\,b \right)\Delta a\]

View Answer
2) Consider an electromagnetic wave propagating in vacuum. Choose the correct statement : JEE Main Online Paper (Held On 10 April 2016)

A)

For an electromagnetic wave propagating in +y direction the electric field is \[\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( x,t \right)\hat{z}\]and the magnetic field is \[\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{z}}\left( x,t \right)\hat{y}\]

B)

For an electromagnetic wave propagating in +y direction the electric field is \[\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( x,t \right)\hat{y}\]and he magnetic field is\[\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{yz}}\left( x,t \right)\hat{z}\]

C)

For an electromagnetic wave propagating in +x direction the electric field is \[\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( y,z,t \right)\left( \hat{y}+\hat{z} \right)\]and the magnetic field is\[\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{yz}}\left( y,z,t \right)\left( \hat{y}+\hat{z} \right)\]

D)

For an electromagnetic wave propagating in +x direction the electric field is \[\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( x,t \right)\left( \hat{y}-\hat{z} \right)\]and eh magnetic field is \[B=\frac{1}{\sqrt{2}}{{B}_{yz}}\left( x,t \right)\left( \hat{y}+\hat{z} \right)\]

View Answer
3) A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 divisions when \[R=2400\,\,\Omega \].Deflection becomes 20 divisions when resistance taken form resistance box is\[4900\,\,\,\Omega \]. Then we can conclude: JEE Main Online Paper (Held On 10 April 2016)

A)

Resistance required on R.B. For a deflection of 10 divisions is \[9800\,\,\,\Omega \].

B)

Full scale deflection current is 2 mA.

C)

Current sensitivity of galvanometer is \[20\mu A/\] division.

D)

Resistance of galvanometer is \[200\,\,\Omega \]

View Answer
4) A carnot freezer takes heat from water at \[^{o}C\] inside it and rejects it to the room at a temperature of\[{{27}^{o}}C\]. The latent heat of ice is\[336\times {{10}^{3}}J\,k{{g}^{-1}}\]. If 5 kg of water at \[{{0}^{o}}C\]is converted into ice at \[{{0}^{o}}C\]by the freezer, then the energy consumed by the freezer is close to: JEE Main Online Paper (Held On 10 April 2016)

A)

\[1.68\times {{10}^{6}}J\]

B)

\[1.71\times {{10}^{7}}J\]

C)

\[1.51\times {{10}^{5}}J\]

D)

1\[1.67\times {{10}^{5}}J\]

View Answer
5) A realistic graph depicting the variation of the reciprocal of input resistance in an input characteristics measurement in a common emitter transistor configuration is : JEE Main Online Paper (Held On 10 April 2016)

A)

B)

C)

D)

View Answer
6) A particle of mass m is acted upon by a force F given by the empirical law \[F=\frac{R}{{{t}^{2}}}V(t)\].If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot : JEE Main Online Paper (Held On 10 April 2016)

A)

log v(t) against t

B)

v(t) against\[{{t}^{2}}\]

C)

log v(t) against\[\frac{1}{{{t}^{2}}}\]

D)

log v(t) against\[\frac{1}{t}\]

View Answer
7) A fighter plane of length 20m, wing span (distance from tip of one wing to the tip of the other wing) of 15m and height 5m is flying towards east over Delhi. Its speed is \[240\,m{{s}^{-1}}\]The earth's magnetic field over Delhi is \[5\times {{10}^{-5}}\]T with the declination angle \[\sim {{0}^{o}}\] and dip of \[\theta \]such that sin\[\theta =\frac{2}{3}\].If the voltage developed is \[{{V}_{B}}\] between the lower and upper side of the plane and \[{{V}_{w}}\]. between the tips the wings then\[{{V}_{B}}\] and VW are closed to: JEE Main Online Paper (Held On 10 April 2016)

A)

\[{{V}_{B}}=40mV,{{V}_{w}}=135mV\] with left side of pilot at higher voltage.

B)

\[{{V}_{B}}=40mV,{{V}_{w}}=135mV\] with right side of pilot at high voltage.

C)

\[{{V}_{B}}=45mV,{{V}_{w}}=120mV\] with left side of pilot at higher voltage.

D)

\[{{V}_{B}}=45mV,{{V}_{w}}=120mV\]with right side of pilot at higher voltage.

