# Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 23 April 2013)

### done JEE Main Online Paper (Held On 23 April 2013) Total Questions - 90

• question_answer1) The ratio of the coefficient of volume expansion of glass container to that of a viscous liquid kept inside the container is 1: 4. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures?   [JEE Main Online Paper ( Held On 23  April 2013 )

A)
2: 5

B)
1 : 4

C)
1 : 64

D)
1 : 8

• question_answer2) Correct set up to verify Ohm?s law is :     [JEE Main Online Paper ( Held On 23  April 2013 )

A)

B)

C)

D)

• question_answer3) Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angel of contact $\theta$and the height h up to which water rises change. These changes are:     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\theta$increases and h also increases

B)
$\theta$decreases and h also decreases

C)
$\theta$increases and h decreases

D)
$\theta$decreases and h increases

• question_answer4)                 A particle of mass 2 kg is moving such hat at time t, its position, in meter, is given by $\overset{\to }{\mathop{\operatorname{r}}}\,(\operatorname{t})=5\hat{i}-2{{\operatorname{t}}^{2}}\hat{j}.$The angular momentum of the particle at $\operatorname{t}=2s$ about the origin in kg ${{\operatorname{m}}^{-2}}$${{\operatorname{s}}^{-2}}$ is :     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
$-80\hat{k}$

B)
$\left( 10\hat{i}-16\hat{j} \right)$

C)
$-40\hat{k}$

D)
$40\hat{k}$­­

• question_answer5)                 Which of the following statement is Not correct?     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
Ground  wave signals are more stable than the sky wave signals.

B)
The critical frequency of an ionospheric layer is the highest frequency that will be reflected back by the layer when it is vertically incident.

C)
Electromagnetic waves of frequencies higher than about 30 MHz cannot penetrate the ionosphere.

D)
Sky wave signals in the broadcast frequency range are stronger at night than in the day time.

• question_answer6) Electrons are accelerated through a potentialdifference V and protons are acceleratedthrough a potential difference 4 V. The de-Broglie wavelengths are  ${{\lambda }_{e}}$ and ${{\lambda }_{\operatorname{p}}}$ for electrons and protons respectively. The ratio of $\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}$ is given by: (given${{\operatorname{m}}_{e}}$is mass of electron and${{\operatorname{m}}_{\operatorname{p}}}$is mass of proton)     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=\sqrt{\frac{{{\operatorname{m}}_{\operatorname{p}}}}{{{\operatorname{m}}_{\operatorname{e}}}}}$

B)
$\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=\sqrt{\frac{{{\operatorname{m}}_{e}}}{{{\operatorname{m}}_{\operatorname{P}}}}}$

C)
$\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=\frac{1}{2}\sqrt{\frac{{{\operatorname{m}}_{e}}}{{{\operatorname{m}}_{\operatorname{P}}}}}$

D)
$\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=2\sqrt{\frac{{{\operatorname{m}}_{\operatorname{P}}}}{{{\operatorname{m}}_{e}}}}$

• question_answer7)                 A thin tube sealed at both is 100 cm long. Itlies horizontally, the middle 20 cm contacting mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced?                                                 (Given: cross section of the tube can be assumed to be uniform)     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
2.95 cm

B)
5.18 cm

C)
8.65 cm

D)
0.0 cm

• question_answer8)                 Which  of the four resistances P, Q, R and S generate the greatest amount of heat when a current flows from A to B?     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
Q

B)
S

C)
P

D)
R

• question_answer9)                 Bob of a simple pendulum of length $l$is mode of iron. The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is T then:     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
$T=2\pi \sqrt{\frac{l}{g}}$and damping is smaller than in air alone.

B)
$T=2\pi \sqrt{\frac{l}{g}}$and damping is larger than in air alone.

C)
$T>2\pi \sqrt{\frac{l}{g}}$and damping is smaller than in air alone.

D)
$T<2\pi \sqrt{\frac{l}{g}}$and damping is larger than in air alone.

• question_answer10)                 The plot given below is the average power delivered to an LRC circuit versus frequency. The quality factor of the circuit is:                   [JEE Main Online Paper ( Held On 23  April 2013 )

A)
5.0

B)
2.0

C)
2.5

D)
0.4

• question_answer11) A rectangular loop of wire, supporting a mass m, hangs with one end in a uniform magnetic filed$\overset{\to }{\mathop{\operatorname{B}}}\,$pointing out of the plane of the paper. A clockwise current is set up such that i> mg/Ba, where a is the width of the loop. Then:                 [JEE Main Online Paper ( Held On 23  April 2013 )

A)
The weight rises due to a vertical force caused by the magnetic field and work is done on the system.

B)
The weight do not rise due to vertical for caused by the magnetic field and work is done on the system.

C)
The weight rises due to a vertical force caused by the magnetic field but no work is done on the system.

D)
The weight rises due to a vertical force caused by the magnetic field and work is extracted from the magnetic field.

