# Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 19 April 2014)

### done JEE Main Online Paper (Held On 19 April 2014)

• question_answer1) Match List - I (Event) with List-II (Order of the time interval for happening of the event) and select the correct option from the options given below the lists:

 List - I List - II (a) Rotation period of earth (i) ${{10}^{5}}s$ (2) Revolution period of earth (ii) ${{10}^{7}}s$ (3) Period of light wave (iii) ${{10}^{-15}}s$ (4) Period of sound wave (iv) ${{10}^{-3}}s$
JEE Main Online Paper (Held On 19 April 2016)

A) (1)-(i), (2)-(ii), (3)-(iii), (4)-(iv)

B) (1)-(ii), (2)-(i), (3)-(iv), (4)-(iii)

C) (1)-(i), (2)-(ii), (3)-(iv), (4)-(iii)

D) (1)-(ii), (2)-(i), (3)-(iii), (4)-(iv)

• question_answer2) A bullet looses ${{\left( \frac{1}{n} \right)}^{th}}$of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be:     JEE Main Online Paper (Held On 19 April 2016)

A) $\frac{{{n}^{2}}}{2n-1}$

B) $\frac{2{{n}^{2}}}{n-1}$

C) infinite

D) n

• question_answer3) A heavy box is to dragged along a rough horizontal floor. To do so, person A pushes it at an angle $30{}^\circ$ from the horizontal and requires a minimum force ${{F}_{A}},$ while person B pulls the box at an angle $60{}^\circ$ from the horizontal and needs minimum force FB. If the coefficient of friction between the box and the floor is $\frac{\sqrt{3}}{5},$the ratio $\frac{{{F}_{A}}}{{{F}_{B}}}$is     JEE Main Online Paper (Held On 19 April 2016)

A) $\sqrt{3}$

B) $\frac{5}{\sqrt{3}}$

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

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

• question_answer4) Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration ?a? perpendicular to the axis of the cylinder. What is F friction at point P? It is assumed that the cylinder does not slip. JEE Main Online Paper (Held On 19 April 2016)

A) Mg

B) Ma

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

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

• question_answer5) A particle is released on a vertical smooth semicircular track from point X so that OX makes angle q from the vertical (see figure). The normal reaction of the track on the particle vanishes at point Y where OY makes angle $\phi$ with the horizontal. Then: JEE Main Online Paper (Held On 19 April 2016)

A) $\sin \phi =\cos \phi$

B) $\sin \phi =\frac{1}{2}\cos \theta$

C) $\sin \phi =\frac{2}{3}\cos \theta$

D) $\sin \phi =\frac{3}{4}\cos \theta$

• question_answer6) A ball of mass 160 g is thrown up at an angle of $60{}^\circ$ to the horizontal at a speed of $10m{{s}^{-1}}.$The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly $(g=10m{{s}^{-2}})$     JEE Main Online Paper (Held On 19 April 2016)

A) $1.73kg{{m}^{2}}/s$

B) $3.0kg{{m}^{2}}/s$

C) $3.46kg{{m}^{2}}/s$

D) $6.0kg{{m}^{2}}/s$

• question_answer7) The gravitational field in a region is given by $\overset{\to }{\mathop{g}}\,=5N/kg\hat{i}+12N/kg\hat{j}.$The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point (7 m, ? 3 m) is:     JEE Main Online Paper (Held On 19 April 2016)

A) 71 J

B) 13 58 J

C) 71 J

D) 1 J

• question_answer8) The velocity of water in a river is 18 km/h near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water $={{10}^{-2}}$ poise.    JEE Main Online Paper (Held On 19 April 2016)

A) ${{10}^{-1}}N/{{m}^{2}}$

B) ${{10}^{-2}}N/{{m}^{2}}$

C) ${{10}^{-3}}N/{{m}^{2}}$

D) ${{10}^{-4}}N/{{m}^{2}}$

• question_answer9) In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross section of the tube at A and B is $6m{{m}^{2}}$and $10m{{m}^{2}}$10 mm2 respectively. The rate at which water flows through the tube is $(g=10\,m{{s}^{-2}})$     JEE Main Online Paper (Held On 19 April 2016)

A) 7.5 cc/s

B) 8.0 cc/s

C) 10.0 cc/s

D) 12.5 cc/s

• question_answer10) A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given, surface tension of liquid T, density $\rho$)     JEE Main Online Paper (Held On 19 April 2016)