View Answer
8) To get an output of 1 from the circuit shown in figure the input must be : JEE Main Online Paper (Held On 10 April 2016)

A)

=1, b =1, c = 0

B)

a = 1, b =0, c = 0

C)

a =0, b = 0, c = 1

D)

a =1, b =0, c = 1

View Answer
9) To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are: JEE Main Online Paper (Held On 10 April 2016)

A)

Four

B)

Two

C)

Three

D)

Five

View Answer
10) An astronaut of mass m is working on a satellite orbiting the earth at a distance h. from the earth's surface. The radius of the earth is R, while its mass is M. The gravitational pull FG on the astronaut is: JEE Main Online Paper (Held On 10 April 2016)

A)

\[{{F}_{G}}\frac{G{{M}_{m}}}{{{\left( R+h \right)}^{2}}}\]

B)

zero since astronaut feels weightless

C)

\[\frac{G{{M}_{m}}}{{{\left( R+h \right)}^{2}}}<{{F}_{G}}<\frac{G{{M}_{m}}}{{{R}^{2}}}\]

D)

\[0<{{F}_{G}}<\frac{G{{M}_{m}}}{{{R}^{2}}}\]

View Answer
11) In the figure shown/ ABC is a uniform wire. If centre of mass wire lies vertically below point A, then\[\frac{BC}{AB}\] JEE Main Online Paper (Held On 10 April 2016)

A)

1.85

B)

1.5

C)

3

D)

1.37

View Answer
12) A neutron moving with a speed 'v' makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is: JEE Main Online Paper (Held On 10 April 2016)

A)

10.2 eV

B)

12.1 eV

C)

20.4 eV

D)

16.8 eV

View Answer
13) Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to : (Take the radius of the drum to be 1.25m and its axle to be horizontal): JEE Main Online Paper (Held On 10 April 2016)

A)

1.3

B)

0.4

C)

27.0

D)

8.0

View Answer
14) A photoelectric surface is illuminated successively by monochromatic light of wavelengths \[\]and\[\frac{}{3}\]. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 time that in the first case, the work function of the surface is : JEE Main Online Paper (Held On 10 April 2016)

A)

\[\frac{3hc}{}\]

B)

\[\frac{hc}{}\]

C)

\[\frac{hc}{3}\]

D)

\[\frac{hc}{2}\]

View Answer
15) A,B,C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C in (BD) holds ture .Then which of the combination is not a meaningful quantity? JEE Main Online Paper (Held On 10 April 2016)

A)

\[{{A}^{2}}-{{B}^{2}}{{C}^{2}}\]

B)

\[\frac{A}{B}-C\]

C)

\[\frac{C}{BD}-\frac{A{{D}^{2}}}{C}\]

D)

\[\frac{(A-C)}{D}\]

View Answer
16) A thin 1m long rod has a radius of 5 mm. A force of \[50\,\,\pi kN\]is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false? JEE Main Online Paper (Held On 10 April 2016)

A)

The maximum value of Y that can be determined is \[{{10}^{14}}N/{{m}^{2}}\]

B)

\[\frac{\Delta Y}{Y}\]?gets minimum contribution from the uncertainty in the length.

C)

The figure of merit is the larges for the length of the rod.

D)

\[\frac{\Delta Y}{Y}\]gets its maximum contribution from the uncertainty in strain.

View Answer
17) Figure shows a network of capacitors where the number indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be \[1\mu F\]is: JEE Main Online Paper (Held On 10 April 2016)

A)

\[\frac{33}{23}\mu F\]

B)

\[\frac{31}{23}\mu F\]

C)

\[\frac{32}{23}\mu F\]

D)

\[\frac{34}{23}\mu F\]

View Answer
18) Which of the following shown the correct relationship between the pressure 'P' and density 'P' of an ideal gas at constant temperature? JEE Main Online Paper (Held On 10 April 2016)

A)

B)

C)

D)

View Answer
19) A hemispherical glass body of radius 10cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen: JEE Main Online Paper (Held On 10 April 2016)

A)

20 cm below flat surface

B)

30 cm below flat surface

C)

16 cm below flat surface

D)

14 cm below flat surface

View Answer
20) In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rest son top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer longer stays in contact with the piston, is closed to : JEE Main Online Paper (Held On 10 April 2016)

A)

0.7 Hz

B)

1.2 Hz

C)

1.9 Hz

D)

0.1 Hz

View Answer
21) Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30cm. The wavelength of light 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year \[=9.46\times {{10}^{15}}\]m) of the order of: JEE Main Online Paper (Held On 10 April 2016)

A)

\[{{10}^{8}}km\]

B)

\[{{10}^{6}}km\]

C)

\[{{10}^{11}}km\]

D)

\[{{10}^{10}}km\]

View Answer
22) A conducting metal circular -wire loop of radius r is placed perpendicular to a magnetic field which varies with time as \[B={{B}_{0e}}^{-t/\tau }\], where B0 and \[\tau \]are constants, at t = 0 . If the resistance of the loop is R then the heat generated in the loop after a long time \[(t-\infty )\] is: JEE Main Online Paper (Held On 10 April 2016)

A)

\[\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}R}{\tau }\]

B)

\[\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}}{2\tau R}\]

C)

\[\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}}{\tau R}\]

D)

\[\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}}{2\tau R}\]