• question_answer12)                 A copper wire of length 1.0 m and a steel wire of length 0.5 m having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm. if the young?s modulii of copper and steel are respectively $1.0\times {{10}^{11}}{{\operatorname{Nm}}^{-2}}$and$2.0\times {{10}^{11}}\,N{{m}^{-2}}$, the total extension of the composite wire is:     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
1.75 mm

B)
2.0 mm

C)
1.50mm

D)
1.25 mm

• question_answer13)                 500 g of water and 100 g of ice at ${{0}^{0}}\operatorname{C}$are in a calorimeter whose water equivalent is $40g.$$10\,g$of  steam at ${{100}^{0}}C$ is added to it Then water in the calorimeter is : (Latent heat of ice =80 cal/g, Latent heat of stem = 540 cal/g)     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
580g

B)
590gs

C)
600g

D)
610g

• question_answer14)                 A boy of mass 20 kg is standing on a 80 kg free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing 25 m from a wall. If he walks 10 m on the cart toward the wall, then the final distance of the boy from the wall will be:     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
15 m

B)
12.5 m

C)
15.5 m

D)
17 m

• question_answer15)                 Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential:     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
less than the charged conductor more than at infinity

B)
more than the charged conductor and less than at infinity.

C)
more than the charged conductor and more than at infinity.

D)
less than the charged conductor and less than at infinity

• 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: Very large size telescopes are reflecting telescopes instead of refracting telescopes.                 Statement 2: It is easier to provide mechanical support to large size mirrors than large size lenses.     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
Statement1 is true and Statement 2 is false.

B)
Statement1 is false and Statement2 is true.

C)
Statement1 and Statement 2 are true and Statement 2 is correct explanation for Statement 1.

D)
Statement 1 and Statement 2 are true and Statement 2 is not the correct explanation for Statement 1.

• question_answer17)                 A sonometer wire of length 114 cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1:3:4?     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
At 36 cm and 84 cm from one end

B)
At 24 cm and 72 cm from one end

C)
At 48cm and 96 cm form one end

D)
At 72 cm and 96 cm from one end

• question_answer18) A particle of charge $16\times {{10}^{-16}}$ C moving with velocity  $10{{\operatorname{ms}}^{-1}}$ along $x-$ axis enters enters a region where magnetic field of induction $\overset{\to }{\mathop{\operatorname{B}}}\,$ is along the $y$-axis and an electric field of magnitude ${{10}^{4}}{{\operatorname{V}}^{-1}}$ is along the negative z-axis. If the charged particle continues moving along $x-axis$, the magnitude of magnitude  of $\overset{\to }{\mathop{\operatorname{B}}}\,$is :     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
$16\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}$

B)
$2\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}$

C)
$1\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}$

D)
$4\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}$

• question_answer19) A light ray falls on square glass slab as shown in the diagram. The index of refraction of the glass, if total internal reflection is to occur at the vertical face, is equal to:     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\left( \sqrt{2}+1 \right)/2$

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

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

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

• question_answer20)                 In the Bohr?s model of hydrogen- like atom the force between the nucleus and the electron is modified as                 $\operatorname{F}=\frac{{{e}^{2}}}{4\pi {{\in }_{0}}}\left( \frac{1}{{{\operatorname{r}}^{2}}}+\frac{\beta }{{{\operatorname{r}}^{3}}} \right),$ Where $\beta$is a constant. For this atom, the radius of the ${{\operatorname{n}}^{\operatorname{th}}}$ orbit in terms of the Bohr radius $\left( {{a}_{0}}\frac{{{\in }_{0}}{{\operatorname{h}}^{2}}}{\operatorname{m}\pi {{e}^{2}}} \right)$ is     [JEE Main Online Paper ( Held On 23  April 2013 )

A)
${{\operatorname{r}}_{\operatorname{n}}}={{\operatorname{a}}_{0}}\operatorname{n}-\beta$

B)
${{\operatorname{r}}_{\operatorname{n}}}={{\operatorname{a}}_{0}}{{\operatorname{n}}^{2}}+\beta$

C)
${{\operatorname{r}}_{\operatorname{n}}}={{\operatorname{a}}_{0}}{{\operatorname{n}}^{2}}-\beta$

D)
${{\operatorname{r}}_{\operatorname{n}}}={{\operatorname{a}}_{0}}\operatorname{n}+\beta$

• question_answer21)                 A projectile of mass M is fired so that the horizontal range is 4 km At the highest point the projectile explodes in two parts of masses M/4 and 3M/4 respectively and the heavier part states falling down vertically with zero initial speed. The horizontal range (distance from point of firing of the lighter part is):     JEE Main Online Paper ( Held On 23  April 2013 )

