# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 10 April 2015)

### done JEE Main Paper (Held On 10 April 2015) Total Questions - 90

• question_answer1) A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it is rolling without slipping then the value of 'F' is: JEE Main Online Paper (Held On 10 April 2015)

A)
$ma$

B)
$2 ma$

C)
$\frac{5}{3}$

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

• question_answer2) When current in a coil changes from 5 A to 2 A in 0.1 s, an average voltage of 50 V is produced. The self-inductance of the coils is: JEE Main Online Paper (Held On 10 April 2015)

A)
3H

B)
1.67 H

C)
6 H

D)
0.67 H

• question_answer3) If a body moving in a circular path maintains constant speed of $\frac{3}{2}ma$, then which of the following correctly describes relation between acceleration and radius? JEE Main Online Paper (Held On 10 April 2015)

A)

B)

C)

D)

• question_answer4) An electromagnetic wave travelling in the x-direction has frequency of $2\times {{10}^{14}}Hz$and electric field amplitude of $27V{{m}^{-1}}.$From the options given below, which one describes the magnetic field for this wave? JEE Main Online Paper (Held On 10 April 2015)

A)
$\overset{\to }{\mathop{B}}\,(x.t)=(9\times {{10}^{-8}}T)\hat{i}$ $\sin \left[ 2\pi (1.5\times {{10}^{-8}}x-2\times {{10}^{14}}t) \right]$

B)
$\overset{\to }{\mathop{B}}\,(x,t)=(3\times {{10}^{-8}}T)\hat{j}$ $\sin \left[ 1.5\times {{10}^{-6}}x-2\times {{10}^{14}}t) \right]$

C)
$\overset{\to }{\mathop{B}}\,(x,t)=(3\times {{10}^{-8}}T)\hat{j}$ $\sin \left[ 2\pi (1.5\times {{10}^{-8}}x-2\times {{10}^{14}}t) \right]$

D)
$\overset{\to }{\mathop{B}}\,(x,t)=(9\times {{10}^{-8}}T)\hat{k}$ $\sin \left[ 2\pi (1.5\times {{10}^{-6}}x-2\times {{10}^{14}}t) \right]$

E)
None of the above

• question_answer5) A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R << L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing  Is t and its distance from the galaxy?s axis is r, then: JEE Main Online Paper (Held On 10 April 2015)

A)
$T\propto {{r}^{2}}$

B)
$T\propto r$

C)
${{T}^{2}}\propto {{r}^{3}}$

D)
$T\propto \sqrt{r}$

• question_answer6) If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter$\frac{2}{\sqrt{\pi }}cm$then the Reynolds number for the flow is (density of water $={{10}^{3}}kg/{{m}^{3}}$and viscosity of water $={{10}^{-3}}Pa.s$) close to: JEE Main Online Paper (Held On 10 April 2015)

A)
11,000

B)
5500

C)
550

D)
1100

• question_answer7) If two  glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by: JEE Main Online Paper (Held On 10 April 2015)

A)
$\frac{4T}{R}$

B)
$\frac{2T}{R}$

C)
$\frac{T}{2R}$

D)
$\frac{T}{4R}$

E)
None of the above

• question_answer8) A thin disc of radius b = 2a has a concentric hole of radius $'\sigma '$ in it (see figure). It carries uniform surface charge 'w' on it. If the electric field on its axis at height 'h' (h<<a) from its centre is given as $'C\overset{\scriptscriptstyle\smile}{h}'$then value  of ?C? is: JEE Main Online Paper (Held On 10 April 2015)

A)
$\frac{\sigma }{a{{\varepsilon }_{0}}}$

B)
$\frac{\sigma }{4a{{\varepsilon }_{0}}}$

C)
$\frac{\sigma }{2a{{\varepsilon }_{0}}}$

D)
$\frac{\sigma }{8a{{\varepsilon }_{0}}}$

• question_answer9) If the capacitance of a Nano capacitor is measured in tern-is of a unit V made by combining the electronic charge 'e', Bohr radius $'{{a}_{0}}',$ Planck's constant 'h' and speed of light 'c' then : JEE Main Online Paper (Held On 10 April 2015)

A)
$u=\frac{hc}{{{e}^{2}}{{a}_{0}}}$

B)
$u=\frac{{{e}^{2}}h}{c{{a}_{0}}}$

C)
$u=\frac{{{e}^{2}}{{a}_{0}}}{hc}$

D)
$u=\frac{{{e}^{2}}c}{h{{a}_{0}}}$

• question_answer10) Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about one of its diagonals, then : JEE Main Online Paper (Held On 10 April 2015)