View Answer
23) A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by \[{{n}^{2}}R\,{{t}^{2}}\]where n is a constant. The power delivered to the particle by the force acting on it, is: JEE Main Online Paper (Held On 10 April 2016)

A)

\[M\,\,n\,{{R}^{2}}\,{{t}^{2}}\]

B)

\[\frac{1}{2}M{{n}^{2}}{{R}^{2}}{{t}^{2}}\]

C)

\[M\,{{n}^{2}}{{R}^{2}}t\]

D)

\[M\,n\,{{R}^{2}}\,t\]

View Answer
24) The ratio (R) of output resistance \[{{r}_{0}}\], and the input resistance \[{{r}_{1}}\]in measurements of input and out put characteristics of a transistor is typically in the range: JEE Main Online Paper (Held On 10 April 2016)

A)

\[R\sim 0.1-0.01\]

B)

\[R\sim 0.1-1.0\]

C)

\[R\sim {{10}^{2}}-{{10}^{^{3}}}\]

D)

\[R\sim 1-{{10}^{{}}}\]

View Answer
25) A modulated signal \[{{C}_{m}}\,\,(t)\]has the form \[{{C}_{m}}\,\,(t)=30\,\sin \,300\pi t+10\,(\cos \,200\pi t-\cos 400\pi t)\].The carrier frequency fc, the modulating frequency (message frequency) \[{{f}_{\omega }}\], and the modulation index \[\mu \]are respectively given by : JEE Main Online Paper (Held On 10 April 2016)

A)

\[{{f}_{c}}=200\,Hz\,;\,{{f}_{\omega }}=30Hz\,;\,\mu =\frac{1}{2}\]

B)

\[{{f}_{c}}=150\,Hz\,;\,{{f}_{\omega }}=50Hz\,;\,\mu =\frac{2}{3}\]

C)

\[{{f}_{c}}=200\,Hz\,;\,{{f}_{\omega }}=50Hz\,;\,\mu =\frac{1}{2}\]

D)

\[{{f}_{c}}=150\,Hz\,;\,{{f}_{\omega }}=30Hz\,;\,\mu =\frac{1}{3}\]

View Answer
26) The resistance of an electrical toaster has a temperature dependence given by \[R\,\,(T)={{R}_{0}}[1+\alpha (T-{{T}_{0}}]\]in its range of operation. At \[{{T}_{0}}=300\,K,\,R=100\Omega \]. And at\[T=500\,K,\,R=120\Omega \]. The toaster is connected to a voltage source at 200 V and its temperature is raised at a constant rate form300 to 500 K in 30s. The total work done in raising the temperature is: JEE Main Online Paper (Held On 10 April 2016)

A)

\[400\,In\frac{1.5}{1.3}J\]

B)

300 J

C)

\[200\,In\frac{2}{3}J\]

D)

\[400\,In\frac{5}{6}J\]

View Answer
27) Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed 'v' in a uniform magnetic field B going into the plane of the paper (see figure) . If charge densities \[{{\sigma }^{1}}\]and \[{{\sigma }^{2}}\] are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) JEE Main Online Paper (Held On 10 April 2016)

A)

             \[{{\sigma }_{1}}=\frac{-{{\varepsilon }_{0}}vB}{2},\,{{\sigma }_{2}}=\frac{-2{{\varepsilon }_{0}}vB}{2}\]

B)

             \[{{\sigma }_{1}}={{\sigma }_{2}}={{\varepsilon }_{0}}vB\]

C)

\[{{\sigma }_{1}}=\frac{{{\varepsilon }_{0}}vB}{2},\,{{\sigma }_{2}}=\frac{-{{\varepsilon }_{0}}vB}{2}\]

D)

             \[{{\sigma }_{1}}={{\varepsilon }_{0}}vB,\,{{\sigma }_{2}}=-{{\varepsilon }_{0}}vB\]

View Answer
28) Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is :

A)

12000 J

B)

12000 J

C)

4500 J

D)

9300 J

View Answer
29) A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beat per second. If the velocity of sound in air is340 m/s, the frequency of horn of the toy car is close to: JEE Main Online Paper (Held On 10 April 2016)

A)

340 Hz

B)

170 Hz

C)

510 Hz

D)

680 Hz

View Answer
30) Within a spherical charge distribution of charge density\[\rho (r)\], N equipotential surfaces of potential\[{{V}_{0}},\,{{V}_{0}}+\Delta V,{{V}_{0}}+2\Delta v\], ???..\[{{V}_{0}}+N\Delta V(\Delta V<0)\]are drawn and have increasing radii \[{{r}_{0}},{{r}_{1}}{{r}_{2}},.......{{r}_{N}}\],respectively. If the difference in the radii of the surface is constant for all values of \[{{V}_{0}}\] and \[\Delta V\] then: JEE Main Online Paper (Held On 10 April 2016)

A)

\[\rho (r)\alpha r\]

B)

\[\rho (r)\alpha \frac{1}{{{r}^{2}}}\]

C)

\[\rho (r)\alpha \frac{1}{r}\]

D)

\[\rho (r)\]= constant

View Answer
31) The correct statement about the synthesis of erythritol \[(C{{(C{{H}_{2}}OH)}_{4}})\]used in the preparation of PETN is: JEE Main Online Paper (Held On 10 April 2016)

A)

The synthesis requires two aldol condensations and two Cannizzaro reactions.

