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question_answer1) Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth \[={{R}_{E}}\])?
JEE Main Online Paper (Held On 07 May 2012)
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
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question_answer2) A car of mass 1000 kg is moving at a speed of 30m/s. Brakes are applied to bring the car to rest. If the net retarding force is 5000 N, the car comes to stop after travelling dm in t s. Then
JEE Main Online Paper (Held On 07 May 2012)
A)
\[d=150,t=5\]
done
clear
B)
\[d=120,t=8\]
done
clear
C)
\[d=180,t=6\]
done
clear
D)
\[d=90,t=6\]
done
clear
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question_answer3) A perfect gas at \[27{}^\circ C\] is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to
JEE Main Online Paper (Held On 07 May 2012)
A)
\[327{}^\circ C\]
done
clear
B)
\[200{}^\circ C\]
done
clear
C)
\[54{}^\circ C\]
done
clear
D)
\[300{}^\circ C\]
done
clear
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question_answer4)
A square hole of side length i is made at a depth of h and a circular hole of radius r is made at adepth of 4h from the surface of water in a water tank kept on a horizontal surface. If \[\ell <<h, r<<h\]and the rate of water flow from the holes is the same, then r is equal to 
JEE Main Online Paper (Held On 07 May 2012)
A)
\[\frac{\ell }{\sqrt{2\pi }}\]
done
clear
B)
\[\frac{\ell }{\sqrt{3\pi }}\]
done
clear
C)
\[\frac{\ell }{3\pi }\]
done
clear
D)
\[\frac{\ell }{2\pi }\]
done
clear
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question_answer5) A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100 kN force stretches it along its length. Young's modulus of structural steel is\[2\times {{10}^{11}}N{{m}^{-2}}.\]The percentage strain is about
JEE Main Online Paper (Held On 07 May 2012)
A)
0.16%
done
clear
B)
0.32%
done
clear
C)
0.08%
done
clear
D)
0.24%
done
clear
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question_answer6) The heat radiated per unit area in 1 hour by a furnace whose temperature is 3000 K is \[(\sigma =5.7\times {{10}^{-8}}W\,{{m}^{-2}}{{K}^{-4}})\]
JEE Main Online Paper (Held On 07 May 2012)
A)
\[1.7\times {{10}^{10}}J\]
done
clear
B)
\[1.1\times {{10}^{12}}J\]
done
clear
C)
\[2.8\times {{10}^{8}}J\]
done
clear
D)
\[4.6\times {{10}^{6}}J\]
done
clear
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question_answer7) Broadcasting antennas are generally
JEE Main Online Paper (Held On 07 May 2012)
A)
vertical type
done
clear
B)
both vertical and horizontal type
done
clear
C)
omni directional type
done
clear
D)
horizontal type
done
clear
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question_answer8) The velocity of certain ions that pass undeflected through crossed electric field E = 7.7 k V/m and magnetic field B = 0.14T is
JEE Main Online Paper (Held On 07 May 2012)
A)
18km/s
done
clear
B)
77km/s
done
clear
C)
55km/s.
done
clear
D)
1078 km/s
done
clear
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question_answer9) Following are expressions for four plane simple harmonic waves (i)\[{{y}_{1}}=A\cos 2\pi \left( {{n}_{1}}t+\frac{x}{{{\lambda }_{1}}} \right)\] (ii\[{{y}_{2}}=A\cos 2\pi \left( {{n}_{1}}t+\frac{x}{{{\lambda }_{1}}}+\pi \right)\] (iii)\[{{y}_{3}}=A\cos 2\pi \left( {{n}_{1}}t+\frac{x}{{{\lambda }_{2}}} \right)\] (iv)\[{{y}_{4}}=A\cos 2\pi \left( {{n}_{2}}t-\frac{x}{{{\lambda }_{2}}} \right)\] The pairs of waves which will produce destructive interference and stationary waves respectively in a medium, are
JEE Main Online Paper (Held On 07 May 2012)
A)
(iii, iv), (i, ii)
done
clear
B)
(i, iii), (ii, iv)
done
clear
C)
(i,iv),(ii,iii)
done
clear
D)
(i, ii), (iii, iv)
done
clear
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question_answer10) An engine pumps water continuously through a hose. Water leaves the hose with velocity v and m is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is
A)
\[m{{v}^{3}}\]
done
clear
B)
\[m{{v}^{2}}\]
done
clear
C)
\[\frac{1}{2}m{{v}^{2}}\]
done
clear
D)
\[\frac{1}{2}m{{v}^{3}}\]
done
clear
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question_answer11) The electron of a hydrogen atom makes a transition from the \[{{(n+1)}^{th}}\]orbit to the \[{{n}^{th}}\] orbit. For large n the wavelength of the emitted radiation is proportional to
JEE Main Online Paper (Held On 07 May 2012)
A)
n
done
clear
B)
\[{{n}^{3}}\]
done
clear
C)
\[{{n}^{4}}\]
done
clear
D)
\[{{n}^{2}}\]
done
clear
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question_answer12)
The graph of an object's motion (along the x-axis) is shown in the figure. The instantaneous velocity of the object at points A and B are \[{{v}_{A}}\]and \[{{v}_{B}}\] respectively. Then 
JEE Main Online Paper (Held On 07 May 2012)
A)
\[{{v}_{A}}={{v}_{B}}=0.5m/s\]
done
clear
B)
\[{{v}_{A}}=0.5m/s<{{v}_{B}}\]
done
clear
C)
\[{{v}_{A}}=0.5m/s>{{v}_{B}}\]
done
clear
D)
\[{{v}_{A}}={{v}_{B}}=2m/s\]
done
clear
