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) \[{{10}^{-3}}s\] |
A) (1)-(i), (2)-(ii), (3)-(iii), (4)-(iv) done clear
B) (1)-(ii), (2)-(i), (3)-(iv), (4)-(iii) done clear
C) (1)-(i), (2)-(ii), (3)-(iv), (4)-(iii) done clear
D) (1)-(ii), (2)-(i), (3)-(iii), (4)-(iv) done clear
View Answer play_arrowquestion_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) \[\frac{{{n}^{2}}}{2n-1}\] done clear
B) \[\frac{2{{n}^{2}}}{n-1}\] done clear
C) infinite done clear
D) n done clear
View Answer play_arrowquestion_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) \[\sqrt{3}\] done clear
B) \[\frac{5}{\sqrt{3}}\] done clear
C) \[\sqrt{\frac{3}{2}}\] done clear
D) \[\frac{2}{\sqrt{3}}\] done clear
View Answer play_arrowquestion_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 done clear
B) Ma done clear
C) \[\frac{Ma}{2}\] done clear
D) \[\frac{Ma}{3}\] done clear
View Answer play_arrowquestion_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) \[\sin \phi =\cos \phi \] done clear
B) \[\sin \phi =\frac{1}{2}\cos \theta \] done clear
C) \[\sin \phi =\frac{2}{3}\cos \theta \] done clear
D) \[\sin \phi =\frac{3}{4}\cos \theta \] done clear
View Answer play_arrowquestion_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) \[1.73kg{{m}^{2}}/s\] done clear
B) \[3.0kg{{m}^{2}}/s\] done clear
C) \[3.46kg{{m}^{2}}/s\] done clear
D) \[6.0kg{{m}^{2}}/s\] done clear
View Answer play_arrowquestion_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 done clear
B) 13 58 J done clear
C) 71 J done clear
D) 1 J done clear
View Answer play_arrowquestion_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) \[{{10}^{-1}}N/{{m}^{2}}\] done clear
B) \[{{10}^{-2}}N/{{m}^{2}}\] done clear
C) \[{{10}^{-3}}N/{{m}^{2}}\] done clear
D) \[{{10}^{-4}}N/{{m}^{2}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 8.0 cc/s done clear
C) 10.0 cc/s done clear
D) 12.5 cc/s done clear
View Answer play_arrowquestion_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) \[\sqrt{\frac{T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}\] done clear
B) \[\sqrt{\frac{2T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}\] done clear
C) \[\sqrt{\frac{4T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}\] done clear
D) \[\sqrt{\frac{6T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}\] done clear
View Answer play_arrowquestion_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) \[\frac{M\alpha }{4\pi {{R}^{2}}\sigma }\ln \left( \frac{3}{2} \right)\] done clear
B) \[\frac{M\alpha }{4\pi {{R}^{2}}\sigma }\ln \left( \frac{16}{3} \right)\] done clear
C) \[\frac{M\alpha }{16\pi {{R}^{2}}\sigma }\ln \left( \frac{16}{3} \right)\] done clear
D) \[\frac{M\alpha }{16\pi {{R}^{2}}\sigma }\ln \left( \frac{3}{2} \right)\] done clear
View Answer play_arrowquestion_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 done clear
B) decreases by 250 J done clear
C) increases by 50 J done clear
D) decreases by 50 J done clear
View Answer play_arrowquestion_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 done clear
B) \[\frac{273{{k}_{B}}}{2Mg}\] done clear
C) \[\frac{546{{k}_{B}}}{3Mg}\] done clear
D) \[\frac{819{{k}_{B}}}{2Mg}\] done clear
View Answer play_arrowquestion_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 done clear
B) 6 cm/s done clear
C) 12 cm/s done clear
D) 16 cm/s done clear
View Answer play_arrowquestion_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 done clear
B) 1000 Hz done clear
C) 166 Hz done clear
D) 100 Hz done clear
View Answer play_arrowquestion_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 done clear
B) 0.02 Nm2/C done clear
C) 0.005 Nm2/C done clear
D) 3.14 Nm2/C done clear
View Answer play_arrowquestion_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) \[{{\in }_{0}}\left( {{\in }_{1}}+{{\in }_{2}} \right)A/d\] done clear
B) \[{{\in }_{0}}\left( {{\in }_{2}}+{{\in }_{1}} \right)A/2d\] done clear
C) \[{{\in }_{0}}A/\left[ d/n\left( {{\in }_{2}}+{{\in }_{1}} \right) \right]\] done clear
D) \[{{\in }_{0}}A/\left( {{\in }_{2}}-{{\in }_{1}} \right)A/\left[ d/n\left( {{\in }_{2}}/{{\in }_{1}} \right) \right]\] done clear
View Answer play_arrowquestion_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 done clear