B)

Alpha hydrogens of ethanol and methanol are involved in this reaction.

C)

The synthesis requires four aldol condensations between methanol and ethanol.

D)

The synthesis requires three aldol condensations and one Cannizzaro reaction.

View Answer
32) The following statements concern elements in the periodic table. Which of the following is true? JEE Main Online Paper (Held On 10 April 2016)

A)

The Group 13 elements are all metals.

B)

All the elements in Group 17 are gases.

C)

Elements of Group 16 have lower ionization enthalpy values compared to those of Group 15 in the corresponding periods.

D)

For Group 15 elements, the stability of +5 oxidation state increases down the group.

View Answer
33) Identify the incorrect statement: JEE Main Online Paper (Held On 10 April 2016)

A)

Rhombic and monoclinic sulphur have S8 molecules.

B)

\[{{S}_{8}}\] ring has a crown shape.

C)

\[{{S}_{2}}\] is paramagnetic like oxygen.

D)

The S-S-S bond angles in the \[{{S}_{8}}\]and \[{{S}_{6}}\] rings are the same.

View Answer
34) Assertion: Among the carbon allotropes, diamond is an insulator, Whereas, graphite is a good conductor of electricity. Reason: Hybridization of carbon in diamond and graphite are \[s{{p}^{3}}\]and \[s{{p}^{2}},\]respectively. JEE Main Online Paper (Held On 10 April 2016)

A)

Both assertion and reason are correct, but the reason is not the correct explanation for the assertion.

B)

Assertion is incorrect statement, but the reason is correct.

C)

Both assertion and reason are correct, and the reason is the correct explanation for the assertion.

D)

Both assertion and reason are incorrect.

View Answer
35) The "N" which does not contribute to the basicity for the compound is : JEE Main Online Paper (Held On 10 April 2016)

A)

N 7

B)

N 1

C)

N 9

D)

N 3

View Answer
36) Bromination of cyclohexene under conditions given below yields: JEE Main Online Paper (Held On 10 April 2016)

A)

B)

C)

D)

View Answer
37) The commercial name for calcium oxide is: JEE Main Online Paper (Held On 10 April 2016)

A)

Quick lime

B)

Milk of lime

C)

Slaked lime

D)

Limestone

View Answer
38) Which one of the following reagents is not suitable for the elimination reaction ? JEE Main Online Paper (Held On 10 April 2016)

A)

NaI

B)

                                                                                 \[NaOH/{{H}_{2}}O-EtOH\]

C)

                                                                                       \[NaOH/{{H}_{2}}O\]

D)

                                                                                            \[NaOEt/EtOH\]

View Answer
39) Which of the following is a bactericidal antibiotic?

A)

Erythromycin

B)

Tetracycline

C)

Ofloxacin

D)

Chloramphenicol

View Answer
40) A solid XY kept in an evacuated sealed container undergoes decomposition to form a mixture of gases X and Y at temperature T. The equilibrium pressure is 10 bar in this vessel.                                                                                                 \[{{K}_{P}}\] for this reaction is : JEE Main Online Paper (Held On 10 April 2016)

A)

25

B)

5

C)

0

D)

100

View Answer
41) The transition metal ions responsible for color in ruby and emerald are, respectively : JEE Main Online Paper (Held On 10 April 2016)

A)

\[\text{C}{{\text{r}}^{\text{3+}}}\,\text{and}\,\,\text{C}{{\text{r}}^{\text{3+}}}\]

B)

\[\text{C}{{\text{o}}^{\text{3+}}}\,\text{and}\,\,\text{C}{{\text{o}}^{\text{3+}}}\]

C)

\[\text{C}{{\text{o}}^{\text{3+}}}\,\text{and}\,\,\text{C}{{\text{r}}^{\text{3+}}}\]

D)

\[\text{C}{{\text{r}}^{\text{3+}}}\,\text{and}\,\,\text{C}{{\text{o}}^{\text{3+}}}\]

View Answer
42) Which of the following polymers is synthesized using a free radical polymerization technique? JEE Main Online Paper (Held On 10 April 2016)

A)

Teflon

B)

Melamine polymer

C)

Nylon 6,6

D)

Terylene

View Answer
43) Extraction of copper by smelting uses silica as an additive to remove : JEE Main Online Paper (Held On 10 April 2016)

A)

FeS

B)