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question_answer13) A circular hole of diameter R is cut from a disc of mass M and radius R, -the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[\left( \frac{15}{32} \right)M{{R}^{2}}\]
done
clear
B)
\[\left( \frac{1}{8} \right)M{{R}^{2}}\]
done
clear
C)
\[\left( \frac{3}{8} \right)M{{R}^{2}}\]
done
clear
D)
\[\left( \frac{13}{32} \right)M{{R}^{2}}\]
done
clear
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question_answer14) In a Young's double slit experiment with light of wavelength\[\lambda ,\] fringe pattern on the screen has fringe width \[\beta .\] When two thin transparent glass(refractive index \[\mu \])plates of thickness \[{{t}_{1}}\] and \[{{t}_{2}}\]\[({{t}_{1}}>{{t}_{2}})\]are placed in the path of the two beams respectively, the fringe pattern will shift by a distance
JEE Main Online Paper (Held On 07 May 2012)
A)
\[\frac{\beta (\mu -1)}{\lambda }\left( \frac{{{t}_{1}}}{{{t}_{2}}} \right)\]
done
clear
B)
\[\frac{\mu \beta }{\lambda }\frac{{{t}_{1}}}{{{t}_{2}}}\]
done
clear
C)
\[\frac{\beta \left( \mu -1 \right)}{\lambda }\left( {{t}_{1}}-{{t}_{2}} \right)\]
done
clear
D)
\[\left( \mu -1 \right)\frac{\lambda }{\beta }\left( {{t}_{1}}+{{t}_{2}} \right)\]
done
clear
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question_answer15) 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: In an adiabatic process, change in internal energy of a gas is equal to work done on/by the gas in the process. Statement 2: The temperature of a gas remains constant in an adiabatic process.
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
done
clear
B)
Statement 1 is true. Statement 2 is false.
done
clear
C)
Statement 1 is false, Statement 2 is true.
done
clear
D)
Statement 1 is false. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
done
clear
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question_answer16) 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: The possibility of an electric bulb fusing is higher at the time of switching ON. Statement 2: Resistance of an electric bulb when it is not lit up is much smaller than when it is lit up.
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true. Statement 2 is false
done
clear
B)
Statement 1 is false, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
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 false, Statement 2 is true.
done
clear
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question_answer17) Given that K= energy, V= velocity, T= time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?
JEE Main Online Paper (Held On 07 May 2012)
A)
\[[K{{V}^{-2}}{{T}^{-2}}]\]
done
clear
B)
\[[{{K}^{2}}{{V}^{2}}{{T}^{-2}}]\]
done
clear
C)
\[[{{K}^{2}}{{V}^{-2}}{{T}^{-2}}]\]
done
clear
D)
\[[K{{V}^{2}}{{T}^{2}}]\]
done
clear
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question_answer18) A particle gets displaced by\[\Delta \over line{r}=\left( 2\hat{i}+3\hat{j}+4\hat{k} \right)m\]under the action of a force\[\vec{F}=\left( 7\hat{i}+4\hat{j}+3\hat{k} \right).\]The change in its kinetic energy is
JEE Main Online Paper (Held On 07 May 2012)
A)
38 J
done
clear
B)
70J
done
clear
C)
52.5 J
done
clear
D)
126 J
done
clear
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question_answer19)
Two circuits (a) and (b) have charged capacitors of capacitance C, 2C and 3C with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches 
JEE Main Online Paper (Held On 07 May 2012)
A)
No charge flows in (a) but charge flows from R to L in (b)
done
clear
B)
Charges flow from L to R in both (a) and (b)
done
clear
C)
Charges flow from R to L in (a) and from L to R in(b)
done
clear
D)
No charge flows in (a) but charge flows from L to R in (b)
done
clear
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question_answer20)
In an LCR circuit shown in the following figure, what will be the readings of the voltmeter across the resistor and ammeter if an a.c. source of 220Vand 100 Hz is connected to it as shown? 
JEE Main Online Paper (Held On 07 May 2012)
A)
800V,8A
done
clear
B)
110V.1.1A
done
clear
C)
300V, 3 A
done
clear
D)
220V, 2.2 A
done
clear
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question_answer21) 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: In the resonance tube experiment, if the tuning fork is replaced by another identical turning fork but with its arm having been filled, the length of the air column should be increased to obtain resonance again. Statement 2: On filling the arms, the frequency of a tuning fork increases.
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
done
clear
B)
Statement 1 is true, Statement 2 is false.
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 not a correct explanation of Statement 1.
done
clear
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question_answer22) A bar magnet of length 6 cm has a magnetic moment of \[4J\,{{T}^{-1}}.\]Find the strength of magnetic field at a distance of 200 cm from the centre of the magnet along its equatorial line.