A)
16 km

B)
1 km

C)
10 km

D)
2 km

• question_answer22)                 If the time period $t$ of the oscillation of a drop of liquid of density $d$radius $r,$vibrating under surface tension s is given by the formula $t=\sqrt{{{r}^{2b}}{{s}^{c}}{{d}^{a/2}}.}$It is observe that the time period is directly proportional to $\sqrt{\frac{d}{s}.}$ The value of $b$ should therefore be:     JEE Main Online Paper ( Held On 23  April 2013 )

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

B)
$\sqrt{3}$

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

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

• question_answer23)                 A parallel plate capacitor of area 60 ${{\operatorname{cm}}^{2}}$ and separation 3 mm is charged  initially to $90\mu \operatorname{C}.$ If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of $2.5\times {{10}^{-8}}\operatorname{C}/s,$ then what is the magnetic field between the plates?     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$2.5\times {{10}^{-8}}\operatorname{T}$

B)
$2.0\times {{10}^{-7}}\operatorname{T}$

C)
$1.63\times {{10}^{-11}}\operatorname{T}$

D)
Zero

• question_answer24)                 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 internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.                 Statement 1: A perfect gas is heated keeping pressure constant pressure is lower than that at constant volume.     JEE Main Online Paper ( Held On 23  April 2013 )

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

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

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

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

• question_answer25)                 nidentical waves each of intensity ${{\operatorname{I}}_{0}}$ interfere with each other. The ratio of maximum intensities if the interference is (i) coherent and (ii) incoherent is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
${{\operatorname{n}}^{2}}$

B)
$\frac{1}{\operatorname{n}}$

C)
$\frac{1}{{{\operatorname{n}}^{2}}}$

D)
$\operatorname{n}$

• question_answer26)                 A 70 Kg man leaps vertically into the air from a crouching position. To take the leap the man pushes the pushes the ground with a constant force F to raise himself. The center of gravity rises by 0.5 m before he leaps. After the leap the c.g. rises by another 1 m. The maximum power delivered by the muscles is: (Take g=10 $\text{m}{{\text{s}}^{\text{2}}}$).     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\text{6}\text{.26}\times \text{1}{{\text{0}}^{\text{3}}}$ Watts at the start

B)
$\text{6}\text{.26}\times \text{1}{{\text{0}}^{\text{3}}}$ Watts at take off

C)
$\text{6}\text{.26}\times \text{1}{{\text{0}}^{\text{4}}}$ Watts at the start

D)
$\text{6}\text{.26}\times \text{1}{{\text{0}}^{\text{4}}}$ Watts at take off

• question_answer27) A system of four gates is set up as shown. The ?truth table? corresponding to this systemis:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
 A B Y 0 0 1 0 1 0 1 0 0 1 1 1

B)
 A B Y 0 0 0 0 1 0 1 0 1 1 1 0

C)
 A B Y 0 0 1 0 1 0 1 0 1 1 1 0

D)
 A B Y 0 0 1 0 1 1 1 0 0 1 1 0

• question_answer28) A body of mass 'm' is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is 1 cm. If the angular velocity is doubled, elongation in the spring is 5 cm. The original length of the spring is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
15 cm

B)
12 cm

C)
16 cm

D)
10 cm

• question_answer29)                 Select the correct statement form the following:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
Electromagnetic waves cannot travel in vacuum

B)
Electromagnetic waves are longitudinal waves

C)
Electromagnetic waves are produced by charge moving with uniform velocity.

D)
­­­ Electromagnetic waves carry both energy and momentum as they processes through space.

• question_answer30) A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of $25.5{{\operatorname{KVm}}^{-1}}$. The density of liquid is$1.26\times {{10}^{3}}$. The radius of the drop is (neglect buoyancy)     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$4.3\times {{10}^{-7}}\operatorname{m}$

B)
$7.8\times {{10}^{-7}}\operatorname{m}$

C)
$0.078\times {{10}^{-7}}\operatorname{m}$

D)
$3.4\times {{10}^{-7}}\operatorname{m}$

• question_answer31) Which of the following polymer is a polyamide?     JEE Main Online Paper ( Held On 23  April 2013 )

A)
Terylene

B)
Nylon

C)
Rubber

D)
vulcanized rubber

• question_answer32)                 The magnetic moment of the complex anion ${{[\operatorname{Cr}(\operatorname{NO})(\operatorname{N}{{\operatorname{H}}_{3}})(\operatorname{C}{{\operatorname{N}}_{4}})]}^{2-}}$is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
5.91 BM

B)
3.87 BM

C)
1.73 BM

D)
2.82 BM

• question_answer33) Glycosidic linkage is actually an:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
Carbonyl bond

B)
Ether bond

C)
Ester bond

D)
Amide bond

• question_answer34)                 Equimolar solution of the following compounds are prepared separately in water. Which will have the lowest pH value?     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\operatorname{Be}{{\operatorname{CI}}_{2}}$