A)
$I=\frac{m{{a}^{2}}}{12}$

B)
$I>\frac{m{{a}^{2}}}{12}$

C)
$I=\frac{m{{a}^{2}}}{24}$

D)
$\frac{m{{a}^{2}}}{24}<I<\frac{m{{a}^{2}}}{12}$

• question_answer11) A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is $\theta$, then$\theta$, is close to : JEE Main Online Paper (Held On 10 April 2015)

A)
${{60}^{o}}$

B)
${{15}^{o}}$

C)
${{1}^{o}}$

D)
${{30}^{o}}$

• question_answer12) Suppose the drift velocity Vi in a material varied with the applied electric field E as ${{\upsilon }_{d}}\propto \sqrt{E}.$Then V - I graph for a wire made of such a material is best given by : JEE Main Online Paper (Held On 10 April 2015)

A)

B)

C)

D)

• question_answer13) In an unbiased n-p Junction electrons diffuse from n - region to p - region because : JEE Main Online Paper (Held On 10 April 2015)

A)
only electrons move from n to p  holes in p- region and not the vice - versa

B)
holes in p - region attract them

C)
electrons travel across the junction due to potential difference

D)
electron concentration in n - region is more as compared to that in p-region

• question_answer14) A simple harmonic oscillator of angular frequency $2rad\,{{s}^{-1}}$is acted upon by an external force F = sint N. If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is proportional to: JEE Main Online Paper (Held On 10 April 2015)

A)
$\sin t+\frac{1}{2}\cos 2t$

B)
$\sin t-\frac{1}{2}\sin 2t$

C)
$\cot t-\frac{1}{2}\sin 2t$

D)
$\sin t+\frac{1}{2}\sin 2t$

• question_answer15) A parallel beam of electrons travelling in x-direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum ${{p}_{y}}$ in the y-direction then for a majority of electrons passing through the slit (h is Planck's constant) : JEE Main Online Paper (Held On 10 April 2015)

A)
$|{{p}_{y}}|d>h$

B)
$|{{p}_{y}}|d>>h$

C)
$|{{p}_{y}}|d<h$

D)
$|{{p}_{y}}|d\simeq h$

• question_answer16) In the circuits  and  switches ${{S}_{1}}$ and ${{S}_{2}}$ are closed at t = 0 and are kept closed for a long time. '1'he variation of currents in the two circuits for $t\ge 0$ are roughly shown by (figures are schematic and not drawn to scale) : JEE Main Online Paper (Held On 10 April 2015)

A)

B)

C)

D)

• question_answer17) A proton (mass m) accelerated by a potential difference V flies through a uniform transverse magnetic field B. The field occupies a region of space by width 'd?. If $'\alpha '$ be the angle of deviation of proton from initial direction of motion (see figure), the value of sin a will be : JEE Main Online Paper (Held On 10 April 2015)

A)
${{q}^{V}}\sqrt{\frac{Bd}{2m}}$

B)
$Bd\sqrt{\frac{q}{2mV}}$

C)
$\frac{B}{2}\sqrt{\frac{qd}{mV}}$

D)
$\frac{B}{d}\sqrt{\frac{q}{2mV}}$

• question_answer18) de-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to $(|e|=1.6\times {{10}^{-19}}C,{{m}_{e}}=9.1\times {{10}^{-31}}kg,h=6.6\times {{10}^{-34}}Js)$ JEE Main Online Paper (Held On 10 April 2015)

A)
$0.5\,\overset{\text{o}}{\mathop{\text{A}}}\,$

B)
$1.7\,\overset{\text{o}}{\mathop{\text{A}}}\,$

C)
$2.4\,\overset{\text{o}}{\mathop{\text{A}}}\,$

D)
$1.2\,\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer19) Diameter of a steel ball is measured using a Vernier callipers which lias divisions of cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as :  S. No. MS (cm) VS divisions 1. 0.5 8 2. 0.5 4 3. 0.5 6
If the zero error is - 0.03 cm, then mean corrected diameter is : JEE Main Online Paper (Held On 10 April 2015)

A)
0.56 cm

B)
0.53 cm

C)
0.52 cm

D)
0.59 cm

• question_answer20) If one were to apply Bohr model to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the nth  level will be : JEE Main Online Paper (Held On 10 April 2015)

A)
$n\left( \frac{hqB}{2\pi m} \right)$

B)
$n\left( \frac{hqB}{8\pi m} \right)$

C)
$n\left( \frac{hqB}{4\pi m} \right)$

D)
$n\left( \frac{hqB}{\pi m} \right)$

• question_answer21) x and y displacements of a particle are given as x(t)=a $\sin \omega t$ and $y(t)=a\sin 2\omega t.$ Its trajectory will look like : JEE Main Online Paper (Held On 10 April 2015)