B) 0.90 A done clear
C) 1.35 A done clear
D) 1.80 A done clear
View Answer play_arrowquestion_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 done clear
B) 1 mV done clear
C) 0.75 mV done clear
D) 0.5 mV done clear
View Answer play_arrowquestion_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) \[{{B}_{s}}=-B\] done clear
B) \[{{B}_{s}}=0\] done clear
C) \[{{B}_{s}}=B\] done clear
D) \[{{B}_{s}}<B\]but\[Bs\ne 0\] done clear
View Answer play_arrowquestion_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) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_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 done clear
B) M, R, V, X, U, G and I done clear
C) G, X, U, V, I, M and R done clear
D) I, M, R, U, V, X and G done clear
View Answer play_arrowquestion_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 done clear
B) 0.4 done clear
C) 0.8 done clear
D) 0.9 done clear
View Answer play_arrowquestion_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 done clear
B) increases with decreasing value of \[\beta \] done clear
C) increases with increasing value of \[n\sin \beta \] done clear
D) increases with increasing value of\[\frac{1}{n\sin 2\beta }\] done clear
View Answer play_arrowquestion_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 done clear
B) 6 done clear
C) 12 done clear
D) 24 done clear
View Answer play_arrowquestion_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 |
A) (1)-(i), (2)-(ii), (3)-(iii), (4)-(iv) done clear
B) (1)-(i), (2)-(ii), (3)-(iv), (4)-(iii) done clear
C) (1)-(iii), (2)-(iv), (3)-(i), (4)-(ii) done clear
D) (1)-(iv), (2)-(iii), (3)-(ii), (4)-(i) done clear
View Answer play_arrowquestion_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 done clear
B) 13094 years done clear
C) 19039 years done clear
D) 39049 years done clear
View Answer play_arrowquestion_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 done clear
B) OR Gate done clear
C) XOR Gate done clear
D) NOR Gate done clear
View Answer play_arrowquestion_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 done clear
B) 8 - 25 MHz done clear
C) 1 - 3 MHz done clear
D) 150 - 1500 kHz done clear
View Answer play_arrowquestion_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) \[9.81m/{{s}^{2}}\] done clear
B) \[9.87m/{{s}^{2}}\] done clear
C) \[9.91m/{{s}^{2}}\] done clear
D) \[10.0m/{{s}^{2}}\] done clear
View Answer play_arrowquestion_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) \[7.50\times {{10}^{4}}{{s}^{-1}}\] done clear
B) \[4.76\times {{10}^{14}}{{s}^{-1}}\] done clear
C) \[3.15\times {{10}^{15}}{{s}^{-1}}\] done clear
D) \[1.24\times {{10}^{15}}{{s}^{-1}}\] done clear
View Answer play_arrowquestion_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 done clear
B) Increases non-linearly with increasing temperature done clear
C) Decreases linearly with increasing temperature done clear
D) Decreases non-linearly with increasing temperature done clear
View Answer play_arrowquestion_answer33) Which one of the following molecules is paramagnetic? JEE Main Online Paper (Held On 19 April 2016)
A) \[{{N}_{2}}\] done clear
B) NO done clear
C) CO done clear
D) \[{{O}_{3}}\] done clear
View Answer play_arrowquestion_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) \[S=\{{{K}_{sp}}/{{(6912)}^{1/7}}\}\] done clear
B) \[S={{\{{{K}_{sp}}/144\}}^{1/7}}\] done clear
C) \[S={{\{{{K}_{sp}}/6912\}}^{1/7}}\] done clear
D) \[S={{\{{{K}_{sp}}/6912\}}^{7}}\] done clear
View Answer play_arrowquestion_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) \[1.94\times {{10}^{-2}}atm\] done clear
B) \[5.82\times {{10}^{-2}}atm\] done clear
C) \[7.66\times {{10}^{-2}}atm\] done clear
D) \[38.8\times {{10}^{-2}}atm\] done clear
View Answer play_arrowquestion_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) \[\frac{1}{3}\frac{d\left[ A \right]}{dt}=\frac{d\left[ C \right]}{dt}=k{{\left[ A \right]}^{n}}{{\left[ B \right]}^{m}}\] done clear
B) \[-\frac{d\left[ A \right]}{dt}=\frac{d\left[ C \right]}{dt}=k{{\left[ A \right]}^{n}}{{\left[ B \right]}^{m}}\] done clear
C) \[+\frac{1}{3}\frac{d\left[ A \right]}{dt}=-\frac{d\left[ C \right]}{dt}=k{{\left[ A \right]}^{n}}{{\left[ B \right]}^{m}}\] done clear