FeO

C)

\[C{{u}_{2}}S\]

D)

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

View Answer
44) Initially, the root mean square (rms) velocity of \[{{N}_{2}}\]molecules at certain temperature is u. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be : JEE Main Online Paper (Held On 10 April 2016)

A)

2 u

B)

14 u

C)

u / 2

D)

4 u

View Answer
45) Gold numbers of some colloids are : Gelatin : 0.005 - 0.01, Gum Arabic : 0.15 - 0.25 ; Ole ate : 0.04 - 1.0 ; Starch : 15 - 25. Which among these is a better protective colloid ? JEE Main Online Paper (Held On 10 April 2016)

A)

Gelatin

B)

Starch

C)

Gum Arabic

D)

Ole ate

View Answer
46) Fluorination of an aromatic ring is easily accomplished by treating a diazonium salt with HBF4. Which of the following conditions is correct about this reaction? JEE Main Online Paper (Held On 10 April 2016)

A)

Only heat

B)

\[NaN{{O}_{2}}/Cu\]

C)

\[C{{u}_{2}}O/{{H}_{2}}O\]

D)

\[NaF/Cu\]

View Answer
47) Identify the correct statement: JEE Main Online Paper (Held On 10 April 2016)

A)

Corrosion of iron can be minimized by forming an impermeable barrier at its surface.

B)

Iron corrodes in oxygen-free water.

C)

Iron corrodes more rapidly in salt water because its electrochemical potential is higher.

D)

Corrosion of iron can be minimized by forming a contact with another metal with a higher reduction potential.

View Answer
48) An aqueous solution of a salt \[M{{X}_{2}}\] at certain temperature has a van't Hoff factor of 2. The degree of dissociation for this solution of the salt is : JEE Main Online Paper (Held On 10 April 2016)

A)

0.67

B)

0.33

C)

0.80

D)

0.50

View Answer
49) Oxidation of succinate ion produces ethylene and carbon dioxide gases. On passing 0.2 Faraday electricity through an aqueous solution of potassium succinate, the total volume of gases (at both cathode and anode) at STP (1 atm and 273 K) is : JEE Main Online Paper (Held On 10 April 2016)

A)

6.72 L

B)

2.24 L

C)

4.48 L

D)

8.96 L

View Answer
50) If 100 mole of \[{{H}_{2}}{{O}_{2}}\]decompose at 1 bar and 300 K, the work done (kJ) by one mole of\[{{O}_{2}}(g)\] as it expands against 1 bar pressure is : \[2{{H}_{2}}{{O}_{2}}(l)2{{H}_{2}}O(l)+{{O}_{2}}(g)\] \[(R=8.3J\,{{K}^{-1}}mo{{l}^{-1}})\] JEE Main Online Paper (Held On 10 April 2016)

A)

498.00

B)

62.25

C)

124.50

D)

249.00

View Answer
51) Which of the following is an example of homoleptic complex ? JEE Main Online Paper (Held On 10 April 2016)

A)

\[[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]\]

B)

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

C)

\[[Co{{(N{{H}_{3}})}_{5}}Cl]C{{l}_{2}}\]

D)

\[[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]\]

View Answer
52) The bond angle H - X - H is the greatest in the compound : JEE Main Online Paper (Held On 10 April 2016)

A)

\[N{{H}_{3}}\]

B)

\[P{{H}_{3}}\]

C)

\[C{{H}_{4}}\]

D)

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

View Answer
53) The rate law for the reaction below is given by the expression k [A][B] \[A+B\to \]Product If the concentration of B is increased from 0.1 to 0.3 mole, keeping the value of A at 0.1 mole, the rate constant will be : JEE Main Online Paper (Held On 10 April 2016)

A)

9 k

B)

3 k

C)

k/3

D)

k

View Answer
54) Sodium extract is heated with concentrated \[HN{{O}_{3}}\] before testing for halogens because : JEE Main Online Paper (Held On 10 April 2016)

A)

Ag reacts faster with halides in acidic medium.

B)

Silver halides are totally insoluble in nitric acid.

C)

\[A{{g}_{2}}S\]and \[AgCN\] are soluble in acidic medium.

D)

\[{{S}^{2-}}\]and \[C{{N}^{-}},\]if present, are decomposed by conc. \[HN{{O}_{3}}\]and hence do not interfere in the test.