A) $\sqrt{\frac{T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}$

B) $\sqrt{\frac{2T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}$

C) $\sqrt{\frac{4T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}$

D) $\sqrt{\frac{6T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}$

• question_answer11) A black coloured solid sphere of radius R and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature ${{T}_{0}}.$ The initial temperature of the sphere is $3{{T}_{0}}.$If the specific heat of the material of the sphere varies as $\alpha {{T}^{3}}$per unit mass with the temperature T of the sphere, where $\alpha$ is a constant, then the time taken for the sphere to cool down to temperature $2{{T}_{0}}$  will be ($\sigma$is Stefan Boltzmann constant)     JEE Main Online Paper (Held On 19 April 2016)

A) $\frac{M\alpha }{4\pi {{R}^{2}}\sigma }\ln \left( \frac{3}{2} \right)$

B) $\frac{M\alpha }{4\pi {{R}^{2}}\sigma }\ln \left( \frac{16}{3} \right)$

C) $\frac{M\alpha }{16\pi {{R}^{2}}\sigma }\ln \left( \frac{16}{3} \right)$

D) $\frac{M\alpha }{16\pi {{R}^{2}}\sigma }\ln \left( \frac{3}{2} \right)$

• question_answer12) A gas is compressed from a volume of $2{{m}^{3}}$to a volume of $1{{m}^{3}}$ at a constant pressure of $100N/{{m}^{2}}.$Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas:     JEE Main Online Paper (Held On 19 April 2016)

A) increases by 250 J

B) decreases by 250 J

C) increases by 50 J

D) decreases by 50 J

• question_answer13) A gas molecule of mass M at the surface of the Earth has kinetic energy equivalent to $0{}^\circ C$. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. (${{k}_{B}}$ is Boltzmann constant).     JEE Main Online Paper (Held On 19 April 2016)

A) 0

B) $\frac{273{{k}_{B}}}{2Mg}$

C) $\frac{546{{k}_{B}}}{3Mg}$

D) $\frac{819{{k}_{B}}}{2Mg}$

• question_answer14) A body is in simple harmonic motion with time period half second (T = 0.5 s) and amplitude one cm (A = 1 cm). Find the average velocity in the interval in which it moves form equilibrium position to half of its amplitude.     JEE Main Online Paper (Held On 19 April 2016)

A) 4 cm/s

B) 6 cm/s

C) 12 cm/s

D) 16 cm/s

• question_answer15) The total length of a sonometer wire between fixed ends is 110 cm. Two bridges are placed to divide the length of wire in ratio 6 : 3 : 2. The tension in the wire is 400 N and the mass per unit length is 0.01 kg/m. What is the minimum common frequency with which three parts can vibrate?     JEE Main Online Paper (Held On 19 April 2016)

A) 1100 Hz

B) 1000 Hz

C) 166 Hz

D) 100 Hz

• question_answer16) The electric field in a region of space is given by, $\vec{E}={{E}_{o}}\hat{i}+2{{E}_{o}}\hat{j}$where ${{E}_{o}}=100N/C.$The flux of the field through a circular surface of radius 0.02 m parallel to the YZ plane is nearly:     JEE Main Online Paper (Held On 19 April 2016)

A) 0.125 Nm2/C

B) 0.02 Nm2/C

C) 0.005 Nm2/C

D) 3.14 Nm2/C

• question_answer17) The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from ${{\in }_{1}}$ at one plate to ${{\in }_{2}}$at the other. The capacitance of capacitor is:     JEE Main Online Paper (Held On 19 April 2016)

A) ${{\in }_{0}}\left( {{\in }_{1}}+{{\in }_{2}} \right)A/d$

B) ${{\in }_{0}}\left( {{\in }_{2}}+{{\in }_{1}} \right)A/2d$

C) ${{\in }_{0}}A/\left[ d/n\left( {{\in }_{2}}+{{\in }_{1}} \right) \right]$

D) ${{\in }_{0}}A/\left( {{\in }_{2}}-{{\in }_{1}} \right)A/\left[ d/n\left( {{\in }_{2}}/{{\in }_{1}} \right) \right]$

• question_answer18) Four bulbs B1, B2, B3 and B4 of 100 W each are connected to 220 V main as shown in the figure. The reading in an ideal ammeter will be:     JEE Main Online Paper (Held On 19 April 2016)

A) 0.45 A

B) 0.90 A

C) 1.35 A

D) 1.80 A

• question_answer19) A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plate of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of $10m{{s}^{-1}}$ (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is:     JEE Main Online Paper (Held On 19 April 2016)