D) \[-\frac{1}{3}\frac{d\left[ A \right]}{dt}=\frac{d\left[ C \right]}{dt}=k{{\left[ A \right]}^{n}}{{\left[ B \right]}^{m}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 14.1 done clear
C) 10.0 done clear
D) 28.2 done clear
View Answer play_arrowquestion_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 done clear
B) 4 and 4.00 done clear
C) 5 and 3.42 done clear
D) 3 and 5.42 done clear
View Answer play_arrowquestion_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 done clear
B) 4 done clear
C) 1 done clear
D) 3 done clear
View Answer play_arrowquestion_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) done clear
B) \[\Delta {{H}_{mixing}}>0\] (zero) done clear
C) A - B interaction is stronger than A - A and B - B interactions done clear
D) A - A, B - B and A - B interactions are identical. done clear
View Answer play_arrowquestion_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 done clear
B) \[S{{n}^{4+}}\]is the reducing agent because it undergoes oxidation done clear
C) \[{{H}_{2}}S{{O}_{3}}\]is the reducing agent because it undergoes oxidation done clear
D) \[{{H}_{2}}S{{O}_{3}}\]is the reducing agent because it undergoes reduction done clear
View Answer play_arrowquestion_answer42) Which one of the following has largest ionic radius? JEE Main Online Paper (Held On 19 April 2016)
A) \[L{{i}^{+}}\] done clear
B) \[O_{2}^{2-}\] done clear
C) \[{{B}^{3+}}\] done clear
D) \[{{F}^{-}}\] done clear
View Answer play_arrowquestion_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)
A) Linkage isomerism done clear
B) Ionisation isomerism done clear
C) Coordinate isomerism done clear
D) Geometrical isomerism done clear
View Answer play_arrowquestion_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 done clear
B) 4 done clear
C) 6 done clear
D) 5 done clear
View Answer play_arrowquestion_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 done clear
B) RbCl and \[BeC{{l}_{2}}\] done clear
C) \[MgC{{l}_{2}}\] and \[BeC{{l}_{2}}\] done clear
D) RbCl and \[MgC{{l}_{2}}\] done clear
View Answer play_arrowquestion_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 done clear
B) \[ds{{p}^{2}},\]zero done clear
C) \[ds{{p}^{2}},\]one done clear
D) \[s{{p}^{3}},\]zero done clear
View Answer play_arrowquestion_answer47) Which of these statements is not true? JEE Main Online Paper (Held On 19 April 2016)
A) \[N{{O}^{+}}\]is not isoelectronic with\[{{O}_{2}}\] done clear
B) B is always covalent in its compounds done clear
C) In aqueous solution, the \[T{{l}^{+}}\] ion is much more stable than Tl (III) done clear
D) \[LiAl{{H}_{4}}\]is a versatile reducing agent in organic synthesis. done clear
View Answer play_arrowquestion_answer48) Example of a three-dimensional silicate is: JEE Main Online Paper (Held On 19 April 2016)
A) Zeolites done clear
B) Ultramarines done clear
C) Feldspars done clear
D) Beryls done clear
View Answer play_arrowquestion_answer49) Amongst the following, identify the species with an atom in + 6 oxidation state: JEE Main Online Paper (Held On 19 April 2016)
A) \[{{[Mn{{O}_{4}}]}^{-}}\] done clear
B) \[{{[Cr{{(CN)}_{6}}]}^{3-}}\] done clear
C) \[C{{r}_{2}}{{O}_{3}}\] done clear
D) \[Cr{{O}_{2}}C{{l}_{2}}\] done clear
View Answer play_arrowquestion_answer50) Which one of the following ores is known as Malachite: JEE Main Online Paper (Held On 19 April 2016)
A) \[C{{u}_{2}}O\] done clear
B) \[C{{u}_{2}}S\] done clear
C) \[CuFe{{S}_{2}}\] done clear
D) \[Cu{{(OH)}_{2}}.CuC{{O}_{3}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 1-Propanol done clear
C) 2-Propanol done clear
D) Propionic acid done clear
View Answer play_arrowquestion_answer52) Which one of the following is an example of thermosetting polymers? JEE Main Online Paper (Held On 19 April 2016)
A) Neoprene done clear
B) Buna-N done clear
C) Nylon 6, 6 done clear
D) Bakelite done clear
View Answer play_arrowquestion_answer53) The correct IUPAC name of the following compound is: JEE Main Online Paper (Held On 19 April 2016)
A) 4 - methyl - 3 - ethylhexane done clear
B) 3 - ethyl - 4 - methylhexane done clear
C) 3, 4 - ethylmethylhexane done clear
D) 4 - ethyl - 3 - methylhexane done clear