JEE Main Online Paper (Held On 07 May 2012)
A)
\[4\times {{10}^{-8}}\text{tesla}\]
done
clear
B)
\[3.5\times {{10}^{-8}}\text{tesla}\]
done
clear
C)
\[5\times {{10}^{-8}}\text{tesla}\]
done
clear
D)
\[3\times {{10}^{-8}}\text{tesla}\]
done
clear
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question_answer23)
The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line 
JEE Main Online Paper (Held On 07 May 2012)
A)
OA
done
clear
B)
OC
done
clear
C)
OD
done
clear
D)
OB
done
clear
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question_answer24)
In the Rutherford experiment, a-particles are scattered from a nucleus as shown. Out of the four paths, which path is not possible? 
JEE Main Online Paper (Held On 07 May 2012)
A)
D
done
clear
B)
B
done
clear
C)
C
done
clear
D)
A
done
clear
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question_answer25) The electric potential V(x) in a region around the origin is given by \[V(x)=4{{x}^{2}}\]volts. The electric charge enclosed in a cube of 1 m side with its centre at the origin is (in coulomb).
JEE Main Online Paper (Held On 07 May 2012)
A)
\[8{{\varepsilon }_{0}}\]
done
clear
B)
\[-4{{\varepsilon }_{0}}\]
done
clear
C)
0
done
clear
D)
(d)\[-8{{\varepsilon }_{0}}\]
done
clear
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question_answer26) Two polaroids have their polarizing directions parallel so that the intensity of a transmitted light is maximum. The angle through which either Polaroid must be turned if the intensity is to drop by one-half is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[135{}^\circ \]
done
clear
B)
\[90{}^\circ \]
done
clear
C)
\[120{}^\circ \]
done
clear
D)
\[180{}^\circ \]
done
clear
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question_answer27) Which of the following processes play a part in the formation of a rainbow? (i) Refraction (ii) Total internal reflection (iii) Dispersion (iv) Interference
JEE Main Online Paper (Held On 07 May 2012)
A)
(i),(ii)and(iii)
done
clear
B)
(i)and(ii)
done
clear
C)
(i), (ii) and (iv)
done
clear
D)
(iii) and (iv)
done
clear
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question_answer28) A sample originally contained 1020 radioactive atoms, which emit a-particles. The ratio of \[\text{ }\!\!\alpha\!\!\text{ -}\]particles emitted in the third year to that emitted during the second year is 0.3. How many \[\text{ }\!\!\alpha\!\!\text{ -}\]particles were emitted in the first year?
JEE Main Online Paper (Held On 07 May 2012)
A)
\[3\times {{10}^{18}}\]
done
clear
B)
\[3\times {{10}^{19}}\]
done
clear
C)
\[5\times {{10}^{18}}\]
done
clear
D)
\[7\times {{10}^{19}}\]
done
clear
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question_answer29) A solid sphere having mass m and radius r rolls down an inclined plane. Then its kinetic energy is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[\frac{5}{7}\]rotational and \[\frac{2}{7}\]translational
done
clear
B)
\[\frac{2}{7}\]rotational and \[\frac{5}{7}\]translational
done
clear
C)
\[\frac{2}{5}\]rotational and \[\frac{3}{5}\]translational
done
clear
D)
\[\frac{1}{2}\]rotational and \[\frac{1}{2}\]translational
done
clear
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question_answer30)
Which logic gate with inputs A and B performs the same operation as that performed by the following circuit? 
JEE Main Online Paper (Held On 07 May 2012)
A)
NAND gate
done
clear
B)
OR gate
done
clear
C)
NOR gate
done
clear
D)
AND gate
done
clear
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question_answer31) Which one of the following compounds is an anti-fertility drug?
JEE Main Online Paper (Held On 07 May 2012)
A)
Aspirin
done
clear
B)
Chloro my cetin
done
clear
C)
Saheli
done
clear
D)
Penicillin
done
clear
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question_answer32) The most basic compound among the following is
JEE Main Online Paper (Held On 07 May 2012)
A)
Acetanilide
done
clear
B)
Benzyl amine
done
clear
C)
p-Nitro aniline
done
clear
D)
Aniline
done
clear
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question_answer33) A battery is constructed of Cr and \[N{{a}_{2}}C{{r}_{2}}{{O}_{7}}.\]The unbalanced chemical equation when such a battery discharges is following: \[N{{a}_{2}}C{{r}_{2}}{{O}_{7}}+Cr+{{H}^{+}}\to C{{r}^{3+}}+{{H}_{2}}O+N{{a}^{+}}\] If one Faraday of electricity is passed through the battery during the charging, the number of moles of \[C{{r}^{3+}}\] removed from the solution is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[\frac{4}{3}\]
done
clear
B)
\[\frac{1}{3}\]
done
clear
C)
\[\frac{3}{3}\]
done
clear
D)
\[\frac{2}{3}\]
done
clear
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question_answer34) The limiting line in Balmer series will have a frequency of (Rydberg constant, \[{{R}_{\infty }}=3.29\times {{10}^{15}}\]cycles/s)
JEE Main Online Paper (Held On 07 May 2012)
A)
\[8.22\times {{10}^{14}}{{s}^{-1}}\]
done
clear
B)
\[3.29\times {{10}^{15}}{{s}^{-1}}\]
done
clear
C)
\[3.65\times {{10}^{14}}{{s}^{-1}}\]
done
clear
D)
\[5.26\times {{10}^{13}}{{s}^{-1}}\]
done
clear
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question_answer35) Which of the following cannot be represented by resonance structures?