A) 2 mV

B) 1 mV

C) 0.75 mV

D) 0.5 mV

• question_answer20) An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field ${{B}_{s}}$ inside the  superconductor will be such that:     JEE Main Online Paper (Held On 19 April 2016)

A) ${{B}_{s}}=-B$

B) ${{B}_{s}}=0$

C) ${{B}_{s}}=B$

D) ${{B}_{s}}<B$but$Bs\ne 0$

• question_answer21) Figure shows a circular area of radius R where a uniform magnetic field $\vec{B}$is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric fieldE(r)?     JEE Main Online Paper (Held On 19 April 2016)

A) B) C) D) • question_answer22) If microwaves, X rays, infrared, gamma rays, ultra-violet, radio waves and visible parts of the electromagnetic spectrum by are denoted M, X, I, G, U, R and V then which of the following is the arrangement in ascending order of wavelength ?     JEE Main Online Paper (Held On 19 April 2016)

A) R, M, I, V, U, X and G

B) M, R, V, X, U, G and I

C) G, X, U, V, I, M and R

D) I, M, R, U, V, X and G

• question_answer23) A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is  ${{\theta }_{iC}}$and Brewster's angle of incidence is ${{\theta }_{iB}},$ such that $\sin {{\theta }_{iC}}/\sin {{\theta }_{iB}}$$=\eta =1.28.$ = h = 1.28. The relative refractive index of the two media is:     JEE Main Online Paper (Held On 19 April 2016)

A) 0.2

B) 0.4

C) 0.8

D) 0.9

• question_answer24) The diameter of the objective lens of microscope makes an angle $\beta$ at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index n. Then the resolving power of the microscope     JEE Main Online Paper (Held On 19 April 2016)

A) increases with decreasing value of n

B) increases with decreasing value of $\beta$

C) increases with increasing value of $n\sin \beta$

D) increases with increasing value of$\frac{1}{n\sin 2\beta }$

• question_answer25) In a Young's double slit experiment, the distance between the two identical slits is 6.1 times larger than the slit width. Then the number of intensity maxima observed within the central maximum of the single slit diffraction pattern is:     JEE Main Online Paper (Held On 19 April 2016)

A) 3

B) 6

C) 12

D) 24

• question_answer26) Match List - I (Experiment performed) with List-II (Phenomena discovered/associated) and select the correct option from the options given below the lists:

 List -I List-II (1) Davisson and Germer experiment (i) Wave nature of electrons (2) Millikan?s oil drop experiment (ii) Charge of an electron (3) Rutherford experiment (iii) Quantization of energy levels (4) Franch-Hertz experiment (iv) Existence of nuleus
JEE Main Online Paper (Held On 19 April 2016)

A) (1)-(i), (2)-(ii), (3)-(iii), (4)-(iv)

B) (1)-(i), (2)-(ii), (3)-(iv), (4)-(iii)

C) (1)-(iii), (2)-(iv), (3)-(i), (4)-(ii)

D) (1)-(iv), (2)-(iii), (3)-(ii), (4)-(i)

• question_answer27) A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of ${{C}^{14}}$is 5730 years, then age of the wooden piece placed in the museum is approximately:     JEE Main Online Paper (Held On 19 April 2016)

A) 10439 years

B) 13094 years

C) 19039 years

D) 39049 years

• question_answer28) Given: A and B are input terminals. Logic 1 = > 5 V Logic 0 = < 1 V Which logic gate operation, the above circuit does?     JEE Main Online Paper (Held On 19 April 2016)

A) AND Gate

B) OR Gate

C) XOR Gate

D) NOR Gate

• question_answer29) Long range radio transmission is possible when the radio waves are reflected from the ionosphere. For this to happen the frequency of the radio waves must be in the range:     JEE Main Online Paper (Held On 19 April 2016)

A) 80 - 150 MHz

B) 8 - 25 MHz

C) 1 - 3 MHz

D) 150 - 1500 kHz

• question_answer30) In an experiment for determining the gravitational acceleration g of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure. What is the value of g at the place?     JEE Main Online Paper (Held On 19 April 2016)

A) $9.81m/{{s}^{2}}$

B) $9.87m/{{s}^{2}}$

C) $9.91m/{{s}^{2}}$

D) $10.0m/{{s}^{2}}$

• question_answer31) Ionization energy of gaseous Na atoms is $495.5\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}$ The lowest possible frequency of light that ionizes a sodium atom is $(h=6.626\times {{10}^{-34}}Js,{{N}_{A}}=6.022\times {{10}^{23}}mo{{l}^{-1}})$     JEE Main Online Paper (Held On 19 April 2016)

