# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 25 April 2013)

### done JEE Main Paper (Held On 25 April 2013) Total Questions - 90

• question_answer1) A mass of 50g of water in a closed vessel, with surroundings at a constant temperature takes 2 minutes to cool form ${{30}^{0}}C$to ${{25}^{0}}C$. A mass of 100g of another liquid in identical vessel with identical surroundings takes the same time to cool from ${{30}^{0}}C$to ${{25}^{0}}C$. The specific heat of the liquid is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$2.0\operatorname{kc}\operatorname{a}\operatorname{l}/\operatorname{kg}$

B)
$7\operatorname{kc}\operatorname{a}\operatorname{l}/\operatorname{kg}$

C)
$3\operatorname{kc}\operatorname{a}\operatorname{l}/\operatorname{kg}$

D)
$0.5\operatorname{kc}\operatorname{a}\operatorname{l}/\operatorname{kg}$

• question_answer2)                 A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, form a fixed point by a mass less  spring, such that it is half submerged in a liquid of density $\sigma$at equilibrium position. When the cylinder is given a downward push and released, it stats oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Smaller than $2\pi$${{\left[ \frac{\operatorname{M}}{\operatorname{k}+\operatorname{A}\sigma g} \right]}^{1/2}}$

B)
$2\pi \sqrt{\frac{\operatorname{M}}{\operatorname{k}}}$

C)
Larger than $2\pi {{\left[ \frac{\operatorname{M}}{(\operatorname{k}+\operatorname{A}\sigma g)} \right]}^{1/2}}$

D)
$2\pi {{\left[ \frac{\operatorname{M}}{(\operatorname{k}+\operatorname{A}\sigma g)} \right]}^{1/2}}$

• question_answer3)                 Which of the following circuits correctly represents the following truth table?                 $\frac{\begin{matrix} A & B & C \\ \end{matrix}}{\begin{matrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{matrix}}$     JEE Main Online Paper ( Held On 25  April 2013 )

A)

B)

C)

D)

• question_answer4)                 One of the two small circular coils, (none of them having any self-inductance) is suspended with a V-shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a de supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Both the same carry currents in the same direction

B)
Coils will attract each other, even if the supply is as source.

C)
Force is proportional to ${{\operatorname{d}}^{-4}}$, d = distance between the centres of the coils.

D)
Force is proportional to ${{\operatorname{d}}^{-2}}$

• question_answer5)                 This question has Statement-1 and that Statements-2. Of the four choice given after the Statements, choose the one that best describes the two Statements.                 Statement 1: No work is required to be done to move a fest charge between any two pints on an equipotential surface.                 Statement 2: Electric lines of force at the equipotential surfaces are mutually perpendicular to each other     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1

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

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

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

• question_answer6)                 A thin glass plate of thikness$\frac{2500}{3}\lambda (\lambda$ is wavelength of light used) and refractive index  $\mu =1.5$ is inserted between one the slits and the screen Yong?s double slit experiment. At a point on the screen equidistant form the slits, the ratio of the intensities before and after the introduction of the glass plate is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
2 : 1

B)
1 : 4

C)
4 : 1

D)
4 : 3

• question_answer7)                 The maximum range of a bullet fired form a toy pistol mounted on a cart at rest is ${{\operatorname{R}}_{0}}=40$ m. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $\upsilon =20$ m/s, on a horizontal surface?                 (g=10 m/$\text{m/}{{\text{s}}^{\text{2}}}$)     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\text{3}{{\text{0}}^{\text{0}}}$

B)
$\text{6}{{\text{0}}^{\text{0}}}$

C)
$\text{7}{{\text{5}}^{\text{0}}}$

D)
$\text{4}{{\text{5}}^{\text{0}}}$

• question_answer8) The surface charge density of a thin charge disc of radius R is $\sigma$. The value of the electric field at the centre of the disc is $\frac{\sigma }{2{{\in }_{0}}}.$With respect to the field at the centre, the electric field along the axis at a distance R From the centre of the disc:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
reduces by 70.7%

B)
reduces by 29.3%

C)
reduces by 9.7%

D)
reduces by 14.6%

• question_answer9)                 Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A Passing over a frictionless fixed pulley as shown in the figure. The system is then released. If  $\operatorname{M}=2$ m, then the stress produced in the wire is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\frac{2\operatorname{mg}}{3A}$

B)
$\frac{4\operatorname{mg}}{3A}$

C)
$\frac{\operatorname{mg}}{A}$

D)
$\frac{3\operatorname{mg}}{4A}$

• question_answer10)                 The gravitational field in a region is given by: $\vec{E}=(5N/kg)\,\hat{i}+(12\,N/kg)\,\hat{j}$                 If the potential at the origin is taken to be zero, then the ratio of the potential at the points (12m,0)and (0,5m) is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Zero

