Solved papers for JEE Main & Advanced JEE Main Paper (Held On 22 April 2013)

JEE Main Paper (Held On 22 April 2013) Total Questions - 90

1) Orbits of a particle moving in a circle are such that the perimeter of orbit equals an integer number of de - Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will therefore be proportional to: JEE Main Online Paper (Held On 22 April 2013)

A)

\[{{n}^{2}}\]

B)

\[n\]

C)

\[{{n}^{1/2}}\]

D)

\[{{n}^{1/4}}\]

View Answer
2) Two blocks of mass \[{{M}_{1}}=20\,kg\] and \[{{\operatorname{M}}_{2}}=12\operatorname{K}\operatorname{g},\] are connected by a metal rod of mass 8 kg. The system is pulled vertically up applying a force of 480 N as shown. The tension at mid-point of the rod is: JEE Main Online Paper (Held On 22 April 2013)

A)

\[144\] N

B)

\[96\] N

C)

\[240\] N

D)

\[192\] N

View Answer
3) An LCR circuit as shown in the figure is connected to voltage source \[{{\operatorname{V}}_{\operatorname{ac}}}\] whose frequency can be varied. The frequency, at which the voltage across the resistor is maximum, is: JEE Main Online Paper (Held On 22 April 2013)

A)

902 Hz

B)

143 Hz

C)

23 Hz

D)

345 Hz

View Answer
4) A body stars from rest on a long inclined plane of slope\[{{45}^{o}}\]. The coefficient of friction between the body and the plane varies as \[\mu =0.3\,x,\] where \[x\] is distance travelled down the down the plane. The body will have maximum speed (for g=10 m/\[{{\text{s}}^{\text{2}}}\]) when \[x\]= : JEE Main Online Paper (Held On 22 April 2013)

A)

9.8 m

B)

27 m

C)

12 m

D)

3.33 ms

View Answer
5) A and B are two sources generating sound waves. A listener is situated at C. The frequency of the source at A is 500 Hz A, now, moves towards C with a speed 4 m/s. The number of beats heard at C is 6. When A moves away from C with speed 4 m/s, the number of beats heard at C is 18. The speed of sound is 340 m/s. The frequency of the source at B is:                 JEE Main Online Paper (Held On 22 April 2013)

A)

500 Hz

B)

506 Hz

C)

512 Hz

D)

494 Hz

View Answer
6) A dc source of emf \[{{E}_{1}}=100\,V\] and internal resistance \[\operatorname{r}=0.5\Omega ,\] a storage battery of emf \[{{\operatorname{E}}_{2}}=90\operatorname{V}\] and an external resistance R are connected as shown in figure. For what value of R no current will pass through the battery?                 JEE Main Online Paper (Held On 22 April 2013)

A)

\[5.5\,\,\Omega \]

B)

\[3.5\,\,\Omega \]

C)

\[4.5\,\,\Omega \]

D)

\[2.5\,\,\Omega \]

View Answer
7) The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is :(mass of the moon \[=7.36\times {{10}^{22}}\,kg\], radius of the moon?s orbit \[=3.8\times {{10}^{8}}\,m\]) JEE Main Online Paper (Held On 22 April 2013)

A)

\[6.73\times {{10}^{-5}}\operatorname{m}/{{\operatorname{s}}^{2}}\]

B)

\[6.73\times {{10}^{-.3}}\operatorname{m}/{{\operatorname{s}}^{2}}\]

C)

\[6.73\times {{10}^{-.2}}\operatorname{m}/{{\operatorname{s}}^{2}}\]

D)

\[6.73\times {{10}^{-.4}}\operatorname{m}/{{\operatorname{s}}^{2}}\]

View Answer
8) An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its initial value. If the final pressure of gas is 128 atmosphers, the value of \['\gamma '\] the gas is: JEE Main Online Paper (Held On 22 April 2013)

A)

1.5

B)

1.4

C)

1.3

D)

1.6

View Answer
9) A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of \[{{30}^{0}}\] with the horizontal. The ball strikes the ground at B. What is the value of the distance AB?                 (Moment of inertia of spherical shell of mass m and radius R about its diameter \[=\frac{2}{3}{{\operatorname{mR}}^{2}})\] JEE Main Online Paper (Held On 22 April 2013)

A)

1.87 m

B)

2.08 m

C)

1.57 m

D)

1.77 m

View Answer
10) The dimensions of angular momentum, latent heat and capacitance are, respectively. JEE Main Online Paper (Held On 22 April 2013)

A)

\[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{1}}{{\operatorname{A}}^{2}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{2}}\]

B)

\[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{4}}{{\operatorname{A}}^{2}}\]

C)

\[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},\operatorname{M}{{\operatorname{L}}^{2}}\operatorname{T}{{\operatorname{A}}^{2}}\]

D)

\[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{4}}{{\operatorname{A}}^{2}}\]

View Answer
11) Air of density 1.2 \[\operatorname{Kg}{{\operatorname{m}}^{-3}}\] is blowing across the horizontal wings of on aero plane in such a way that its speeds above and below the wings are \[150\,\,m{{s}^{-1}}\]and \[100\,\,m{{s}^{-1}}\], respectively. The pressure difference between the upper and lower JEE Main Online Paper (Held On 22 April 2013)

A)

\[60\operatorname{N}{{\operatorname{m}}^{-2}}\]

B)

\[180\operatorname{N}{{\operatorname{m}}^{-2}}\]

C)

\[7500\operatorname{N}{{\operatorname{m}}^{-2}}\]

D)

\[12500\operatorname{N}{{\operatorname{m}}^{-2}}\]