A) $7.50\times {{10}^{4}}{{s}^{-1}}$

B) $4.76\times {{10}^{14}}{{s}^{-1}}$

C) $3.15\times {{10}^{15}}{{s}^{-1}}$

D) $1.24\times {{10}^{15}}{{s}^{-1}}$

• question_answer32) Choose the correct statement with respect to the vapour pressure of a liquid among the following:     JEE Main Online Paper (Held On 19 April 2016)

A) Increases linearly with increasing temperature

B) Increases non-linearly with increasing temperature

C) Decreases linearly with increasing temperature

D) Decreases non-linearly with increasing temperature

• question_answer33) Which one of the following molecules is paramagnetic?     JEE Main Online Paper (Held On 19 April 2016)

A) ${{N}_{2}}$

B) NO

C) CO

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

• question_answer34) Zirconium phosphate $[Z{{r}_{3}}{{(P{{O}_{4}})}_{4}}]$dissociates into three zirconium cations of charge + 4 and four phosphate anions of charge ? 3. If molar solubility of zirconium phosphate is denoted by S and its solubility product by ${{K}_{sp}}$ then which of the following relationship between S and ${{K}_{sp}}$is correct?     JEE Main Online Paper (Held On 19 April 2016)

A) $S=\{{{K}_{sp}}/{{(6912)}^{1/7}}\}$

B) $S={{\{{{K}_{sp}}/144\}}^{1/7}}$

C) $S={{\{{{K}_{sp}}/6912\}}^{1/7}}$

D) $S={{\{{{K}_{sp}}/6912\}}^{7}}$

• question_answer35) For the decomposition of the compound, represented as$N{{H}_{2}}COON{{H}_{4}}(s)2N{{H}_{3}}(g)+C{{O}_{2}}(g)$ the ${{K}_{p}}=2.9\times {{10}^{-5}}at{{m}^{3}}.$ If the reaction is started with 1 mol of the compound, the total pressure at equilibrium would be :     JEE Main Online Paper (Held On 19 April 2016)

A) $1.94\times {{10}^{-2}}atm$

B) $5.82\times {{10}^{-2}}atm$

C) $7.66\times {{10}^{-2}}atm$

D) $38.8\times {{10}^{-2}}atm$

• question_answer36) For the reaction, $3A+2B\to C+D,$ the differential rate law can be written as:     JEE Main Online Paper (Held On 19 April 2016)

A) $\frac{1}{3}\frac{d\left[ A \right]}{dt}=\frac{d\left[ C \right]}{dt}=k{{\left[ A \right]}^{n}}{{\left[ B \right]}^{m}}$

B) $-\frac{d\left[ A \right]}{dt}=\frac{d\left[ C \right]}{dt}=k{{\left[ A \right]}^{n}}{{\left[ B \right]}^{m}}$

C) $+\frac{1}{3}\frac{d\left[ A \right]}{dt}=-\frac{d\left[ C \right]}{dt}=k{{\left[ A \right]}^{n}}{{\left[ B \right]}^{m}}$

D) $-\frac{1}{3}\frac{d\left[ A \right]}{dt}=\frac{d\left[ C \right]}{dt}=k{{\left[ A \right]}^{n}}{{\left[ B \right]}^{m}}$

• question_answer37) Sulphur dioxide and oxygen were allowed to diffuse through a porous partition. $20d{{m}^{3}}$of $S{{O}_{2}}$ diffuses through the porous partition in 60 seconds. The volume of ${{O}_{2}}$ in $d{{m}^{3}}$which diffuses under the similar condition in 30 seconds will be (atomic mass of sulphur = 32 u):     JEE Main Online Paper (Held On 19 April 2016)

A) 7.09

B) 14.1

C) 10.0

D) 28.2

• question_answer38) The observed osmotic pressure for a 0.10 M solution of $Fe{{(N{{H}_{4}})}_{2}}{{(S{{O}_{4}})}_{2}}$at 25°C is 10.8 atm. The expected and experimental (observed) values of van?t Hoff factor (i) will be respectively: $(R=0.082Lamt\,{{k}^{-1}}mo{{l}^{-1}})$     JEE Main Online Paper (Held On 19 April 2016)

A) 5 and 4.42

B) 4 and 4.00

C) 5 and 3.42

D) 3 and 5.42

• question_answer39) The total number of octahedral void (s) per atom present in a cubic close packed structure is:     JEE Main Online Paper (Held On 19 April 2016)

A) 2

B) 4

C) 1

D) 3

• question_answer40) For an ideal solution of two components A and B, which of the following is true?     JEE Main Online Paper (Held On 19 April 2016)

A) $\Delta {{H}_{mixing}}<0$ (zero)

B) $\Delta {{H}_{mixing}}>0$ (zero)

C) A - B interaction is stronger than A - A and B - B interactions

D) A - A, B - B and A - B interactions are identical.

