Solved papers for JEE Main & Advanced JEE Main Paper (Held On 12 April 2014)

JEE Main Paper (Held On 12 April 2014) Total Questions - 90

1) From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{ch}{2\pi \varepsilon _{o}^{2}}\]

B)

\[\frac{{{e}^{2}}}{2\pi \varepsilon _{o}^{{}}Gm_{e}^{2}}\](\[{{m}_{e}}=\] mass of electron)

C)

\[\frac{{{\mu }_{o}}{{\varepsilon }_{o}}}{{{c}^{2}}}\frac{G}{h{{e}^{2}}}\]

D)

\[\frac{2\pi \sqrt{{{\mu }_{o}}{{\varepsilon }_{o}}}}{c{{e}^{2}}}\frac{h}{G}\]

View Answer
2) A person climbs up a stalled escalator in 60 s. If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

37 s

B)

27 s

C)

24 s

D)

45 s

View Answer
3)                 Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{u}{12}\left( \hat{i}+\sqrt{3}\hat{j} \right)\]

B)

\[\frac{u}{12}\left( \hat{i}-\sqrt{3}\hat{j} \right)\]

C)

\[\frac{u}{12}\left( -\hat{i}+\sqrt{3}\hat{j} \right)\]

D)

\[\frac{u}{12}\left( -\hat{i}-\sqrt{3}\hat{j} \right)\]

View Answer
4) A bullet of mass 4g is fired horizontally with a speed of 300 m/s into 0.8 kg block of wood at rest on a table. If the coefficient of friction between the block and the table is 0.3, how far will the block slide approximately? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

0.19 m

B)

0.379 m

C)

0.569 m

D)

0.758 m

View Answer
5) A spring of unstretched length l has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{1}{2}m{{v}^{2}}\]

B)

\[m{{v}^{2}}\]

C)

\[\frac{1}{3}m{{v}^{2}}\]

D)

\[\frac{1}{6}m{{v}^{2}}\]

View Answer
6) A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The centre of circle is marked by 'C'. The angular momentum from the origin O can be written as: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[va(1+cos2\theta )\]

B)

\[va(1+cos\theta )\]

C)

\[vacos2\theta \]

D)

\[va\]

View Answer
7) Two hypothetical planets of masses m1 and m2 are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ?d?? (Speed of \[{{m}_{1}}\] is \[{{v}_{1}}\] and that of \[{{m}_{2}}\] is \[{{v}_{2}}\]) [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[{{v}_{1}}={{v}_{2}}\]

B)

\[{{v}_{1}}={{m}_{2}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}\] \[{{v}_{2}}={{m}_{1}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}\]

C)

\[{{v}_{1}}={{m}_{1}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}\]\[{{v}_{2}}={{m}_{2}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}\]

D)

\[{{v}_{2}}={{m}_{2}}\sqrt{\frac{2G}{{{m}_{1}}}}\] \[{{v}_{2}}={{m}_{2}}\sqrt{\frac{2G}{{{m}_{2}}}}\]

View Answer
8) Steel ruptures when a shear of \[3.5\times {{10}^{8}}N{{m}^{-2}}\]is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[1.4\times {{10}^{4}}N\]

B)

\[2.7\times {{10}^{4}}N\]

C)

\[3.3\times {{10}^{4}}N\]

D)

\[1.1\times {{10}^{4}}N\]

View Answer
9) A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius 'a'. The time in which it will be emptied is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{2A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]

B)

\[\frac{\sqrt{2}A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]

C)

\[\frac{2\sqrt{2}A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]

D)

\[\frac{A}{\sqrt{2}\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]

View Answer
10) Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S change in total surface area, T is the surface tension and P atmospheric pressure, then which of the following relation is correct? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

4PV + 3ST = 0

B)

3PV + 4ST = 0

C)

2PV + 3ST = 0

D)

3PV + 2ST = 0

View Answer
11) Hot water cools from \[60{}^\circ C\] to \[50{}^\circ C\] in the first 10 minutes and to \[42{}^\circ C\] in the next 10 minutes. The temperature of the surroundings is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[25{}^\circ C\]

B)

\[10{}^\circ C\]

C)

\[15{}^\circ C\]

D)

\[20{}^\circ C\]