View Answer play_arrowquestion_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) \[-C{{H}_{3}}\] done clear
B) \[-OC{{H}_{3}}\] done clear
C) \[-COC{{H}_{3}}\] done clear
D) \[-C{{H}_{2}}OH\] done clear
View Answer play_arrowquestion_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 done clear
B) Methylalcohol done clear
C) Methylcyanide done clear
D) Nitromethane done clear
View Answer play_arrowquestion_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 done clear
B) Benzoic acid done clear
C) o-Nitrophenol done clear
D) Benzene sulphonic acid done clear
View Answer play_arrowquestion_answer57) Williamson synthesis of ether is an example of: JEE Main Online Paper (Held On 19 April 2016)
A) Nucleophilic addition done clear
B) Electrophilic addition done clear
C) Electrophilic substitution done clear
D) Nucleophilic substitution done clear
View Answer play_arrowquestion_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 done clear
B) van der Waals forces done clear
C) Dipole - Dipole interactions done clear
D) Hydrogen bonding done clear
View Answer play_arrowquestion_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 done clear
B) Lactic acid done clear
C) Butyric acid done clear
D) Acetic acid done clear
View Answer play_arrowquestion_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) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_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 done clear
B) one-one but not onto done clear
C) onto but not one-one done clear
D) neither one-one nor onto. done clear
View Answer play_arrowquestion_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) \[{{y}^{2}}-4x+2=0\] done clear
B) \[{{y}^{2}}+4x-4=0\] done clear
C) \[{{y}^{2}}-4x-4=0\] done clear
D) \[{{y}^{2}}+4x+2=0\] done clear
View Answer play_arrowquestion_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 done clear
B) exactly one solution done clear
C) exactly two solution done clear
D) exactly four solution done clear
View Answer play_arrowquestion_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 done clear
B) Symmetric done clear
C) neither symmetric nor skewsymmetric done clear
D) I or - I, where I is an identity matrix. done clear
View Answer play_arrowquestion_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 done clear
B) depends only on n done clear
C) depends both on a and n done clear
D) is independent of both a and n done clear
View Answer play_arrowquestion_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] done clear
B) [10, 12) done clear
C) (11, 13] done clear
D) (14, 17) done clear
View Answer play_arrowquestion_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 done clear
B) \[^{10}{{C}_{4}}\] done clear
C) 4n done clear
D) \[^{253}{{C}_{4}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 8 done clear
C) 12 done clear
D) 16 done clear
View Answer play_arrowquestion_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 done clear
B) 689 done clear
C) 1287 done clear
D) 1399 done clear
View Answer play_arrowquestion_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 done clear
B) \[\frac{1}{2}\] done clear
C) 2 done clear
D) \[\frac{1}{4}\] done clear
View Answer play_arrowquestion_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. done clear
B) continuous as well as differentiable. done clear
C) neither continuous nor differentiable. done clear
D) differentiable but not continuous. done clear
View Answer play_arrowquestion_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) \[\left( 0,\frac{1}{2} \right)\] done clear
B) \[\left[ \frac{1}{2},\frac{1}{\sqrt{2}} \right)\] done clear
C) \[\left[ \frac{1}{\sqrt{2},}\sqrt{2} \right]\] done clear
D) \[\left( \sqrt{2},\infty \right)\] done clear
View Answer play_arrowquestion_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) \[\frac{1}{6}\] done clear
B) \[\frac{1}{9}\] done clear
C) \[\frac{1}{36}\] done clear
D) \[\frac{1}{24}\] done clear
View Answer play_arrowquestion_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) \[\frac{{{x}^{5m}}}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}\] done clear
B) \[\frac{{{x}^{4m}}}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}\] done clear