JEE Main Online Paper (Held On 07 May 2012)
A)
Dimethyl ether
done
clear
B)
Nitrate anion
done
clear
C)
Carboxylate anion
done
clear
D)
Toluene
done
clear
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question_answer36) Which of the oxide groups among the following cannot be reduced by carbon?
A)
\[C{{u}_{2}}O,Sn{{O}_{2}}\]
done
clear
B)
\[CaO,{{K}_{2}}O\]
done
clear
C)
\[PbO,F{{e}_{2}}{{O}_{4}}\]
done
clear
D)
\[F{{e}_{2}}{{O}_{3}},ZnO\]
done
clear
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question_answer37) Among the following, the species having the smallest bond is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[N{{O}^{-}}\]
done
clear
B)
\[N{{O}^{+}}\]
done
clear
C)
\[{{O}_{2}}\]
done
clear
D)
NO
done
clear
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question_answer38) Based on lattice energy and other considerations, which one of the following alkali metal chloride is expected to have the highest melting point?
JEE Main Online Paper (Held On 07 May 2012)
A)
NaCI
done
clear
B)
KCl
done
clear
C)
LiCI
done
clear
D)
RbCl
done
clear
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question_answer39) The entropy of a sample of a certain substance increases by \[0.836\,J\,{{K}^{-1}}\] on adding reversibly0.3344 J of heat at constant temperature. The temperature of the sample is:
JEE Main Online Paper (Held On 07 May 2012)
A)
2.5K
done
clear
B)
0.3K
done
clear
C)
0.016K
done
clear
D)
0.4K
done
clear
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question_answer40) The electron affinity of chlorine is 3.7 eV. 1 gram of chlorine is completely converted to \[C{{l}^{-1}}\] ion in a gaseous state. (1 eV = 23.06 kcal \[mo{{l}^{-1}}\]).Energy released in the process is
JEE Main Online Paper (Held On 07 May 2012)
A)
4.8kcal
done
clear
B)
7.2kcal
done
clear
C)
8.2 kcal
done
clear
D)
2.4 kcal
done
clear
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question_answer41) Copper wire test for halogens is known as
JEE Main Online Paper (Held On 07 May 2012)
A)
Duma's Test
done
clear
B)
Beilstein' s Test
done
clear
C)
Liebig'sTest
done
clear
D)
Lassigne's Test
done
clear
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question_answer42) For 1 mol of an ideal gas at a constant temperature T, the plot of (log P) against (log V) is a(P: Pressure, V\ Volume)
JEE Main Online Paper (Held On 07 May 2012)
A)
Straight line parallel to x-axis.
done
clear
B)
Straight line with a negative slope.
done
clear
C)
Curve starting at origin.
done
clear
D)
Straight line passing through origin.
done
clear
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question_answer43) Which one of the following is a chain growth polymerisation?
JEE Main Online Paper (Held On 07 May 2012)
A)
Nucleic acid
done
clear
B)
Polystyrene
done
clear
C)
Protein
done
clear
D)
Starch
done
clear
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question_answer44) The d-electron configurations of \[C{{r}^{2+}},M{{n}^{2+}},F{{e}^{2+}}\]and \[C{{o}^{2+}}\]are \[{{d}^{4}},{{d}^{5}},{{d}^{6}}\]and \[{{d}^{7}}\] respectively. Which one of the following will exhibit the lowest paramagnetic behaviour? (Atomic no. Cr =24, Mn = 25, Fe = 26, Co = 27).
JEE Main Online Paper (Held On 07 May 2012)
A)
\[{{[Co{{({{H}_{2}}O)}_{6}}]}^{2+}}\]
done
clear
B)
\[{{[Cr{{({{H}_{2}}O)}_{6}}]}^{2+}}\]
done
clear
C)
\[{{[Mn{{({{H}_{2}}O)}_{6}}]}^{2+}}\]
done
clear
D)
\[{{[Fe{{({{H}_{2}}O)}_{6}}]}^{2+}}\]
done
clear
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question_answer45) If x is the mass of the gas adsorbed on mass m of the adsorbent at pressure p, Freundlic had sorption isotherm gives a straight line on plotting
JEE Main Online Paper (Held On 07 May 2012)
A)
\[x/m\,vs\,p\]
done
clear
B)
\[x/m\,vs1/\,p\]
done
clear
C)
\[\log x/m\,vs\,\log \,p\]
done
clear
D)
\[\log x/m\,\,vs\,p\]
done
clear
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question_answer46) The solubility (in mol\[{{L}^{-1}}\]) of AgCl\[({{K}_{sp}}=1.0\times {{10}^{-10}})\] in a 0.1 M KC1 solution will be
JEE Main Online Paper (Held On 07 May 2012)
A)
\[1.0\times {{10}^{-9}}\]
done
clear
B)
\[1.0\times {{10}^{-10}}\]
done
clear
C)
\[1.0\times {{10}^{-5}}\]
done
clear
D)
\[1.0\times {{10}^{-11}}\]
done
clear
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question_answer47) Among the following which is the best description of water in the solid phase?