• question_answer41) Consider the reaction: ${{H}_{2}}S{{O}_{3}}(aq)+S{{n}^{4+}}(aq)+{{H}_{2}}O(l)$ $\to S{{n}^{2+}}(aq)+HSO_{4}^{-}(aq)+3{{H}^{+}}(aq)$ Which of the following statements is correct?     JEE Main Online Paper (Held On 19 April 2016)

A) $S{{n}^{4+}}$is the oxidizing agent because it undergoes oxidation

B) $S{{n}^{4+}}$is the reducing agent because it undergoes oxidation

C) ${{H}_{2}}S{{O}_{3}}$is the reducing agent because it undergoes oxidation

D) ${{H}_{2}}S{{O}_{3}}$is the reducing agent because it undergoes reduction

• question_answer42) Which one of the following has largest ionic radius?     JEE Main Online Paper (Held On 19 April 2016)

A) $L{{i}^{+}}$

B) $O_{2}^{2-}$

C) ${{B}^{3+}}$

D) ${{F}^{-}}$

• question_answer43) An octahedral complex with molecular composition $N{{H}_{3}}.Cl.S{{O}_{4}}$has two isomers, A and B. The solution of A gives a white precipitate with $AgN{{O}_{3}}$ solution and the solution of B gives white precipitate with $BaC{{l}_{2}}$ solution. The type of isomerism exhibited by the complex is:     JEE Main Online Paper (Held On 19 April 2016)

B) Ionisation isomerism

C) Coordinate isomerism

D) Geometrical isomerism

• question_answer44) How many electrons are involved in the following redox reaction? $C{{r}_{2}}O_{7}^{2-}+F{{e}^{2+}}+{{C}_{2}}O_{4}^{2-}$$\to C{{r}^{3+}}+F{{e}^{3+}}+C{{O}_{2}}$(Unbalanced)     JEE Main Online Paper (Held On 19 April 2016)

A) 3

B) 4

C) 6

D) 5

• question_answer45) Amongst $LiCl,RbCl,BeC{{l}_{2}}$ and $MgC{{l}_{2}}$ the compounds with the greatest and the least ionic character, respectively are:     JEE Main Online Paper (Held On 19 April 2016)

A) LiCl and RbCl

B) RbCl and $BeC{{l}_{2}}$

C) $MgC{{l}_{2}}$ and $BeC{{l}_{2}}$

D) RbCl and $MgC{{l}_{2}}$

• question_answer46) Nickel (Z = 28) combines with a uninegative monodentate ligand to form a diamagnetic complex ${{[Ni{{L}_{4}}]}^{2-}}.$The hybridisation involved and the number of unpaired electrons present in the complex are respectively:   JEE Main Online Paper (Held On 19 April 2016)

A) $s{{p}^{3}},$ two

B) $ds{{p}^{2}},$zero

C) $ds{{p}^{2}},$one

D) $s{{p}^{3}},$zero

• question_answer47) Which of these statements is not true?     JEE Main Online Paper (Held On 19 April 2016)

A) $N{{O}^{+}}$is not isoelectronic with${{O}_{2}}$

B) B is always covalent in its compounds

C) In aqueous solution, the $T{{l}^{+}}$ ion is much more stable than Tl (III)

D) $LiAl{{H}_{4}}$is a versatile reducing agent in organic synthesis.

• question_answer48) Example of a three-dimensional silicate is:     JEE Main Online Paper (Held On 19 April 2016)

A) Zeolites

B) Ultramarines

C) Feldspars

D) Beryls

• question_answer49) Amongst the following, identify the species with an atom in + 6 oxidation state:     JEE Main Online Paper (Held On 19 April 2016)

A) ${{[Mn{{O}_{4}}]}^{-}}$

B) ${{[Cr{{(CN)}_{6}}]}^{3-}}$

C) $C{{r}_{2}}{{O}_{3}}$

D) $Cr{{O}_{2}}C{{l}_{2}}$

• question_answer50) Which one of the following ores is known as Malachite:     JEE Main Online Paper (Held On 19 April 2016)