B)
1

C)
$\frac{144}{25}$

D)
$\frac{25}{144}$

• question_answer11)                 A sample of gas expands from ${{\operatorname{V}}_{1}}$to ${{\operatorname{V}}_{2}}$. In which of the following, the work dine will begreatest?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Same in all processes

B)
Isobaric process

C)
Isothermal process

D)
A diabetic process

• question_answer12) A block is paced on a rough horizontal plane. A time dependent horizontal force F=kt acts on the block, where k is a positive constant. The acceleration ? time graph of the block is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)

B)

C)

D)

• question_answer13)                 Six equal resistances are connected between points P, Q and R a shown in figure. The net resistance will be maximum between:   JEE Main Online Paper ( Held On 25  April 2013 )

A)
P and R

B)
P and Q

C)
Q and R

D)
Any two points

• question_answer14)                  The earth?s magnetic filed lines resemble of a dipole at the centre of the earth. It the magnetic moment of this dipole is close to$8\times {{10}^{22}}$$\text{A}{{\text{m}}^{\text{2}}}$, the value of earth?s magnetic filed near the equator is close to (radius of earth =$\text{6}\text{.4}\times \text{1}{{\text{0}}^{\text{6}}}\operatorname{m}$)     JEE Main Online Paper ( Held On 25  April 2013 )

A)
0.6 Gauss

B)
1.2 Gauss

C)
1.8 Gauss

D)
032 Gauss

• question_answer15)                 A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. It will emit:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
2 lines in the Lyman series and I line in the Balmar series

B)
3 lines in the Lyman series

C)
1 line in the Lyman series and 2 lines in the balmar series

D)
3 lines in the balmer series

• question_answer16)                 A metal sample carrying a current along X-axis with density ${{J}_{x}}$is subjected to a magnetic filed${{\operatorname{B}}_{z}}$(along-z axis). The electric field ${{\operatorname{E}}_{y}}$developed along Y-axis is directly proportional to ${{\operatorname{J}}_{x}}$as well as ${{B}_{z}}$. The constant of proportionality as has SI unit.     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\frac{{{m}^{2}}}{A}$

B)
$\frac{{{m}^{3}}}{A\operatorname{s}}$

C)
$\frac{{{m}^{2}}}{A\operatorname{s}}$

D)
$\frac{{{\operatorname{A}}_{\operatorname{S}}}}{{{\operatorname{m}}^{3}}}$

• question_answer17) A printed page is pressed by a glass of water. The refractive index of the glass and water is 1.5 and 1.33, respectively. If the thickness of the bottom of glass is 1 cm and depth of depth of water is 5 cm, how much the page will appear to be shifted if viewed from the top?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
1.033 cm

B)
3.581 cm

C)
1.3533 cm

D)
1.90 cm

• question_answer18)                 In a transverse wave the distance between ac rest and neighboring trough at the same instant is 4.0 cm the distance between a crest and trough at the same place is 1.0 cm. Then ext crest appears at the same palace after a time interval of $0.4s.$The maximum speed of the vibrating particle the medium is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\frac{3\pi }{2}\operatorname{cm}/s$

B)
$\frac{5\pi }{2}\operatorname{cm}/s$

C)
$\frac{\pi }{2}\operatorname{cm}/s$

D)
$2\pi$ cm/s

• question_answer19) Which of the following modulated signal has the  best noise-tolerance?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
long-wave

B)
short - wave

C)
medium-wave

D)
amplitude-modulated

• question_answer20)                 When resonance is produced in series LCR circuit, then which of the following is not correct?   JEE Main Online Paper ( Held On 25  April 2013 )

A)
Current in the circuit  is in phase with the applied voltage.

B)
Inductive and  capacitive reactance?s are equal.

C)
If R reduced, the voltage across capacitor will increase.

D)
Impedance of circuit is maximum.

• question_answer21)                 In an experiment, a small steel ball falls through a liquid at a constant speed of 10cm/s. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
5 cm/s

B)
Zero

C)
10 cm/s

D)
(d) 20 cm/s

• question_answer22)                 A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance ${{C}_{0}}$. Now one-third of the materialism replaced by another material with dielectric constant 2K, so that effectively there are two capacitors one with area $\frac{1}{3}\operatorname{A},$ dielectric constant 2 K and another with area $\frac{2}{3}\operatorname{A},$and dielectric constant K. If the capacitance of this new capacitor is C then $C/{{C}_{0}}$is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$1$