View Answer
12) 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 Young?s double slit experiment, the number of fringes observed in the filed of view is small with longer wave length of light and is large with shorter wave length of light. Statement 2: In the double slit experiment the fringe width depends directly on the wave length of light. JEE Main Online Paper (Held On 22 April 2013)

A)

Statement 1 is true Statement 2 is true and the Statement 2 is not the correct explanation of the Statement 1

B)

Statement 1 is false and the Statement 2 is true

C)

Statement 1 true and statement 2 is true and the Statement 2 is true explanation of the Statement 1

D)

Statement 1 is true and the Statement 2 is false

View Answer
13) To find the resistance of galvanometer by the half deflection method the following circuit is used with resistances \[{{\operatorname{R}}_{1}}=9970\Omega ,{{\operatorname{R}}_{2}}=30\Omega \] and \[{{\operatorname{R}}_{3}}=0\]. The deflection in the galvanometer is d. With \[{{\operatorname{R}}_{3}}=107\Omega \]the deflection changed to \[\frac{\operatorname{d}}{2}.\] The galvanometer resistance is approximately:                JEE Main Online Paper (Held On 22 April 2013)

A)

\[107\Omega \]

B)

\[137\Omega \]

C)

\[107/2\Omega \]

D)

\[77\,\Omega \]

View Answer
14) The focal length of the objective and the eyepiece of a telescope are 50 cm and 5 cm respectively. If the telescope is focused for distinct vision on a scale distant 2m from its objective, then its magnifying power will be: JEE Main Online Paper (Held On 22 April 2013)

A)

\[-4\]

B)

\[-8\]

C)

\[+8\]

D)

\[-2\]

View Answer
15) In a series L-C-R circuit, \[\text{C}=\text{1}{{0}^{-11}}\] Farad, \[\text{L}=\text{1}{{0}^{-5}}\] Henry and \[\text{R}=100\] Ohm, when a constant D.C. voltage E is applied to the circuit, the capacitor acquires a charge \[\text{1}{{\text{0}}^{-9}}\operatorname{C}.\] The D.C. source is replaced by a sinusoidal voltage source in which the peak voltage \[{{\operatorname{E}}_{0}}\] is equal to the constant D.C voltage E. At resonance the peak value of the charge acquired by the capacitor will be : JEE Main Online Paper (Held On 22 April 2013)

A)

\[{{10}^{-15}}\operatorname{C}\]

B)

\[{{10}^{-6}}\operatorname{C}\]

C)

\[{{10}^{-10}}\operatorname{C}\]

D)

\[{{10}^{-8}}\operatorname{C}\]

View Answer
16) A point charge of magnitude + \[1\mu C\] is fixed at (0, 0, 0). An isolated uncharged spherical conductor, is fixed with its center at (4, 0, 0). The potential and the induced electric field at the sphere is : JEE Main Online Paper (Held On 22 April 2013)

A)

\[1.8\times {{10}^{5}}\] and \[-5.625\times {{10}^{6}}\,V/m\]

B)

\[0\operatorname{V}\] and \[0\operatorname{V}/\operatorname{m}\]

C)

\[2.25\times {{10}^{5}}\operatorname{V}\] and \[-5.625\times {{10}^{6}}\operatorname{V}/\operatorname{m}\]

D)

\[2.25\times {{10}^{5}}\operatorname{V}\] and V/m

View Answer
17) A uniform wire (Young?s modulus\[2\times {{10}^{11}}{{\operatorname{Nm}}^{-2}}\]) is subjected to longitudinal tensile stress of\[5\times {{10}^{7}}{{\operatorname{Nm}}^{-2}}\]. If the overall volume change in the wire is 0.02%, the fractional decrease in the radius of the wire is close to: JEE Main Online Paper (Held On 22 April 2013)

A)

\[1.0\times {{10}^{-4}}\]

B)

\[1.5\times {{10}^{-4}}\]

C)

\[0.25\times {{10}^{-4}}\]

D)

\[5\times {{10}^{-4}}\]

View Answer
18) The half ? life of a radioactive element A is the same as the mean-life of another radioactive element B. Initially both substances have the same number of atoms, then : JEE Main Online Paper (Held On 22 April 2013)

A)

A and B both decay at the same rate always

B)

A and B will decay at the same rate initially

C)

A will decay at a faster rate B initially

D)

B will decay at faster rate A initially

View Answer
19) A Ball projected from ground at an angle of \[{{45}^{0}}\] just clears a wall in front. If point of projection is 4m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is: JEE Main Online Paper (Held On 22 April 2013)

A)

4.4 m

B)

2.4 m

C)

3.6 m

D)

1.6 m

View Answer
20) A plane electromagnetic wave in a non-magnetic dielectric medium is given by \[\overset{\to }{\mathop{\operatorname{E}}}\,={{\overset{\to }{\mathop{\operatorname{E}}}\,}_{0}}\]\[(4\times {{10}^{-7}}x-50t)\] with distance being in meter and time in seconds. The dielectric constant of the medium is : JEE Main Online Paper (Held On 22 April 2013)

A)

2.4

B)

5.8

C)

8.2

D)

4.8

View Answer
21) To establish an instantaneous current of 2 A through a \[1\mu \operatorname{F}\] capacitor; the potential difference across the capacitor plates should be changed at the rate of : JEE Main Online Paper (Held On 22 April 2013)

A)

\[2\times {{10}^{4}}\operatorname{V}/s\]

B)

\[4\times {{10}^{6}}\operatorname{V}/s\]

C)

\[2\times {{10}^{6}}\operatorname{V}/s\]

D)

\[4\times {{10}^{4}}\operatorname{V}/s\]

View Answer
22) Choose the correct sketch of the magnetic field lies of a circular current loop shown by the dot and the cross \[\otimes \] JEE Main Online Paper (Held On 22 April 2013)