View Answer
12) A Carnot engine absorbs 1000 J of heat energy from a reservoir at \[127{}^\circ C\] and rejects 600 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[20%\text{ }and\,\,-43{}^\circ C\]

B)

\[40%\text{ }and\,\,-33{}^\circ C\]

C)

\[50%\text{ }and\,\,-20{}^\circ C\]

D)

\[70%\text{ }and\,\,-10{}^\circ C\]

View Answer
13) At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 \[\text{m}{{\text{s}}^{\text{-1}}}\]. The gas is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

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

B)

\[C{{l}_{2}}\]

C)

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

D)

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

View Answer
14) Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[a+bx-c{{x}^{2}}\]

B)

\[b{{x}^{2}}\]

C)

\[a-bx+c{{x}^{2}}\]

D)

\[-bx\]

View Answer
15) A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed v. The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz. The source A receives waves, reflected from ground of frequency nearly: (Speed of sound = 343 m/s) [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

2150 Hz

B)

2500 Hz

C)

1800 Hz

D)

2400 Hz

View Answer
16) A spherically symmetric charge distribution is characterized by a charge density having the following variations: \[\rho (r)={{\rho }_{o}}\left( 1-\frac{r}{R} \right)\]for r < R\[\rho (r)=0\]for \[r\ge R\] Where r is the distance from the centre of the charge distribution \[{{\rho }_{o}}\]is a constant. The electric field at an internal point (r < R) is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{{{\rho }_{o}}}{4{{\varepsilon }_{0}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)\]

B)

\[\frac{{{\rho }_{o}}}{{{\varepsilon }_{o}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)\]

C)

\[\frac{{{\rho }_{o}}}{3{{\varepsilon }_{o}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)\]

D)

\[\frac{{{\rho }_{o}}}{12{{\varepsilon }_{o}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)\]

View Answer
17) The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: \[K(x)={{K}_{o}}+\lambda x\] (\[\lambda =\] a constant) The capacitance C, of the capacitor, would be related to its vacuum capacitance Co for the relation : [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[C=\frac{\lambda d}{\ln (1+{{K}_{o}}\lambda d)}{{C}_{o}}\]

B)

\[C=\frac{\lambda }{d.ln(1+{{K}_{o}}\lambda d)}{{C}_{o}}\]

C)

\[C=\frac{\lambda d}{ln(1+\lambda d/{{K}_{o}})}{{C}_{o}}\]

D)

\[C=\frac{\lambda }{d.ln(1+{{K}_{o}}/\lambda d)}{{C}_{o}}\]

View Answer
18) The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors \[3\Omega ,9\Omega \]and \[9\Omega \] and a capacitor of 5.0 \[\mu F.\]                       How much is the current I in the circuit in steady state? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

1.6 A

B)

0.67 A

C)

2.5 A

D)

0.25 A

View Answer
19) A positive charge 'q' of mass 'm' is moving along the + x axis. We wish to apply a uniform magnetic field B for time \[\Delta t\]so that the charge reverses its direction crossing the y axis at a distance d. Then: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[B=\frac{mv}{qd}\]and\[\Delta t=\frac{\pi d}{v}\]

B)

\[B=\frac{mv}{2qd}\]and\[\Delta t=\frac{\pi d}{2v}\]

C)

\[B=\frac{2mv}{qd}\]and\[\Delta t=\frac{\pi d}{2v}\]

D)

\[B=\frac{2mv}{qd}\]and\[\Delta t=\frac{\pi d}{v}\]

View Answer
20) Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field \[{{B}_{1}},\] at its centre when a current I passes through it. The ratio \[{{B}_{1}}:{{B}_{2}}\] is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

1 : 1

B)

1 : 3

C)

1 : 9

D)

9 : 1

View Answer
21) A sinusoidal voltage V(t) = 100 sin (500t) is applied across a pure inductance of L = 0.02 H. The current through the coil is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

10 cos (500 t)

B)

- 10 cos (500t)

C)

10 sin (500t)

D)

- 10 sin (500t)

View Answer
22) A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

1.34 V/m

B)

2.68 V/m

C)

4.02 V/m

D)