B)
$\frac{4}{3}$

C)
$\frac{2}{3}$

D)
$\frac{1}{3}$

• question_answer23)                 A series LR circuit is connected to an ac source of frequency is equal to $2R.$ A capacitance of capacitive reactance equal to R is added in series with L and R The ratio of the new power factor to the old one is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\sqrt{\frac{2}{3}}$

B)
$\sqrt{\frac{2}{5}}$

C)
$\sqrt{\frac{3}{2}}$

D)
$\sqrt{\frac{5}{2}}$

• question_answer24)                 In an experiment on photoelectric effect, a student plots stopping potential ${{V}_{0}}$against reciprocal of the wavelength $\lambda$ of the incident light for two different metals A and B These are shown is the figure.                 Looking at the graphs, you can most appropriately say that:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Work function of metal B is greater that that of metal A

B)
for light of certain wavelength falling on both metal, maximum kinetic energy of  those emitted from B.

C)
Work function of metal A is greater than that of metal B

D)
Students data is not correct

• question_answer25)                 The source that illuminates the double-slit in ?double?slit interference experiment? emits two distinct monochromatic waves of wavelength 500 nm and 600 nm each of them producing its own pattern on the screen. At the central point of the pattern when path difference is zero, maxima of booth the patterns coincide and the resulting interference pattern is most distinct at the region of zero path  difference. But as one moves out of this central region, the two fringe systems are gradually out of step such that maximum due to one wave length coincides with the minimum due to the other and the other and the combined fringe system becomes completely indistinct. This may happen when path difference in nm is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
2000

B)
3000

C)
1000

D)
1500

• question_answer26)                 This question has Statement -1 and Statement -2. Of the four choices given after the Statements, choose the one that best describes the two Statement.                 Statement-1: Out of radio waves and microwaves, the radio waves undergo more diffraction.                 Statement-2: Radio waves have greater frequency compared to microwaves.     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Statement -1 is true, Statement -2 is true and Statement -2 is the correct explanation of Statement 1.

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

C)
Statement -1 is true, Statement -2 is true.

D)
(d) Statement -1 is true, Statement 2 is true butStatement-2 is not the correct explanation of Statement -1.

• question_answer27)                 A ring of mass M and radius R is rotating about its axis with angular velocity $\omega$. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\frac{\operatorname{m}(\operatorname{M}+2m)}{\operatorname{M}}{{\omega }^{2}}{{R}^{2}}$

B)
$\frac{\operatorname{Mm}}{(\operatorname{M}+m)}{{\omega }^{2}}{{R}^{2}}$

C)
$\frac{\operatorname{Mm}}{(\operatorname{M}+2m)}{{\omega }^{2}}{{R}^{2}}$

D)
(d)$\frac{\left( \operatorname{M}+m \right)\operatorname{M}}{(\operatorname{M}+2m)}{{\omega }^{2}}{{R}^{2}}$

• question_answer28) A wind powered generator converts wind energy into electrical energy. Assume that the generator coverts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed $\upsilon$, the electrical power output will be most likely proportional to :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
${{\upsilon }^{4}}$

B)
${{\upsilon }^{2}}$

C)
$\upsilon$

D)
${{\upsilon }^{3}}$

• question_answer29)                 A copper ball of radius 1 cm and work function 4.47  eV us irradiated with ultraviolet radiation of wavelength $2500{{\operatorname{A}}_{\circ }}$. The effect of irradiation results in the emission of electrons form the ball. Further the ball will acquire                charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$5.5\times {{10}^{-13}}C$

B)
$7.5\times {{10}^{-13}}C$

C)
$4.5\times {{10}^{-12}}C$

D)
$2.5\times {{10}^{-11}}C$

• question_answer30)                 In the isothermal expansion of 10g of gas from volume V to 2V the work done by the gas is 575J. What is the root mean square speed of the molecules of the gas at that temperature?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
398 m/s

B)
520m/s

C)
499m/s

D)
532m/s

• question_answer31)                 The catenation tendency of C, Si and Ge is in the order Ge < Si < C. The bond energies $\left( \operatorname{in}\operatorname{K}\operatorname{J}\operatorname{mo}{{1}^{-1}} \right)$of C-C, Si-Si and Ge-Ge bonds are respectively:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
348, 297, 260

B)
297, 348, 260

C)
348, 260, 297

D)
260, 297, 348

• question_answer32)                 In which of the following exothermic reactions, the heat liberated per mole is the highest?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$CaO+{{H}_{2}}O\to Ca{{(OH)}_{2}}$

B)
$\operatorname{SrO}+{{\operatorname{H}}_{2}}\operatorname{O}\to \operatorname{Sr}{{(\operatorname{OH})}_{2}}$

C)
$\operatorname{Ba}\operatorname{O}+{{\operatorname{H}}_{2}}\operatorname{O}\to \operatorname{B}a{{(\operatorname{OH})}_{2}}$