A)

B)

C)

D)

View Answer
23) Two small equal point charges of magnitude q are suspended from a common point on the ceiling by insulating massless strings of equal lengths. They come to equilibrium with each string making angle \[\theta \] from the vertical. If the mass of each charge is m, then the electrostatic potential at the centre of line joining them will be \[\left( \frac{1}{4\pi {{\in }_{0}}}=\operatorname{k} \right).\] JEE Main Online Paper (Held On 22 April 2013)

A)

\[2\sqrt{\operatorname{k}\operatorname{mg}\tan \theta }\]

B)

\[\sqrt{\operatorname{k}\operatorname{mg}\tan \theta }\]

C)

\[4\sqrt{\operatorname{k}\operatorname{mg}/\tan \theta }\]

D)

\[4\sqrt{\operatorname{k}\operatorname{mg}\,\,\tan \theta }\]

View Answer
24) The image of an illuminated square is obtained on screen with the help of a converging lens. The distance of the square of the square from the lens is 40 cm. The area of the image is 9 times that of the square. The focal length of the lens is : JEE Main Online Paper (Held On 22 April 2013)

A)

36 cm

B)

27 cm

C)

60 cm

D)

30 cm

View Answer
25) A certain amount of gas is taken through a cyclic process (A B C D A) that has two isobars, one isochore and one isothermal. The cycle can be represented on a P-V indicator diagram as: JEE Main Online Paper (Held On 22 April 2013)

A)

B)

C)

D)

View Answer
26)                 Figure shows a circuit in which three identical diodes are used. Each diode has forward resistance of 20 \[\Omega \] and infinite backward resistance. Resistors \[{{\operatorname{R}}_{1}}={{\operatorname{R}}_{2}}={{\operatorname{R}}_{3}}=50\Omega \]. Battery voltage is 6 V. The current though \[{{\operatorname{R}}_{3}}\]. JEE Main Online Paper (Held On 22 April 2013)

A)

50 mA

B)

100 mA

C)

60 mA

D)

25 mA

View Answer
27) A mass m = 1.0kg is put on a flat pan attached to vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500 N/m. What is the amplitude A of the motion, so that the mass m tends to get detached from the pan? (Take g = 10 m/\[{{\operatorname{s}}^{2}}\]). The spring is stiff enough so that it does not get distorted during the motion.                 JEE Main Online Paper (Held On 22 April 2013)

A)

\[\operatorname{A}>2.0\operatorname{cm}\]

B)

\[\operatorname{A}=2.0\operatorname{cm}\]

C)

\[\operatorname{A}<2.0\operatorname{cm}\]

D)

\[\operatorname{A}<1.5\operatorname{cm}\]

View Answer
28) A current \[i\] is flowing in a straight conductor of length L. The magnetic induction at a point on its axis at a distance \[\frac{\operatorname{L}}{4}\] from its centre will be: JEE Main Online Paper (Held On 22 April 2013)

A)

Zero

B)

\[\frac{{{\mu }_{0}}\operatorname{i}}{2\pi L}\]

C)

\[\frac{{{\mu }_{0}}\operatorname{i}}{\sqrt{2L}}\]

D)

\[\frac{4{{\mu }_{0}}\operatorname{i}}{\sqrt{5}\,\pi L}\]

View Answer
29) This question has Statement-1 and Statement-2. Of four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: Short wave transmission is achieved due to the total internal reflection of the e-m wave from an appropriate height in the ionosphere. Statement 2: Refractive index of a plasma is independent of the frequency of e-m waves. JEE Main Online Paper (Held On 22 April 2013)

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 but Statement 2 is not the correct explanation of Statement 1

D)

Statement 1 is true, Statement 2 is true but Statement 2 is the correct explanation of Statement 1

View Answer
30) Given that 1g of water in liquid phase has volume \[\text{1c}{{\text{m}}^{3}}\]and in vopour phase \[\text{1671}\,\,\text{c}{{\text{m}}^{3}}\] at atmospheric pressure and the latent heat of vaporization of water is 2256 J/g; the change in the internal energy in Joules for 1 g of water at 373 K when it changes from liquid phase to vapour phase at the same temperature is: JEE Main Online Paper (Held On 22 April 2013)

A)

2256

B)

167

C)

2089

D)

1

View Answer
31) Oxidation state of sulphur in anions \[\operatorname{S}\operatorname{O}_{3}^{2-},{{\operatorname{S}}_{2}}\operatorname{O}_{4}^{2-},\] and \[{{\operatorname{S}}_{2}}\operatorname{O}_{6}^{2-}\] increases in the orders: JEE Main Online Paper (Held On 22 April 2013)

A)

\[{{\operatorname{S}}_{2}}\operatorname{O}_{6}^{2-}<{{\operatorname{S}}_{2}}\operatorname{O}_{4}^{2-}<\operatorname{S}\operatorname{O}_{3}^{2-}\]

B)

\[\operatorname{S}\operatorname{O}_{3}^{2-}<{{\operatorname{S}}_{2}}\operatorname{O}_{4}^{2-}<{{\operatorname{S}}_{2}}\operatorname{O}_{6}^{2-}\]

C)

\[{{\operatorname{S}}_{2}}\operatorname{O}_{4}^{2-}<\operatorname{S}\operatorname{O}_{3}^{2-}<{{\operatorname{S}}_{2}}\operatorname{O}_{6}^{2-}\]

D)

\[{{S}_{2}}O_{4}^{2-}<{{S}_{2}}O_{6}^{2-}<SO_{3}^{2-}\]

View Answer
32) A major component of Borsch regent is obtained by reacting hydrazine hydrate with of the following? JEE Main Online Paper (Held On 22 April 2013)

