Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 12 May 2012)

done JEE Main Online Paper (Held On 12 May 2012)

  • question_answer1) A hypothetical atom has only three energy levels. The ground level has energy, \[{{E}_{1}}=-8eV.\]The two excited states have energies, \[{{E}_{2}}=-6eV\]and\[{{E}_{3}}=-2eV.\]Then which of the following wavelengths will not be present in the emission spectrum of this atom?     JEE Main Online Paper (Held On 12 May 2012)

    A) 207 nm                

    B)                        465 nm

    C)                        310 nm                

    D)                        620 nm

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  • question_answer2) A given ideal gas with \[\gamma =\frac{{{C}_{p}}}{{{C}_{v}}}=1.5\]at a temperature T. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be   JEE Main Online Paper (Held On 12 May 2012)

    A) \[2\sqrt{2}T\]                   

    B)                        4 T

    C)                        2 T                                         

    D)                        8 T

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  • question_answer3) A resistance R and a capacitance C are connected in series to a battery of negligible internal resistance through a key. The key is closed at t = If after t sec the voltage across the capacitance was seven times the voltage across R, the value of t is   JEE Main Online Paper (Held On 12 May 2012)

    A) \[3RC\ell n2\]                   

    B)                        \[2RC\,\ell n2\]

    C)                        \[2RC\,\ell n7\]                

    D)                        \[3RC\,\ell n7\]

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  • question_answer4) The magnetic force acting on charged particle of charge \[2\mu C\]in magnetic field of 2 F acting in y-direction, when the particle velocity is \[\left( 2\hat{i}+3\hat{j} \right)\times {{10}^{6}}m{{s}^{-1}}\]is   JEE Main Online Paper (Held On 12 May 2012)

    A) 8 N in z-direction             

    B)                        8 N in y-direction

    C)                        4 N in y-direction             

    D)                        4 N in z-direction

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  • question_answer5) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A pure semiconductor has negative temperature coefficient of resistance. Statement 2: On raising the temperature,  more charge carriers are released into the conduction band.   JEE Main Online Paper (Held On 12 May 2012)

    A) Statement 1 is false. Statement 2 is true.

    B)                        Statement 1 is true. Statement 2 is false.

    C)                        Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

    D)                        Statement 1 is true. Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

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  • question_answer6) A projectile moving vertically upwards with a velocity of 200 \[\text{m}{{\text{s}}^{-1}}\]breaks into two equal parts at a height of 490 m. One part starts moving vertically upwards with a velocity of 400 \[\text{m}{{\text{s}}^{-1}}\]. How much time it will take, after the break up with the other part to hit the ground?   JEE Main Online Paper (Held On 12 May 2012)

    A) \[2\sqrt{10}s\]                 

    B)                        5 s

    C)                        10 s       

    D)                        \[\sqrt{10}s\]

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  • question_answer7) n moles of an ideal gas undergo a process \[A\to B\]as shown in the figure. Maximum temperature of the gas during the process is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[\frac{8{{P}_{0}}{{V}_{0}}}{nR}\]            

    B)                        \[\frac{3{{P}_{0}}{{V}_{0}}}{2nR}\]

    C)                        \[\frac{9{{P}_{0}}{{V}_{0}}}{2nR}\]                          

    D)                        \[\frac{9{{P}_{0}}{{V}_{0}}}{4nR}\]

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  • question_answer8) A student measured the diameter of a wire using a screw gauge with the least count 0.001 cm and listed the measurements. The measured value should be recorded as   JEE Main Online Paper (Held On 12 May 2012)

    A) 5.3200cm            

    B)                        5.3cm            

    C)                        5.32cm                                 

    D)                        5.320cm

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  • question_answer9) The first diffraction minimum due to the single slit diffraction is seen at \[\theta ={{30}^{o}}\]for a light of wavelength \[5000\overset{\text{o}}{\mathop{\text{A}}}\,\] falling perpendicularly on the slit. The width of the slit is   JEE Main Online Paper (Held On 12 May 2012)

    A) \[2.5\times {{10}^{-5}}cm\]                        

    B) \[1.25\times {{10}^{-5}}cm\]

    C) \[10\times {{10}^{-5}}cm\]         

    D) \[5\times {{10}^{-5}}cm\]

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  • question_answer10) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: Bats emitting ultrasonic waves can detect the location of a prey by hearing the waves reflected from it. Statement 2: When the source and the detector are moving, the frequency of reflected waves is changed.   JEE Main Online Paper (Held On 12 May 2012)

    A) Statement 1 is false. Statement 2 is true.

    B)                        Statement 1 is true, Statement 2 is false.

    C)                        Statement 1 is true. Statement 2 is true, Statement 2 is not the correct explanation of Statement 1. 