5.36 V/m

View Answer
23) The refractive index of the material of a concave lens is m. It is immersed in a medium of refractive index \[{{\mu }_{1}}.\] A parallel beam of light is incident on the lens. The path of the emergent rays when \[{{\mu }_{1}}>\mu \] is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

B)

C)

D)

View Answer
24) Interference pattern is observed at 'P' due to superimposition of two rays coming out from a source 'S' as shown in the figure. The value of 'l' for which maxima is obtained at 'P' is: (R is perfect reflecting surface) [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[1=\frac{1n\lambda }{\sqrt{3}-1}\]

B)

\[1=\frac{(2n-1)\lambda }{2\left( \sqrt{3}-1 \right)}\]

C)

\[1=\frac{(2n-1)\lambda \sqrt{3}}{4\left( 2-\sqrt{3} \right)}\]

D)

\[1=\frac{(2n-1)\lambda }{\sqrt{3}-1}\]

View Answer
25) In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength. If wavelength of red light is \[\text{6600}\overset{\text{o}}{\mathop{\text{A}}}\,\], then wavelength of first maximum will be: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\text{3300}\overset{\text{o}}{\mathop{\text{A}}}\,\]

B)

\[\text{4400}\overset{\text{o}}{\mathop{\text{A}}}\,\]

C)

\[\text{5500}\overset{\text{o}}{\mathop{\text{A}}}\,\]

D)

\[\text{6600}\overset{\text{o}}{\mathop{\text{A}}}\,\]

View Answer
26) A beam of light has two wavelengths of \[\text{497200}\overset{\text{o}}{\mathop{\text{A}}}\,\] and \[\text{6216}\overset{\text{o}}{\mathop{\text{A}}}\,\] with a total intensity of \[3.6\times {{10}^{-3}}W{{m}^{-2}}\] equally distributed among the two wavelengths. The beam falls normally on an area of 1 \[c{{m}^{2}}\] of a clean metallic surface of work function 2.3 eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in 2s is approximately: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[6\times {{10}^{11}}\]

B)

\[9\times {{10}^{11}}\]

C)

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

D)

\[15\times {{10}^{11}}\]

View Answer
27) A piece of bone of an animal from a ruin is found to have \[^{14}C\] activity of 12 disintegrations per minute per gm of its carbon content. The 14C activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die? (Given half life of 14C is t1/2 = 5760 years) [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

1672 years

B)

2391 years

C)

3291 years

D)

4453 years

View Answer
28) For LED's to emit light in visible region of electromagnetic light, it should have energy band gap in the range of: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

eV to 0.4 eV

B)

0.5 eV to 0.8 eV

C)

0.9 eV to 1.6 eV

D)

1.7 eV to 3.0 eV

View Answer
29) For sky wave propagation, the radio waves must have a frequency range in between: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

MHz to 2 MHz

B)

5 MHz to 25 MHz

C)

35 MHz to 40 MHz

D)

45 MHz to 50 MHz

View Answer
30) In the experiment of calibration of voltmeter, a standard cell of e.m.f. 1.1 volt is balanced against 440 cm of potential wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding reading of voltmeter is 0.5 volt. The error in the reading of volmeter will be: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

0. 15 volt

B)

0.15 volt

C)

0.5 volt

D)

? 0.05 volt

View Answer
31) If m and e are the mass and charge of the revolving electron in the orbit of radius r for hydrogen atom, the total energy of the revolving electron will be: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{1}{2}\frac{{{e}^{2}}}{r}\]

B)

\[-\frac{{{e}^{2}}}{r}\]

C)

\[m{{e}^{2}}\]

D)

\[1\,{{e}^{2}}\]

View Answer
32) The de-Broglie wavelength of a particle of mass 6.63 g moving with a velocity of 100 \[m{{s}^{-1}}\] is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[{{10}^{-33}}m\]

B)

\[{{10}^{-35}}m\]

C)

\[{{10}^{-31}}m\]

D)

\[{{10}^{-25}}m\]

View Answer
33) What happens when an inert gas is added to an equilibrium keeping volume unchanged? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

More product will form

B)

Less product will form

C)

More reactant will form

D)