B)
$\operatorname{Sr}{{\operatorname{CI}}_{2}}$

C)
$\operatorname{Ca}{{\operatorname{CI}}_{2}}$

D)
${{\operatorname{M}}_{g}}{{\operatorname{CI}}_{2}}$

• question_answer35)                 The numbers of protons, electrons and neutrons in molecule of heavy water are respectively:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
8,10,11

B)
10,10,10

C)
10,11,10

D)
11,10,10

• question_answer36)                 Number of atoms in the following samples of substances is the largest in:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
4.0 g of hydrogen

B)
71.0g chlorine

C)
127.0 g of iodine

D)
48.0g magnesium

• question_answer37)                 Which has bipyramidal shape?     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\operatorname{X}{{\operatorname{eOF}}_{4}}$

B)
$\operatorname{X}{{\operatorname{eO}}_{3}}$

C)
$\operatorname{X}{{\operatorname{eO}}_{3}}{{\operatorname{F}}_{2}}$

D)
$\operatorname{X}\operatorname{eO}{{\operatorname{F}}_{2}}$

• question_answer38)                 Which is the correct order of second ionization potential of C,N, O and F in the following ?     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\operatorname{O}>\operatorname{N}>\operatorname{F}>C$

B)
$O>\operatorname{F}>\operatorname{N}>C$

C)
$\operatorname{F}>\operatorname{O}>\operatorname{N}>C$

D)
$\operatorname{C}>\operatorname{N}>\operatorname{O}>\operatorname{F}$

• question_answer39)                 Natural glucose is termed D-glucose because:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$-OH$on the second carbon is on the right side in Fischer projection

B)
$-OH$n the sixth carbon is on the right side in Fischer projection

C)
$-OH$on the fifth carbon is on the right side in Fischer projection

D)
It is dextrorotatory

• question_answer40)                 The shape of $\operatorname{IF}_{6}^{-}$is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
Trgonally distorted octahedron

B)
pyramidal

C)
Octahedral

D)
Square antiprism

• question_answer41)                 ${{\operatorname{N}}_{2}}(g)+3{{\operatorname{H}}_{2}}(g)\rightleftharpoons 2{{\operatorname{NH}}_{3}}(g),{{\operatorname{K}}_{1}}$                                      [A]                          ${{\operatorname{N}}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2NO(g),{{\operatorname{K}}_{2}}$                        [B]                 ${{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\rightleftharpoons {{H}_{2}}O(g),{{\operatorname{K}}_{3}}$                          [C]                 The equation for the equilibrium constant of the reaction $2{{\operatorname{NH}}_{3}}(g)+\frac{5}{2}{{O}_{2}}(g)\rightleftharpoons$$2\operatorname{NH}O(g)+3{{\operatorname{H}}_{3}}\operatorname{O}(g),({{K}_{4}})$ in terms of ${{K}_{1}},{{K}_{2}},$ and ${{K}_{3}}$is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\frac{{{\operatorname{K}}_{1}}{{\operatorname{K}}_{2}}}{{{\operatorname{K}}_{3}}}$

B)
$\frac{{{\operatorname{K}}_{1}}\operatorname{K}_{3}^{2}}{{{\operatorname{K}}_{2}}}$

C)
${{\operatorname{K}}_{1}}{{\operatorname{K}}_{2}}{{\operatorname{K}}_{3}}$

D)
$\frac{{{\operatorname{K}}_{2}}\operatorname{K}_{3}^{3}}{{{\operatorname{K}}_{1}}}$

• question_answer42)                 ${{\operatorname{H}}_{1}}-$Receptor antagonists is a term associated with:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
Antisptics

B)
Anti his tam ins

C)
Antacids

D)
Analgesics

• question_answer43)                 The correct order of viscosity of the following liquids will be:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
Water < methyl alcohol < dimethyl ether < glycerol

B)
methyl alcohol < glycerol < water < dimethyl ether

C)
dimethyl ether < methyl alcohol < water < glycerol

D)
glycerol< dimethyl ether < water < methyl alcohol

• question_answer44)                 What is the ­­$\operatorname{p}\operatorname{H}$ of a${{10}^{-4}}$ M ${{\operatorname{OH}}^{-}}$ solution at $330\operatorname{K},$ if ${{\operatorname{K}}_{w}}$at 330K is ${{10}^{-13.6}}?$     JEE Main Online Paper ( Held On 23  April 2013 )

A)
4

B)
9.0

C)
10

D)
9.6

• question_answer45)                 The order of reactivity of the given haloalkanes towards nuclephlile is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$R\,I<R\,Br<R\,Cl$

B)
$R\,\,Cl>R\,\,Br>R\,\,I$

C)
$R\,\,Br>R\,\,Cl>R\,\,I$

D)
$R\,\,Br>R\,\,I\,\,>\,R\,\,Cl$

• question_answer46)                 Identify the incorrect statement:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
In${{(\operatorname{S}{{\operatorname{i}}_{3}}{{\operatorname{O}}_{9}})}^{6-}}$, tetrahedral $Si{{O}_{4}}$ units share two oxygen atoms.