    D)                        Statement 1 is true. Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

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  • question_answer11) Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of r from the centre is proportional to     JEE Main Online Paper (Held On 12 May 2012)

    A) r             

    B)                        \[{{r}^{-1}}\]

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

    D)                        \[{{r}^{-2}}\]

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  • question_answer12) A doubly ionised Li atom is excited from its ground state (n=1) to n=3 state. The wavelengths of the spectral lines are given by \[{{\lambda }_{32}},{{\lambda }_{31}}\]and\[{{\lambda }_{21}}.\]The ratio \[{{\lambda }_{32}}/{{\lambda }_{31}}\]and\[{{\lambda }_{21}}/{{\lambda }_{31}}\]are, respectively     JEE Main Online Paper (Held On 12 May 2012)

    A) 8.1,0.67               

    B)                        8.1,1.2

    C)                        6.4,1.2                  

    D)                        6.4,0.67

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  • question_answer13) Which of the following Statements is correct?   JEE Main Online Paper (Held On 12 May 2012)

    A) The rate of radioactive decay cannot be controlled but that of nuclear fission can be controlled.

    B)                        Nuclear forces are short range, attractive and charge dependent.

    C)                        Nuclei of atoms having same number of neutrons are known as isobars.

    D)                        Wavelength of matter waves is given by de Broglie formula but that of photons is not given by the same formula d. Nuclear fission can be controlled but not of nuclear fusion.

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  • question_answer14) The distance travelled by a body moving along a line in time / is proportional to t3. The acceleration-time (a,t) graph for the motion of the body will be     JEE Main Online Paper (Held On 12 May 2012)

    A)                             

    B)  

    C)                           

    D)  

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  • question_answer15) A wave represented by the equation \[{{y}_{1}}=a\cos (kx-\omega t)\]is superimposed with another wave to form a stationary wave such that the point x ? 0 is node. The equation for the other wave is   JEE Main Online Paper (Held On 12 May 2012)

    A) \[a\cos (kx-\omega t+\pi )\]      

    B)                        \[a\cos (kx-\omega t+\pi )\]

    C)                        \[a\cos \left( kx+\omega t+\frac{\pi }{2} \right)\]            

    D)                        \[a\cos \left( kx-\omega t+\frac{\pi }{2} \right)\]

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  • question_answer16) An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of a so that the insect does not slip is given by   JEE Main Online Paper (Held On 12 May 2012)

    A) \[\cot \alpha =3\]           

    B)                        \[\sec \alpha =3\]

    C)                        \[\cos ec\,\alpha =3\]                   

    D)                        \[\cos \,\alpha =3\]

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  • question_answer17) Water is flowing through a horizontal tube having cross-sectional areas of its two ends being A and A' such that the ratio A/A' is 5. If the pressure difference of water between the two ends is \[3\times {{10}^{5}}N{{m}^{-2}},\] the velocity of water with which it enters the tube will be (neglect gravity effects)   JEE Main Online Paper (Held On 12 May 2012)

    A) \[5\,m\,{{s}^{-1}}\]                        

    B)                        \[10\,m\,{{s}^{-1}}\]

    C)                        \[25\,m\,{{s}^{-1}}\]                      

    D)                        \[50\sqrt{10}\,m\,{{s}^{-1}}\]

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  • question_answer18) A solid sphere is rolling on a surface as shown in figure, with a translational velocity \[v\,m\,{{s}^{-1}}.\] If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is   JEE Main Online Paper (Held On 12 May 2012)

    A) \[\sqrt{2gh}\]                   

    B)                        \[\sqrt{\frac{7}{5}gh}\]

    C)                        \[\sqrt{\frac{7}{2}gh}\]                

    D)                        \[\sqrt{\frac{10}{7}gh}\]

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  • question_answer19) Three resistors of \[4\Omega ,6\Omega \]and \[12\Omega \]are connected in parallel and the combination is connected in series with a 1.5 V battery of\[1\Omega \]internal resistance. The rate of Joule heating in the \[4\Omega \]resistor is   JEE Main Online Paper (Held On 12 May 2012)

    A) 0.55W                  

    B)                        0.33 W

    C)                        0.25 W                 

    D)                        0.86 W

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  • question_answer20) We wish to make a microscope with the help of two positive lenses both with a focal length of 20 mm each and the object is positioned 25 mm from the objective lens. How far apart the lenses should be so that the final image is formed at infinity?   JEE Main Online Paper (Held On 12 May 2012)

    A) 20mm                                  

    B)                        100mm

    C)                        120mm    

    D)                        80mm

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  • question_answer21) Magnetic flux through a coil of resistance \[10\Omega \]is changed by \[\Delta \phi \]in 0.1 s. The resulting current in the coil varies with time as shown in the figure. Then\[|\Delta \phi |\]is equal to (in weber)   JEE Main Online Paper (Held On 12 May 2012)

    A) 6                                             

    B)                        4

    C)                        2    

    D)                        8

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  • question_answer22) A series combination of\[{{n}_{1}}\] capacitors, each of capacity \[{{C}_{1}}\] is charged by source of potential difference 4 V. When another parallel combination of \[{{n}_{2}}\]capacitors each of capacity \[{{C}_{2}}\] is charged by a source of potential difference V, it has the same total energy stored in it as the first combination has. The value of \[{{C}_{2}}\] in terms of \[{{C}_{1}}\]is then     JEE Main Online Paper (Held On 12 May 2012)