A)

B)

C)

D)

View Answer
33) Given                 Reaction                                Energy Change (in KJ)                 \[\operatorname{L}\operatorname{i}(\operatorname{s})\to \operatorname{Li}(g)\]                                           161                 \[\operatorname{L}\operatorname{i}(g)\to {{\operatorname{Li}}^{+}}(g)\]                             520                 \[\frac{1}{2}{{\operatorname{F}}_{2}}(g)\to \operatorname{F}(g)\]                          77\[{{\operatorname{F}}_{2}}(g)+{{e}^{-}}\to {{\operatorname{F}}^{-}}(g)\]               (Electron gain                                                                                 enthalpy)                 \[\operatorname{L}{{\operatorname{i}}^{+}}(g)+{{\operatorname{F}}^{-}}(g)\to Li\,\,\operatorname{F}(s)\]   -1047                 \[\operatorname{L}\operatorname{i}(\operatorname{s})+\frac{1}{2}{{\operatorname{F}}_{2}}(g)\to \operatorname{Li}\operatorname{F}(s)\]       -617                 Based on data provided, the value of electron gain enthalpy of fluorine would be: JEE Main Online Paper (Held On 22 April 2013)

A)

\[-300\operatorname{k}\operatorname{J}{{\operatorname{mol}}^{-1}}\]

B)

\[-350\operatorname{k}\operatorname{J}{{\operatorname{mol}}^{-1}}\]

C)

\[-328\operatorname{k}\operatorname{J}{{\operatorname{mol}}^{-1}}\]

D)

\[-228\operatorname{k}\operatorname{J}{{\operatorname{mol}}^{-1}}\]

View Answer
34) A molecule M associates in given solvent according to the equation \[\operatorname{M}\underset{{}}{\overset{{}}{\longleftrightarrow}}{{(\operatorname{M})}_{\operatorname{n}.}}\] For a certain concentration of M, The van? t Hoff factor was found to 0.9 and the fraction of associated molecules was 0.2 The value of n is: JEE Main Online Paper (Held On 22 April 2013)

A)

3

B)

5

C)

2

D)

4

View Answer
35) The solubility order for alkali metal fluoride in water is: JEE Main Online Paper (Held On 22 April 2013)

A)

LiF < RbF < KF < NaF

B)

RbF < KF < NaF < LiF

C)

LiF > NaF > KF > RbF

D)

LiF < NaF < KF < RbF

View Answer
36) \[\text{Xe}{{\operatorname{O}}_{4}}\] molecule is tetrahedral having: JEE Main Online Paper (Held On 22 April 2013)

A)

Two \[p\pi -d\pi \] bonds

B)

One \[p\pi -d\pi \] bond

C)

Four \[p\pi -d\pi \] bonds

D)

Three \[p\pi -d\pi \] bonds

View Answer
37) The reaction \[\operatorname{X}\to \operatorname{Y}\] is an exothermic reaction. Activation energy of the reaction for X into \[\operatorname{Y}\] is 150 \[150\operatorname{K}\operatorname{J}{{\operatorname{mol}}^{-1}}\]. Enthalpy of reaction is \[135\operatorname{K}\operatorname{J}{{\operatorname{mol}}^{-1}}\]. The activation energy for the reverse reaction, \[\operatorname{Y}\to \operatorname{X}\] will be: JEE Main Online Paper (Held On 22 April 2013)

A)

\[280\operatorname{kJ}{{\operatorname{mol}}^{-1}}\]

B)

\[285\operatorname{kJ}{{\operatorname{mol}}^{-1}}\]

C)

\[270\operatorname{kJ}{{\operatorname{mol}}^{-1}}\]

D)

\[15\operatorname{kJ}{{\operatorname{mol}}^{-1}}\]

View Answer
38) For which of the following compounds Kjeldahl method can be used to determine the percentage of Nitrogen? JEE Main Online Paper (Held On 22 April 2013)

A)

Nitrobenzene

B)

Pyridine

C)

Alanine

D)

Diazomethane

View Answer
39) Which of the following statements about aspirin is not true JEE Main Online Paper (Held On 22 April 2013)

A)

It is effective in reliving pain

B)

It is a neurologically active drug

C)

It has antiblood clotting action

D)

It belongs to narcotic analgesics

View Answer
40) The density of 3M solution of sodium chloride is 1.252\[~\text{gm}{{\text{L}}^{-1}}\]. The molality of the solution will be: (molar mass,\[\text{NaCI }=\text{85}.\text{5 g mo}{{\text{l}}^{\text{-1}}}\]) JEE Main Online Paper (Held On 22 April 2013)

A)

2.60 m

B)

2.18 m

C)

2.79 m

D)

3.00 m

View Answer
41) Which of the following structures represents thymine? JEE Main Online Paper (Held On 22 April 2013)

A)

B)

C)

D)

View Answer
42) The polymer used for optical lenses is: JEE Main Online Paper (Held On 22 April 2013)

A)

polypropylene

B)

polyvinyl chloride

C)

polythene

D)

polymethyl methacrylate

View Answer
43) Which of the following is diamagnetic? JEE Main Online Paper (Held On 22 April 2013)

A)

\[[\operatorname{F}e{{({{\operatorname{CN}}_{6}})}^{3-}}\]

B)

\[{{[\operatorname{Co}(\operatorname{O}\operatorname{X})]}^{3-}}\]

C)

\[{{[\operatorname{Fe}{{\operatorname{F}}_{6}}]}^{3-}}\]

D)

\[{{[\operatorname{Co}{{\operatorname{F}}_{6}}]}^{3-}}\]