A)

B)

C)

D)

• question_answer22) Shown in the figure are two point charges +Q and -Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If ${{\sigma }_{1}}$ is the surface charge on the inner surface and ${{Q}_{1}}$ net charge on it and ${{\sigma }_{2}}$ the surface charge on the outer surface and ${{Q}_{2}}$ net charge on it then : JEE Main Online Paper (Held On 10 April 2015)

A)
${{\sigma }_{1}}\ne 0,{{Q}_{1}}=0$ ${{\sigma }_{2}}\ne 0,{{Q}_{2}}=0$

B)
${{\sigma }_{1}}\ne 0,{{Q}_{1}}=0$ ${{\sigma }_{2}}=0,{{Q}_{2}}=0$

C)
${{\sigma }_{1}}\ne 0,{{Q}_{1}}\ne 0$ ${{\sigma }_{2}}\ne 0,{{Q}_{2}}\ne 0$

D)
${{\sigma }_{1}}=0,{{Q}_{1}}=0$ ${{\sigma }_{2}}=0,{{Q}_{2}}=0$

• question_answer23) A block of mass m=10 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of nails 50 g moving with speed r, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed $\frac{\upsilon }{10}$ after being dropped from height H, then neglecting energy losses and taking $g=10m{{s}^{-2}},$the value of H is close to: JEE Main Online Paper (Held On 10 April 2015)

A)
0.2 km

B)
0.4 km

C)
0.5 km

D)
0.3 km

E)
None of the above

• question_answer24) A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance $\left( \frac{x}{2} \right)$from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity $3m{{s}^{-1}}.$The total initial energy of the spring is: JEE Main Online Paper (Held On 10 April 2015)

A)
15J

B)
0.6 J

C)
0.8 J

D)
0.3 J

• question_answer25) A bat moving at $10m{{s}^{-1}}$ towards a wall sends a sound signal of ROOO Hz towards it. On reflection it hears a sound of frequency f. The value of f in Hz is dose to (speed of sound $=320m{{s}^{-1}}$) JEE Main Online Paper (Held On 10 April 2015)

A)
8516

B)
8000

C)
8424

D)
8258

• question_answer26) An ideal gas goes through a reversible cycle $a\to b\to c\to d$has the V - T diagram shown below. Process $d\to a$and $b\to c$ are adiabatic. The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) : JEE Main Online Paper (Held On 10 April 2015)

A)

B)

C)

D)

• question_answer27) A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15 A. If it is equivalent to a magnet of the same size and magnetization $\overset{\to }{\mathop{M}}\,$(magnetic moment/volume), then $|\overset{\to }{\mathop{M}}\,|$is: JEE Main Online Paper (Held On 10 April 2015)

A)
$30000\,A{{m}^{-1}}$

B)
$3\pi \,A{{m}^{-1}}$

C)
$30000\pi \,A{{m}^{-1}}$

D)
$300\,A{{m}^{-1}}$

• question_answer28) In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as ${{T}^{q}}.$ A good estimate for q is : JEE Main Online Paper (Held On 10 April 2015)

A)
1

B)
$\frac{1}{4}$

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

D)
2

• question_answer29) You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm- The radius of curvature of the mirror would then be : JEE Main Online Paper (Held On 10 April 2015)

A)
-24 cm

B)
24 cm

C)
60 cm

D)
30 cm

• question_answer30) A 10V battery with internal resistance $1\Omega$and a 15 V battery with internal resistance $0.6\Omega$ are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to : JEE Main Online Paper (Held On 10 April 2015)

A)
11.9 V

B)
13.1 V

C)
12.5 V

D)
24.5 V

• question_answer31) In the isolation of metals, calcination process usually results in: JEE Main Online Paper (Held On 10 April 2015)

A)
metal oxide

B)
metal carbonate

C)
metal hydroxide

D)
metal sulphide

• question_answer32) Permanent hardness in water cannot be cured by : JEE Main Online Paper (Held On 10 April 2015)

A)
Ion exchange method

B)
Treatment with washing soda

C)
Boiling

D)
Calgon's method

• question_answer33) Gaseous ${{N}_{2}}{{O}_{4}}$ dissociates into gaseous $N{{O}_{2}}$according to the reaction ${{N}_{2}}{{O}_{4}}(g)\rightleftharpoons 2N{{O}_{2}}(g)$ At 300 K and 1 atm pressure, the degree of dissociation of ${{N}_{2}}{{O}_{4}}$ is 0.2. If one mole of ${{N}_{2}}{{O}_{4}}$ gas is contained in a vessel, then the density of the equilibrium mixture is: JEE Main Online Paper (Held On 10 April 2015)

