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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
done
clear
B)
465 nm
done
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C)
310 nm
done
clear
D)
620 nm
done
clear
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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)
\[2\sqrt{2}T\]
done
clear
B)
4 T
done
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C)
2 T
done
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D)
8 T
done
clear
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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)
\[3RC\ell n2\]
done
clear
B)
\[2RC\,\ell n2\]
done
clear
C)
\[2RC\,\ell n7\]
done
clear
D)
\[3RC\,\ell n7\]
done
clear
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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
done
clear
B)
8 N in y-direction
done
clear
C)
4 N in y-direction
done
clear
D)
4 N in z-direction
done
clear
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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.
done
clear
B)
Statement 1 is true. Statement 2 is false.
done
clear
C)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
done
clear
D)
Statement 1 is true. Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
done
clear
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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)
\[2\sqrt{10}s\]
done
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B)
5 s
done
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C)
10 s
done
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D)
\[\sqrt{10}s\]
done
clear
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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)
\[\frac{8{{P}_{0}}{{V}_{0}}}{nR}\]
done
clear
B)
\[\frac{3{{P}_{0}}{{V}_{0}}}{2nR}\]
done
clear
C)
\[\frac{9{{P}_{0}}{{V}_{0}}}{2nR}\]
done
clear
D)
\[\frac{9{{P}_{0}}{{V}_{0}}}{4nR}\]
done
clear
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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
done
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B)
5.3cm
done
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C)
5.32cm
done
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D)
5.320cm
done
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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)
\[2.5\times {{10}^{-5}}cm\]
done
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B)
\[1.25\times {{10}^{-5}}cm\]
done
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C)
\[10\times {{10}^{-5}}cm\]
done
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D)
\[5\times {{10}^{-5}}cm\]
done
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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.
done
clear
B)
Statement 1 is true, Statement 2 is false.
done
clear
C)
Statement 1 is true. Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
done
clear
D)
Statement 1 is true. Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
done
clear
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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
done
clear
B)
\[{{r}^{-1}}\]
done
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C)
\[{{r}^{2}}\]
done
clear
D)
\[{{r}^{-2}}\]
done
clear
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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
done
clear
B)
8.1,1.2
done
clear
C)
6.4,1.2
done
clear
D)
6.4,0.67
done
clear
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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.
done
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B)
Nuclear forces are short range, attractive and charge dependent.
done
clear
C)
Nuclei of atoms having same number of neutrons are known as isobars.
done
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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.
done
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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)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
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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)
\[a\cos (kx-\omega t+\pi )\]
done
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B)
\[a\cos (kx-\omega t+\pi )\]
done
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C)
\[a\cos \left( kx+\omega t+\frac{\pi }{2} \right)\]
done
clear
D)
\[a\cos \left( kx-\omega t+\frac{\pi }{2} \right)\]
done
clear
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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)
\[\cot \alpha =3\]
done
clear
B)
\[\sec \alpha =3\]
done
clear
C)
\[\cos ec\,\alpha =3\]
done
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D)
\[\cos \,\alpha =3\]
done
clear
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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)
\[5\,m\,{{s}^{-1}}\]
done
clear
B)
\[10\,m\,{{s}^{-1}}\]
done
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C)
\[25\,m\,{{s}^{-1}}\]
done
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D)
\[50\sqrt{10}\,m\,{{s}^{-1}}\]
done
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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)
\[\sqrt{2gh}\]
done
clear
B)
\[\sqrt{\frac{7}{5}gh}\]
done
clear
C)
\[\sqrt{\frac{7}{2}gh}\]
done
clear
D)
\[\sqrt{\frac{10}{7}gh}\]
done
clear
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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
done
clear
B)
0.33 W
done
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C)
0.25 W
done
clear
D)
0.86 W
done
clear
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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
done
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B)
100mm
done
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C)
120mm
done
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D)
80mm
done
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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
done
clear
B)
4
done
clear
C)
2
done
clear
D)
8
done
clear
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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)
\[16\frac{{{n}_{2}}}{{{n}_{1}}}{{C}_{1}}\]
done
clear
B)
\[\frac{2{{C}_{1}}}{{{n}_{1}}{{n}_{2}}}\]
done
clear
C)
\[2\frac{{{n}_{2}}}{{{n}_{1}}}{{C}_{1}}\]
done
clear
D)
\[\frac{16{{C}_{1}}}{{{n}_{1}}{{n}_{2}}}\]
done
clear
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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)
done
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B)
(i), (iii), (iv)
done
clear
C)
(i),(ii)
done
clear
D)
(i),(ii),(iii),(iv)
done
clear
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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)
\[m\frac{v_{0}^{2}}{x_{0}^{2}}\]
done
clear
B)
\[m\frac{{{v}_{0}}}{2{{x}_{0}}}\]
done
clear
C)
\[2m\frac{{{v}_{0}}}{{{x}_{0}}}\]
done
clear
D)
\[\frac{2}{3}m{{\left( \frac{{{v}_{0}}}{{{x}_{0}}} \right)}^{2}}\]
done
clear
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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
done
clear
B)
1.2 T and directed into the plane of page
done
clear
C)
0.6 T and directed into the plane of page
done
clear
D)
1.2 T and directed out of page
done
clear
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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.