View Answer
44) Bond order normally gives idea of stability of a molecular species. All the molecules viz. \[{{\operatorname{H}}_{2}},\] \[\operatorname{L}{{\operatorname{i}}_{2}}\] and \[{{\operatorname{B}}_{2}}\] have the same bond order yet they are not equally stable. The Their stability order is: JEE Main Online Paper (Held On 22 April 2013)

A)

\[{{\text{H}}_{\text{2}}}>{{\text{B}}_{\text{2}}}>\text{L}{{\text{i}}_{\text{2}}}\]

B)

\[\text{L}{{\text{i}}_{\text{2}}}\text{}{{\text{H}}_{\text{2}}}>{{\text{B}}_{\text{2}}}\]

C)

\[{{\operatorname{Li}}_{2}}>{{\text{B}}_{\text{2}}}>{{\operatorname{H}}_{2}}\]

D)

\[{{\text{B}}_{\text{2}}}>{{\operatorname{H}}_{2}}>{{\operatorname{Li}}_{2}}\]

E)

(e) None of these

View Answer
45) Which one of the following arrangements represents the correct order of solubilities of sparingly soluble soluble salts\[\operatorname{H}{{\operatorname{g}}_{2}}{{\operatorname{CI}}_{2}},C{{r}_{2}}{{(S{{O}_{4}})}_{3}},\]\[BaS{{O}_{4}}\] and \[\text{CrC}{{\text{l}}_{3}}\] respectively? JEE Main Online Paper (Held On 22 April 2013)

A)

\[BaS{{O}_{4}}>H{{g}_{2}}C{{l}_{2}}>C{{r}_{2}}{{(S{{O}_{4}})}_{3}}>CrC{{l}_{3}}\]

B)

\[BaS{{O}_{4}}>H{{g}_{2}}C{{l}_{2}}>CrC{{l}_{3}}>C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]

C)

\[BaS{{O}_{4}}>CrC{{l}_{3}}>H{{g}_{2}}C{{l}_{2}}>C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]

D)

\[H{{g}_{2}}C{{l}_{2}}>BaS{{O}_{4}}>CrC{{l}_{3}}>C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]

View Answer
46) The wave number of the first emission line in the Balmer series of H-Spectrum is: (R= Rydberg constant): JEE Main Online Paper (Held On 22 April 2013)

A)

\[\frac{5}{36}\operatorname{R}\]

B)

\[\frac{9}{400}\operatorname{R}\]

C)

\[\frac{7}{6}\operatorname{R}\]

D)

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

View Answer
47) What is the structure of the major product when phenol is treated with bromine water? JEE Main Online Paper (Held On 22 April 2013)

A)

B)

C)

D)

View Answer
48) \[NaOH\] is a strong base. What will be pH of \[5.0\times {{10}^{-2}}\,M\,\,NaOH\] solution? \[(\log \,2\,=\,0.3)\] JEE Main Online Paper (Held On 22 April 2013)

A)

14.00

B)

13.70

C)

13.00

D)

12.70

View Answer
49) Flocculation value of \[BaC{{l}_{2}}\] is much less then that of \[KCl\] for sol A and flocculation value of \[\operatorname{N}{{\operatorname{a}}_{2}}\operatorname{S}{{\operatorname{O}}_{4}}\] is much less than that of \[\text{NaBr}\]for sol B. The correct statement among the following is: JEE Main Online Paper (Held On 22 April 2013)

A)

Both the sols A and B are negatively charged

B)

Sol A is positively charged and Sol B is negatively charged

C)

Both the sols A and B are positively charged

D)

Sol A is negatively charged and sol B is positively charged

View Answer
50) Amongst the following alcohols which would react fastest with conc. HCI and \[ZnC{{l}_{2}}\]? JEE Main Online Paper (Held On 22 April 2013)

A)

pentanol

B)

2-methylbutanol

C)

2-pentanol

D)

2-methy lbutan-2ol

View Answer
51) Values of dissociation constant, \[{{\text{K}}_{\text{a}}}\]are given as follows:                 Acid                                        \[{{\text{K}}_{\text{a}}}\]                 \[\operatorname{HCN}\]                                    \[6.2\times {{10}^{-10}}\]                   \[HF\]                                     \[7.2\times {{10}^{-4}}\]                 \[HN{{O}_{2}}\]                                     \[4.0\times {{10}^{-4}}\]                 Correct order of increasing base strength of the base \[{{\operatorname{CN}}^{-}},{{\operatorname{F}}^{-}}\] and \[\operatorname{NO}_{2}^{-}\]will be: JEE Main Online Paper (Held On 22 April 2013)

A)

\[{{\operatorname{F}}^{-}}<{{\operatorname{CN}}^{-}}<\operatorname{NO}_{2}^{-}\]

B)

\[NO_{2}^{-}<C{{N}^{-}}<{{F}^{-}}\]

C)

\[{{\operatorname{F}}^{-}}<\operatorname{NO}_{2}^{-}<{{\operatorname{CN}}^{-}}\]

D)

\[\operatorname{NO}_{2}^{-}<\operatorname{F}_{{}}^{-}<\operatorname{CN}_{{}}^{-}\]

View Answer
52) Clemmensen reduction of a ketone is carried out in the presence of : JEE Main Online Paper (Held On 22 April 2013)

A)

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

B)

\[Zn-Hg\] with \[HCl\]

C)

Glycol with \[KOH\]

D)

\[{{H}_{2}}\] with \[Pt\] as catalyst

View Answer
53) Which of the following statements is incorrect? JEE Main Online Paper (Held On 22 April 2013)

A)

\[\operatorname{F}{{\operatorname{e}}^{2}}^{+}\]ion also gives blood red colour with \[{{\operatorname{SCN}}^{-}}\]ion

B)

\[F{{e}^{3+}}\]ion given blood red colour with \[SC{{N}^{-}}\] ion.