Equilibrium will remain unchanged

View Answer
34) The amount of \[BaS{{O}_{4}}\]formed upon mixing 100 mL of 20.8% \[{{H}_{2}}S{{O}_{4}}\] solution with 50 mL of 9.8% \[{{H}_{2}}S{{O}_{4}}\]solution with 50 mL of 9.8% \[{{H}_{2}}S{{O}_{4}}\] solution will be: (Ba = 137, Cl = 35.5, S = 32, H = 1 and O = 16) [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

23.3 g

B)

11.65 g

C)

30.6 g

D)

33.2 g

View Answer
35) The rate coefficient (k) for a particular reactions is \[1.3\times {{10}^{-4}}{{M}^{-1}}\]\[{{s}^{-1}}\] at \[100{}^\circ C\], and \[1.3\times {{10}^{-3}}\] at \[150{}^\circ C\]. What is the energy of activation (EA) (in kJ) for this reaction? (R = molar gas constant\[=8.31J{{K}^{-1}}kJ\]) [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

16

B)

60

C)

99

D)

132

View Answer
36) How many electrons would be required to deposit 6.35 g of copper at the cathode during the electrolysis of an aqueous solution of copper sulphate? (Atomic mass of copper \[=63.5u,{{N}_{A}}=\] Avogadro's constant): [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{{{N}_{A}}}{20}\]

B)

\[\frac{{{N}_{A}}}{10}\]

C)

\[\frac{{{N}_{A}}}{5}\]

D)

\[\frac{{{N}_{A}}}{2}\]

View Answer
37) The \[\left( S{}^\circ \right)\] of the following substances are: \[C{{H}_{4}}(g)186.2J{{K}^{-1}}mo{{l}^{-1}}\] \[{{O}_{2}}(g)205.2J{{K}^{-1}}mo{{l}^{-1}}\] \[{{H}_{2}}O(g)69.9J{{K}^{-1}}mo{{l}^{-1}}\] The entropy change \[(\Delta {{S}^{o}})\]for the reaction : \[C{{H}_{4}}(g)+2{{O}_{2}}(g)\to C{{O}_{2}}(g)+2{{H}_{2}}O(l)\]is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[-312.5J{{K}^{-1}}mo{{l}^{-1}}\]

B)

\[-242.8J{{K}^{-1}}mo{{l}^{-1}}\]

C)

\[-108.1J{{K}^{-1}}mo{{l}^{-1}}\]

D)

\[-37.6J{{K}^{-1}}mo{{l}^{-1}}\]

View Answer
38) The conjugate base of hydrazoic acid is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[{{N}^{-3}}\]

B)

\[N_{3}^{-}\]

C)

\[N_{2}^{-}\]

D)

\[HN_{3}^{-}\]

View Answer
39) In a monoclinic unit cell, the relation of sides and angles are respectively: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[a=b\ne c\]and \[\alpha =\beta =\gamma ={{90}^{o}}\]

B)

\[a\ne b\ne c\]and \[\alpha =\beta =\gamma ={{90}^{o}}\]

C)

\[a\ne b\ne c\]and \[\beta =\gamma ={{90}^{o}}\ne \alpha \]

D)

\[a\ne b\ne c\]and \[\alpha \ne \beta \ne \gamma \ne {{90}^{o}}\]

View Answer
40) The standard enthalpy of formation \[({{\Delta }_{f}}{{H}^{o}}_{298})\]for methane, \[C{{H}_{4}}\]is\[-74.9kJ\,mo{{l}^{-1}}.\]In order to calculate the average energy given out in the formation of a C ? H bond from this it is necessary to know which one of the following? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

The dissociation energy of the hydrogen molecule, \[{{H}_{2}}\].

B)

The first four ionisation energies of carbon.

C)

The dissociation energy of \[{{H}_{2}}\]and enthalpy and sublimation of carbon (graphite).

D)

The first four ionisation energies of carbon and electron affinity of hydrogen.