done
clear
B)
low resistivity and high temperature coefficient.
done
clear
C)
low resistivity and low temperature coefficient.
done
clear
D)
high resistivity and high temperature coefficient.
done
clear
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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)
\[\frac{{{m}_{2}}}{{{m}_{1}}}\]
done
clear
B)
\[\frac{{{m}_{1}}}{{{m}_{2}}}\]
done
clear
C)
\[\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\]
done
clear
D)
\[\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\]
done
clear
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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.
done
clear
B)
(b) Statement 1 is false, Statement 2 is true.
done
clear
C)
(c) Statement 1 is true, Statement 2 is true. Statement 2 is correct explanation of the Statement 1.
done
clear
D)
(d) Statement 1 is true, Statement 2 is false.
done
clear
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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
done
clear
B)
1031
done
clear
C)
1025
done
clear
D)
1043
done
clear
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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
done
clear
B)
3
done
clear
C)
infinite
done
clear
D)
5
done
clear
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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
done
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B)
Friedel-Crafts reaction
done
clear
C)
Gattermann reaction
done
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D)
Azo-eoupling reaction
done
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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
done
clear
B)
trigonal
done
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C)
octahedral
done
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D)
pyramidal
done
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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
done
clear
B)
from sp2 to sp3
done
clear
C)
from sp3 to sp2
done
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D)
from sp3 to sp3
done
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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)
\[N{{H}_{3}}\]
done
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B)
\[Mg{{(N{{O}_{3}})}_{2}}\]
done
clear
C)
\[M{{g}_{3}}{{N}_{2}}\]
done
clear
D)
\[MgO\]
done
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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
done
clear
B)
equal to 10 ppm
done
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C)
equal to 5 ppm
done
clear
D)
less than 5 ppm
done
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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%
done
clear
B)
73.5%
done
clear
C)
7.35%
done
clear
D)
2.47%
done
clear
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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)
\[{{[Cr{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]}^{+}}\]
done
clear
B)
\[{{[Co{{(en)}_{2}}C{{l}_{2}}]}^{+}}\]
done
clear
C)
\[{{[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]}^{+}}\]
done
clear
D)
\[{{[Zn{{(en)}_{2}}]}^{2+}}\]
done
clear
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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
done
clear
B)
Boron
done
clear
C)
Carbon
done
clear
D)
Oxygen
done
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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
done
clear
B)
9.72 BM
done
clear
C)
7.9 BM
done
clear
D)
10.60 BM
done
clear
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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
done
clear
B)
20ml
done
clear
C)
2ml
done
clear
D)
40ml
done
clear
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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
done
clear
B)
dissolve alumina in molten cryolite
done
clear
C)
remove the impurities of alumina
done
clear
D)
increase the electrical conductivity
done
clear
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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
done
clear
B)
Acrylonitrile and vinyl chloride
done
clear
C)
Adipic acid and ethylene glycol
done
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D)
Phenol and formaldehyde
done
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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
done
clear
B)
chemisorption is endothermic but physisorption is exothermic
done
clear
C)
both are exothermic
done
clear
D)
physisorption is endothermic but chemisorption is exothermic.
done
clear
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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.
done
clear
B)
The reaction of methyl magnesium bromide with acetone gives butano1-2.
done
clear
C)
Alkyl halides follow the following reactivity sequence on reaction with alkeries. \[R-I>R-Br>R-Cl>R-I\]
done
clear
D)
\[{{C}_{2}}{{H}_{4}}C{{l}_{2}}\] may exist in two isomeric forms
done
clear
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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
done
clear
B)
lone bond energy
done
clear
C)
absence of bond polarity
done
clear
D)
uneven electron distribution.
done
clear
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question_answer46) Amylopectin is a polymer of
JEE Main Online Paper (Held On 12 May 2012)
A)
\[\alpha -D-\] glucose
done
clear
B)
amino acid
done
clear
C)
\[\beta -D-\] glucose
done
clear
D)
amylase.