    A) \[16\frac{{{n}_{2}}}{{{n}_{1}}}{{C}_{1}}\]                              

    B)                        \[\frac{2{{C}_{1}}}{{{n}_{1}}{{n}_{2}}}\]

    C)                        \[2\frac{{{n}_{2}}}{{{n}_{1}}}{{C}_{1}}\]

    D)                                        \[\frac{16{{C}_{1}}}{{{n}_{1}}{{n}_{2}}}\]

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  • question_answer23) It is preferable to measure the e.m.f. of a cell by potentiometer than by a voltmeter because of the following possible reasons. (i) In case of potentiometer, no current flows through the cell. (ii) The length of the potentiometer allows greater precision. (iii) Measurement by the potentiometer is quicker. (iv) The sensitivity of the galvanometer, when using a potentiometer is not relevant. Which of these reasons are correct?   JEE Main Online Paper (Held On 12 May 2012)

    A) (i),(iii),(iv)           

    B)                        (i), (iii), (iv)

    C)                        (i),(ii)                                    

    D)                        (i),(ii),(iii),(iv)

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  • question_answer24) Two bodies A and B of mass m and 2m respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A' third body C of mass m is placed on the floor. The body C moves with a velocity \[{{v}_{0}}\] along the line joining A and B and collides elastically with A. At a certain time after the collision it is found that the instantaneous velocities of A and B are same and the compression of the spring is \[{{x}_{0}}\]. The spring constant k will be   JEE Main Online Paper (Held On 12 May 2012)

    A) \[m\frac{v_{0}^{2}}{x_{0}^{2}}\]                             

    B)                        \[m\frac{{{v}_{0}}}{2{{x}_{0}}}\]

    C)                        \[2m\frac{{{v}_{0}}}{{{x}_{0}}}\]                              

    D)                        \[\frac{2}{3}m{{\left( \frac{{{v}_{0}}}{{{x}_{0}}} \right)}^{2}}\]

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  • question_answer25) The circuit in figure consists of wires at the top and bottom and identical springs as the left and right sides. The wire at the bottom has a mass of 10 g and is 5 cm long. The wire is hanging as shown in the figure. The springs stretch 0.5 cm under the weight of the wire and the circuit has a, total resistance of \[12\Omega .\] When the lower wire is subjected to a static magnetic field, the springs, stretch an additional 0.3 cm. The magnetic field is     JEE Main Online Paper (Held On 12 May 2012)

    A) 0.6 T and directed out of page

    B)                        1.2 T and directed into the plane of page

    C)                        0.6 T and directed into the plane of page

    D)                        1.2 T and directed out of page

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  • question_answer26) In a sensitive meter bridge apparatus the bridge wire should possess   JEE Main Online Paper (Held On 12 May 2012)

    A) high resistivity and low temperature coefficient.

    B)                        low resistivity and high temperature coefficient.

    C)                        low resistivity and low temperature coefficient.

    D)                        high resistivity and high temperature coefficient.

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  • question_answer27) A spring is compressed between two blocks of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of \[{{v}_{1}}\] and \[{{v}_{2}}\] as shown. The blocks travel distances \[{{x}_{1}}\] and \[{{x}_{2}}\] respectively before coming  to rest. The ratio \[\left( \frac{{{x}_{1}}}{{{x}_{2}}} \right)\] is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[\frac{{{m}_{2}}}{{{m}_{1}}}\] 

    B)                        \[\frac{{{m}_{1}}}{{{m}_{2}}}\]

    C)                        \[\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\]                    

    D)                        \[\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\]

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  • question_answer28) This question has Statement land Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.                 Statement 1: When moment of inertia/of a body rotating about an axis with angular speed \[\omega \]increases, its angular momentum L is unchanged but the kinetic energy K increases if there is no torque applied on it.                 Statement 2: \[L=I\omega ,\] kinetic energy of rotation \[=\frac{1}{2}I{{\omega }^{2}}\]   JEE Main Online Paper (Held On 12 May 2012)               

    A)                 (a) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.                

    B)                 (b) Statement 1 is false, Statement 2 is true.                

    C)                 (c) Statement 1 is true, Statement 2 is true. Statement 2 is correct explanation of the Statement 1.                

    D)                 (d) Statement 1 is true, Statement 2 is false.                

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  • question_answer29) A 10 kW transmitter emits radio waves of wavelength 500 m. The number of photons emitted per second by the transmitter is of the order of   JEE Main Online Paper (Held On 12 May 2012)

    A) 1037                                       

    B)                        1031

    C)                        1025                                       

    D)                        1043

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  • question_answer30) The maximum number of possible interference maxima for slit separation equal to 1. 8A,, where X is the wavelength of light used, in a Young's double slit experiment is   JEE Main Online Paper (Held On 12 May 2012)

    A) zero                                      

    B)                        3

    C)                        infinite                                 

    D)                        5

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  • question_answer31) The conversion of benzene diazonium chloride to bromobenzene can be accomplished by     JEE Main Online Paper (Held On 12 May 2012)