C)

On Passing \[{{H}_{2}}S\] into \[N{{a}_{2}}Zn{{O}_{2}}\] solution, a white ppt of \[ZnS\] is formed

D)

Cupric ion react with excess of ammonia solution to give deep blue colour of \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] ion.

View Answer
54) The Order of increasing sizes of atomic radii among the elements O, S, Se and As is: JEE Main Online Paper (Held On 22 April 2013)

A)

\[As-S<O<Se\]

B)

\[Se<S<As<O\]

C)

\[O<S<As<Se\]

D)

\[O<S<Se<As\]

View Answer
55) In Williamason synthesis of mixed ether having a primary and a tertiary alkyl group if tertiary halide is used, then: JEE Main Online Paper (Held On 22 April 2013)

A)

Rate of reaction will be slow due to slow cleavage of carbon ? halogen bond

B)

Alkene will be the main product

C)

Simple ether will form instead of mixed ether

D)

Expected mixed ether will be formed

View Answer
56) Which of the following would not give 2-phenylbutane as the major product in a Friedel-Crafts alkylation reaction? JEE Main Online Paper (Held On 22 April 2013)

A)

1-butene + HF

B)

2-butanol+ \[{{\operatorname{H}}_{2}}{{\operatorname{SO}}_{4}}\]

C)

Butanoykhloride \[+AlC{{l}_{3}}\] then \[Zn,\,HCl\]

D)

Butyl chloride \[+AlC{{l}_{3}}\]

View Answer
57) Arrange in the correct order of stability (decreasing order) for the following molecules : JEE Main Online Paper (Held On 22 April 2013)

A)

(I) > (II) > (III) > (IV)

B)

(IV) > (III) > (II)\[\approx \](I)

C)

(I) > (II) \[\approx \] (III) > (IV)

D)

(III) > (I) \[\approx \] (II) > (IV)

View Answer
58) Which one of the following statements about packing in solids in incorrect? JEE Main Online Paper (Held On 22 April 2013)

A)

Coordination number in bee mode of packing is 8

B)

Coordination number in hcp mode of packing is 12.

C)

Void space in hcp mode of packing is 32%

D)

Void space in ccp mode of packing in 26%

View Answer
59) The Wurtz-Fitting reaction involues condensation of: JEE Main Online Paper (Held On 22 April 2013)

A)

two molecules of aryl halides

B)

one molecule of each of aryl- halide and phenol

C)

one molecule of each aryl-halide and phenol

D)

two molecules of aralkyl-halides

View Answer
60) In Goldschmidt alumino thermic process which of the following reducing agents is used: JEE Main Online Paper (Held On 22 April 2013)

A)

calcium

B)

coke

C)

AI- powder

D)

sodium

View Answer
61) The number of ways in which an examiner can assign 30 marks to 8 question, giving not less than 2 marks to any question, is: JEE Main Online Paper (Held On 22 April 2013)

A)

\[^{30}{{C}_{7}}\]

B)

\[^{21}{{C}_{8}}\]

C)

\[^{21}{{C}_{7}}\]

D)

\[^{30}{{C}_{8}}\]

View Answer
62) If the system of linear equations \[{{x}_{1}}+2{{x}_{2}}+3{{x}_{3}}=6\] \[{{x}_{1}}+3{{x}_{2}}+5{{x}_{3}}=9\] \[2{{x}_{1}}+5{{x}_{2}}+a{{x}_{3}}=b\] is consistent and has infinite number of solutions, then: JEE Main Online Paper (Held On 22 April 2013)

A)

\[a=8,b\] can be any real number

B)

\[b=15,\]a cab be any real number

C)

\[a=R-\{8\}\] and \[\operatorname{b}\in \operatorname{R}-[15]\]

D)

\[\operatorname{a}=8,b=15\]

View Answer
63) Given sum of the first n terms of an A.P. is \[2n+3{{n}^{2}}\]. Anther A.P. is formed with the same first term and double of the common difference, the sum of n terms of the new A.P. is : JEE Main Online Paper (Held On 22 April 2013)

A)

\[n+4{{n}^{2}}\]

B)

\[6{{n}^{2}}-n\]

C)

\[{{n}^{2}}+4n\]

D)

\[3n+2{{n}^{2}}\]

View Answer
64) Statement 1: The function \[{{x}^{2}}({{\operatorname{e}}^{x}}+{{\operatorname{e}}^{-x}})\]is increasing for all \[x>0.\] Statement 2: The functions \[{{x}^{2}}{{e}^{x}}\] and \[{{x}^{2}}{{e}^{-x}}\] are increasing for all \[x>0\] and the sum of two increasing functions in any interval (a, b) is an increasing function in (a, b). JEE Main Online Paper (Held On 22 April 2013)

A)

Statement 1 is false; Statement 2 is true.

B)

Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

C)

Statement 1 is true; Statement 2 is false.