View Answer
41) Which of the following xenon-oxo compounds may not be obtained by hydrolysis of xenon fluorides? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

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

B)

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

C)

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

D)

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

View Answer
42) Excited hydrogen atom emits light in the ultraviolet region at \[2.47\times {{10}^{15}}Hz.\]With this frequency, the energy of a single photon is: \[(h=6.63\times {{10}^{-34}}Js)\] [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[8.041\times {{10}^{-40}}J\]

B)

\[2.680\times {{10}^{-19}}J\]

C)

\[1.640\times {{10}^{-18}}J\]

D)

\[6.111\times {{10}^{-17}}J\]

View Answer
43) Which one of the following exhibits the large number of oxidation states? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

Ti (22)

B)

V (23)

C)

Cr (24)

D)

Mn (25)

View Answer
44) Copper becomes green when exposed to moist air for a long period. This is due to: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

the formation of a layer of cupric oxide on the surface of copper.

B)

the formation of a layer of basic carbonate of copper on the surface of copper.

C)

the formation of a layer of cupric hydroxide on the surface of copper.

D)

the formation of basic copper sulphate layer on the surface of the metal.

View Answer
45) Among the following species the one which causes the highest \[CFSE,{{\Delta }_{0}}\]as a ligand is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

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

B)

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

C)

\[{{F}^{-}}\]

D)

CO

View Answer
46) Similarity in chemical properties of the atoms of elements in a group of the Periodic table is most closely related to: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

atomic numbers

B)

atomic masses

C)

number of principal energy levels

D)

number of valence electrons

View Answer
47) Which of the following arrangements represents the increasing order (smallest to largest) of ionic radii of the given species \[{{O}^{2-}},{{S}^{2-}},{{N}^{3-}},{{p}^{3-?}}\] [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[{{O}^{2-}}<{{N}^{3-}}<{{S}^{2-}}<{{p}^{3-}}\]

B)

\[{{O}^{2-}}<{{p}^{3-}}<{{N}^{3-}}<{{S}^{2-}}\]

C)

\[{{N}^{3}}<{{O}^{2-}}<{{p}^{3-}}<{{S}^{2-}}\]

D)

\[{{N}^{3-}}<{{S}^{2-}}<{{O}^{2-}}<{{p}^{3-}}\]

View Answer
48) Global warming is due to increase of: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

methane and nitrous oxide in atmosphere

B)

methane and \[C{{O}_{2}}\] in atmosphere

C)

methane and \[{{O}_{3}}\] in atmosphere

D)

methane and CO in atmosphere

View Answer
49) Hydrogen peroxide acts both as an oxidising and as a reducing agent depending upon the nature of the reacting species. In which of the following cases \[{{H}_{2}}{{O}_{2}}\]acts as a reducing agent in acid medium? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[MnO_{4}^{-}\]

B)

\[C{{r}_{2}}O_{7}^{2-}\]

C)

\[SO_{3}^{2-}\]

D)

KI

View Answer
50) Which one of the following complexes will most likely absorb visible light? (At nos. Sc = 21, Ti = 22, V = 23, Zn = 30) [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[{{[Sc{{({{H}_{2}}O)}_{6}}]}^{3+}}\]

B)

\[{{[Ti{{(N{{H}_{3}})}_{6}}]}^{4+}}\]

C)

\[{{[V{{(N{{H}_{3}})}_{6}}]}^{3+}}\]

D)

\[{{[Zn{{(N{{H}_{3}})}_{6}}]}^{2+}}\]

View Answer
51) on mercuration-demercuration produces the major product: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

B)

C)

D)

View Answer
52) In the Victor-Meyer's test, the colour given by \[1{}^\circ ,\text{ }2{}^\circ \text{ }and\text{ }3{}^\circ \] alcohols are respectively: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

Red, colourless, blue

B)

Red, blue, colourless

C)

Colourless, red, blue

D)

Red, blue, violet

View Answer
53) Conversion of benzene diazonium chloride to chlorobenzene is an example of which of the following reactions? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

Claisen

B)

Friedel-craft

C)

Sandmeyer

D)

Wurtz

View Answer
54) In the presence of peroxide, HCl and HI do not give anti- Markownikoff's addition of alkenes because: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

One of the steps is endothermic in HCl and HI

B)

Both HCl and HI are strong acids

C)

HCl is oxidizing and the HI is reducing

D)

All the steps are exothermic is HCl and HI

View Answer
55) The major product obtained in the photo catalyzed bromination of 2--methylbutane is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

1-bromo-2-methylbutane

B)

1-bromo-3-methylbutane

C)

2-bromo-3-methylbutane

D)