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

B) $C{{u}_{2}}S$

C) $CuFe{{S}_{2}}$

D) $Cu{{(OH)}_{2}}.CuC{{O}_{3}}$

• question_answer51) The major product formed when 1, 1, 1-trichloro-propane is treated with aqueous potassium hydroxide is:     JEE Main Online Paper (Held On 19 April 2016)

A) Propyne

B) 1-Propanol

C) 2-Propanol

D) Propionic acid

• question_answer52) Which one of the following is an example of thermosetting polymers?     JEE Main Online Paper (Held On 19 April 2016)

A) Neoprene

B) Buna-N

C) Nylon 6, 6

D) Bakelite

• question_answer53) The correct IUPAC name of the following compound is: JEE Main Online Paper (Held On 19 April 2016)

A) 4 - methyl - 3 - ethylhexane

B) 3 - ethyl - 4 - methylhexane

C) 3, 4 - ethylmethylhexane

D) 4 - ethyl - 3 - methylhexane

• question_answer54) Which one of the following substituents at para-position is most effective in stabilizing the phenoxide O - ion? JEE Main Online Paper (Held On 19 April 2016)

A) $-C{{H}_{3}}$

B) $-OC{{H}_{3}}$

C) $-COC{{H}_{3}}$

D) $-C{{H}_{2}}OH$

• question_answer55) The final product formed when Methyl amine is treated with $NaN{{O}_{2}}$ and HCl is:     JEE Main Online Paper (Held On 19 April 2016)

A) Diazomethane

B)  Methylalcohol

C) Methylcyanide

D) Nitromethane

• question_answer56) Which one of the following compounds will not be soluble in sodium bicarbonate?     JEE Main Online Paper (Held On 19 April 2016)

A) 2, 4, 6 - Trinitrophenol

B) Benzoic acid

C) o-Nitrophenol

D) Benzene sulphonic acid

• question_answer57) Williamson synthesis of ether is an example of:     JEE Main Online Paper (Held On 19 April 2016)

C) Electrophilic substitution

D) Nucleophilic substitution

• question_answer58) The reason for double helical structure of DNA is the operation of:     JEE Main Online Paper (Held On 19 April 2016)

A) Electrostatic attractions

B) van der Waals forces

C) Dipole - Dipole interactions

D) Hydrogen bonding

• question_answer59) Among the following organic acids, the acid present in rancid butter is:     JEE Main Online Paper (Held On 19 April 2016)

A) Pyruvic acid

B) Lactic acid

C) Butyric acid

D) Acetic acid

• question_answer60) In a set of reactions p-nitrotoluene yielded a product E. $\xrightarrow[HCl]{NaN{{O}_{2}}}D\xrightarrow[HBr]{CuBr}E$ The product E would be:     JEE Main Online Paper (Held On 19 April 2016)

A) B) C) D) • question_answer61) Let $f:R\to R$be defined by $f(x)=\frac{\left| x \right|-1}{\left| x \right|+1}$then f is:     JEE Main Online Paper (Held On 19 April 2016)

A) both one-one and onto

B) one-one but not onto

C) onto but not one-one

D) neither one-one nor onto.

• question_answer62) For all complex numbers z of the form $1+i\alpha ,\alpha \in R,$if ${{z}^{2}}=x+iy,$then     JEE Main Online Paper (Held On 19 April 2016)

A) ${{y}^{2}}-4x+2=0$

B) ${{y}^{2}}+4x-4=0$

C) ${{y}^{2}}-4x-4=0$

D) ${{y}^{2}}+4x+2=0$

• question_answer63) The equation $\sqrt{3{{x}^{2}}+x+5}x-3,$where x is real, has;     JEE Main Online Paper (Held On 19 April 2016)

A) no solution

B) exactly one solution

C) exactly two solution

D) exactly four solution

• question_answer64) Let A and B be any two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB - BA is:     JEE Main Online Paper (Held On 19 April 2016)

A) skewsymmetric

B) Symmetric

C)  neither symmetric nor skewsymmetric

D) I or - I, where I is an identity matrix.