done
clear
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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)
\[4\pi {{a}_{0}}\]
done
clear
B)
\[8\pi {{a}_{0}}\]
done
clear
C)
\[6\pi {{a}_{0}}\]
done
clear
D)
\[2\pi {{a}_{0}}\]
done
clear
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question_answer48) Chemically heroin is
JEE Main Online Paper (Held On 12 May 2012)
A)
morphine monoacetate
done
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B)
morphine dibenzbate
done
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C)
morphine diacetate
done
clear
D)
morphine monobenzoate
done
clear
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question_answer49)
In the given reaction, the product 'A' is
JEE Main Online Paper (Held On 12 May 2012)
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
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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
done
clear
B)
1000
done
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C)
250
done
clear
D)
200
done
clear
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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
done
clear
B)
1.5
done
clear
C)
1
done
clear
D)
2
done
clear
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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
done
clear
B)
3
done
clear
C)
27
done
clear
D)
36
done
clear
View Answer play_arrow
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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
done
clear
B)
5.6g
done
clear
C)
8.09g
done
clear
D)
6.6g
done
clear
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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)
\[OH>{{H}_{2}}O>C{{N}^{-}}\]
done
clear
B)
\[O{{H}^{-}}>C{{N}^{-}}>{{H}_{2}}O\]
done
clear
C)
\[{{H}_{2}}O>C{{N}^{-}}>O{{H}^{-}}\]
done
clear
D)
\[C{{N}^{-}}>{{H}_{2}}O>O{{H}^{-}}\]
done
clear
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A)
(iv)>(i)>(ii)>(iii)
done
clear
B)
(ii)>(iii)>(i)>(iv)
done
clear
C)
(iii)>(i)>(iv)>(ii)
done
clear
D)
(i)>(ii)>(iii)>(iv)
done
clear
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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)
\[0\,J\,mo{{l}^{-1}}\,\]
done
clear
B)
\[2490\,J\,mo{{l}^{-1}}\,\]
done
clear
C)
\[-2490\,J\,mo{{l}^{-1}}\,\]
done
clear
D)
\[-7482\,J\,mo{{l}^{-1}}\,\]
done
clear
View Answer play_arrow
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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
done
clear
B)
Rosenmund reduction
done
clear
C)
Wolf-Kishner reduction
done
clear
D)
Clemmenson reduction
done
clear
View Answer play_arrow
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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)
\[u>v>\alpha \]
done
clear
B)
\[v>u>\alpha \]
done
clear
C)
\[\alpha >u>v\]
done
clear
D)
\[u>\alpha >v\]
done
clear
View Answer play_arrow
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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)
\[C{{H}_{3}}Cl\]
done
clear
B)
done
clear
C)
\[C{{H}_{2}}C{{l}_{2}}\]
done
clear
D)
done
clear
View Answer play_arrow
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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
done
clear
B)
8,2,5
done
clear
C)
5,2,16
done
clear
D)
5,8,4
done
clear
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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.
done
clear
B)
ab = cd
done
clear
C)
ac = bd
done
clear
D)
a, b, c, d are in G.P.
done
clear
View Answer play_arrow
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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
done
clear
B)
8
done
clear
C)
1
done
clear
D)
4
done
clear
View Answer play_arrow
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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.
done
clear
B)
Statement 1 is false, Statement 2 is true.
done
clear
C)
Statement 1 is true. Statement 2 is true; Statement 2 is a correct explanation of Statement!.
done
clear
D)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1,
done
clear
View Answer play_arrow
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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
done
clear
B)
1/5
done
clear
C)
35/19
done
clear
D)
19/35
done
clear
View Answer play_arrow
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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.
done
clear
B)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
done
clear
C)
Statement 1 is false, Statement 2 is true
done
clear
D)
Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
done
clear
View Answer play_arrow
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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)
\[\frac{2\hat{j}+\hat{k}}{\sqrt{5}}\]
done
clear
B)
\[\frac{3\hat{i}+2\hat{j}-2\hat{k}}{\sqrt{17}}\]
done
clear
C)
\[\frac{3\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{17}}\]
done
clear
D)
\[\frac{2\hat{i}+2\hat{j}-2\hat{k}}{3}\]
done
clear
View Answer play_arrow
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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
done
clear
B)
twelve
done
clear
C)
seven
done
clear
D)
five
done
clear
View Answer play_arrow
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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)
\[\left( \frac{3}{2},\infty \right)\]
done
clear
B)
\[\left( 1,\frac{3}{2} \right)\]
done
clear
C)
\[\left( -\infty ,0 \right)\]
done
clear
D)
\[\left( 0,\frac{1}{2} \right)\]
done
clear
View Answer play_arrow
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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)
done
clear
B)
(-4,-7)
done
clear
C)
(-4,7)
done
clear
D)
(4,7)
done
clear
View Answer play_arrow
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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.