JEE Main Online Paper (Held On 07 May 2012)
A)
Covalent solid
done
clear
B)
Molecular solid
done
clear
C)
Ionic solid
done
clear
D)
Network solid
done
clear
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question_answer48) All of the following statements apply to proteins except
JEE Main Online Paper (Held On 07 May 2012)
A)
Proteins generally have no definite melting point
done
clear
B)
Proteins contain the grouping 'CONH'
done
clear
C)
Proteins have high molecular weight
done
clear
D)
Proteins can only contain the elements C, H, O and N.
done
clear
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question_answer49) \[{{K}_{1}},{{K}_{2}}\]and\[{{K}_{3}}\] are the equilibrium constants of the following reactions (I), (II) and (III)respectively: (i)\[{{N}_{2}}+2{{O}_{2}}2N{{O}_{2}}\](ii)\[2N{{O}_{2}}{{N}_{2}}+2{{O}_{2}}\] (iii)\[N{{O}_{2}}\frac{1}{2}{{N}_{2}}+{{O}_{2}}\] The correct relation from the following is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[{{K}_{1}}=\frac{1}{{{K}_{2}}}=\frac{1}{{{K}_{3}}}\]
done
clear
B)
\[{{K}_{1}}=\frac{1}{{{K}_{2}}}=\frac{1}{{{({{K}_{3}})}^{2}}}\]
done
clear
C)
\[{{K}_{1}}=\sqrt{{{K}_{2}}}={{K}_{3}}\]
done
clear
D)
\[{{K}_{1}}=\frac{1}{{{K}_{2}}}={{K}_{3}}\]
done
clear
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question_answer50) The concentrated sulphuric acid that is peddled commercial is \[95%{{H}_{2}}S{{O}_{4}}\] by weight. If the density of this commercial acid is 1.834 g\[c{{m}^{-3}},\] the molarity of this solution is
JEE Main Online Paper (Held On 07 May 2012)
A)
17.8 M
done
clear
B)
12.0 M
done
clear
C)
10.5M
done
clear
D)
15.7M
done
clear
View Answer play_arrow
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question_answer51) A solid has a 'bcc' structure. If the distance of nearest approach between two atoms is 1.73A,the edge length of the cell is
JEE Main Online Paper (Held On 07 May 2012)
A)
314.20pm
done
clear
B)
1.41pm
done
clear
C)
200pm
done
clear
D)
216pm
done
clear
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question_answer52) Reaction rate between two substance A and B is expressed as following:\[\text{rate}\,\text{=k }\!\![\!\!\text{ A}{{\text{ }\!\!]\!\!\text{ }}^{\text{n}}}{{\text{ }\!\![\!\!\text{ B }\!\!]\!\!\text{ }}^{\text{m}}}\] If the concentration of A is doubled and concentration of B is made half of initialcon centration, the ratio of the new rate to the earlier rate will be:
JEE Main Online Paper (Held On 07 May 2012)
A)
\[m+n\]
done
clear
B)
\[n-m\]
done
clear
C)
\[\frac{1}{{{2}^{\left(m+n \right)}}}\]
done
clear
D)
\[{{2}^{\left( n-m \right)}}\]
done
clear
View Answer play_arrow
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question_answer53) How many cyclic structures are possible for\[{{C}_{4}}{{H}_{6}}?\]
JEE Main Online Paper (Held On 07 May 2012)
A)
3
done
clear
B)
5
done
clear
C)
6
done
clear
D)
4
done
clear
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question_answer54) Which is not the correct Statement? (At.nos.\[\text{Ce}=\text{58},\text{Lu}=\text{71},\text{La}=\text{57},\text{Yb}=\text{7}0\])
JEE Main Online Paper (Held On 07 May 2012)
A)
Colour of \[Y{{b}^{3+}}\] ion is pink.
done
clear
B)
\[L{{a}^{3+}}\]is diamagnetic.
done
clear
C)
\[C{{e}^{4+}}\] has\[{{f}^{0}}\] configuration.
done
clear
D)
\[L{{u}^{3+}}\]had\[{{f}^{14}}\] configuration.
done
clear
View Answer play_arrow
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question_answer55) In which of the following arrangements, the sequence is not strictly according to the property written against it?
JEE Main Online Paper (Held On 07 May 2012)
A)
\[C{{O}_{2}}<Si{{O}_{2}}<Sn{{O}_{2}}<Pb{{O}_{2}}\]: increasing oxidising power
done
clear
B)
\[N{{H}_{3}}<P{{H}_{3}}<As{{H}_{3}}<Sb{{H}_{3}}\]: increasing basic strength
done
clear
C)
\[HF < HCl < HBr < HI\]: increasing acid strength
done
clear
D)
\[B<C<O<N\]: increasing first ionization enthalpy.