D)
$\operatorname{M}g\operatorname{O}+{{\operatorname{H}}_{2}}\operatorname{O}\to \operatorname{Mg}{{(\operatorname{OH})}_{2}}$

• question_answer33) Give               (A) $n=5,\,\,{{m}_{l}}=+1$                (B) $n=2,\,\,l+1,\,\,\,{{m}_{l}}=-1$,${{\operatorname{m}}_{s}}=-1/2$     JEE Main Online Paper ( Held On 25  April 2013 )

A)
25 and 1

B)
8 and 1

C)
2 and 4

D)
4 and  1

• question_answer34)                 Which one of the following cannot function as an oxidizing agent?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
${{I}^{-}}$

B)
${{S}_{(s)}}$

C)
$NO_{3}^{-}(aq)$

D)
$C{{r}_{2}}O_{7}^{2-}$

• question_answer35)                 Given                                 In the above compounds correct order of reactivity in electrophilic substitution reactions will be:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$b>a>c>d$

B)
$d>c>b>a$

C)
$a>b>c>d$

D)
$b>c>a>d$

• question_answer36) Which one of the following is the wrong assumption of kinetic theory of gases?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Momentum and energy always remain conserved

B)
Pressure is the result of elasticcollision of molecules with the container's wall

C)
Molecule are separated by great distances compared to their sizes.

D)
All the molecule move in straight line between collision and with some velocity

• question_answer37) A radioactive isotope having a half?life period of 3 days received after 12 days. If 3g of the isotope is left in the container, what would be the initial mass of the isotope?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
12g

B)
36g

C)
48g

D)
24g

• question_answer38)                 Which of the following statement is not correct?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Amylopectin is branched polymer of $\alpha$-glucose.

B)
Cellulose is a linear polymer of $\beta$glucose.

C)
Glycogen is the food reserve of plants

D)
All proteins are polymers of $\alpha -$amino acids

• question_answer39) The major product in the following reaction                                 is     JEE Main Online Paper ( Held On 25  April 2013 )

A)

B)

C)

D)

• question_answer40) The ratio $\frac{\operatorname{Kp}}{\operatorname{Kc}}$ for the reaction$CO(g)+\frac{1}{2}{{O}_{2}}(g)\rightleftharpoons C{{O}_{2}}(g)$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\frac{1}{\sqrt{RT}}$

B)
${{(RT)}^{1/2}}$

C)
RT

D)
1

• question_answer41)                 Copper crystallizes in fcc with a unit length of 361 pm. What is the radius of copper atom?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
157 pm

B)
128 pm

C)
108 pm

D)
181 pm

• question_answer42)                 In which of the following sets, all the given Species are is structural?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
${{\operatorname{CO}}_{2}},\operatorname{N}{{\operatorname{O}}_{2}},Cl{{O}_{2}}Si{{O}_{2}}$

B)
$PC{{l}_{3}},AlC{{l}_{3}}BC{{l}_{3}}SbC{{l}_{3}}$

C)
${{\operatorname{BF}}_{3}},N{{F}_{3}},P{{F}_{3}},Al{{F}_{3}}$

D)
$\operatorname{BF}_{4}^{-}CC{{l}_{4}},NH_{4}^{+},PCl_{4}^{+}$

• question_answer43)                 Given that :                 (i) ${{\Delta }_{f}}{{H}^{0}}$of${{N}_{2}}O$ is $82\operatorname{k}\operatorname{j}$$\operatorname{mo}{{\operatorname{l}}^{-1}}$                 (ii)  Bond energies of N$\equiv$N, N=N, O=O and N=O are 946,418,498 and 607 Kj${{\operatorname{mol}}^{-1}}$ respectively.                 The resonance energy of ${{N}_{2}}$ O is     JEE Main Online Paper ( Held On 25  April 2013 )

A)
-88 Kj

B)
-66 Kj

C)
-62 Kj

D)
-44 Kj

• question_answer44)                 What would be the pH of a solution obtained by mixing 5g of acetic acid and 7.5g of sodium acetate and making the volume equal to 500 mL?                 $(\operatorname{Ka}=1.75\times {{10}^{-5}},\operatorname{pka}=4.6)$     JEE Main Online Paper ( Held On 25  April 2013 )

A)
pH =4.70

B)
pH< 4.70

C)
pH of solution will be equal to pH of acetic acid

D)
4.76 < pH< 5.0

• question_answer45)                 6 litres of an alkene require 27 litres of oxygen at constant temperature and pressure for complete combustion. The alkene is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Ethene

B)
Propene

C)
1-Butene

D)
2-Butene

• question_answer46)                 Bakelite is obtained from phenol by reacting with :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Acetal