2-bromo-2-methylbutane

View Answer
56) Which of the following molecules has two sigma (s) and two \[{{p}_{i}}(\pi )\]bonds? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[{{C}_{2}}{{H}_{4}}\]

B)

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

C)

\[{{C}_{2}}{{H}_{2}}C{{l}_{2}}\]

D)

HCN

View Answer
57) Which one of the following acids does not exhibit optical isomerism? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

Lactic acid

B)

Tartaric acid

C)

Maleic acid

D)

\[\text{ }\!\!\alpha\!\!\text{ -}\]amino acids

View Answer
58) Aminoglycosides are usually used as: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

antibiotic

B)

analgesic

C)

hypnotic

D)

antifertility

View Answer
59) Which of the following will not show mutarotation? [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

Maltose

B)

Lactose

C)

Glucose

D)

Sucrose

View Answer
60) Phthalic acid reacts with resorcinol in the presence of concentrated \[{{H}_{2}}S{{O}_{4}}\]to give: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

Phenolphthalein

B)

Alizarin

C)

Coumarin

D)

Fluorescein

View Answer
61) A relation on the set \[a=\{x:|x|<3,x\in Z\},\]where Z is the set of integers is defined by \[R=\{x,y):y=|x|,x\ne -1\}.\]Then the number of elements in the power set of R is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

32

B)

16

C)

8

D)

64

View Answer
62) Let \[z\ne -i\] be any complex number such that \[\frac{z-i}{z+i}\]is a purely imaginary number. Then\[z+\frac{1}{z}\]is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

0

B)

any non-zero real number other than 1.

C)

any non-zero real number.

D)

a purely imaginary number.

View Answer
63) The sum of the roots of the equation, \[{{x}^{2}}+|2x-3|-4=0,\] is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[2\]

B)

\[-2\]

C)

\[\sqrt{2}\]

D)

\[-\sqrt{2}\]

View Answer
64) If \[\left| \begin{matrix}    {{a}^{2}} & {{b}^{2}} & {{c}^{2}} \\    {{(a+\lambda )}^{2}} & {{(b+\lambda )}^{2}} & {{(a+\lambda )}^{2}} \\    {{(a-\lambda )}^{2}} & {{(b-\lambda )}^{2}} & {{(c+\lambda )}^{2}} \\ \end{matrix} \right|=\] \[k\lambda \left| \begin{matrix}    {{a}^{2}} & {{b}^{2}} & {{c}^{2}} \\    a & b & c \\    1 & 1 & 1 \\ \end{matrix} \right|,\lambda \ne 0\]then k is equal to: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[4\lambda abc\]

B)

\[-4\lambda abc\]

C)

\[4{{\lambda }^{2}}\]

D)

\[-4{{\lambda }^{2}}\]

View Answer
65) If\[A=\left[ \begin{matrix}    1 & 2 & x \\    3 & -1 & 2 \\ \end{matrix} \right]\]and\[B=\left[ \begin{align} & y \\ & x \\ & 1 \\ \end{align} \right]\]be such that\[AB=\left[ \begin{align} & 6 \\ & 8 \\ \end{align} \right],\]then: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[y=2x\]

B)

\[y=2x\]

C)

\[y=x\]

D)

\[y=-x\]

View Answer
66) 8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places, is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

160

B)

120

C)

60

D)

48

View Answer
67) If\[{{\left( 2+\frac{x}{3} \right)}^{55}}\]is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive terms of the expansion are equal, then these terms are: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

7th and 8th

B)

8th and 9th

C)

28th and 29th

D)

27th and 28th

View Answer
68) Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of \[\frac{1}{a}\]and\[\frac{1}{b}.\]If\[\frac{1}{M}:G\]is 4 : 5 then a : b can be: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

1 : 4

B)

1 : 2

C)

2 : 3

D)

3 : 4

View Answer
69) The least positive integer n such that \[1-\frac{2}{3}-\frac{2}{{{3}^{2}}}-....-\frac{2}{{{3}^{n-1}}}<\frac{1}{100},\]is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

4

B)

5

C)

7

D)

7

View Answer
70) Let \[f,g:R\to R\]be two functions defined by \[f(x)=\left\{ \begin{align} & x\sin \left( \frac{1}{x} \right),x\ne 0 \\ & 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,x=0 \\ \end{align} \right.,\]and \[g(x)=xf(x)\] Statement I: f is a continuous function at x = 0. Statement II: g is a differentiable function at x = 0. [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

Both statement I and II are false.