done
clear
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question_answer56)
The IUPAC name of the compound
is
JEE Main Online Paper (Held On 07 May 2012)
A)
1,2-Propoxide
done
clear
B)
Propylene oxide
done
clear
C)
1,2-Oxo propane
done
clear
D)
1,2-Epoxy propane
done
clear
View Answer play_arrow
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question_answer57) Green house gases can be arranged in 'Global Warming Potential' sequence as
JEE Main Online Paper (Held On 07 May 2012)
A)
\[{{N}_{2}}O>CFC>C{{H}_{4}}>C{{O}_{2}}\]
done
clear
B)
\[CFC>{{N}_{2}}O>C{{H}_{4}}>C{{O}_{2}}\]
done
clear
C)
\[CFC>C{{O}_{2}}>{{N}_{2}}O>C{{H}_{4}}\]
done
clear
D)
\[C{{O}_{2}}>CFC>{{N}_{2}}O>C{{H}_{4}}\]
done
clear
View Answer play_arrow
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question_answer58) Among the following the order of reactivity towards nucieophilic addition is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[C{{H}_{3}}CHO>C{{H}_{3}}COC{{H}_{3}}>HCHO\]
done
clear
B)
\[HCHO>C{{H}_{3}}CHO>C{{H}_{3}}COC{{H}_{3}}\]
done
clear
C)
\[C{{H}_{3}}CHO>HCHO>C{{H}_{3}}COC{{H}_{3}}\]
done
clear
D)
\[C{{H}_{3}}COC{{H}_{3}}>C{{H}_{3}}CHO>HCHO\]
done
clear
View Answer play_arrow
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question_answer59) \[{{C}_{2}}{{H}_{5}}Br\xrightarrow[{}]{AgCN}X\xrightarrow[Zn-Hg/HCl]{\operatorname{Re}duction}Y,\]Here Y is
JEE Main Online Paper (Held On 07 May 2012)
A)
Ethyl methyl amine
done
clear
B)
n-propylamine
done
clear
C)
Isopropylamine
done
clear
D)
Ethylamine
done
clear
View Answer play_arrow
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question_answer60) The ratio of number of oxygen atoms (0) in 16.0 gozone \[({{O}_{3}}),\] 28.0 g carbon monoxide (CO) and16.0 oxygen \[({{O}_{2}})\] is (Atomic mass: C = 12,0 = 16and Avogadro's constant\[{{N}_{A}}=6.0\times {{10}^{23}}mo{{l}^{-1}}\])
JEE Main Online Paper (Held On 07 May 2012)
A)
3:1:2
done
clear
B)
1:1:2
done
clear
C)
3:1:1
done
clear
D)
1:1:1
done
clear
View Answer play_arrow
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question_answer61) If\[A=\left( \begin{matrix} \alpha -1 \\ 0 \\ 0 \\ \end{matrix} \right),B=\left( \begin{matrix} \alpha +1 \\ 0 \\ 0 \\ \end{matrix} \right)\]be two matrices, then \[A{{B}^{T}}\]is a non-zero matrix for |a| not equal to
JEE Main Online Paper (Held On 07 May 2012)
A)
2
done
clear
B)
0
done
clear
C)
1
done
clear
D)
3
done
clear
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question_answer62) If a circular iron sheet of radius 30 cm is heated such that its area increases at the uniform rate of\[6\pi c{{m}^{2}}hr,\]then the rate (in mm/hr) at which the radius of the circular sheet increases is
JEE Main Online Paper (Held On 07 May 2012)
A)
1.0
done
clear
B)
0.1
done
clear
C)
1.1
done
clear
D)
2.0
done
clear
View Answer play_arrow
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question_answer63) The difference between the fourth term and the first term of a Geometrical Progresssion is 52. If the sum of its first three terms is 26, then the sum of the first six terms of the progression is
JEE Main Online Paper (Held On 07 May 2012)
A)
63
done
clear
B)
189
done
clear
C)
728
done
clear
D)
364
done
clear
View Answer play_arrow
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question_answer64) The value of k for which the equation\[(k-2){{x}^{2}}+8x+k+4=0\]has both roots real, distinct and negative is
JEE Main Online Paper (Held On 07 May 2012)
A)
6
done
clear
B)
3
done
clear
C)
4
done
clear
D)
1
done
clear
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question_answer65) Let y (x) be a solution of \[\frac{\left( 2+\sin x \right)}{\left( 1+y \right)}\frac{dy}{dx}=\cos x.\] If \[y(0)=2,\]then \[y\left( \frac{\pi }{2} \right)\]equals
JEE Main Online Paper (Held On 07 May 2012)
A)
\[\frac{5}{2}\]
done
clear
B)
2
done
clear
C)
\[\frac{7}{2}\]
done
clear
D)
3
done
clear
View Answer play_arrow
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question_answer66) If the eccentricity of a hyperbola \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]which passes through (k, 2), is \[\frac{\sqrt{13}}{3},\] then the value of \[{{k}^{2}}\] is
JEE Main Online Paper (Held On 07 May 2012)
A)
18
done
clear
B)
8
done
clear
C)
1
done
clear
D)
2
done
clear
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question_answer67) If \[\int\limits_{e}^{x}{tf(t)dt}=\sin x-x\cos x-\frac{{{x}^{2}}}{2},\]for all\[x\in R-\{0\},\]then the value of\[f\left( \frac{\pi }{6} \right)\] is
JEE Main Online Paper (Held On 07 May 2012)
A)
1/2
done
clear
B)
1
done
clear
C)
0
done
clear
D)
-1/2
done
clear
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question_answer68) If the number of 5-element subsets of the set\[A=\{{{a}_{1}},{{a}_{2}},....,{{a}_{20}}\}\] of 20 distinct elements is k times the number of 5-element subsets containing\[{{a}_{4}},\]then k is
JEE Main Online Paper (Held On 07 May 2012)
A)
5
done
clear
B)
\[\frac{20}{7}\]
done
clear
C)
4
done
clear
D)
\[\frac{10}{3}\]
done
clear
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question_answer69) If the system of equations \[x+y+z=6\] \[x+2y+3z=10\] \[x+2y+\lambda z=0\] has a unique solution, then \[\lambda \] is not equal to
JEE Main Online Paper (Held On 07 May 2012)
A)
1
done
clear
B)
0
done
clear
C)
2
done
clear
D)
3
done
clear
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question_answer70) If the straight lines \[\text{x}+\text{3y}=\text{4},\text{3x}+\text{y}=\text{4}\]and \[\text{x}+\text{y}=0\]form a triangle, then the triangle is
JEE Main Online Paper (Held On 07 May 2012)
A)
scalene
done
clear
B)
equilateral triangle
done
clear
C)
isosceles
done
clear
D)
right angled isosceles
done
clear
View Answer play_arrow
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question_answer71) Let fix)be an indefinite integral of \[{{\cos }^{3}}x.\] Statement 1:f(x) is a periodic function of period\[\pi .\] Statement 2: \[{{\cos }^{3}}x\] is a periodic function.