B)
${{\operatorname{CH}}_{3}}\operatorname{CHO}$

C)
${{\operatorname{CH}}_{3}}\operatorname{CHO}$

D)
Chlorobenzene

• question_answer47)                 How many grams of methyl alcohol should added to 10 litre tank of water to prevent its freezing at 268 K?                 (${{\operatorname{K}}_{f}}$for water is 1.86 K kg ${{\operatorname{mol}}^{-1}}$)     JEE Main Online Paper ( Held On 25  April 2013 )

A)
880.07 g

B)
899.04 g

C)
866.02 g

D)
868.06 g

• question_answer48)                 In which of the following octahedral complex species the magnitude of ${{\Delta }_{0}}$ will be maximum?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
${{\left[ \text{Co}\left( {{\text{H}}_{\text{2}}}{{\operatorname{O}}_{6}} \right) \right]}^{2+}}$

B)
${{\left[ \text{Co}\left( \operatorname{C}{{\operatorname{N}}_{6}} \right) \right]}^{3+}}$

C)
${{\left[ \text{Co}{{\left( {{\operatorname{C}}_{2}}{{O}_{4}} \right)}_{3}} \right]}^{3-}}$

D)
${{\left[ \text{Co}{{\left( \operatorname{N}{{\operatorname{H}}_{3}} \right)}_{6}} \right]}^{3+}}$

• question_answer49)                 In nucleophilic substitution reaction, order of halogens as incoming (attacking) nucleophiles:                 ${{\operatorname{I}}^{-}}>{{\operatorname{Br}}^{-}}>{{\operatorname{CI}}^{-}}$                 The order of halogens as departing nucleophile should be :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$B{{r}^{-}}>{{I}^{-}}>C{{l}^{-}}$

B)
${{I}^{-}}>B{{r}^{-}}>C{{l}^{-}}$

C)
$C{{l}^{-}}>B{{r}^{-}}>{{I}^{-}}$

D)
$C{{l}^{-}}>{{I}^{-}}>B{{r}^{-}}$

• question_answer50)                 The Gibbs energy for the decomposition of$A{{l}_{2}}{{O}_{3}}$at ${{500}^{0}}C$ is as follows:                 $\frac{2}{3}A{{l}_{2}}{{O}_{3}}\to 4/3Al+{{O}_{2}},{{\Delta }_{r}}G=+940\,kJ\,mo{{l}^{-1}}$                 The potential difference needed for the electrolytic reduction of aluminium oxide at${{500}^{0}}C$ should be atleast:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
4.5 V

B)
3.0 V

C)
5.0 V

D)
2.5 V

• question_answer51)                 Cannizaro?s reaction is not given by :     JEE Main Online Paper ( Held On 25  April 2013 )

A)

B)

C)
$C{{H}_{3}}CHO$

D)
$HCHO$

• question_answer52)                 Pheol on heating with $CHC{{l}_{3}}$and $\text{NaOH}$gives Salicylaldehyde. The reaction is called:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Remer- Tiemenanraeaction

B)
Claisen reaction

C)
Cannizzareo?s reaction

D)
Hell-volhard-Zelinsky reaction

• question_answer53)                 The inter nuclear distances in O-O bonds for $\operatorname{O}_{2}^{+},{{\operatorname{O}}_{2}},\operatorname{O}_{2}^{-}$ and $\operatorname{O}_{2}^{2-}$ respectively are:

A)
$1.30\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.49\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.12\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.21\,\overset{\text{o}}{\mathop{\text{A}}}\,$

B)
$1.49\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.21\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.12\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.30\,\overset{\text{o}}{\mathop{\text{A}}}\,$

C)
$1.21\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.12\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.49\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.30\,\overset{\text{o}}{\mathop{\text{A}}}\,\,$

D)
$1.12\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.21\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.30\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,1.49\,\overset{\text{o}}{\mathop{\text{A}}}\,\,$

• question_answer54)                 Among the following vitamins the one whose deficiency causes rickets (bone deficiency) is     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Vitamin A

B)
Vitamin B

C)
Vitamin D

D)
Vitamin C

• question_answer55)                 Which one of the following arrangements represent the correct order of the proton affinity of the given species:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
${{I}^{-}}<{{F}^{-}}<H{{S}^{-}}<NH_{2}^{-}$

B)
${{\operatorname{HS}}^{-}}<\operatorname{NH}_{2}^{-}>{{\operatorname{F}}^{-}}<{{\operatorname{I}}^{-}}$

C)
${{\operatorname{F}}^{-}}<{{\operatorname{I}}^{-}}<\operatorname{NH}_{2}^{-}<{{\operatorname{HS}}^{-}}$