B)
Trialkylchlorosilaneon hydrolysis gives ${{R}_{3}}SiOH$

C)
$SiC{{l}_{4}}$undergoes hydrolysis to give ${{H}_{4}}Si{{O}_{4}}$

D)
${{(\operatorname{S}{{\operatorname{i}}_{3}}{{\operatorname{O}}_{9}})}^{6-}}$has cyclic structure

• question_answer47)                 When a small amount of $\operatorname{K}\operatorname{M}\operatorname{n}{{\operatorname{O}}_{4}}$is added to concentrated${{\operatorname{H}}_{2}}\operatorname{S}{{\operatorname{O}}_{4}},$ a green oily compound is obtained which is highly explosive in nature. Compound may be:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\operatorname{M}\operatorname{n}\operatorname{S}{{\operatorname{O}}_{4}}$

B)
$\operatorname{M}{{\operatorname{n}}_{2}}{{\operatorname{O}}_{7}}$

C)
$\operatorname{M}\operatorname{n}{{\operatorname{O}}_{2}}$

D)
$\operatorname{M}{{\operatorname{n}}_{2}}{{\operatorname{O}}_{3}}$

• question_answer48) The reaction of phenol with benzoyl benzoateis known as :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
Claisen reaction

B)
Schotten-Baumann reaction

C)
Reimer - Tiemeann reaction

D)
Gatterman- Koch reaction

• question_answer49) ­­                Identify incorrect statement:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$C{{u}_{2}}O$ is colourless

B)
Cupper (I) compounds

C)
Copper (I) compounds are diamagnetic

D)
${{\operatorname{Cu}}_{2}}\operatorname{S}$ is black

• question_answer50)                 Vapour pressure of pure benzene is 119 torr and that of toluene is 37.0 torr at the same temperature. Mole fraction of toluene in vapour phase which is equilibrium with a solution of benzene and toluene having a mole fraction of toluene 0.50 will be:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
0.137

B)
0.237

C)
0.435

D)
0.205

• question_answer51)                 In a face centred cubic lattice, atoms of A form the corner points and atoms of B form the face  points. If two atoms of A are missing form the corner points, the formula of the ionic compound is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
${{\operatorname{AB}}_{3}}$

B)
${{\operatorname{AB}}_{4}}$

C)
${{\operatorname{A}}_{2}}{{B}_{5}}$

D)
${{\operatorname{AB}}_{2}}$

• question_answer52)                 The de Broglie wavelength of a car of mass 100 kg and velocity 36 km/hr is:                 $(h=6.63\times {{10}^{-34}}\,Js)$     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$6.626\times {{10}^{-34}}\operatorname{m}$

B)
$6.626\times {{10}^{-38}}\operatorname{m}$

C)
$6.626\times {{10}^{-31}}\operatorname{m}$

D)
$6.626\times {{10}^{-30}}\operatorname{m}$

• question_answer53)                 Given:                 $E_{1/2/C{{l}_{2}}/c{{l}^{-}}}^{0}=1.36\,V,\,E_{C{{r}^{3+}}/Cr}^{0}=-0.74\,V$,                 $E_{C{{r}_{2}}O_{7}^{2-}/C{{r}^{3+}}}^{0}=1.33\,V,\,E_{MnO_{4}^{-}/MnO_{{}}^{2+}}^{0}=1.51\,V$                 The correct order of reducing power of the species $(Cr,C{{r}^{3+}},M{{n}^{2+}}\text{and}\,\,C{{l}^{-}})$be:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$M{{n}^{2+}}<C{{l}^{-}}<C{{r}^{3+}}<Cr$

B)
$M{{n}^{2+}}<C{{r}^{3}}^{-}<C{{l}^{-}}<Cr$

C)
$C{{r}^{3+}}<C{{l}^{-}}<M{{n}^{2+}}<Cr$

D)
$C{{r}^{3+}}<C{{l}^{-}}<Cr<M{{n}^{2}}^{+}$

• question_answer54)                 Smoke is an example of:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
Solid disperse in solid

B)
Gas dispersed in liquid

C)
Solid dispersed in gas                   Smoke is an example of solid particles dispersed in gas.

D)
Gas dispersed in solid

• question_answer55)                 Which of the following statements/ relationships is not correct in thermodynamic changes?     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\Delta U=0$(isothermal reversible expansion of a gas)

B)
$w=-nRT\ln \frac{{{V}_{2}}}{{{V}_{1}}}$(isothermal reversible expansion of an ideal gas)

C)
$w=-nRT\ln \frac{{{V}_{2}}}{{{V}_{1}}}$(isothermal reversible expansion of an ideal gas)

D)
For a system of constant volume heat involved directly changes to internal energy.