    A) Reimer- Tiemann reacton

    B) Friedel-Crafts reaction

    C) Gattermann reaction

    D) Azo-eoupling reaction

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  • question_answer32) The radius of a calcium ion is 94 pm and of the oxide ion is 146 pm. The possible crystal structure of calcium oxide will be     JEE Main Online Paper (Held On 12 May 2012)

    A) tetrahedral        

    B)                        trigonal

    C)                        octahedral       

    D)                        pyramidal

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  • question_answer33) The formation of molecular complex \[B{{F}_{3}}-N{{H}_{3}}\]results in a change in hybridization of boron     JEE Main Online Paper (Held On 12 May 2012)

    A) from sp2 to dsp2              

    B)                        from sp2 to sp3

    C)                        from sp3 to sp2                 

    D)                        from sp3 to sp3

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  • question_answer34) A metal Mon heating in nitrogen gas gives Y. Y on treatment with \[{{H}_{2}}O\] gives a colourless gas which when passed through \[CuS{{O}_{4}}\] solution gives a blue colour. V is     JEE Main Online Paper (Held On 12 May 2012)

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

    B)                        \[Mg{{(N{{O}_{3}})}_{2}}\]

    C)                        \[M{{g}_{3}}{{N}_{2}}\]

    D)                        \[MgO\]

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  • question_answer35) Water sample is reported to be highly polluted if BOD (Biological Oxygen Demand) value of sample becomes     JEE Main Online Paper (Held On 12 May 2012)

    A) more than 17 ppm          

    B)                        equal to 10 ppm

    C)                        equal to 5 ppm                 

    D)                        less than 5 ppm

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  • question_answer36) A solution containing 0.85 g of \[znC{{l}_{2}}\] in 125.0 g of water freezes at \[-0.23{}^\circ C\]. The apparent degree of dissociation of the salt is (\[{{K}_{f}}\] for water = 1.86 K kg \[\text{mo}{{\text{l}}^{-1}}\], atomic mass: Zn = 65.3 and Cl = 35.5)   JEE Main Online Paper (Held On 12 May 2012)

    A) 1.36%                                   

    B) 73.5%

    C) 7.35%                                   

    D) 2.47%

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  • question_answer37) Which of the following complex ions will exhibit optical isomerism? (en = 1,2-diamine ethane).     JEE Main Online Paper (Held On 12 May 2012)

    A) \[{{[Cr{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]}^{+}}\]      

    B)                        \[{{[Co{{(en)}_{2}}C{{l}_{2}}]}^{+}}\]

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

    D)                        \[{{[Zn{{(en)}_{2}}]}^{2+}}\]

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  • question_answer38) Which among the following elements has the highest first ionization enthalpy?     JEE Main Online Paper (Held On 12 May 2012)

    A) Nitrogen             

    B)                        Boron

    C)                        Carbon                                

    D)                        Oxygen

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  • question_answer39) Magnetic moment of \[G{{d}^{3+}}ion(Z=64)\]is     JEE Main Online Paper (Held On 12 May 2012)

    A) 3.62 BM               

    B)                        9.72 BM

    C)                        7.9 BM        

    D)                        10.60 BM

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  • question_answer40) An aqueous solution of oxalic acid dehydrate contains its 6.3 g in 250 ml. The volume of 0.1N NaOH required to completely neutralize 10 ml of this solution     JEE Main Online Paper (Held On 12 May 2012)

    A) 4ml                                        

    B)                        20ml

    C)                        2ml                                        

    D)                        40ml

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  • question_answer41) In the electrolysis of alumina to obtain aluminium metal, cryolite is added mainly to     JEE Main Online Paper (Held On 12 May 2012)

    A) lower the melting point of alumina

    B)                        dissolve alumina in molten cryolite

    C)                        remove the impurities of alumina

    D)                        increase the electrical conductivity

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  • question_answer42) Synthetic polymer bakelite can be prepared from following compounds     JEE Main Online Paper (Held On 12 May 2012)

    A) Styrene and vinyl chloride

    B)                        Acrylonitrile and vinyl chloride

    C)                        Adipic acid and ethylene glycol

    D)                        Phenol and formaldehyde

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  • question_answer43) The correct statement for both the processes of physisorption and chemisorption is     JEE Main Online Paper (Held On 12 May 2012)

    A) both are endothermic

    B)                        chemisorption is endothermic but physisorption is exothermic

    C)                        both are exothermic

    D)                        physisorption is endothermic but chemisorption is exothermic.

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  • question_answer44) Which of the following statements is wrong?   JEE Main Online Paper (Held On 12 May 2012)

    A) Ethyl chloride on reduction with Zn-Cu couple and alcohol gives ethane.

    B)                        The reaction of methyl magnesium bromide with acetone gives butano1-2.