D)

Statement 1 is true; Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

View Answer
65) Mean of 5 observations is 7. If four of these observations are 6, 7, 8, 10 and one is missing then      the variance of all the five observations is : JEE Main Online Paper (Held On 22 April 2013)

A)

4

B)

6

C)

8

D)

2

View Answer
66) The area of the region (in sq. units), in the first quadrant, bounded by the parabola \[y=9{{x}^{2}}\] and the lines \[x=0,\] \[y=1\] and \[y=4\] is: JEE Main Online Paper (Held On 22 April 2013)

A)

\[7/9\]

B)

\[14/3\]

C)

\[7/3\]

D)

\[14/9\]

View Answer
67) If the \[x-\] intercept of some line L is double as that of the line, \[3x+4y=12\] and the \[y-\]intercept of L is half as that of the same line. Then the slope of L is : jEE Main Online Paper (Held On 22 April 2013)

A)

-3

B)

-3/8

C)

-3/2

D)

-3/16

View Answer
68) The sum \[\frac{3}{{{1}^{2}}}+\frac{5}{{{1}^{2}}+{{2}^{2}}}+\frac{7}{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}+...\] upto 11 ?terms is: JEE Main Online Paper (Held On 22 April 2013)

A)

\[\frac{7}{2}\]

B)

\[\frac{11}{4}\]

C)

\[\frac{11}{2}\]

D)

\[\frac{60}{11}\]

View Answer
69) The integral \[\int\limits_{7\pi /4}^{7\pi /3}{\sqrt{{{\tan }^{2}}}x\operatorname{d}x}\] is equal to : JEE Main Online Paper (Held On 22 April 2013)

A)

\[\log 2\sqrt{2}\]

B)

\[\log 2\]

C)

\[2\log 2\]

D)

\[\log \sqrt{2}\]

View Answer
70) Let \[\operatorname{R}=\{(3,3),(5,5),(9,9)(12,12),\] \[(5,12),(3,9),(3,12)(3,5),\}\] be a relation on the set A = {3, 5, 9, 12} . Then, R is : JEE Main Online Paper (Held On 22 April 2013)

A)

reflexive, symmetric but not transitive.

B)

symmetric, transitive but not reflexive

C)

an equivalence relation.

D)

reflexive, transitive but not symmetric

View Answer
71) If a complex number z satisfies the equation \[z+\sqrt{2}\left| z+1 \right|+i=0,\operatorname{then}\left| z \right|\] is equal to : JEE Main Online Paper (Held On 22 April 2013)

A)

2

B)

\[\sqrt{3}\]

C)

\[\sqrt{5}\]

D)

\[1\]

View Answer
72) If the 7th term in binomial expansion of \[{{\left( \frac{3}{^{3}\sqrt{84}}+\sqrt{3}\operatorname{In}x \right)}^{9}},x>0,\] equal to 729, then \[x\]cab be :                               JEE Main Online Paper (Held On 22 April 2013)

A)

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

B)

\[e\]

C)

\[\frac{e}{2}\]

D)

\[2e\]

View Answer
73) Statement 1: The line \[x-2y=2\] meets the parabola, \[{{y}^{2}}+2x=0\] only at the point \[(-2,-2):\] Statement 2: The line \[y=mx-\frac{1}{2m}(\operatorname{m}\#0)\]is tangent to the parabola, \[{{y}^{2}}=-2x\] at the point \[\left( -\frac{1}{2{{\operatorname{m}}^{2}}},\frac{1}{\operatorname{m}} \right).\] JEE Main Online Paper (Held On 22 April 2013)

A)

Statement 1 is true; Statement 2 is false.

B)

Statement 1 is true; Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

C)

Statement 1 is false; Statement 2 is true.

D)

Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

View Answer
74) If a circle C passing though (4, 0) touches the circle \[{{x}^{2}}+{{y}^{2}}+4x-6y-12=0\] externally at point (1, -1), then the radius of the circle C is: JEE Main Online Paper (Held On 22 April 2013)

A)

5

B)

\[2\sqrt{5}\]

C)

4

D)

\[\sqrt{57}\]

View Answer
75) Let Q be the foot of perpendicular from the origin to the plane \[4x-3y+z+13=0\] and R be point (-1, 1, -6) on the plane Then length QR is : JEE Main Online Paper (Held On 22 April 2013)

A)

\[\sqrt{14}\]

B)

\[\sqrt{\frac{19}{2}}\]

C)

\[3\sqrt{\frac{7}{2}}\]

D)

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

View Answer
76) Given two independent events, if the probability that exactly one of them occurs is \[\frac{26}{49}\] and the probability that nine of them occurs is \[\frac{15}{49},\] then the probability of more probable of the two events is : JEE Main Online Paper (Held On 22 April 2013)

A)

\[4/7\]

B)

\[6/7\]

C)

\[3/7\]

D)

\[5/7\]

View Answer
77) The statement \[p\to (q\to p)\] is equivalent to: JEE Main Online Paper (Held On 22 April 2013)

A)

\[\operatorname{p}\to \operatorname{q}\]

B)

\[\operatorname{p}\left( \operatorname{p}\,\vee \operatorname{q} \right)\]

C)

\[\operatorname{p}\to \left( \operatorname{p}\to \operatorname{q} \right)\]

D)

\[\operatorname{p}\to \left( \operatorname{p}\wedge \operatorname{q} \right)\]

View Answer
78) The maximum area of a right angled triangle with hypotenuse h is : JEE Main Online Paper (Held On 22 April 2013)

A)

\[\frac{{{\operatorname{h}}^{2}}}{2}\sqrt{2}\]

B)

\[\frac{{{\operatorname{h}}^{2}}}{2}\]

C)

\[\frac{{{\operatorname{h}}^{2}}}{\sqrt{2}}\]

D)

\[\frac{{{\operatorname{h}}^{2}}}{4}\]

View Answer
79) If \[\int{\frac{{{x}^{2}}-x+1}{{{x}^{2}}+1}e{{\cot }^{-1}}}x\operatorname{d}x=\operatorname{A}(x){{\operatorname{e}}^{{{\cot }^{-1}}}}x+C,\] then A\[\left( x \right)\] is equal to : JEE Main Online Paper (Held On 22 April 2013)

A)

\[-x\]

B)

\[x\]

C)

\[\sqrt{1-x}\]

D)

\[\sqrt{1+x}\]