View Answer
55) Which one of the following substances used in dry cleaning is a better strategy to control environmental pollution? JEE Main Online Paper (Held On 10 April 2016)

A)

Nitrogen dioxide

B)

Sulphur dioxide

C)

Tetrachloroethylene

D)

Carbon dioxide

View Answer
56) Consider the reaction sequence below : JEE Main Online Paper (Held On 10 April 2016)

A)

B)

C)

D)

View Answer
57) Observation of "Rhumann's purple" is a confirmatory test for the presence of : JEE Main Online Paper (Held On 10 April 2016)

A)

Reducing sugar

B)

Starch

C)

Protein

D)

Cupric ion

View Answer
58) Aqueous solution of which salt will not contain ions with the electronic configuration \[1{{s}^{2}}2{{s}^{2}}{{p}^{6}}3{{s}^{2}}3{{p}^{6}}\] ? JEE Main Online Paper (Held On 10 April 2016)

A)

\[NaCl\]

B)

\[Ca{{I}_{2}}\]

C)

\[NaF\]

D)

\[KBr\]

View Answer
59) The volume of 0.1 N dibasic acid sufficient to neutralize 1 g of a base that furnishes 0.04 mole of \[O{{H}^{-}}\] in aqueous solution is : JEE Main Online Paper (Held On 10 April 2016)

A)

400 mL

B)

600 mL

C)

200 mL

D)

80 mL

View Answer
60) Identify the reaction which does not liberate hydrogen : JEE Main Online Paper (Held On 10 April 2016)

A)

Allowing a solution of sodium in liquid ammonia to stand.

B)

Reaction of zinc with aqueous alkali.

C)

Reaction of lithium hydride with \[{{B}_{2}}{{H}_{6}}.\]

D)

Electrolysis of acidified water using Pt electrodes.

View Answer
61)           Let C be a curve given by\[y(x)=1+\sqrt{4x-3},x>\frac{3}{4}\]. If P is a point on C, such that the tangent at P has slope\[\frac{2}{3}\], then a point through which the normal at P passes, is JEE Main Online Paper (Held On 10 April 2016)

A)

(3, - 4)

B)

(1, 7)

C)

(4, - 3)

D)

(2, 3)

View Answer
62) Let \[a{{ }_{1}},{{a}_{2}},{{a}_{3}}........\,\,{{a}_{n}}..........\]be in A.P. If \[{{a}_{3}}+{{a}_{7}}+{{a}_{11}}+{{a}_{15}}=72\] then the sum of its first 17 terms is equal to JEE Main Online Paper (Held On 10 April 2016)

A)

153

B)

306

C)

612

D)

204

View Answer
63) If \[A>0,\,B>0\]and \[B=\frac{\pi }{6}\], then the minimum value of tanA + tanB is JEE Main Online Paper (Held On 10 April 2016)

A)

\[2-\sqrt{3}\]

B)

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

C)

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

D)

\[4-2\sqrt{3}\]

View Answer
64) The contrapositive of the following statement, ?If the side of a square doubles, then its area increases four times", is                 JEE Main Online Paper (Held On 10 April 2016)

A)

If the area of a square does not increase four times, then its side is not doubled.

B)

If the area of a square increases four times, then its side is not doubled.

C)

If the area of a square increases four times, then its side is doubled.

D)

If the side of a square is not doubled, then its area does not increase four times.

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65) Let A be a \[3\times 3\] matrix such that \[{{A}^{2}}-5A+7I=0\]. Statement. - I : \[{{A}^{-1}}=\frac{1}{7}(5I-A)\]. Statement -II : The polynomial \[{{A}^{3}}-2{{A}^{2}}-3A+I\] can be reduced to \[5(A-41)\]. Then JEE Main Online Paper (Held On 10 April 2016)

A)

Statement- I is false, but Statement-II is true.

B)

Both the statements are false.

C)

Both the statements are true.

D)

Statement-I is true, but Statement-II is false.

View Answer
66) Equation of the tangent to the circle, at the point (1, - 1), whose centre is the point of intersection of the straight lines \[x-y=1\] and \[2x+y=3\] is JEE Main Online Paper (Held On 10 April 2016)

A)

\[3x-y-4=0\]

B)

\[x+4y+3=0\]

C)

\[x-3y-4=0\]

D)

\[4x+y-3=0\]

View Answer
67) The sum\[\sum\limits_{r=1\grave{\ }}^{10}{({{r}^{2}}+1)\times (r!)}\]is equal to JEE Main Online Paper (Held On 10 April 2016)

A)

\[10\times (11!)\]

B)

\[101\times (10!)\]

C)

\[(11!)\]

D)

\[11\times (11!)\]

View Answer
68) Let ABC be a triangle whose circumventer is at P. If the position vectors of A,B,C and P are \[\overrightarrow{a}\,,\,\overrightarrow{b},\,\,\overrightarrow{c}\]and\[\frac{\overrightarrow{a}\,,\,+\overrightarrow{b},\,+\,\overrightarrow{c}}{4}\]respectively, then the position vector of the orthocenter of this triangle, is JEE Main Online Paper (Held On 10 April 2016)

A)

\[\overrightarrow{0}\]

B)

\[-\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{2} \right)\]

C)

\[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\]

D)

\[\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{2} \right)\]