D)
$NH_{2}^{1}<H{{S}^{-}}<{{I}^{-}}<{{F}^{-}}$

• question_answer56)                 Carbylamines forms from aliphatic or aromatic primary amine via which of the following intermediates?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Carbanion

B)
Carbine

C)
Carbonation

D)

• question_answer57)                 10 mL of 2 (M) of $\operatorname{NaOH}$ solution is added to 200 mL of 0.5 (M) of NaOH solution. What in the final concentration?              JEE Main Online Paper ( Held On 25  April 2013 )

A)
0.57 (M)

B)
5.7 (M)

C)
11.4 (M)

D)
1.14 (M)

• question_answer58)                 The structure of which of the following chloro species can be explained on basis of $ds{{p}^{2}}$ hybridization?     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\operatorname{Pd}Cl_{4}^{2-}$

B)
$\operatorname{Fe}Cl_{4}^{2-}$

C)
${{C}_{O}}Cl_{4}^{2-}$

D)
$NiCl_{4}^{2-}$

• question_answer59)                 Which of the following reagent (s) used for the conversion                     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\text{glycol}/\text{LiAI}{{\text{H}}_{4}}/{{\operatorname{H}}_{3}}{{\operatorname{O}}^{+}}$

B)
$\text{glycol}/\text{NaH/}{{\operatorname{H}}_{3}}{{\operatorname{O}}^{+}}$

C)
$\operatorname{L}\operatorname{i}\operatorname{A}{{\operatorname{IH}}_{4}}$

D)
${{\operatorname{NaBH}}_{4}}$

• question_answer60)                 A solution of copper sulphate$({{\operatorname{CuSO}}_{4}})$is electrolyzed for 10 minutes with a current of 1.5 ampers. The mass of copper deposited at the cathode (at. Mass of Cu=63u) is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
0.3892g

B)
0.2938 g

C)
0.2398 g

D)
0.3928 g

• question_answer61)                 Given a sequence of 4 numbers, first  three of with are in G.P. and the last there are in A.P. with common difference six If first and last terms of this sequence are equal then the last term is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
16

B)
8

C)
4

D)
2

• question_answer62)                 Statement I: The only circle having radius$\sqrt{10}$ and a diameter along line is ${{x}^{2}}+{{y}^{2}}-6x+2y=0.$                 Statement II:$2x+y=5$ is a normal to the circle ${{x}^{2}}+{{y}^{2}}-6x-2y=0.$     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Statement I is false; statement II is true.

B)
Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I.

C)
Statement I is true; Statement II is false.

D)
Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.

• question_answer63)                 If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle ${{60}^{o}}$on the circumference of the first circle, then the of the first circle, then the radius of the are is:            JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\sqrt{3}$

B)
$\frac{1}{2}$

C)
$1$

D)
$\sqrt{2}$

• question_answer64)                 If the image of point P(2,3) in a line L is Q(4,5), the image of point R(0,0) in the same line is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
(2, 2)

B)
(4, 5)

C)
(3, 4)

D)
(7, 7)

• question_answer65)                 Consider the system of equations:                 $x+ay=0,$$y+az=0$and$z+ax=0$. Then the set of all real values of ?a? for with the system has a unique solution is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$R-\{1\}$

B)
$R-\{-1\}$

C)
$\{1,-1\}$

D)
$\{1,0,-1\}$

• question_answer66)                 A common tangent to the conics and $2{{x}^{2}}-4{{y}^{2}}=9$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$x-y=\frac{3}{2}$

B)
$x+y=1$

C)
$x+y=\frac{9}{2}$

D)
$x-y=1$

• question_answer67)                 Let                 $\operatorname{S}=\left\{ \left( \begin{matrix} {{a}_{11}} & {{a}_{12}} \\ {{a}_{21}} & {{a}_{22}} \\ \end{matrix} \right):{{a}_{\operatorname{i}\operatorname{j}}}\in \{0,1,2\},{{a}_{11}}={{a}_{22}} \right\}$                 Then the number of non ? singular matrices in the set S is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
27

B)
24

C)
10

D)
20

• question_answer68)                 Let $x$$\in$(0, 1). The set of all $x$ such that$\text{si}{{\text{n}}^{-\text{1}}}x>{{\cos }^{-1}}x,$ is the interval :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left( \frac{1}{2},\frac{1}{\sqrt{2}} \right)$

B)
$\left( \frac{1}{\sqrt{2}},1 \right)$

C)
$\left( 0,1 \right)$

D)
$\left( 0,\frac{\sqrt{3}}{2} \right)$

• question_answer69)                 Let A (-3,2) and B(-2,1) be the vertices of a triangle ABC. If the centroid of this triangle lies on the line $3x+4y+2=0,$ the vertex C lies on the line:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$4x+3y+5=0$