    C)                        Alkyl halides follow the following reactivity sequence on reaction with alkeries. \[R-I>R-Br>R-Cl>R-I\]

    D)                        \[{{C}_{2}}{{H}_{4}}C{{l}_{2}}\] may exist in two isomeric forms

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  • question_answer45) Although \[C{{N}^{-}}\]ion and \[{{N}_{2}}\] molecule are isoelectronic, yet \[{{N}_{2}}\] molecule is chemically inert because of     JEE Main Online Paper (Held On 12 May 2012)

    A) presence of more number of electrons in bonding orbitals

    B)                        lone bond energy

    C)                        absence of bond polarity

    D)                        uneven electron distribution.

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  • question_answer46) Amylopectin is a polymer of   JEE Main Online Paper (Held On 12 May 2012)

    A) \[\alpha -D-\] glucose   

    B)                        amino acid

    C)                        \[\beta -D-\] glucose     

    D)                        amylase.

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  • question_answer47) If the radius of first orbit of H atom is \[{{a}_{0}},\] the de- Broglie wavelength of an electron in the third orbit is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[4\pi {{a}_{0}}\]                             

    B)                        \[8\pi {{a}_{0}}\]

    C)                        \[6\pi {{a}_{0}}\]

    D)                        \[2\pi {{a}_{0}}\]

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  • question_answer48) Chemically heroin is     JEE Main Online Paper (Held On 12 May 2012)

    A) morphine monoacetate

    B)                        morphine dibenzbate

    C)                        morphine diacetate  

    D) morphine monobenzoate

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  • question_answer49) In the given reaction, the product 'A' is              JEE Main Online Paper (Held On 12 May 2012)

    A)  

    B)  

    C)  

    D)  

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  • question_answer50) The ppm level of \[{{F}^{-}}\]in a 500 g sample of a tooth paste containing 0.2 g \[{{F}^{-}}\]is     JEE Main Online Paper (Held On 12 May 2012)

    A) 400   

    B)                        1000

    C)                        250                                        

    D)                        200

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  • question_answer51) In a chemical reaction A is converted into B. The rates of reaction, starting with initial concentrations of A as \[2\times {{10}^{-3}}M\] and \[1\times {{10}^{-3}}M,\]are equal to \[2.40\times {{10}^{-4}}M{{s}^{-1}}\]and \[0.60\times {{10}^{-4}}M{{s}^{-1}}\] respectively. The order of reaction with respect to reactant A will be     JEE Main Online Paper (Held On 12 May 2012)

    A) 0      

    B)                               1.5

    C)                        1                                             

    D)                        2

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  • question_answer52) 8 mol of\[A{{B}_{3}}(g)\]are introduced into a 1.0 dm3 vessel. If it dissociates as  \[2A{{B}_{3}}(g){{A}_{2}}(g)+3{{B}_{2}}(g).\]At equilibrium, 2 mol of \[{{A}_{2}}\] are found to be present. The equilibrium constant of this reaction is     JEE Main Online Paper (Held On 12 May 2012)

    A) 2                                             

    B)                        3

    C)                        27     

    D)                        36

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  • question_answer53) 5 g of benzene on nitration gave 6.6 g of nitrobenzene. The theoretical yield of the nitrobenzene will be     JEE Main Online Paper (Held On 12 May 2012)

    A) 4.5 g                                      

    B)                        5.6g

    C)                        8.09g                                    

    D)                        6.6g

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  • question_answer54) Given (i)\[HCN(aq)+{{H}_{2}}O(l){{H}_{3}}{{O}^{+}}(aq)+C{{N}^{-}}(aq)\]\[{{K}_{a}}=6.2\times {{10}^{-10}}\] (ii)\[C{{N}^{-}}(aq)+{{H}_{2}}O(l)HCN(aq)+O{{H}^{-}}(aq)\] \[{{K}_{b}}=1.6\times {{10}^{-5}}.\] These equilibria show the following order of the relative base strength,     JEE Main Online Paper (Held On 12 May 2012)

    A) \[OH>{{H}_{2}}O>C{{N}^{-}}\]

    B)                        \[O{{H}^{-}}>C{{N}^{-}}>{{H}_{2}}O\]

    C)                        \[{{H}_{2}}O>C{{N}^{-}}>O{{H}^{-}}\]

    D)                        \[C{{N}^{-}}>{{H}_{2}}O>O{{H}^{-}}\]

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  • question_answer55) In the below mentioned compounds the decreasing order of reactivity towards electrophilic substitution is (i)??..                                  (ii)                             (iii)                                          (iv)                                   JEE Main Online Paper (Held On 12 May 2012)

    A)  (iv)>(i)>(ii)>(iii)               

    B)                        (ii)>(iii)>(i)>(iv)

    C)                        (iii)>(i)>(iv)>(ii)

    D)                        (i)>(ii)>(iii)>(iv)

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  • question_answer56) The difference between the reaction enthalpy change \[({{\Delta }_{r}}H)\]arid reaction internal energy change \[({{\Delta }_{r}}U)\] for the reaction: \[2{{C}_{6}}{{H}_{6}}(l)+15{{O}_{2}}(g)\xrightarrow[{}]{{}}12C{{O}_{2}}(g)+6{{H}_{2}}O(l)\]at 300 K is \[(R=8.314\,J\,mo{{l}^{-1}}\,{{K}^{-1}})\]   JEE Main Online Paper (Held On 12 May 2012)