A)
3.11 g/L

B)
6.22 g/L

C)
4.56 g/L

D)
1.56 g/L

• question_answer34) Complete hydrolysis of starch gives : JEE Main Online Paper (Held On 10 April 2015)

A)
galactose and fructose in equimolar amounts

B)
glucose and fructose in equimolar  amounts

C)
glucose only

D)
glucose and galactose in equimolar amounts

• question_answer35) The correct statement on the isomerism associated with the following complex ions, ${{[Ni{{({{H}_{2}}O)}_{5}}N{{H}_{3}}]}^{2+}},$ ${{[Ni{{({{H}_{2}}O)}_{4}}{{(N{{H}_{3}})}_{2}}]}^{2+}}$and ${{[Ni{{({{H}_{2}}O)}_{3}}{{(N{{H}_{3}})}_{3}}]}^{2+}}$is: JEE Main Online Paper (Held On 10 April 2015)

A)
and  show geometrical andoptical isomerism

B)
and  show geometrical and optical isomerism

C)
and  show only geometrical isomerism

D)
and  show only geometrical isomerism

• question_answer36) The least number of oxy acids are formed by: JEE Main Online Paper (Held On 10 April 2015)

A)
Chlorine

B)
Nitrogen

C)
Fluorine

D)
Sulphur

• question_answer37) 1.4 g of an organic compound was digested according to Kjeldahl's method and the ammonia evolved was absorbed in 60 mL of $M/10\,{{H}_{2}}S{{O}_{4}}$ solution. The excess sulphuric acid required 20 mL of M/10 NaOH solution tor neutralization. The percentage of nitrogen in the compound is: JEE Main Online Paper (Held On 10 April 2015)

A)
24

B)
5

C)
10

D)
3

• question_answer38) . JEE Main Online Paper (Held On 10 April 2015)

A)
Antihistamine

B)
Antacid

C)
Insecticide

D)
Analgesic

• question_answer39) The geometry of $XeO{{F}_{4}}$ by VSEPR theory is: JEE Main Online Paper (Held On 10 April 2015)

A)
octahedral

B)
pentagonal planar

C)
square pyramidal

D)
trigonal bipyramidal

• question_answer40) Arrange the following amines in the order of increasing basicity. JEE Main Online Paper (Held On 10 April 2015)

A)

B)

C)

D)

• question_answer41) If the principal quantum number n = 6, the correct sequence of filling of electrons will be: JEE Main Online Paper (Held On 10 April 2015)

A)
$ns\to np\to (n-1)d\to (n-2)f$

B)
$ns\to (n-1)d\to (n-2)f\to np$

C)
$ns\to (n-2)f\to (n-1)d\to np$

D)
$ns\to (n-2)f\to np\to (n-1)d$

• question_answer42) The correct order of thermal stability of hydroxides is: JEE Main Online Paper (Held On 10 April 2015)

A)
$Ba{{(OH)}_{2}}<Sr{{(OH)}_{2}}<Ca{{(OH)}_{2}}<Mg{{(OH)}_{2}}$

B)
$Ba{{(OH)}_{2}}<Ca{{(OH)}_{2}}<Sr{{(OH)}_{2}}<Mg{{(OH)}_{2}}$

C)
$Mg{{(OH)}_{2}}<Sr{{(OH)}_{2}}<Ca{{(OH)}_{2}}<Ba{{(OH)}_{2}}$

D)
$Mg{{(OH)}_{2}}<Ca{{(OH)}_{2}}<Sr{{(OH)}_{2}}<Ba{{(OH)}_{2}}$

• question_answer43) A sample of a hydrate of barium chloride weighing 61 g was heated until all the water of hydration is removed. The dried sample weighed 52 g. The formula of the hydrated salt is : (atomic mass, Ba = 137 amu, Cl=35.5 amu) JEE Main Online Paper (Held On 10 April 2015)

A)
$BaC{{l}_{2}}.3{{H}_{2}}O$

B)
$BaC{{l}_{2}}.2{{H}_{2}}O$

C)
$BaC{{l}_{2}}.{{H}_{2}}O$

D)
$BaC{{l}_{2}}.4{{H}_{2}}O$

• question_answer44)  A is: JEE Main Online Paper (Held On 10 April 2015)

A)

B)

C)

D)

• question_answer45) Match the polymers in column-A with their main uses in column-B and choose the correct answer : JEE Main Online Paper (Held On 10 April 2015)  Column-A Column-B A Polystyrene (i) Paints and lacquers B Glyptal (ii) Rain coats C Polyvinyl Chloride (iii) Manufacture of toys D Bakelite (iv) Computer discs