• question_answer56)                 Bond distance in HF is $9.17\times {{10}^{-11}}\operatorname{m}.$ Dipole moment of HF is $6.104\times {{10}^{-30}}\operatorname{Cm}.$ The percent ionic character in HF will be (electron charge = $6.104\times {{10}^{-19}}\operatorname{C}$)     JEE Main Online Paper ( Held On 23  April 2013 )

A)
61.0 %

B)
38.0%

C)
35.5 %

D)
41.5 %

• question_answer57)                 The rate constant of a zero order reaction is $2.0\times {{10}^{-2}}$mol${{\operatorname{L}}^{-1}}$${{\operatorname{s}}^{-1}}$. If the concentration of the reactant after 25 seconds is 0.5 M. What is the initial concentration?   JEE Main Online Paper ( Held On 23  April 2013 )

A)
0.5 M

B)
1.25 M

C)
12.5 M

D)
1.0 M

• question_answer58)                 Which of the following is the product of aldol condensation?     JEE Main Online Paper ( Held On 23  April 2013 )

A)

B)

C)

D)

• question_answer59)                 The order of amines in gaseous state is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
${{1}^{0}}>{{2}^{0}}>{{3}^{0}}>\operatorname{N}{{\operatorname{H}}_{3}}$

B)
${{3}^{0}}>{{2}^{0}}>\operatorname{N}{{\operatorname{H}}_{3}}>{{1}^{0}}$

C)

D)
${{\operatorname{NH}}_{3}}>{{1}^{0}}>{{2}^{0}}>{{3}^{0}}$

• question_answer60)                 Monocarboxylic acids are functional isomers of:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
Ethers

B)
Amines

C)
Esters

D)
Alcohols

• question_answer61) The integral $\int{\frac{x\operatorname{d}x}{2-{{x}^{2}}+\sqrt{2-{{x}^{2}}}}}$equals :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\log \left| 1+\sqrt{2+{{x}^{2}}} \right|+C$

B)
$-\log \left| 1+\sqrt{2-{{x}^{2}}} \right|+C$

C)
$-x\log \left| 1-\sqrt{2-{{x}^{2}}} \right|+C$

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

• question_answer62)                 If the curves$\frac{{{x}^{2}}}{\alpha }+\frac{{{y}^{2}}}{4}=1$ and ${{y}^{3}}=16x$ intersect at right angles, then a value of $\alpha$is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
2

B)
$4/3$

C)
$1/2$

D)
$3/4$

• question_answer63)                 Statement 1: The system of linear equations                 $x+(\sin \alpha )y+(\cos \alpha )z=0$                 $x+(\cos \alpha )y+(\sin \alpha )z=0$                 $x-(\sin \alpha )y-(\cos \alpha )z=0$                 has non-trivial solution of only one value of a lying in the interval $0,\frac{\pi }{2}.$                 Statement 2 : The equation in $\alpha$                 $\left| \begin{matrix} \cos \alpha & \sin \alpha & \cos \alpha \\ \sin \alpha & \cos \alpha & \sin \alpha \\ \cos \alpha & -\sin \alpha & -\cos \alpha \\ \end{matrix} \right|=0$                              has only one solution lying in the interval  $\left( 0,\frac{\pi }{2}. \right)$     JEE Main Online Paper ( Held On 23  April 2013 )

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

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

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

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

• question_answer64)                 For integers m and n both greater than 1, consider the following  three statement:                 P: m divides n                 Q :  m divides  ${{\text{n}}^{2}}$                 R:  m is prime, then     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$Q\wedge R\to P$

B)
$P\wedge Q\to R$

C)
$Q\to R$

D)
$Q\to P$

• question_answer65)                 The sum of the rational terms in the binomial expansion of ${{\left( {{2}^{\frac{1}{2}}}+{{3}^{\frac{1}{5}}} \right)}^{10}}$is     JEE Main Online Paper ( Held On 23  April 2013 )

A)
25

B)
32

C)
9

D)
41

• question_answer66)                 If the extremities of the base of an isosceles triangle are the points (2a, 0) and (0, a) and the equation of one of the sides is $x=2a,$ then the area of the square units, is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\frac{5}{4}{{\operatorname{n}}^{2}}$

B)
$\frac{5}{2}{{\operatorname{n}}^{2}}$

C)
$\frac{25{{a}^{2}}}{4}$

D)
$5{{a}^{2}}$

• question_answer67)                 The sum of the series:             ${{(2)}^{2}}+2{{(4)}^{2}}+3{{(6)}^{2}}+.....\operatorname{upto}10\operatorname{trems}\operatorname{is}:$     JEE Main Online Paper ( Held On 23  April 2013 )

A)
11300

B)
12100

C)
12100

D)
12300

• question_answer68)                 If the circle ${{x}^{2}}+{{y}^{2}}-6x-8y+(25-{{a}^{2}})=0$touches the axis of $x,$ then a equals.     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$0$