B)
$3x+4y+3=0$

C)
$4x+3y+3=0$

D)
$3x+4y+5=0$

• question_answer70)                 Let ABC be a triangle with vertices at points A (2,3,5), B (-1,3,2) and C ($\lambda ,5,\mu$) in three dimensional space. If the median through A is equally inclined with the axes, the is$\left( \lambda ,\mu \right)$equal to:                    JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left( 10,7 \right)$

B)
$\left( 7,5 \right)$

C)
$\left( 7,10 \right)$

D)
$\left( 5,7 \right)$

• question_answer71)                 If the integral $\int{\frac{\cos 8x+1}{\cot 2x-\tan 2x}dx=A\cos }$$8x+k,$where K is an arbitrary constant, then A is equal to :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$-\frac{1}{16}$

B)
$\frac{1}{16}$

C)
$\frac{1}{8}$

D)
$-\frac{1}{8}$

• question_answer72)                 The equation of the curve passing through the origin and satisfying the differential equation                 $(1+{{x}^{2}})\frac{\operatorname{dy}}{\operatorname{dx}}+2xy=4{{x}^{2}}$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$(1+{{x}^{2}})y={{x}^{3}}$

B)
$3(1+{{x}^{2}})y=2{{x}^{3}}$

C)
$1(1+{{x}^{2}})y=3{{x}^{3}}$

D)
$3(1+{{x}^{2}})y=4{{x}^{3}}$

• question_answer73)                 For$0\le x\le \frac{\pi }{2},$ the value of$\int\limits_{0}^{{{\sin }^{2}}x}{{{\sin }^{-1}}(\sqrt{t})\operatorname{dt}+}\int\limits_{0}^{{{\cos }^{2}}x}{{{\cos }^{-1}}(\sqrt{t})\operatorname{dt}}$equals:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\frac{\pi }{4}$

B)
0

C)
1

D)
$-\frac{\pi }{4}$

• question_answer74)                 Let f: $\left[ -2,3 \right]\to \left[ 8,\infty \right]$be a continuous function such that $f(1-x)=f(x)$ for all $x\in [-1,3].$                 If ${{\operatorname{R}}_{1}}$is the numerical value of the area of the region bounded by $y=f(x),x=-2$, $x=3$and          the axis of $x$ and${{R}_{2}}=\int\limits_{-2}^{3}{xf(x)\operatorname{d}x,\operatorname{then}:}$     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$3{{R}_{1}}=2{{R}_{2}}$

B)
$2{{R}_{1}}=3{{R}_{2}}$

C)
${{R}_{1}}={{R}_{2}}$

D)
${{R}_{1}}=2{{R}_{2}}$

• question_answer75)                 Let$\vec{a}=2\hat{i}+\hat{j}-2\hat{k},\,\vec{b}=\hat{i}+\hat{j}$. If$\vec{c}$ is a vector such that $\vec{a}\cdot \vec{c}=|\vec{c}|,\,|\vec{c}-\vec{a}|=2\sqrt{2}$and the angle between $\vec{a}\times \vec{b}$ and $\vec{c}$is ${{30}^{o}}$, then $|(\vec{a}\times \vec{b})\times \vec{c}|$ equals:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\frac{1}{2}$

B)
$\frac{3\sqrt{3}}{2}$

C)
3

D)
$\frac{3}{2}$

• question_answer76)                 Let p and q be any two logical statements and $\operatorname{r}:p\to (\sim \operatorname{p}\vee \operatorname{q}).$If r has truth values of p and q are respectively:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
F, F

B)
T, T

C)
T, F

D)
F, T

• question_answer77)                 If the events A and B are mutually exclusive events such that $\operatorname{P}(\operatorname{A})=\frac{3x+1}{3}$$\operatorname{P}(\operatorname{B})=\frac{1+x}{4},$ then the set of possible values of $x$ lies in the interval:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left[ 0,1 \right]$

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

C)
$\left[ -\frac{1}{3},\frac{5}{9} \right]$

D)
$\left[ -\frac{7}{9},\frac{4}{9} \right]$

• question_answer78)                 The equation of a plane though the of intersection of the planes $x+2y=3,$of the planes $x+2y=3,$$y-2z+1=0$ and perpendicular to the first plane is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$2x-y-10z=9$

B)
$2x-y+7z=11$

C)
$2x-y+10z=11$

D)
$2x-y-9z=10$

• question_answer79)                 If for positive integers$\operatorname{r}>1,\operatorname{n},>2,$the coefficients of the ${{(3r)}^{\operatorname{th}}}$and ${{(\operatorname{r}+2)}^{\operatorname{th}}}$  powers of $x$in the expansion of ${{(1+x)}^{2n}}$ are equal, then n is equal to     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$2r+1$