A)
A - (ii),  B- (i),  C- (iii), D- (iv)

B)
A - (iii),  B- (iv),  C- (ii), D- (i)

C)
A - (iii),  B- (i),  C- (ii), D- (iv)

D)
A - (ii),  B- (iv),  C- (iii), D- (i)

• question_answer46) The optically inactive compound from the following is : JEE Main Online Paper (Held On 10 April 2015)

A)
2 - chlorobutane

B)
2-chloropropanal

C)
2- chloro-2-methylbutane

D)
2-chloropentanes

• question_answer47) In the long form of the periodic table, the valence shell electronic configuration of $5{{s}^{2}}5{{p}^{4}}$corresponds to the element present in: JEE Main Online Paper (Held On 10 April 2015)

A)
Group 17 and period 5

B)
Group 16 and period 5

C)
Group 17 and period 6

D)
4 Group 16 and period 6

• question_answer48) The following statements relate to the adsorption of gases on a solid surface. Identify the incorrect statement among them : JEE Main Online Paper (Held On 10 April 2015)

A)
On adsorption, the residual forces on the surface are increased

B)

C)
On adsorption decrease in surface 3 energy appears as heat

D)

• question_answer49) A variable, opposite external potential $({{E}_{ext}})$ is applied to the cell$Zn|Z{{n}^{2+}}(1M)||C{{u}^{2+}}(1M)|Cu,$potential 1.1 V. When ${{E}_{ext}}<1.1V$ and ${{E}_{ext}}>1.1V,$respectively electrons flow from : JEE Main Online Paper (Held On 10 April 2015)

A)
anode to cathode and cathode to 1 anode

B)
cathode to anode in both cases

C)
cathode to anode and anode to cathode

D)
anode to cathode in both cases

• question_answer50) An aqueous solution of a salt X turns blood red on treatment with $SC{{N}^{-}}$ and blue on treatment with ${{K}_{4}}[Fe{{(CN)}_{6}}].X$also gives a positive chromyl chloride test. The salt X is: JEE Main Online Paper (Held On 10 April 2015)

A)
$Cu{{(N{{O}_{3}})}_{2}}$

B)
$FeC{{l}_{3}}$

C)
$CuC{{l}_{2}}$

D)
$Fe{{(N{{O}_{3}})}_{3}}$

• question_answer51) photochemical smog consists of excessive amount of X, in addition to aldehydes, ketones, peroxy acetyl nitrile (PAN), and so forth- X is : JEE Main Online Paper (Held On 10 April 2015)

A)
$C{{O}_{2}}$

B)
CO

C)
$C{{H}_{4}}$

D)
${{O}_{3}}$

• question_answer52) In the presence of a small amount of phosphorous, aliphatic carboxylic acids react with chlorine or bromine to yield a compound in which $\text{ }\!\!\alpha\!\!\text{ -}$hydrogen has been replaced by halogen. This reaction is known as : JEE Main Online Paper (Held On 10 April 2015)

A)
Rosemond reaction

B)
Etard reaction

C)
Wolff - Kischner reaction

D)
Hell - Volhard - Zelinsky reaction

• question_answer53) The cation that will not be precipitated by  ${{H}_{2}}S$ in the presence of dil $HCl$is : JEE Main Online Paper (Held On 10 April 2015)

A)
$C{{u}^{2+}}$

B)
$P{{b}^{2+}}$

C)
$A{{s}^{3+}}$

D)
$C{{o}^{2+}}$

• question_answer54) Which of the following is not an assumption of the kinetic theory of gases ? JEE Main Online Paper (Held On 10 April 2015)

A)
At high pressure, gas particles are difficult to compress.

B)
A gas consists of many identical particles which are in continual motion.

C)
Collisions of gas particles are perfectly elastic.

D)
Gas particles have negligible volume.

• question_answer55) The reaction $2{{N}_{2}}{{O}_{5}}(g)\to 4N{{O}_{2}}(g)+{{O}_{2}}(g)$follows first order kinetics. The pressure of a vessel containing only ${{N}_{2}}{{O}_{5}}$ was found to increase from 50 mm Hg to 87.5 mm Hg in 30 min. The pressure exerted by the gases after 60 min. will be (Assume temperature remains constant) : JEE Main Online Paper (Held On 10 April 2015)

A)
150 mm He

B)
116.05 mm Hg

C)
106.25 mm Hg

D)
125 mm Hg

• question_answer56) A solution at $20{}^\circ C$ is composed of 1.5 mol of benzene and 3.5 mol of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are 74.7 torr and 22.3 torr, respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively : JEE Main Online Paper (Held On 10 April 2015)