• question_answer65) If $\Delta r=\left| \begin{matrix} r & 2r-1 & 3r-2 \\ \frac{n}{2} & n-1 & a \\ \frac{1}{2}n(n-1) & {{(n-1)}^{2}} & \frac{1}{2}(n-1)(3n-4) \\ \end{matrix} \right|$then the value of$\sum\limits_{r=1}^{n-1}{{{\Delta }_{r}}}$     JEE Main Online Paper (Held On 19 April 2016)

A) depends only on a

B) depends only on n

C) depends both on a and n

D) is independent of both a and n

• question_answer66) Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval:     JEE Main Online Paper (Held On 19 April 2016)

A) [8, 9]

B) [10, 12)

C) (11, 13]

D) (14, 17)

• question_answer67) The coefficient of ${{x}^{1012}}$in the expansion of ${{(1+{{x}^{n}}+{{x}^{253}})}^{10}},$ (where $n\le 22$is any positive integer), is     JEE Main Online Paper (Held On 19 April 2016)

A) 1

B) $^{10}{{C}_{4}}$

C) 4n

D) $^{253}{{C}_{4}}$

• question_answer68) The number of terms in an A.P. is even; the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by $10\frac{1}{2},$ then the number of terms in the A.P. is:     JEE Main Online Paper (Held On 19 April 2016)

A) 4

B) 8

C) 12

D) 16

• question_answer69) Let $f(n)=\left[ \frac{1}{3}+\frac{3n}{100} \right]n,$ where [n] denotes the greatest integer less than or equal to n. Then $\sum\limits_{n=1}^{56}{f\left( n \right)}$is equal to:     JEE Main Online Paper (Held On 19 April 2016)

A) 56

B) 689

C) 1287

D) 1399

• question_answer70) If the function$f\left( x \right)=\left\{ \begin{matrix} \frac{\sqrt{2+\cos x}-1}{{{\left( \pi -x \right)}^{2}}}, & x\ne \pi \\ k & ,x=\pi \\ \end{matrix} \right.$is continuous at $x=\pi ,$ then k equals:     JEE Main Online Paper (Held On 19 April 2016)

A) 0

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

C) 2

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

• question_answer71) Let $f:R\to R$be a function such that $\left| f\left( x \right) \right|\le {{x}^{2}},$for all $x\in R.$Then, at x = 0, f is:     JEE Main Online Paper (Held On 19 April 2016)

A) continuous but not differentiable.

B) continuous as well as differentiable.

C) neither continuous nor differentiable.

D) differentiable but not continuous.

• question_answer72) If non-zero real numbers b and c are such that min $f(x)>\max g(x)$ where $f(x)={{x}^{2}}+2bx+2{{c}^{2}}$and $g(x)=-{{x}^{2}}-2cx+{{b}^{2}}$$(x\in R);$ then$\left| \frac{c}{b} \right|$lies in the interval:     JEE Main Online Paper (Held On 19 April 2016)

A) $\left( 0,\frac{1}{2} \right)$

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

C) $\left[ \frac{1}{\sqrt{2},}\sqrt{2} \right]$

D) $\left( \sqrt{2},\infty \right)$

• question_answer73) If the volume of a spherical ball is increasing at the rate of $4\pi cc/\sec ,$then the rate of increase of its radius (in cm/sec), when the volume is $288\pi cc,$     JEE Main Online Paper (Held On 19 April 2016)

A) $\frac{1}{6}$

B) $\frac{1}{9}$

C) $\frac{1}{36}$

D) $\frac{1}{24}$

• question_answer74) If m is a non-zero number and $\int_{{}}^{{}}{\frac{{{x}^{5m-1}}+2{{x}^{4m-1}}}{{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{3}}}}dx=f(x)+c,$then f(x) is:     JEE Main Online Paper (Held On 19 April 2016)

A) $\frac{{{x}^{5m}}}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}$

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

C) $\frac{2m\left( {{x}^{5m}}+{{x}^{4m}} \right)}{{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}$

D) $\frac{\left( {{x}^{5m}}-{{x}^{4m}} \right)}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}$

• question_answer75) Let function F be defined as$F(x)=\int\limits_{1}^{x}{\frac{{{e}^{t}}}{t}}dt,x>0$then the value of the integral$\int\limits_{1}^{x}{\frac{{{e}^{t}}}{t+a}}dt,$where a > 0, is:     JEE Main Online Paper (Held On 19 April 2016)

A) ${{e}^{a}}\left[ F(x)-F(1+a) \right]$

B) ${{e}^{-a}}\left[ F(x+a)-F(a) \right]$

C) ${{e}^{a}}\left[ F(x+a)-F(1+a) \right]$

D) ${{e}^{-a}}\left[ F(x+a)-F(1+a) \right]$

• question_answer76) The area of the region above the x-axis bounded by the curve $y=\tan x,0\le x\le \frac{\pi }{2}$and the tangent to the curve at $x=\frac{\pi }{4}$ is:     JEE Main Online Paper (Held On 19 April 2016)