B)
$2r-1$

C)
3r

D)
$r+1$

• question_answer80)                                 If p and q are non-zero real numbers and${{\alpha }^{3}}+{{\beta }^{3}}=-p,\,\,\alpha \beta =q,$then a quadratic equation whose roots are$\frac{{{\alpha }^{2}}}{\beta },\frac{{{\beta }^{2}}}{\alpha }$is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$p{{x}^{2}}-qx+{{p}^{2}}=0$

B)
$q{{x}^{2}}+px+{{q}^{2}}=0$

C)
$p{{x}^{2}}+qx+{{p}^{2}}=0$

D)
$q{{x}^{2}}-px+{{q}^{2}}=0$

• question_answer81)                 A spherical balloon is being inflated at the rate of 35cc/min. The rate of increase in the surface area (in${{\operatorname{cm}}^{2}}/\min .$) of the balloon when its diameter is 14 cm, is     JEE Main Online Paper ( Held On 25  April 2013 )

A)
10

B)
$\sqrt{10}$

C)
$100$

D)
$10\sqrt{10}$

• question_answer82)                 Let $\operatorname{A}=\{\theta :\sin (\theta )=\tan (\theta )\}$ and $B=\{\theta :\cos (\theta )=1\}$ be two sets. Then:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\operatorname{A}=B$

B)
$\operatorname{A}\not\subset B$

C)
$\operatorname{B}\not\subset \operatorname{A}$

D)
$A\subset B$and$B-A\ne \phi$

• question_answer83)                 Let z satisfy $\left| z \right|=1$ and $\left| z \right|=1-\overset{-}{\mathop{z}}\,$                     Statement I : z is a real number                 Statement II : Principal argument of$z$ is $\frac{\pi }{3}$     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Statement I true: Statement II is true; Statement II is a correct explanation for statement I

B)
Statement I is false; Statement II is true.

C)
Statement I is true; statement II is false.

D)
Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.

• question_answer84)                 Consider the function                 $f(x)=[x]+\left| 1-x \right|,-1\le x\le 3$where$\left[ x \right]$is the greatest integer function.                 Statement I: $f$in not continuous at $x=0,$1,2 and 3.                 Statement II: $f(x)\left( \begin{matrix} -x, & -1\le x<0 \\ 1-x, & 0\le x<1 \\ 1+x, & 1\le x<2 \\ 2+x, & 2\le x\le 3 \\ \end{matrix} \right.$

A)
Statement I is true; Statement II is false.

B)

C)
Statement I is true: Statement II is true; Statement II is a correct explanation for Statement I.

D)
Statement I is false; Statement ii is true.

• question_answer85)                 Let $f(1)=-2$ and $f'(x)\ge 4.2$ for 1 $\le x\le 6.$The possible value of $f(6)$ lies in the interval     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left( 15,19 \right)$

B)
$\left( -\infty ,12 \right)$

C)
$[12,\,15)$

D)
$[19,\,\infty )$

• question_answer86)                                  In a set of 2n observations, half of them ear equal to $'a'$ and the remaining half are equal to $'-a'$ If the standard deviation of all the observations is 2; then the value of $\left| a \right|$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
2

B)
$\sqrt{2}$

C)
4

D)
$2\sqrt{2}$

• question_answer87)                 The value of${{1}^{2}}+{{3}^{2}}+{{5}^{2}}+..........+{{25}^{2}}$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
2925

B)
1469

C)
1728

D)
1456

• question_answer88)                 If an equation of a tangent to the curve,$y=\cos (x+y),-1\le x\le 1+\pi$, is $x+2y=k$then $k$is equal to     JEE Main Online Paper ( Held On 25  April 2013 )

A)
1

B)
2

C)
$\frac{\pi }{4}$

D)
$\frac{\pi }{2}$

• question_answer89)                 5-digit numbers are to be formed using 2,3,5,7,9 without repeating the digits. If p be the number of such numbers that exceed  20000 and $q$ be the number of those that lie between 30000 and 90000 , then p:q is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
6:5

B)
3:2

C)
4:3

D)
5:3

• question_answer90) A point on the ellipse,$4{{x}^{2}}+9{{y}^{2}}=36,$where the normal is parallel to the line, $4x-2y-5=0,$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left( \frac{9}{5},\frac{8}{5}, \right)$

B)
$\left( \frac{8}{5},-\frac{9}{5}, \right)$

C)
$\left( -\frac{9}{5},\frac{8}{5}, \right)$

D)
$\left( -\frac{8}{5},\frac{9}{5} \right)$