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true, Statement 2 is false.
done
clear
B)
Both the Statements are true, but Statement2 is not the correct explanation of Statement1.
done
clear
C)
Both the Statements are true, and Statement2 is correct explanation of Statement 1.
done
clear
D)
Statement 1 is false, Statement 2 is true.
done
clear
View Answer play_arrow
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question_answer72) The parabola\[{{y}^{2}}=x\] divides the circle \[{{x}^{2}}+{{y}^{2}}=2\]into two parts whose areas are in the ratio
JEE Main Online Paper (Held On 07 May 2012)
A)
\[9\pi +2:3\pi -2\]
done
clear
B)
\[9\pi -2:3\pi +2\]
done
clear
C)
\[7\pi -2:2\pi -3\]
done
clear
D)
\[7\pi +2:3\pi +2\]
done
clear
View Answer play_arrow
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question_answer73) The equation of the circle passing through the point (1,2) and through the points of intersection of\[{{x}^{2}}+{{y}^{2}}-4x-6y-21=0\]and \[3x+4y+5=0\] is given by
JEE Main Online Paper (Held On 07 May 2012)
A)
\[{{x}^{2}}+{{y}^{2}}+2x=2y+11=0\]
done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x+2y-7=0\]
done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2x-2y-3=0\]
done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+2x+2y-11=0\]
done
clear
View Answer play_arrow
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question_answer74)
The frequency distribution of daily working expenditure of families in a locality is as follows:
| Expenditure in Rs. (x): |
0-50 |
50-100 |
100-150 |
150-200 |
200-250 |
| No. of families (f): |
24 |
33 |
37 |
B |
25 |
If the mode of the distribution is " 140, then the value of b is
JEE Main Online Paper (Held On 07 May 2012)
A)
34
done
clear
B)
31
done
clear
C)
26
done
clear
D)
36
done
clear
View Answer play_arrow
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question_answer75) The sum of the series\[{{\text{1}}^{\text{2}}}+\text{2}.{{\text{2}}^{\text{2}}}+{{\text{3}}^{\text{2}}}+\text{2}.{{\text{4}}^{\text{2}}}+{{\text{5}}^{\text{2}}}+\text{2}.{{\text{6}}^{\text{2}}}+....+\text{2(2m}{{\text{)}}^{\text{2}}}\]is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[m{{(2m+1)}^{2}}\]
done
clear
B)
\[{{m}^{2}}(m+2)\]
done
clear
C)
\[{{m}^{2}}(2m+1)\]
done
clear
D)
\[m{{(m+2)}^{2}}\]
done
clear
View Answer play_arrow
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question_answer76) The point of intersection of the lines\[({{a}^{3}}+3)x+ay+a-3=0\]and\[({{a}^{5}}+2)x+(a+2)y+2a+3=0\](a real) lies on they-axis for
JEE Main Online Paper (Held On 07 May 2012)
A)
no value of a
done
clear
B)
more than two values of a
done
clear
C)
exactly one value of a
done
clear
D)
exactly two values of a
done
clear
View Answer play_arrow
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question_answer77) ABCD is parallelogram. The position vectors of A and C are respectively,\[3\hat{i}+3\hat{j}+5\hat{k}\] and\[\hat{i}-5\hat{j}-5\hat{k}\].If M is the midpoint of the diagonal\[\overset{\to }{\mathop{OM}}\,\]then the magnitude of the projection of on\[\overset{\to }{\mathop{OC}}\,,\] where O is the origin, is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[7\sqrt{51}\]
done
clear
B)
\[\frac{7}{\sqrt{50}}\]
done
clear
C)
\[7\sqrt{50}\]
done
clear
D)
\[\frac{7}{\sqrt{51}}\]
done
clear
View Answer play_arrow
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question_answer78) The range of the function \[f\left( x \right)=\frac{x}{1+|x|},x\in R,\]is
JEE Main Online Paper (Held On 07 May 2012)
A)
R
done
clear
B)
-1,1
done
clear
C)
R- {0}
done
clear
D)
[-1, 1]
done
clear
View Answer play_arrow
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question_answer79) If two vertical poles 20 m and 80 m high stand apart on a horizontal plane, then the height (in m)of the point of intersection of the lines joining the top of each pole to the foot of other is
JEE Main Online Paper (Held On 07 May 2012)
A)
16
done
clear
B)
18
done
clear
C)
50
done
clear
D)
15
done
clear
View Answer play_arrow
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question_answer80) If \[\vec{a}=\hat{i}-2\hat{j}+3\hat{k},\vec{b}=2\hat{i}+3\hat{j}-\hat{k}\]and\[\vec{c}=\lambda \hat{i}+\hat{j}+(2\lambda -1)\hat{k}\]are coplanar vectors, then\[\lambda \]is equal to
A)
0
done
clear
B)
-1
done
clear
C)
2
done
clear
D)
1
done
clear
View Answer play_arrow
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question_answer81) Statement 1:\[y=mx-\frac{1}{m}\]is always a tangent to the parabola, \[{{y}^{2}}=-4x\]for all non-zero values of w. Statement 2: Every tangent to the parabola, \[{{y}^{2}}=-4x\] will meet its axis at a point whose abscissa is non-negative.