A)
30.5 torr and 0.389

B)
38.0 torr and 0.589

C)
35.8 torr and 0.280

D)
4 35.0 torr and 0.480

• question_answer57) A compound A with molecular formula ${{C}_{10}}{{H}_{13}}Cl$ gives a white precipitate on adding silver nitrate solution. A on reacting with alcoholic K.OH gives compound B as the main product. B on ozonolysis gives C and D. C gives Cannizaro reaction but not aldol condensation. U gives aldol condensation but not Cannizaro reaction. A is : JEE Main Online Paper (Held On 10 April 2015)

A)

B)
${{C}_{6}}{{H}_{5}}-C{{H}_{2}}-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{3}}$

C)

D)
${{C}_{6}}{{H}_{5}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{2}}-Cl$

• question_answer58) Which molecule/ion among the following cannot act as a ligand in complex compounds? JEE Main Online Paper (Held On 10 April 2015)

A)
CO

B)
$C{{N}^{-}}$

C)
$C{{H}_{4}}$

D)
$B{{r}^{-}}$

• question_answer59) The heat of atomization of methane and ethane are 360 kJ/mol and 620 kJ/mol, respectively. The longest wavelength of light capable of breaking the C - C bond is (Avogadro number $=6.02\times {{10}^{23}},h=6.62\times {{10}^{-34}}Js$) JEE Main Online Paper (Held On 10 April 2015)

A)
$1.49\times {{10}^{3}}nm$

B)
$2.48\times {{10}^{4}}nm$

C)
$2.48\times {{10}^{3}}nm$

D)
$1.49\times {{10}^{4}}nm$

• question_answer60) After understanding the assertion and reason, choose the correct option. Assertion : In the bonding molecular orbital (MO) of ${{H}_{2}},$electron density is increased between the nuclei. Reason : The bonding MO is${{\psi }_{A}}+{{\psi }_{B'}}$which shows destructive interference of the combining electron waves. JEE Main Online Paper (Held On 10 April 2015)

A)
Assertion and reason are correct and Option reason is the correct explanation for the assertion.

B)
Assertion is incorrect, reason is correct.

C)
Assertion and reason are correct, but reason is not the correct explanation for the assertion.

D)
Assertion is correct, reason is 4 incorrect.

• question_answer61) A factory is operating in two shirts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs. 54 and per day mean wage of all the workers is Rs. 60, then per day mean wage of the night shift workers (in Rs.) is: JEE Main Online Paper (Held On 10 April 2015)

A)
74

B)
66

C)
75

D)
69

• question_answer62) If Rolle's theorem holds for the function $f(x)=2{{x}^{3}}+b{{x}^{2}}+cx,x\in [-1,1],$at the point $x=\frac{1}{2},$then 2b +c equals    JEE Main Online Paper (Held On 10 April 2015)

A)
2

B)
- 1

C)
-3

D)
1

• question_answer63) The area (in square units) of the region bounded by the curves $y+2{{x}^{2}}=0$and $y+3{{x}^{2}}=1,$is equal to : JEE Main Online Paper (Held On 10 April 2015)

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

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

C)
$\frac{3}{5}$

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

• question_answer64) The points $\left( 0,\frac{8}{3} \right),(1,3)$and (82, 30) : JEE Main Online Paper (Held On 10 April 2015)

A)
form an acute angled triangle.

B)
form a right angled triangle.

C)
form an obtuse angled triangle.

D)
lie on a straight line.

• question_answer65) The least value of the product xyz for which the determinant $\left| \begin{matrix} x & 1 & 1 \\ 1 & y & 1 \\ 1 & 1 & z \\ \end{matrix} \right|$is non-negative, is : JEE Main Online Paper (Held On 10 April 2015)

A)
$- 1$

B)
$-2\sqrt{2}$

C)
$-16\sqrt{2}$

D)
$- 8$

• question_answer66) The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is: JEE Main Online Paper (Held On 10 April 2015)

A)
1120

B)
1960

C)
1880

D)
1240

• question_answer67) If the points $(1,1\lambda )$and (-3, 0, 1) are equidistant    from    the    plane, $3x+4y-12z+13=0,$then $\lambda$ satisfies the equation : JEE Main Online Paper (Held On 10 April 2015)

A)
$3{{x}^{2}}-10x+21=0$

B)
$3{{x}^{2}}-10x+7=0$

C)
$3{{x}^{2}}+10x+7=0$

D)
$3{{x}^{2}}+10x-13=0$

• question_answer68) If $f(x)=2ta{{n}^{-1}}x+{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right),x>1,$then f(5) is equal to : JEE Main Online Paper (Held On 10 April 2015)

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

B)
$\pi$

C)
${{\tan }^{-1}}\left( \frac{65}{156} \right)$

D)
$4{{\tan }^{-1}}(5)$

• question_answer69) If $2+3i$ is one of the roots of the equation $2{{x}^{3}}-9{{x}^{2}}+kx-13=0,k\in R,$ then the real root of this equation : JEE Main Online Paper (Held On 10 April 2015)

A)
exists and is equal to 1.