    A) \[0\,J\,mo{{l}^{-1}}\,\]

    B)                        \[2490\,J\,mo{{l}^{-1}}\,\]

    C)                        \[-2490\,J\,mo{{l}^{-1}}\,\]         

    D)                        \[-7482\,J\,mo{{l}^{-1}}\,\]

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  • question_answer57) \[C{{H}_{3}}CHO\xrightarrow[Zn\left( Hg \right)/Conc.HCl]{[H]}C{{H}_{3}}C{{H}_{3}}\]The reaction;     JEE Main Online Paper (Held On 12 May 2012)

    A) Cannizaro's reaction

    B)                        Rosenmund reduction

    C)                        Wolf-Kishner reduction

    D)                        Clemmenson reduction

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  • question_answer58) \[\alpha ,v\]and u represent most probable velocity, average velocity and root mean square velocity respectively of a gas at a particular temperature. The correct order among the following is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[u>v>\alpha \]               

    B)                        \[v>u>\alpha \]

    C)                        \[\alpha >u>v\]               

    D)                        \[u>\alpha >v\]

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  • question_answer59) Among the following chloro-compound having the lowest dipole moment is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[C{{H}_{3}}Cl\]               

    B)                         

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

    D)                       

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  • question_answer60) In the following balanced reaction,\[X\,MnO_{4}^{-}+Y\,{{C}_{2}}O_{4}^{2-}+Z{{H}^{+}}\]\[X\,M{{n}^{2+}}+2Y\,C{{O}_{2}}+\frac{Z}{2}{{H}_{2}}O\]values of X, Y and Z respectively are     JEE Main Online Paper (Held On 12 May 2012)

    A) 2,5,16   

    B)                        8,2,5

    C)                        5,2,16                                   

    D)                        5,8,4

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  • question_answer61) If a, b, c, d and are distinct real numbers such that \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}){{p}^{2}}-2p\]\[(ab+bc+cd)+\]\[({{b}^{2}}+{{c}^{2}}+{{d}^{2}})\]\[\le 0,\]then   JEE Main Online Paper (Held On 12 May 2012)

    A) a, b, c, d are in A.P.

    B) ab = cd

    C) ac = bd

    D) a, b, c, d are in G.P.

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  • question_answer62) The area of triangle formed by the lines joining the vertex of the parabola, \[{{x}^{2}}=8y,\]to the extremities of its latus rectum is   JEE Main Online Paper (Held On 12 May 2012)

    A) 2                                             

    B)                        8

    C)                        1                                             

    D)                        4

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  • question_answer63) Let A and B be real matrices of the form \[\left[ \begin{matrix}   \alpha  & 0  \\   0 & \beta   \\ \end{matrix} \right]\]and \[\left[ \begin{matrix}    0 & \gamma   \\    \delta  & 0  \\ \end{matrix} \right],\]respectively. Statement 1: AB - BA is always an-invertible matrix. Statement 2: AB - BA is never an identity matrix.   JEE Main Online Paper (Held On 12 May 2012)

    A) Statement 1 is true. Statement 2 is false.

    B)                        Statement 1 is false, Statement 2 is true.

    C)                        Statement 1 is true. Statement 2 is true; Statement 2 is a correct explanation of Statement!.

    D)                        Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1,

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  • question_answer64) If in a triangle \[ABC,\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13},\]then cos A is equal to     JEE Main Online Paper (Held On 12 May 2012)

    A) 5/7                                        

    B)                        1/5

    C)                        35/19                                    

    D)                        19/35

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  • question_answer65) Statement 1: If A and B be two sets having p and q elements respectively, where q > p. Then the total number of functions from set A to set B is \[{{d}^{p}}.\]. Statement 2: The total number of selections of p different objects out of q objects is \[^{q}{{C}_{p}}.\]     JEE Main Online Paper (Held On 12 May 2012)

    A) Statement 1 is true. Statement 2 is false.

    B)                        Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

    C)                        Statement 1 is false, Statement 2 is true

    D)                        Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

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  • question_answer66) A unit vector which is perpendicular to the vector \[2\hat{i}-\hat{j}+2\hat{k}\] and is coplanar with the vectors\[\hat{i}+\hat{j}-\hat{k}\]and \[2\hat{i}+2\hat{j}-\hat{k}\] is   JEE Main Online Paper (Held On 12 May 2012)

    A) \[\frac{2\hat{j}+\hat{k}}{\sqrt{5}}\]                       

    B)                        \[\frac{3\hat{i}+2\hat{j}-2\hat{k}}{\sqrt{17}}\]

    C)                        \[\frac{3\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{17}}\]                

    D)                        \[\frac{2\hat{i}+2\hat{j}-2\hat{k}}{3}\]

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  • question_answer67) The number of terms in the expansion of \[{{\left( {{y}^{1/5}}+{{x}^{1/10}} \right)}^{55}},\]in which powers of x and y are free from radical signs are     JEE Main Online Paper (Held On 12 May 2012)