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true, Statement 2 is true; Statement 2 is 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 false.
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_answer82) Let \[{{Z}_{1}}\]and \[{{Z}_{2}}\]be any two complex number. Statement1:\[\left| {{Z}_{1}}-{{Z}_{2}} \right|\ge \left| {{Z}_{1}} \right|-\left| {{Z}_{2}} \right|\] Statement 2: \[\left| {{Z}_{1}}+{{Z}_{2}} \right|\le \left| {{Z}_{1}} \right|+\left| {{Z}_{2}} \right|\]
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
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 true. Statement 2 is false.
done
clear
D)
Statement 1 is false. Statement 2 is true.
done
clear
View Answer play_arrow
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question_answer83) Let X and Y are two events such that\[P\left( X\cup Y \right)=P(X\cap Y).\] Statement1:\[P(X\cap Y')=P\left( X'\cap Y \right)=0\] Statement 2; \[P(X)+P=2P\left( X\cap Y \right)\]
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is false. Statement 2 is true. Statement 1 is true. Statement 2 is true,
done
clear
B)
Statement 2 is not a correct explanation of Statement 1.
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_answer84) If\[f(y)=1-(y-1)+{{(y-1)}^{2}}-{{(y-1)}^{3}}\]\[+...-{{(y-1)}^{17}},\]then the coefficient of \[{{y}^{2}}\] in it is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[^{17}{{C}_{2}}\]
done
clear
B)
\[^{17}{{C}_{3}}\]
done
clear
C)
\[^{18}{{C}_{2}}\]
done
clear
D)
\[^{18}{{C}_{3}}\]
done
clear
View Answer play_arrow
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question_answer85) The values of a for which the two points (1, a, 1)and (-3, 0, a) lie on the opposite sides of the plane \[\text{3x}+\text{4y}-\text{12z}+\text{13}=0,\] satisfy
JEE Main Online Paper (Held On 07 May 2012)
A)
\[0<a<\frac{1}{3}\]
done
clear
B)
\[-1<a<0\]
done
clear
C)
\[a<-1\]or \[a<\frac{1}{3}\]
done
clear
D)
\[a=0\]
done
clear
View Answer play_arrow
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question_answer86) \[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{x-\sin x}{x} \right)\sin \left( \frac{1}{x} \right)\]
JEE Main Online Paper (Held On 07 May 2012)
A)
equals 1
done
clear
B)
equals 0
done
clear
C)
does not exist
done
clear
D)
equals? 1
done
clear
View Answer play_arrow
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question_answer87) A line with positive direction cosines passes through the point P (2, - 1, 2) and makes equal angles with the coordinate axes. If the line meets the plane \[2x+y+z=9\] at point Q, then the length PQ equals
JEE Main Online Paper (Held On 07 May 2012)
A)
\[\sqrt{2}\]
done
clear
B)
2
done
clear
C)
\[\sqrt{3}\]
done
clear
D)
1
done
clear
View Answer play_arrow
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question_answer88) Let\[f(x)=\sin x,g(x)=x.\] Statement1:\[f(x)\le g(x)\] for x in \[(0,\infty )\] Statement2:\[f(x)\le 1\] for x in \[(0,\infty )\] but \[g(x)\to \infty \]as\[x\to \infty .\]
JEE Main Online Paper (Held On 07 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 a correct explanation for Statement 1.
done
clear
C)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation for Statement!.
done
clear
D)
Statement 1 is false. Statement 2 is true.
done
clear
View Answer play_arrow
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question_answer89) The Statement that is TRUE among the following is
JEE Main Online Paper (Held On 07 May 2012)
A)
The contrapositive of\[3x+2=8\Rightarrow x=2\]is\[x\ne 2\]\[\Rightarrow \]\[3x+2\ne 8.\]
done
clear
B)
The converse of \[=0\Rightarrow x=0\] is \[x\ne 0\Rightarrow \tan x=0.\]
done
clear
C)
\[p\Rightarrow q\] is equivalent to\[p\vee \tilde{\ }q.\]
done
clear
D)
\[p\vee q\]and\[p\wedge q\] have the same truth table.
done
clear
View Answer play_arrow
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question_answer90) If\[x+|y|=2y,\] then y as a function of x, at x = 0 is
A)
differentiable but not continuous
done
clear
B)
continuous but not differentiable
done
clear
C)
continuous as well as differentiable
done
clear
D)
neither continuous nor differentiable
done
clear
View Answer play_arrow