B)
$\pm 4$

C)
$\pm 2$

D)
$\pm 3$

• question_answer69)                 If$\operatorname{S}={{\tan }^{-1}}\left( \frac{1}{{{\operatorname{n}}^{2}}+\operatorname{n}+1} \right)+$                 ${{\tan }^{-1}}\left( \frac{1}{{{\operatorname{n}}^{2}}+3\operatorname{n}+3} \right)+.......$                 $+{{\tan }^{-1}}\left( \frac{1}{1+(\operatorname{n}+19)(\operatorname{n}+20)} \right),$then tan S is equal to :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\frac{20}{401+20\operatorname{n}}$

B)
$\frac{\operatorname{n}}{{{\operatorname{n}}^{2}}+20\operatorname{n}+1}$

C)
$\frac{20}{{{\operatorname{n}}^{2}}+20\operatorname{n}+1}$

D)
$\frac{\operatorname{n}}{401+20\operatorname{n}}$

• question_answer70)                 If $\overset{\to }{\mathop{a}}\,$ and $\overset{\to }{\mathop{b}}\,$ are non-collinear vectors, then the value of $\alpha$for which the vectors $\overset{\to }{\mathop{\operatorname{u}}}\,=(\alpha -2)\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\,$and $\overset{\to }{\mathop{\operatorname{v}}}\,=(2+3\alpha )\overset{\to }{\mathop{a}}\,-\overset{\to }{\mathop{3b}}\,$ are collinear is:     JEE Main Online Paper ( Held On 23  April 2013 )

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

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

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

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

• question_answer71)                 The least integral value $a$ of $x$such that$\frac{x-5}{{{x}^{2}}+5x-14}>0$, satisfies:               JEE Main Online Paper ( Held On 23  April 2013 )

A)
${{\alpha }^{2}}+3\alpha -4=0$

B)
${{\alpha }^{2}}-5\alpha +4=0$

C)
${{\alpha }^{2}}-7\alpha +6=0$

D)
${{\alpha }^{2}}+5\alpha -6=0$

• question_answer72)                 A, B,C, try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets are $\frac{3}{4},\frac{1}{2},\frac{5}{8}.$ The probability that the target  is hit by A or B but not by C is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$21/64$

B)
$7/8$

C)
$7/32$

D)
$9/64$

• question_answer73)                 If two lines ${{\operatorname{L}}_{1}}$and ${{\operatorname{L}}_{2}}$ in space, are defined by                 ${{\operatorname{L}}_{2}}=\{x=\sqrt{\lambda }y+(\sqrt{\lambda }-1)\}$                 $z=\left( \sqrt{\lambda }-1 \right)y+\sqrt{\lambda }\}$and                 ${{L}_{2}}=\{x=\sqrt{\mu }y+(1-\sqrt{\mu }),$                 $z=(1-\sqrt{\mu })y+\sqrt{\mu }\},$                 then${{L}_{1}}$ is perpendicular to ${{L}_{2}},$ for all non-negative reals$\lambda$ and $\mu$ such that:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\sqrt{\lambda }+\sqrt{\mu }=1$

B)
$\lambda \ne \mu$

C)
$\lambda +\mu =0$

D)
$\lambda =\mu$

• question_answer74)                 The number of solutions of the equation$\sin 2x-2\cos x+4\sin x=4$in the interval$[0,5\pi ]$is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
3

B)
5

C)
4

D)
6

• question_answer75)                 If the projections of a line segment of the $x,y$and z-axes in 3-dimensional  space are 2, 3 and 6 respectively, the length of the line segment  is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
12

B)
7

C)
9

D)
6

• question_answer76)                 Let a =Im$\left( \frac{1+{{z}^{2}}}{2iz} \right),$where z is any non- zero complex ?complex number.                 The set $\operatorname{A}=\{a:\left| z \right|1\operatorname{and}z\ne \pm 1\}$ is equal to :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
(-1,1)

B)
[-1,1]

C)
[0, 1)

D)
(-1,0]

• question_answer77)                 Let ${{\theta }_{1}}$be the angle between two lines $2x+3y+{{\operatorname{c}}_{1}}=0$and $-x+5y+{{c}_{2}}=0,$and${{\theta }_{2}}$ be the angle between two lines $2x+3y+{{c}_{1}}=0$,  and$-x+5y+{{c}_{3}}=0,$where, ${{c}_{1}},{{c}_{2}},\,\,{{c}_{3}}$are any real numbers :                 Statement 1: If ${{c}_{2}}$ and ${{c}_{3}}$ are proportional, then ${{\theta }_{1}}={{\theta }_{2}}$                 Statement 2: ${{\theta }_{1}}={{\theta }_{2}}$ for all ${{\operatorname{c}}_{2}}$ and ${{\operatorname{c}}_{3}}$     JEE Main Online Paper ( Held On 23  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 correct explanation for Statement 1.