B)

Both statement I and II are true.

C)

Statement I is true, statement II is false.

D)

Statement I is false, statement II is true.

View Answer
71) If \[f(x)={{x}^{2}}-x+5,x>\frac{1}{2},\]and g(x) is its inverse function, then g'(7) equals: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

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

B)

\[\frac{1}{13}\]

C)

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

D)

\[-\frac{1}{13}\]

View Answer
72) Let f and g be two differentiable functions on R such that f'(x) > 0 and g'(x) < 0 for all \[x\in R\]. Then for all x: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

f (g (x)) > f (g (x - 1))

B)

f (g (x)) > f (g (x + 1))

C)

g(f (x)) > g (f (x - 1))

D)

g(f (x)) < g (f (x + 1))

View Answer
73) If \[1+{{x}^{4}}+{{x}^{5}}=T\sum\limits_{i=0}^{5}{{{a}_{i}}}{{\left( 1+x \right)}^{i}},\]for all x in R, then \[{{a}_{2}}\]is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

-4

B)

6

C)

-8

D)

10

View Answer
74) The integral \[\int_{{}}^{{}}{\frac{\sin x{{\cos }^{2}}x}{{{\left( {{\sin }^{3}}x+{{\cos }^{3}}x \right)}^{2}}}dx}\]is equal to: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{1}{\left( 1+{{\cot }^{3}}x \right)}+c\]

B)

\[-\frac{1}{3\left( 1+{{\cot }^{3}}x \right)}+c\]

C)

\[-\frac{{{\sin }^{3}}x}{\left( 1+{{\cot }^{3}}x \right)}+c\]

D)

\[-\frac{{{\cos }^{3}}x}{3\left( 1+{{\cot }^{3}}x \right)}+c\]

View Answer
75) If [ ] denotes the greatest integer function, then the integral \[\int\limits_{0}^{\pi }{\left[ \cos x \right]}dx\]is equal to: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{\pi }{2}\]

B)

0

C)

-1

D)

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

View Answer
76) If for a continuous function \[f(x),\int\limits_{-\pi }^{t}{\left( f\left( x \right)+x \right)dx}={{\pi }^{2}}-t2,\]for all\[t\ge -\pi ,\]then\[\left( -\frac{\pi }{3} \right)\]is equal to: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\pi \]

B)

\[\frac{\pi }{2}\]

C)

\[\frac{\pi }{3}\]

D)

\[\frac{\pi }{6}\]

View Answer
77) The general solution of the differential equation, \[\sin 2x\left( \frac{dy}{dx}-\sqrt{\tan x} \right)-y=0,\]is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[y\sqrt{\tan x}=x+c\]

B)

\[y\sqrt{\cot x}=\tan x+c\]

C)

\[y\sqrt{\tan x}=\cot x+c\]

D)

\[y\sqrt{\cot x}=x+c\]

View Answer
78) If a line intercepted between the coordinate axes is trisected at a point A(4, 3), which is nearer to x-axis, then its equation is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[4x\text{ }-\text{ }3y\text{ }=\text{ }7\text{ }~\]

B)

\[3x\text{ }+\text{ }2y\text{ }=\text{ }18\]

C)

\[3x\text{ }+\text{ }8y\text{ }=\text{ }36\]

D)

\[x\text{ }+\text{ }3y\text{ }=\text{ }13\]

View Answer
79) If the three distinct lines x + 2ay + a = 0, x + 3by + b = 0 and x + 4ay + a = 0 are concurrent, then the point (a, b) lies on a: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

circle

B)

hyperbola

C)

straight line

D)

parabola

View Answer
80) For the two circles \[{{x}^{2}}+{{y}^{2}}=16\] and \[{{x}^{2}}+{{y}^{2}}-2y=0,\]there is/are [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

one pair of common tangents

B)

two pair of common tangents

C)

three pair of common tangents

D)

no common tangent

View Answer
81) Two tangents are drawn from a point (- 2, - 1) to the curve, \[{{y}^{2}}=4x.\] If \[\alpha \] is the angle between them, then \[|\tan \alpha |\]is equal to: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