A) $\frac{1}{2}\left( \log 2-\frac{1}{2} \right)$

B) $\frac{1}{2}\left( \log 2+\frac{1}{2} \right)$

C) $\frac{1}{2}\left( 1-\log 2 \right)$

D) $\frac{1}{2}\left( 1+\log 2 \right)$

• question_answer77) If$\frac{dy}{dx}+y\tan x=\sin 2x$and$y(0)=1,$then$y(\pi )$ then y(p) is equal to:     JEE Main Online Paper (Held On 19 April 2016)

A) 1

B) -1

C) -5

D) 5

• question_answer78) The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points $({{a}^{2}}+1,{{a}^{2}}+1)$and $(2a,-2a),a\ne 0.$Then for any a, the orthocentre of this triangle lies on the line:     JEE Main Online Paper (Held On 19 April 2016)

A) $y-2ax=0$

B) $y-({{a}^{2}}+1)x=0$

C) $y+x=0$

D) ${{(a-1)}^{2}}x-{{(a+1)}^{2}}y=0$

• question_answer79) If a line L is perpendicular to the line $5x-y=1$, and the area of the triangle formed by the line L and the coordinate axes is 5, then the distance of line L from the line $x+5y=0$ is:     JEE Main Online Paper (Held On 19 April 2016)

A) $\frac{7}{\sqrt{5}}$

B) $\frac{5}{\sqrt{13}}$

C) $\frac{7}{\sqrt{13}}$

D) $\frac{5}{\sqrt{7}}$

• question_answer80) The equation of circle described on the chord $3x+y+5=0$of the circle ${{x}^{2}}+{{y}^{2}}=16$as diameter is:     JEE Main Online Paper (Held On 19 April 2016)

A) ${{x}^{2}}+{{y}^{2}}+3x+y-11=0$

B) ${{x}^{2}}+{{y}^{2}}+3x+y+1=0$

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

D) ${{x}^{2}}+{{y}^{2}}+3x+y-22=0$

• question_answer81) A chord is drawn through the focus of the parabola ${{y}^{2}}=6x$such that its distance from the vertex of this parabola is $\frac{\sqrt{5}}{2},$then its slope can be:     JEE Main Online Paper (Held On 19 April 2016)

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

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

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

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

• question_answer82) The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola $\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{5}=1,$ meet x-axis and y-axis at A and B respectively. Then ${{(OA)}^{2}}-{{(OB)}^{2}},$where O is the origin, equals:     JEE Main Online Paper (Held On 19 April 2016)

A) $-\frac{20}{9}$

B) $\frac{19}{9}$

C) 4

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

• question_answer83) Equation of the line of the shortest distance between the lines $\frac{x}{1}=\frac{y}{-1}=\frac{z}{1}$and $\frac{x-1}{0}=\frac{y+1}{-2}=\frac{z}{1}$is:     JEE Main Online Paper (Held On 19 April 2016)

A) $\frac{x}{1}=\frac{y}{-1}=\frac{z}{-2}$

B) $\frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{-2}$

C) $\frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{1}$

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

• question_answer84) If the angle between the line and the plane is then the value of is:     JEE Main Online Paper (Held On 19 April 2016)

A) B) C) D) • question_answer85) If and then the magnitude of the projection of on is:     JEE Main Online Paper (Held On 19 April 2016)

A) 12

B) 15

C) 14

D) 13

• question_answer86) Let A and E be any two events with positive probabilities: Statement - 1: Statement ? 2: JEE Main Online Paper (Held On 19 April 2016)

A) Both the statements are true

B) Both the statements are false

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

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

• question_answer87) Let and be respectively the mean, mode and variance of n observations and where   is any number. Statement I: Variance of is Statement II: Mean and mode of are and ? M ? a, respectively.     JEE Main Online Paper (Held On 19 April 2016)

A) Statement I and Statement II are both false

B) Statement I and Statement II are both true

C) Statement I is true and Statement II is false

D) Statement I is false and Statement II is true

• question_answer88) The function is a periodic function with period:     JEE Main Online Paper (Held On 19 April 2016)

A) B) C) D) • question_answer89) The principal value of is:     JEE Main Online Paper (Held On 19 April 2016)

A) B) C) D) • question_answer90) The contrapositive of the statement 'if I am not feeling well, then I will go to the doctor' is     JEE Main Online Paper (Held On 19 April 2016)

A) If I am feeling well, then I will not go to the doctor

B) If I will go to the doctor, then I am feeling well

C) If I will not go to the doctor, then I am feeling well

D) If I will go to the doctor, then I am not feeling well.

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