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

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

• question_answer78)                 If $f(x)=\sin (\sin x)$and            $f''(x)+\tan xf(x)+g(x)=0,$then g($x$) is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
${{\cos }^{2}}x\cos (\sin x)$

B)
${{\sin }^{2}}x\cos (\cos x)$

C)
${{\sin }^{2}}x\sin (\cos x)$

D)
${{\cos }^{2}}x\sin (\sin x)$

• question_answer79)                 If${{a}_{1}},{{a}_{2}},{{a}_{.3.......}}{{a}_{n}}......$ are in A.P. such that ${{a}_{4}}-{{a}_{7}}+{{a}_{10}}=\operatorname{m},$ then sum of first 13 terms of this A.P., is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
10 m

B)
12 m

C)
13 m

D)
15 m

• question_answer80)                 A tangent to the hyperbola $\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{2}=1$ meets $x-$axis at P and $y-$axis at $Q.$Lines PR and QR are drawn such that OPRQ is a rectangle (where O is the origin). The R lies on:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
­$\frac{4}{{{x}^{2}}}+\frac{2}{{{y}^{2}}}=1$

B)
$\frac{2}{{{x}^{2}}}-\frac{4}{{{y}^{2}}}=1$

C)
$\frac{2}{{{x}^{2}}}+\frac{4}{{{y}^{2}}}=1$

D)
$\frac{4}{{{x}^{2}}}-\frac{2}{{{y}^{2}}}=1$

• question_answer81)                 Let$f$ be a composite function of $x$ defined by  $f(u)=\frac{1}{{{\operatorname{u}}^{2}}+\operatorname{u}-2},\operatorname{u}(x)=\frac{1}{x-1}.$                 Then the number of points $x$ where f of is discontinuous is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
4

B)
3

C)
2

D)
1

• question_answer82)                 The value of  $\int\limits_{-\pi /2}^{\pi /2}{\frac{{{\sin }^{2}}x}{1+{{2}^{x}}}\operatorname{d}}x$is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$\pi$

B)
$\pi /2$

C)
$4\pi$

D)
$\pi /4$

• question_answer83)                 The cost of running a bus from A to B, is $\operatorname{Rs}.\left( \operatorname{av}\frac{\operatorname{b}}{\operatorname{v}} \right),$ where v km/h is the cost speed of the bus. When the bus travels at 30 km /h, the cost comes out to be Rs. 75 while at 40 km/h, it is Rs. 65 Then the most economical speed (in Km/h)of the bus is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
45

B)
50

C)
60

D)
40

• question_answer84)                 The area under the curve$y=\left| \cos x-\sin x \right|,$$0\le x\le \frac{\pi }{2},$and above $x-\operatorname{axis}$ is:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
$2\sqrt{2}$

B)
$2\sqrt{2}-2$

C)
$2\sqrt{2}+2$

D)
0

• question_answer85)                 Let A, other than I or-I, a$2\times 2$ areal matrix such that${{\operatorname{A}}^{2}}=I,$I being the unit matrix. Let Tr   be the sum of diagonal elements of A.                 Statement 1 :$\operatorname{T}\operatorname{r}(\operatorname{A})=0$                 Statement 1 :$\det (\operatorname{A})=-1$     JEE Main Online Paper ( Held On 23  April 2013 )

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

B)
Statement 1 is true; Statement 2 is true; Statement 2 is not correct explanation for Statement 1.

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

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

• question_answer86)                 On the sides AB,BC, CA of                 $\Delta \operatorname{ABC},$ 3, 4, 5 distinct points (excluding vertices A, B, C) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are:     JEE Main Online Paper ( Held On 23  April 2013 )

A)
210

B)
205

C)
215

D)
220

• question_answer87)                 If the median and the range of four numbers                 $\{x,y,2x+y,x-y\},$ where                 $0<y<x<2y$ are 10 and 28  respectively, then the mean of the numbers is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
18

B)
10

C)
5

D)
14

• question_answer88)                 If curve passes through the point                 $\left( 2,\frac{7}{2} \right)$  and has slope                 $\left( 1-\frac{1}{{{x}^{2}}} \right)$  at any point                 $(x,y)$  on it, then the ordinate of the point on the curve whose abscissa is -2 is:     JEE Main Online Paper ( Held On 23  April 2013 )

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

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

C)
$\frac{5}{2}$

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

• question_answer89)                 The point of intersection of the parabola                 ${{y}^{2}}=4x$  at the ends of its latus rectum is     JEE Main Online Paper ( Held On 23  April 2013 )

A)
(0,2)

B)
(3,0)

C)
(0, 3)

D)
(2,0)

• question_answer90)                 Let                 $\operatorname{R}=\{(x,y):x,y\in \operatorname{N}$ and                 ${{x}^{2}}-4xy$                 $+3{{y}^{2}}=0\},$ where N is the set of all natural  numbers. Then the relation R is :     JEE Main Online Paper ( Held On 23  April 2013 )

A)
reflexive but neither symmetric nor transitive

B)
symmetric and transitive.

C)
reflexive and symmetric.

D)
reflexive and transitive.