B)
does not exist.

C)
exists and is equal to$\frac{1}{2}$.

D)
exists and is equal to$\frac{1}{2}$

• question_answer70) An ellipse passes through the foci of the hyperbola, $9{{x}^{2}}-4{{y}^{2}}=36$and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is$\frac{1}{2},$ then which of the following points does not lie on the ellipse? JEE Main Online Paper (Held On 10 April 2015)

A)
$(\sqrt{13},0)$

B)
$\left( \sqrt{\frac{13}{2}},\sqrt{6} \right)$

C)
$\left( \frac{1}{2}\sqrt{13},\frac{\sqrt{3}}{2} \right)$

D)
$\left( \frac{\sqrt{39}}{2},\sqrt{3} \right)$

• question_answer71) Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is : JEE Main Online Paper (Held On 10 April 2015)

A)
28

B)
31

C)
29.5

D)
26.5

• question_answer72) In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :  5% families own both a car and a phone.   35% families own either a car or a phone.    40,000 families live in the town. Then, JEE Main Online Paper (Held On 10 April 2015)

A)
only  and  are correct.

B)
Only  and  are correct.

C)
All ,  and  are correct.

D)
Only  and  are correct.

• question_answer73) For $x>0,$let $f(x)=\int\limits_{1}^{x}{\frac{\log t}{1+t}}dt.$ Then  $f(x)+f\left( \frac{1}{x} \right)$is equal to: JEE Main Online Paper (Held On 10 April 2015)

A)
$\frac{1}{4}\log {{x}^{2}}$

B)
$\frac{1}{4}{{(\log x)}^{2}}$

C)
$\frac{1}{2}{{(\log x)}^{2}}$

D)
$\log x$

• question_answer74) If the coefficients of the three successive terms in the binomial expansion of ${{(1+x)}^{n}}$are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is : JEE Main Online Paper (Held On 10 April 2015)

A)
8th

B)
6th

C)
9th

D)
7th

• question_answer75) Let $\overset{\to }{\mathop{a}}\,$ arid $\overset{\to }{\mathop{b}}\,$ be two unit vectors such that|$\left| \overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\, \right|=\sqrt{3}.$If$\overset{\to }{\mathop{c}}\,=\overset{\to }{\mathop{a}}\,+2\overset{\to }{\mathop{b}}\,+3\left( \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right),$then $2|\overset{\to }{\mathop{c}}\,|$is equal to: JEE Main Online Paper (Held On 10 April 2015)

A)
$\sqrt{51}$

B)
$\sqrt{37}$

C)
$\sqrt{43}$

D)
$\sqrt{55}$

• question_answer76) Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P. If ${{L}_{1}}$ is the line perpendicular to L and passing through the point (-2, 1),then the point of intersection of I and L JEE Main Online Paper (Held On 10 April 2015)

A)
$\left( \frac{3}{5},\frac{23}{10} \right)$

B)
$\left( \frac{11}{20},\frac{29}{10} \right)$

C)
$\left( \frac{4}{5},\frac{12}{5} \right)$

D)
$\left( \frac{3}{10},\frac{17}{5} \right)$

• question_answer77) In a $\Delta ABC,\frac{a}{b}=2+\sqrt{3}$and $\angle C={{60}^{o}}.$ Then the ordered pair $(\angle A,\angle B)$is equal to: JEE Main Online Paper (Held On 10 April 2015)

A)
$({{105}^{o}},{{15}^{o}})$

B)
$({{45}^{o}},{{75}^{o}})$

C)
$({{15}^{o}},{{105}^{o}})$

D)
$({{75}^{o}},{{45}^{o}})$

• question_answer78) Let the tangents drawn to the circle, ${{x}^{2}}+{{y}^{2}}=16$from the point P(0/ h) meet me r-axis at points A and B. If the area of $\Delta APB$is minimum, men h is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
$4\sqrt{2}$

B)
$4\sqrt{3}$

C)
$3\sqrt{2}$

D)
$3\sqrt{3}$

• question_answer79) $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{{{x}^{2}}}}-\cos x}{{{\sin }^{2}}x}$is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
3