View Answer
69) Let \[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\]. Then f is an increasing function in the interval JEE Main Online Paper (Held On 10 April 2016)

A)

\[\left] \frac{\pi }{4},\frac{\pi }{2} \right[\]

B)

\[\left] \frac{5\pi }{8},\frac{3\pi }{4} \right[\]

C)

\[\left] 0,\frac{\pi }{4} \right[\]

D)

\[\left] \frac{\pi }{2},\frac{5\pi }{8} \right[\]

View Answer
70) Let \[z=1+ai\]be a complex number, a > 0 such that \[{{z}^{3}}\] is a real number. Then the sum \[1+z+{{z}^{2}}+.....+{{z}^{11}}\]is equal to JEE Main Online Paper (Held On 10 April 2016)

A)

\[-1250\sqrt{3}\,i\]

B)

\[1250\sqrt{3}\,i\]

C)

\[-1350\sqrt{3}\,i\]

D)

\[1365\sqrt{3}\,i\]

View Answer
71) Let \[P=\{\theta \,:\,\sin \theta -\cos \theta =\sqrt{2}\cos \theta =\sqrt{2}\cos \theta \}\]and \[Q=\{\theta :\sin +\cos \theta =\sqrt{2}\,\sin \theta \}\] be two sets. Then JEE Main Online Paper (Held On 10 April 2016)

A)

\[Q\,\not\subset P\]

B)

\[P\,\not\subset Q\]

C)

\[P\subset Q\,\]and \[Q-P\ne \phi \]

D)

P = Q

View Answer
72) The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1,2 and 6, then the mean deviation from the mean of the data is JEE Main Online Paper (Held On 10 April 2016)

A)

2.5

B)

2.8

C)

2.6

D)

2.4

View Answer
73) The number of distinct real values of \[\lambda \] for which the lines \[\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{2}=\frac{z+3}{{{}^{2}}}\]and\[\frac{x-3}{1}=\frac{y-2}{{{}^{2}}}=\frac{z-1}{2}\]are coplanar is JEE Main Online Paper (Held On 10 April 2016)

A)

3

B)

2

C)

1

D)

4

View Answer
74) The angle of elevation of the top of a vertical tower from a point A, due east of it is \[{{45}^{o}}\]. The angle of elevation of the top of the same tower from a point B, due south of A is \[{{30}^{o}}\]. If the distance between A and B is \[54\sqrt{2}\]m, then the height of the tower (in metres), is JEE Main Online Paper (Held On 10 April 2016)

A)

54

B)

108

C)

\[54\sqrt{3}\]

D)

36 3

View Answer
75) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{(1-\cos 2x)}^{2}}}{2x\ \tan x-x{{\tan }^{2}}x}\]is JEE Main Online Paper (Held On 10 April 2016)

A)

\[2\]

B)

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

C)

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

D)

\[-2\]

View Answer
76) The solution of the differential equation\[\frac{dy}{dx}+y\frac{y}{2}\sec \,x=\frac{\tan x}{2y}\], where\[\le \,x<\frac{\pi }{2}\] and y(0) = 1, is given by JEE Main Online Paper (Held On 10 April 2016)

A)

\[{{y}^{2}}=1-\frac{x}{\sec x\,+\tan x}\]

B)

\[{{y}^{2}}=1+\frac{x}{\sec x\,+\tan x}\]

C)

\[y=1+\frac{x}{\sec x\,+\tan x}\]

D)

\[y=1-\frac{x}{\sec x\,+\tan x}\]

View Answer
77) P and Q are two distinct points on the parabola, \[{{y}^{2}}=4x\], with parameters t and \[{{t}_{1}}\] respectively. If the normal at p passes through Q, then the minimum value of \[t_{1}^{2}\] is JEE Main Online Paper (Held On 10 April 2016)

A)

4

B)

6

C)

8

D)

2

View Answer
78) A hyperbola whose transverse axis is along the major axis of the conic,\[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=4\] and has vertices at the foci of this conic. If the eccentricity of the hyperbola is\[\frac{3}{2}\], then which of the following points does NOT lie on it? JEE Main Online Paper (Held On 10 April 2016)

A)

\[\left( \sqrt{5},2\sqrt{2} \right)\]

B)

\[\left( 5,2\sqrt{3} \right)\]

C)

\[\left( 0,\,\,2 \right)\]

D)

\[\left( \sqrt{10},\,\,2\sqrt{3} \right)\]

View Answer
79) For \[x\,\in \,R,\,x\,\ne 0\], if y(x) is a differentiable function such that\[x\int\limits_{1}^{x}{y(t)dt=(x+1)\int\limits_{1}^{x}{ty(t)dt}}\], then y(x) equals(where C is a constant) JEE Main Online Paper (Held On 10 April 2016)

A)

\[C{{x}^{3}}{{e}^{\frac{1}{x}}}\]