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

B)

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

C)

\[\sqrt{3}\]

D)

\[3\]

View Answer
82) The minimum area of a triangle formed by any tangent to the ellipse\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{81}=1\]and the co-ordinate axes is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

12

B)

18

C)

26

D)

36

View Answer
83) A symmetrical form of the line of intersection of the planes \[x\text{ }=\text{ }ay\text{ }+\text{ }b\text{ }and\text{ }z\text{ }=\text{ }cy\text{ }+\text{ }d\] is [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\frac{x-b}{a}+\frac{y-1}{1}=\frac{z-d}{c}\]

B)

\[\frac{x-b-a}{a}=\frac{y-1}{1}=\frac{z-d-c}{c}\]

C)

\[\frac{x-a}{b}=\frac{y-0}{1}=\frac{z-c}{d}\]

D)

\[\frac{x-b-a}{b}=\frac{y-1}{0}=\frac{z-d-c}{d}\]

View Answer
84) If the distance between planes, \[4x-2y-4z+1=0\]and \[2y-4z+d=0\] is 7, then d is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[41 or - 42\]

B)

\[42 or - 43\]

C)

\[- 41 or 43\]

D)

\[- 42 or 44\]

View Answer
85) If \[\hat{x},\hat{y}\]and \[\hat{z}\] are three unit vectors in three-dimensional space, then the minimum value of\[|\hat{x}+\hat{y}{{|}^{2}}+|\hat{y}+\hat{z}{{|}^{2}}+|\hat{z}+\hat{x}{{|}^{2}}\] [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

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

B)

3

C)

\[3\sqrt{3}\]

D)

6

View Answer
86) Let\[\overline{X}\]and M.D. be the mean and the mean deviation about X of n observations \[{{x}_{i}},\] i = 1, 2, ........, n. If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are : [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\overline{X},M.D.\]

B)

\[\overline{X}+5,M.D.\]

C)

\[\overline{X},M.D.+5\]

D)

\[\overline{X}+M.D.+5\]

View Answer
87) A number x is chosen at random from the set {1, 2, 3, 4, ...., 100}. Define the event: A = the chosen number x satisfies\[\frac{\left( x-10 \right)\left( x-50 \right)}{\left( x-30 \right)}\ge 0\] Then P (A) is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

0.71

B)

0.70

C)

0.51

D)

0.20

View Answer
88) Statement I : The equation\[{{(si{{n}^{-1}}x)}^{3}}+\]\[{{(co{{s}^{-1}}x)}^{3}}+a{{\pi }^{3}}=0\]has a solution for all\[a\ge \frac{1}{32}.\] Statement II: For any \[x\in R,\] \[{{\sin }^{-1}}x{{\cos }^{-1}}x=\frac{\pi }{C}\]and\[0\le {{\left( {{\sin }^{-1}}x-\frac{\pi }{4} \right)}^{2}}\le \frac{9{{\pi }^{2}}}{16}\] [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

Both statements I and II are true.

B)

Both statements I and II are false.

C)

Statement I is true and statement II is false.

D)

Statement I is false and statement II is true.

View Answer
89) If \[f(\theta )=\left| \begin{matrix} 1 & \cos \theta & 1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1 \\ \end{matrix} \right|\]and A and B are respectively the maximum and the minimum values of f(q), then (A, B) is equal to: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[(3, - 1)\]

B)

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

C)

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

D)

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

View Answer
90) Let p, q, r denote arbitrary statements. Then the logically equivalent of the statement\[p\Rightarrow \left( q\vee r \right)\] is: [JEE Main Online Paper ( Held On 12 Apirl 2014 )

A)

\[\left( p\vee q \right)\Rightarrow r\]

B)

\[\left( p\Rightarrow q \right)\vee \left( p\Rightarrow r \right)\]

C)

\[\left( p\Rightarrow \tilde{\ }q \right)\wedge \left( p\Rightarrow r \right)\]

D)

\[\left( p\Rightarrow q \right)\wedge \left( p\Rightarrow \tilde{\ }r \right)\]

View Answer