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

C)
2

D)
$\frac{5}{4}$

• question_answer80) The value of $\sum\limits_{r=16}^{30}{(r+2)(r-3)}$is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
7785

B)
7775

C)
7780

D)
7770

• question_answer81) If $y+3x=0$ is the equation of a chord of the circle, ${{x}^{2}}+{{y}^{2}}-30x=0,$then the equation of the circle with this chord as diameter is: JEE Main Online Paper (Held On 10 April 2015)

A)
${{x}^{2}}+{{y}^{2}}+3x+9y=0$

B)
${{x}^{2}}+{{y}^{2}}-3x+9y=0$

C)
${{x}^{2}}+{{y}^{2}}-3x-9y=0$

D)
${{x}^{2}}+{{y}^{2}}+3x-9y=0$

• question_answer82) The integral $\int_{{}}^{{}}{\frac{dx}{{{(x+1)}^{\frac{3}{4}}}{{(x-2)}^{\frac{5}{4}}}}}$is equal to: JEE Main Online Paper (Held On 10 April 2015)

A)
$4{{\left( \frac{x-2}{x+1} \right)}^{\frac{1}{4}}}+C$

B)
$-\frac{4}{3}{{\left( \frac{x+1}{x-2} \right)}^{\frac{1}{4}}}+C$

C)
$4{{\left( \frac{x+1}{x-2} \right)}^{\frac{1}{4}}}+C$

D)
$-\frac{4}{3}{{\left( \frac{x-2}{x+1} \right)}^{\frac{1}{4}}}+C$

• question_answer83) The distance, from the origin, of the normal to the curve, $x=2\cos t+2t\sin t,$$y=2\sin t-2t\cos t$at$t=\frac{\pi }{4},$is: JEE Main Online Paper (Held On 10 April 2015)

A)
2

B)
$\sqrt{2}$

C)
$2\sqrt{2}$

D)
4

• question_answer84) If the shortest distance between the lines $\frac{x-1}{\alpha }=\frac{y+1}{-1}=\frac{z}{1},(\alpha \ne -1)$and$x+y+z+1=0=2x-y+z+3$is$\frac{1}{\sqrt{3}},$ a value of $\alpha$ is : JEE Main Online Paper (Held On 10 April 2015)

A)
$-\frac{16}{19}$

B)
$-\frac{19}{16}$

C)
$\frac{19}{32}$

D)
$\frac{32}{19}$

• question_answer85) If$A=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right],$ then which one of the following statements is not correct ? JEE Main Online Paper (Held On 10 April 2015)

A)
${{A}^{4}}-I={{A}^{2}}+I$

B)
${{A}^{3}}+I=A({{A}^{3}}-I)$

C)
${{A}^{3}}-I=A(A-I)$

D)
${{A}^{2}}+I=A({{A}^{2}}-I)$

• question_answer86) Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is : JEE Main Online Paper (Held On 10 April 2015)

A)
$\frac{({{2}^{10}}-1)}{{{2}^{20}}}$

B)
$\frac{({{2}^{10}}-1)}{{{2}^{10}}}$

C)
$\frac{^{20}{{C}_{10}}}{{{2}^{10}}}$

D)
$\frac{^{20}{{C}_{10}}}{{{2}^{20}}}$

• question_answer87) If the tangent to the conic,$y-6={{x}^{2}}$at (2, 10) touches the circle, ${{x}^{2}}+{{y}^{2}}+8x-2y=k$(for some fixed k) at a point $(\alpha ,\beta );$ then $(\alpha ,\beta )$is : JEE Main Online Paper (Held On 10 April 2015)

A)
$\left( -\frac{7}{17},\frac{6}{17} \right)$

B)
$\left( -\frac{8}{17},\frac{2}{17} \right)$

C)
$\left( -\frac{4}{17},\frac{1}{17} \right)$

D)
$\left( -\frac{6}{17},\frac{10}{17} \right)$

• question_answer88) The contrapositive of the statement "If it is raining, then I will not come", is : JEE Main Online Paper (Held On 10 April 2015)

A)
If I will come, then it is raining.

B)
If I will not come, then it is raining.

C)
I will come, then it is not raining.

D)
If I will not come, then it is not raining.

• question_answer89) The largest value of r for which the region represented by the set$\{\omega \in C/|\omega -4-i|\le r\}$is contained in the region represented by the set $\{z\in C/|z-1|\le |z+i|\},$is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
$2\sqrt{2}$

B)
$\sqrt{17}$

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

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

• question_answer90) If y(x) is the solution of the differential equation $(x+2)\frac{dy}{dx}={{x}^{2}}+4x-9,x\ne -2$and $y(0)=0,$then $y(-4)$ is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
-1

B)
2

C)
1

D)
0