    A) six       

    B)                        twelve

    C)                        seven                                   

    D)                        five

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  • question_answer68) If the point (1, a) lies between the straight lines  \[x+y=1\] and \[2(x+y)=3\]then a lies in interval     JEE Main Online Paper (Held On 12 May 2012)

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

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

    C)                        \[\left( -\infty ,0 \right)\]                            

    D)                        \[\left( 0,\frac{1}{2} \right)\]

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  • question_answer69) If two vertices of a triangle are (5, -1) and (-2,3) and its orthocentre is at (0, 0), then the third vertex is                JEE Main Online Paper (Held On 12 May 2012)             

    A) (4,-7)                                    

    B)                        (-4,-7)

    C)                        (-4,7)                                    

    D)                        (4,7)

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  • question_answer70) Statement 1: A function \[f:R\to R\] is continuous at \[{{x}_{0}}\]if and only if \[\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f(x)\] exists and \[\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f\left( x \right)=f\left( {{x}_{0}} \right)\] Statement 2: A function \[f:R\to R\] is discontinuous at \[{{x}_{0}}\] if and only if,\[\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f\left( x \right)\]exists and \[\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f\left( x \right)\ne f\left( {{x}_{0}} \right).\]     JEE Main Online Paper (Held On 12 May 2012)

    A) Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

    B)                        Statement 1 is false. Statement 2 is true.

    C)                        Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

    D)                        Statement 1 is true. Statement 2 is false.

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  • question_answer71) The sum of the series\[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...\] upto 15 terms is     JEE Main Online Paper (Held On 12 May 2012)

    A) 1                                             

    B)                        2

    C)                        3   

    D)                        4

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  • question_answer72) The coordinates of the foot perpendicular from the point (1,0,0) to the line \[\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+10}{8}\]are     JEE Main Online Paper (Held On 12 May 2012)

    A)                 (2.-3.8)                                

    B)                        (1,-1,-10)

    C)                        (5,-8,-4)                               

    D)                        (3,-4,-2)

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  • question_answer73) If\[\vec{u}=\hat{j}+4\hat{k},\vec{v}=\hat{i}+3\hat{k}\] and \[\vec{w}=\cos \theta \hat{i}+\sin \theta \hat{j}\] are vectors in 3-dimensional space, then the maximum possible value of \[\left| \vec{u}\times \vec{v}.\vec{w} \right|\] is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[\sqrt{3}\]                                        

    B)                        \[5\]

    C)                        \[\sqrt{14}\]                                      

    D)                        \[7\]

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  • question_answer74) If the mean of 4,7,2,8,6 and a is 7, then the mean deviation from the median of these observations is     JEE Main Online Paper (Held On 12 May 2012)

    A) 8                                             

    B)                        5

    C)                        1                                             

    D)                        3

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  • question_answer75) Consider a rectangle whose length is increasing at the uniform rate of 2 m/sec, breadth is decreasing at the uniform rate of 3 m/sec and the area is decreasing at the uniform rate of it \[5\,{{m}^{2}}/\sec .\] If after some time the breadth of the rectangle is 2 m then the length of the rectangle is     JEE Main Online Paper (Held On 12 May 2012)

    A) 2m                                         

    B)                        4m

    C)                        1m                                         

    D)                        3m

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  • question_answer76) If \[f'(x)=\sin (\log x)\]and \[y=f\left( \frac{2x+3}{3-2x} \right),\] then\[\frac{dy}{dx}\] equals     JEE Main Online Paper (Held On 12 May 2012)

    A) \[\sin \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]

    B)                        \[\frac{12}{{{\left( 3-2x \right)}^{2}}}\]

    C)                        \[\frac{12}{{{\left( 3-2x \right)}^{2}}}\sin \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]

    D)                        \[\frac{12}{{{\left( 3-2x \right)}^{2}}}\cos \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]

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  • question_answer77) The area of the triangle whose vertices are complex numbers z, iz, z + iz in the Argand diagram is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[2|z{{|}^{2}}\]                

    B)                        \[1/2|z{{|}^{2}}\]

    C)                        \[4|z{{|}^{2}}\]                

    D)                        \[|z{{|}^{2}}\]  

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  • question_answer78) Statement 1: The degrees of the differential equations \[\frac{dy}{dx}+{{y}^{2}}=x\] and \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y\sin x\]are equal. Statement 2: The degree of a differential equation, when it is a polynomial equation in derivatives, is the highest positive integral power of the highest order derivative involved in the differential equation, otherwise degree is not defined.     JEE Main Online Paper (Held On 12 May 2012)

    A) Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement!.

    B)                        Statement 1 is false, Statement 2 is true.

    C)                        Statement 1 is true. Statement 2 is false.

    D)                        Statement 1 is true. Statement 2 is true; Statement 2 is a correct explanation of Statement 1.

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  • question_answer79) Statement 1: If the points (1,2,2), (2,1,2) and (2,2, z) and (1,1,1) are coplanar, then z= 2. Statement 2: If the 4 points P, Q, R and S are coplanar, then the volume of the tetrahedron PQRS is O.     JEE Main Online Paper (Held On 12 May 2012)

    A) Statement 1 is false,. Statement 2 is true.