B)

\[\frac{C}{x}{{e}^{\frac{-1}{x}}}\]

C)

\[\frac{C}{{{x}^{2}}}{{e}^{-\frac{1}{x}}}\]

D)

\[\frac{C}{{{x}^{3}}}{{e}^{-\frac{1}{x}}}\]

View Answer
80) ABC is a triangle in a plane with vertices A(2,3,5), B(-1,3,2) and C\[(\lambda ,\,\,5,\,\,\mu )\]. If the median through A is equally inclined to the coordinate axes, then the value of (\[({{\lambda }^{3}}+{{\mu }^{3}}+5)\]is JEE Main Online Paper (Held On 10 April 2016)

A)

676

B)

1130

C)

1348

D)

1077

View Answer
81) A ray of light is incident along a line which meets another line, \[7x-y+1=0\], at the point (0, 1). The ray is then reflected from this point along the line, \[y+2x=1\]. Then the equation of the line of incidence of the ray of light is JEE Main Online Paper (Held On 10 April 2016)

A)

\[41x+38y-38=0\]

B)

\[41x-38y+38=0\]

C)

\[41x+25y-25=0\]0

D)

\[41x-25y+25=0\]

View Answer
82) A straight line through origin O meets the line \[3y=10-4x\] and \[8x+6y+5=0\] at points A and Respectively. Then O divides the segment AB in the ratio JEE Main Online Paper (Held On 10 April 2016)

A)

3 : 4

B)

1 : 2

C)

2 : 3

D)

4 : 1

View Answer
83) The value of the integral\[\int\limits_{4}^{10}{\frac{[{{x}^{2}}]dx}{[{{x}^{2}}-28x+196]+[{{x}^{2}}]}}\] , where [x] denotes the greatest integer less than or equal to x, is JEE Main Online Paper (Held On 10 April 2016)

A)

3

B)

       7

C)

                6

D)

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

View Answer
84) If \[\frac{^{n+2}{{C}_{6}}}{^{n-2}{{P}_{2}}}=11\], then n satisfies the equation JEE Main Online Paper (Held On 10 April 2016)

A)

\[{{n}^{2}}+n-110=0\]

B)

\[{{n}^{2}}+5n-84=0\]

C)

\[{{n}^{2}}+3n-180=0\]

D)

\[{{n}^{2}}+2n-80=0\]

View Answer
85) If the coefficients of \[{{x}^{-2}}\] and \[{{x}^{-4}}\] in the expansion of, \[{{\left( {{x}^{\frac{1}{3}}}\frac{1}{2{{x}^{\frac{1}{3}}}} \right)}^{18}}\] , (x > 0) )are m and n respectively, then \[\frac{m}{n}\] is equal to JEE Main Online Paper (Held On 10 April 2016)

A)

\[\frac{5}{4}\]

B)

\[\frac{4}{5}\]

C)

\[27\]

D)

\[182\]

View Answer
86) If \[A=\left[ \begin{matrix} -4 & -1 \\ 3 & 1 \\ \end{matrix} \right]\], then the determinant of the matrix \[({{A}^{2016}}-2{{A}^{2015}}-{{A}^{2014}})\] is JEE Main Online Paper (Held On 10 April 2016)

A)

\[2014\]

B)

\[2016\]

C)

\[-175\]

D)

\[- 25\]

View Answer
87) If x is a solution of the equation, \[\sqrt{2x+1}-\sqrt{2x-1}=1\,,\,\,\left( x\le \frac{1}{2} \right)\] , then \[\sqrt{4{{x}^{2}}-1}\] is equal to JEE Main Online Paper (Held On 10 April 2016)

A)

\[2\]

B)

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

C)

\[2\sqrt{2}\]

D)

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

View Answer
88) An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is JEE Main Online Paper (Held On 10 April 2016)

A)

\[\frac{192}{729}\]

B)

\[\frac{256}{729}\]

C)

\[\frac{240}{729}\]

D)

\[\frac{496}{729}\]

View Answer
89) The integral \[\int{\frac{dx}{\left( 1+\sqrt{x} \right)\sqrt{x-{{x}^{2}}}}}\] is equal to (where C is a constant of integration) JEE Main Online Paper (Held On 10 April 2016)

A)

\[-2\sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+C\]

B)

\[-2\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C\]

C)

\[-\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C\]

D)

\[2\sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+C\]

View Answer
90) Let a,b \[\in \] R, \[(a\ne 0)\] If the function f defined as \[f(x)=\left\{ \begin{matrix}    2{{x}^{2}}, & 0\le x<1 \\    a, & {} \\    a, & 1\le x<\sqrt{2} \\    \frac{2{{b}^{2}}-4b}{{{x}^{3}}} & \sqrt{2}\le x<\infty   \\ \end{matrix} \right.\]

A)

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

B)

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

C)

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

D)

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

View Answer