View Answer
80) If two vertices of an equilateral triangle are \[\operatorname{A}(-a,0)\] and \[B(a,\,0),\,a>0\], the third vertex C lies above \[x-\]axis then the equation of the circumcircle of \[\Delta \operatorname{ABC}\] is : JEE Main Online Paper (Held On 22 April 2013)

A)

\[3{{x}^{2}}+3{{y}^{2}}-2\sqrt{3}ay=3{{a}^{2}}\]

B)

\[3{{x}^{2}}+3{{y}^{2}}-2ay=3{{a}^{2}}\]

C)

\[{{x}^{2}}+{{y}^{2}}-2ay={{a}^{2}}\]

D)

\[{{x}^{2}}+{{y}^{2}}-\sqrt{3}ay={{a}^{2}}\]

View Answer
81) The acute angle between two lines such that the direction cosines I, m, n of each of them satisfy the equations I + m + n = 0 and \[{{\operatorname{I}}^{2}}+{{\operatorname{m}}^{2}}-{{\operatorname{n}}^{2}}=0\] is: JEE Main Online Paper (Held On 22 April 2013)

A)

\[{{15}^{0}}\]

B)

\[{{30}^{0}}\]

C)

\[{{60}^{0}}\]

D)

\[{{45}^{0}}\]

View Answer
82) Consider the differential equation \[\frac{dy}{dx}=\frac{{{y}^{3}}}{2(x{{y}^{2}}-{{x}^{2}})}:\] Statement 1: The substitution \[z={{y}^{2}}\] transforms the above equation into a first order homogenous differential equation. Statement 2: The solution of this differential equation is \[{{y}^{2}}e\frac{-{{y}^{2}}}{x}=C.\]

A)

Both statements are false.

B)

Statement 1 is rue and statement 2 is false.

C)

Statement 1 is false. Statement 2 is true

D)

Both statement s are true.

View Answer
83) The number of solution of the equation, \[{{\sin }^{-1}}\] \[x=2\] \[{{\tan }^{-1}}\] \[x\] (in principal values is :) JEE Main Online Paper (Held On 22 April 2013)

A)

1

B)

4

C)

2

D)

3

View Answer
84) For \[>0,\operatorname{t}\in \left( 0,\frac{\pi }{2} \right),\] let \[x=\sqrt{{{a}^{\sin -1}}t}\] and \[y=\sqrt{a{{\cos }^{-1}}\operatorname{t}}.\] Then , \[1+{{\left( \frac{\operatorname{dy}}{dx} \right)}^{2}}\]equals: JEE Main Online Paper (Held On 22 April 2013)

A)

\[\frac{{{x}^{2}}}{{{y}^{2}}}\]

B)

\[\frac{{{y}^{2}}}{{{x}^{2}}}\]

C)

\[\frac{{{x}^{2}}+{{y}^{2}}}{{{y}^{2}}}\]

D)

\[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}}\]

View Answer
85) If p, q, r are 3 real numbers satisfying the matrix equation, \[[p\,q\,r]\left[ \begin{matrix}    3 & 4 & 1 \\    3 & 2 & 3 \\    2 & 0 & 2 \\ \end{matrix} \right]=[3\,\,0\,\,1]\] then \[2\operatorname{p}+\operatorname{q}-\operatorname{r}\] equals: JEE Main Online Paper (Held On 22 April 2013)

A)

-3

B)

-1

C)

4

D)

2

View Answer
86) If \[\hat{a},\hat{b}\] and \[\hat{c}\] are unit vectors satisfying \[\hat{a}-\sqrt{3}\] \[\hat{b}+\hat{c}=\overset{\to }{\mathop{0}}\,\] then the angle between the vectors \[\hat{a}\] and \[\hat{c}\] is : JEE Main Online Paper (Held On 22 April 2013)

A)

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

B)

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

C)

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

D)

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

View Answer
87) Let the equations of two ellipses be                 \[{{\operatorname{E}}_{1}}:\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{2}=1\] and                 \[{{\operatorname{E}}_{2}}:\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{\operatorname{b}}^{2}}}=1\]. If the product of their eccentricities is \[\frac{1}{2},\] then the length of the minor axis of ellipse \[{{\operatorname{E}}_{2}}\] is: JEE Main Online Paper (Held On 22 April 2013)

A)

8

B)

9

C)

4

D)

2

View Answer
88) If \[\alpha \] and \[\beta \] are roots of the equation \[{{x}^{2}}+\operatorname{p}x+\frac{3\operatorname{p}}{4}=0,\] such that \[\left| \alpha -\beta \right|\]=\[\sqrt{10},\]then p belongs to the set: JEE Main Online Paper (Held On 22 April 2013)

A)

{2, -5}

B)

{-3, 2}

C)

{-2, 5}

D)

{3, -5}

View Answer
89) Statement 1: The number of common solution of the trigonometric equations \[2{{\sin }^{2}}\theta -\cos 2\theta =0\] and 2\[{{\cos }^{2}}\theta -3\] \[\sin \theta =0\]in the interval [0, 2\[\pi \]] is two : Statement 2: The number of solutions of the equation, \[2{{\cos }^{2}}\theta -3\]\[\sin \theta =0\] in the interval \[\left[ 0,\pi \right]\] is two JEE Main Online Paper (Held On 22 April 2013)

A)

Statement 1 is true; Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

B)

Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

C)

Statement 1 is false; Statement 2 is true.

D)

Statement 1 is true; Statement 2 is false.

View Answer
90) Let \[f(x)=-1+\left| x-2 \right|,\]and g\[\left( x \right)=1-\left| x \right|;\] then the set of all points where \[fog\] us discontinuous is :

A)

{0, 2}

B)

{0, 1, 2}

C)

{0}

D)

an empty set

View Answer