done
clear
B)
Statement 1 is false. Statement 2 is true.
done
clear
C)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
done
clear
D)
Statement 1 is true. Statement 2 is false.
done
clear
View Answer play_arrow
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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
done
clear
B)
2
done
clear
C)
3
done
clear
D)
4
done
clear
View Answer play_arrow
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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)
done
clear
B)
(1,-1,-10)
done
clear
C)
(5,-8,-4)
done
clear
D)
(3,-4,-2)
done
clear
View Answer play_arrow
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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)
\[\sqrt{3}\]
done
clear
B)
\[5\]
done
clear
C)
\[\sqrt{14}\]
done
clear
D)
\[7\]
done
clear
View Answer play_arrow
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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
done
clear
B)
5
done
clear
C)
1
done
clear
D)
3
done
clear
View Answer play_arrow
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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
done
clear
B)
4m
done
clear
C)
1m
done
clear
D)
3m
done
clear
View Answer play_arrow
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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)
\[\sin \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]
done
clear
B)
\[\frac{12}{{{\left( 3-2x \right)}^{2}}}\]
done
clear
C)
\[\frac{12}{{{\left( 3-2x \right)}^{2}}}\sin \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]
done
clear
D)
\[\frac{12}{{{\left( 3-2x \right)}^{2}}}\cos \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]
done
clear
View Answer play_arrow
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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)
\[2|z{{|}^{2}}\]
done
clear
B)
\[1/2|z{{|}^{2}}\]
done
clear
C)
\[4|z{{|}^{2}}\]
done
clear
D)
\[|z{{|}^{2}}\]
done
clear
View Answer play_arrow
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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!.
done
clear
B)
Statement 1 is false, Statement 2 is true.
done
clear
C)
Statement 1 is true. Statement 2 is false.
done
clear
D)
Statement 1 is true. Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
done
clear
View Answer play_arrow
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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.
done
clear
B)
Statement 1 is true. Statement 2 is false.
done
clear
C)
Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
done
clear
D)
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement!.
done
clear
View Answer play_arrow
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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)
\[2\sqrt{2}\]
done
clear
B)
\[\sqrt{5}\]
done
clear
C)
\[2\sqrt{3}\]
done
clear
D)
\[\sqrt{10}\]
done
clear
View Answer play_arrow
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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
done
clear
B)
16/3
done
clear
C)
2
done
clear
D)
4/3
done
clear
View Answer play_arrow
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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]
done
clear
B)
decreasing on R
done
clear
C)
increasing on [-1/2,1]
done
clear
D)
increasing on R
done
clear
View Answer play_arrow
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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)
\[\frac{1}{2}\log \left( {{x}^{2}}+1 \right)+C\]
done
clear
B)
\[\frac{1}{2}\log \left| {{x}^{2}}+1 \right|+C\]
done
clear
C)
\[\log \left( {{x}^{2}}+1 \right)+C\]
done
clear
D)
\[\log \left| {{x}^{2}}-1 \right|+C\]
done
clear
View Answer play_arrow
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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)
\[\left( p\Rightarrow q \right)\wedge \left( q\Rightarrow p \right)\]
done
clear
B)
\[p\wedge q\]
done
clear
C)
\[\left( p\wedge q \right)\vee \left( q\Rightarrow p \right)\]
done
clear
D)
\[\left( p\wedge q \right)\Rightarrow \left( q\vee p \right)\]
done
clear
View Answer play_arrow
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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)
\[a+b+c\]
done
clear
B)
\[abc\]
done
clear
C)
4
done
clear
D)
1
done
clear
View Answer play_arrow
-
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
done
clear
B)
215
done
clear
C)
210
done
clear
D)
220
done
clear
View Answer play_arrow
-
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)
\[\frac{\pi }{6}\]
done
clear
B)
\[\frac{\pi }{4}\]
done
clear
C)
\[\frac{\pi }{3}\]
done
clear
D)
\[\frac{\pi }{2}\]
done
clear
View Answer play_arrow
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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)
\[G(\pi /4)-G(\pi /16)\]
done
clear
B)
\[2[G(\pi /4)-G(\pi /16)]\]
done
clear
C)
\[\pi [G(1/2)-G(1/4)]\]
done
clear
D)
\[G(1/\sqrt{2})-G(1/2)\]
done
clear
View Answer play_arrow
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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
done
clear
B)
0333
done
clear
C)
0334
done
clear
D)
0332
done
clear
View Answer play_arrow
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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)
\[3\pi -8:\pi +8\]
done
clear
B)
\[\pi -3:3\pi +3\]
done
clear
C)
\[3\pi -4:\pi +4\]
done
clear
D)
\[\pi -2:3\pi +2\]
done
clear
View Answer play_arrow