    B)                        Statement 1 is true. Statement 2 is false.

    C)                        Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

    D)                        Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement!.

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  • question_answer80) If \[{{P}_{1}}\]and \[{{P}_{2}}\] are two points on the ellipse \[\frac{{{x}^{2}}}{4}+{{y}^{2}}=1\]at which the tangents are parallel to the chord joining the points (0,1) and (2,0), then the distance between \[{{P}_{1}}\] and \[{{P}_{2}}\] is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[2\sqrt{2}\]                                      

    B)                        \[\sqrt{5}\]

    C)                        \[2\sqrt{3}\]                                      

    D)                        \[\sqrt{10}\]

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  • question_answer81) The area enclosed by the curves \[y={{x}^{2}},y={{x}^{3}},x=0\]and \[x=0\]where \[p>1,\]is 1/6. The p equals     JEE Main Online Paper (Held On 12 May 2012)

    A) 8/3                        

    B)                        16/3

    C)                        2                                             

    D)                        4/3

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  • question_answer82) If \[f(x)=x{{e}^{x}}^{(1-x)},x\in R,\]then f(x) is     JEE Main Online Paper (Held On 12 May 2012)

    A) decreasing on [-1/2,1]

    B)                        decreasing on R

    C)                        increasing on [-1/2,1]

    D)                        increasing on R

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  • question_answer83) The integral of \[\frac{{{x}^{2}}-x}{{{x}^{3}}-{{x}^{2}}+x-1}\]w.r.t.x is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[\frac{1}{2}\log \left( {{x}^{2}}+1 \right)+C\]

    B)                        \[\frac{1}{2}\log \left| {{x}^{2}}+1 \right|+C\]

    C)                        \[\log \left( {{x}^{2}}+1 \right)+C\]         

    D)                        \[\log \left| {{x}^{2}}-1 \right|+C\]

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  • question_answer84) The logically equivalent preposition of \[p\Leftrightarrow q\]is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[\left( p\Rightarrow q \right)\wedge \left( q\Rightarrow p \right)\]      

    B)                        \[p\wedge q\]

    C)                        \[\left( p\wedge q \right)\vee \left( q\Rightarrow p \right)\]     

    D)                        \[\left( p\wedge q \right)\Rightarrow \left( q\vee p \right)\]

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  • question_answer85) If\[\left| \begin{matrix} -2a & a+b & a+c  \\ b+a & -2b & b+c  \\ c+a & b+c & -2c  \\ \end{matrix} \right|\]\[=\alpha \left( a+b \right)\left( b+c \right)\left( c+a \right)\ne 0\]then \[\alpha \] is equal to     JEE Main Online Paper (Held On 12 May 2012)

    A) \[a+b+c\]                           

    B)                        \[abc\]

    C)                         4

    D)                        1

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  • question_answer86) If \[A=\{x\in {{z}^{+}}:x<10\]and x is a multiple of 3 or 4}, where \[{{z}^{+}}\] is the set of positive integers, then the total number of symmetric relations on A is     JEE Main Online Paper (Held On 12 May 2012)

    A) 25                                           

    B)                        215

    C)                        210                                         

    D)                        220

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  • question_answer87) If the sum of the square of the roots of the equation \[{{x}^{2}}-(\sin \alpha -2)x-(1+\sin \alpha )=0\] is least, then \[\alpha \] is equal to     JEE Main Online Paper (Held On 12 May 2012)

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

    B)                        \[\frac{\pi }{4}\]

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

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

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  • question_answer88) If \[\frac{d}{dx}G(x)=\frac{{{e}^{\tan x}}}{x},x\in (0,\pi /2),\]then \[\int\limits_{1/4}^{1/2}{\frac{2}{x}.{{e}^{\tan (\pi {{x}^{2}})}}}dx\] is equal to     JEE Main Online Paper (Held On 12 May 2012)

    A) \[G(\pi /4)-G(\pi /16)\]

    B)                        \[2[G(\pi /4)-G(\pi /16)]\]

    C)                        \[\pi [G(1/2)-G(1/4)]\]

    D)                        \[G(1/\sqrt{2})-G(1/2)\]

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  • question_answer89) A number w is randomly selected from the set {1,2,3,....., 1000}. The probability that\[\frac{\sum\limits_{i=1}^{n}{{{i}^{2}}}}{\sum\limits_{i=1}^{n}{i}}\] is  an integer is     JEE Main Online Paper (Held On 12 May 2012)

    A) 0.331                                    

    B)                        0333

    C)                        0334                                      

    D)                        0332

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  • question_answer90) If a straight line y - x = 2 divides the region \[{{x}^{2}}+{{y}^{2}}\le 4\]into two parts, then the ratio of the area of the smaller part to the area of the greater part is     JEE Main Online Paper (Held On 12 May 2012)

    A) \[3\pi -8:\pi +8\]                              

    B)                        \[\pi -3:3\pi +3\]

    C)                        \[3\pi -4:\pi +4\]                              

    D)                        \[\pi -2:3\pi +2\]

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