C) \[\frac{2m\left( {{x}^{5m}}+{{x}^{4m}} \right)}{{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}\] done clear
D) \[\frac{\left( {{x}^{5m}}-{{x}^{4m}} \right)}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}\] done clear
View Answer play_arrowquestion_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) \[{{e}^{a}}\left[ F(x)-F(1+a) \right]\] done clear
B) \[{{e}^{-a}}\left[ F(x+a)-F(a) \right]\] done clear
C) \[{{e}^{a}}\left[ F(x+a)-F(1+a) \right]\] done clear
D) \[{{e}^{-a}}\left[ F(x+a)-F(1+a) \right]\] done clear
View Answer play_arrowquestion_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) \[\frac{1}{2}\left( \log 2-\frac{1}{2} \right)\] done clear
B) \[\frac{1}{2}\left( \log 2+\frac{1}{2} \right)\] done clear
C) \[\frac{1}{2}\left( 1-\log 2 \right)\] done clear
D) \[\frac{1}{2}\left( 1+\log 2 \right)\] done clear
View Answer play_arrowquestion_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 done clear
B) -1 done clear
C) -5 done clear
D) 5 done clear
View Answer play_arrowquestion_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) \[y-2ax=0\] done clear
B) \[y-({{a}^{2}}+1)x=0\] done clear
C) \[y+x=0\] done clear
D) \[{{(a-1)}^{2}}x-{{(a+1)}^{2}}y=0\] done clear
View Answer play_arrowquestion_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) \[\frac{7}{\sqrt{5}}\] done clear
B) \[\frac{5}{\sqrt{13}}\] done clear
C) \[\frac{7}{\sqrt{13}}\] done clear
D) \[\frac{5}{\sqrt{7}}\] done clear
View Answer play_arrowquestion_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) \[{{x}^{2}}+{{y}^{2}}+3x+y-11=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+3x+y+1=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+3x+y-2=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+3x+y-22=0\] done clear
View Answer play_arrowquestion_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) \[\frac{\sqrt{5}}{2}\] done clear
B) \[\frac{\sqrt{3}}{2}\] done clear
C) \[\frac{2}{\sqrt{5}}\] done clear
D) \[\frac{2}{\sqrt{3}}\] done clear
View Answer play_arrowquestion_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) \[-\frac{20}{9}\] done clear
B) \[\frac{19}{9}\] done clear
C) 4 done clear
D) \[-\frac{4}{3}\] done clear
View Answer play_arrowquestion_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) \[\frac{x}{1}=\frac{y}{-1}=\frac{z}{-2}\] done clear
B) \[\frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{-2}\] done clear
C) \[\frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{1}\] done clear
D) \[\frac{x}{-2}=\frac{y}{1}=\frac{z}{2}\] done clear
View Answer play_arrowquestion_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) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer85) If andthen the magnitude of the projection ofon is: JEE Main Online Paper (Held On 19 April 2016)
A) 12 done clear
B) 15 done clear
C) 14 done clear
D) 13 done clear
View Answer play_arrowquestion_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 done clear
B) Both the statements are false done clear
C) Statement-1 is true, Statement-2 is false done clear
D) Statement-1 is false, Statement-2 is true done clear
View Answer play_arrowquestion_answer87) Let and be respectively the mean, mode and variance of n observations andwhere is any number. Statement I: Variance of is Statement II: Mean and mode of areand ? M ? a, respectively. JEE Main Online Paper (Held On 19 April 2016)
A) Statement I and Statement II are both false done clear
B) Statement I and Statement II are both true done clear
C) Statement I is true and Statement II is false done clear
D) Statement I is false and Statement II is true done clear
View Answer play_arrowquestion_answer88) The function is a periodic function with period: JEE Main Online Paper (Held On 19 April 2016)
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer89) The principal value of is: JEE Main Online Paper (Held On 19 April 2016)
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_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 done clear
B) If I will go to the doctor, then I am feeling well done clear
C) If I will not go to the doctor, then I am feeling well done clear
D) If I will go to the doctor, then I am not feeling well. done clear
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