Solved papers for JEE Main & Advanced JEE Main Paper (Held On 09-Jan-2019 Evening)

JEE Main Paper (Held On 09-Jan-2019 Evening) Total Questions - 90

1) In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of band width 6 MHz are (Take velocity of light \[c\text{ }=\text{ }3\text{ }\times \text{ }{{10}^{8}}\,m/s,\text{ }h=6.6\,\,\times \,\,{{10}^{-\,34}}J-s)\] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[3.75\text{ }\times \text{ }{{10}^{6}}\]

B)

            \[4.87\text{ }\times \text{ }{{10}^{5}}\]

C)

\[6.25\text{ }\times \text{ }{{10}^{5}}\]

D)

            \[3.86\text{ }\times \text{ }{{10}^{6}}\]

View Answer
2) The magnetic field associated with a light wave is given, at the origin, by \[B\text{ }=\text{ }{{B}_{0}}\] \[[sin(3.14\,\times \,\,{{10}^{7}})ct+sin(6.28\,\,\times \,{{10}^{6}})ct]\] If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons? \[\left( c=3\text{ }\times \text{ }{{10}^{8}}\text{ }m{{s}^{-\,1}},\text{ }h\,\,=\,\,6.6\,\,\times \,\,{{10}^{-34}}\,J-s \right)\] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[6.82\text{ }eV\]

B)

            \[8.52\text{ }eV\]

C)

\[12.5\text{ }eV\]

D)

            \[7.55\text{ }eV\]

View Answer
3)      The top of a water tank is open to air and its water level maintained. It is giving out \[0.74\text{ }{{m}^{3}}\] water per minute through a circular opening of 2 cm radius is its wall. The depth of the centre of the opening from the level of water in the tank is close to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

6.0 m

B)

                                      9.6 m

C)

2.9 m

D)

            4.8 m

View Answer
4) A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by \[20%\] The value of ratio m/M is close to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

0.37

B)

0.57

C)

0.77

D)

0.17

View Answer
5) A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants \[{{K}_{1}},\text{ }{{K}_{2}},\text{ }{{K}_{3}},\text{ }{{K}_{4}}\] arranged as shown in the figure. The effective dielectric constant K will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{2}}+{{K}_{4}})}{{{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}}}\]

B)

\[K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{2}}+{{K}_{4}})}{2({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}\]

C)

\[K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{3}}+{{K}_{4}})}{({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}\]

D)

\[K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{4}})({{K}_{2}}+{{K}_{3}})}{2({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}\]

E)

None of these

View Answer
6) A carbon resistance has a following colour code. What is the value of the resistance? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[5.3\,M\,\Omega \,\,\pm \,\,5\,%\]

B)

                          \[530\,k\,\Omega \,\,\pm \,\,5%\]

C)

\[6.4\,k\,\Omega \,\,\pm \,10%\]

D)

            \[6.4\,M\Omega \,\,\pm \,\,5%\]

View Answer
7) A series AC circuit containing an inductor\[\left( 20\text{ }mH \right)\], a capacitor \[\left( 120\text{ }\mu F \right)\] and a resistor \[\left( 60\text{ }\Omega \right)\] is driven by an AC source of\[24\text{ }V/50\text{ }Hz\]. The energy dissipated in the circuit in 60 s is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[5.65\text{ }\times \text{ }{{10}^{2}}J\]

B)

\[2.26\text{ }\times {{10}^{3}}J\]

C)

\[5.17\text{ }\times \text{ }{{10}^{2}}\,J~\]

D)

            \[3.39\text{ }\times \text{ }{{10}^{3}}\,J\]

View Answer
8) A force acts on a 2 kg object so that its position is given as a function of time as\[x=3{{t}^{2}}+5\]. What is the work done by this force in first 5 seconds? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

950 J

B)

900 J

C)

875 J

D)

            850 J

View Answer
9)             One of the two identical conducting wires of length L is bent in the form of a circular   loop and the other one into a circular coil. If the same current is passed in both, the ratio of the magnetic field at the central of the loop \[({{B}_{L}}),\,\,\,\,i.e.\,\,\,\frac{{{B}_{L}}}{{{B}_{C}}}\]will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{1}{N}\]

B)

N

C)

\[{{N}^{2}}\]

D)

            \[\frac{1}{{{N}^{2}}}\]

View Answer
10) In a young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength \[\lambda \text{ }=\text{ }500\text{ }nm\] is incident on the slits. The total number of bright fringes that are observed in the angular range \[-30{}^\circ \le \,\theta \le 30{}^\circ \] is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

640

B)

641

C)

320

D)

321

View Answer
11) Two Carnot engines A and B are operated in series. The first one, A, receives heat at \[{{T}_{1}}\left( =600\text{ }K \right)\] and rejects to a reservoir at temperature Ta. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at\[{{T}_{3}}(=400\text{ }K)\]. Calculate the temperature \[{{T}_{2}}\] if the work outputs of the engines are equal: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

500K

B)

300K

C)

600 K

D)

            400 K

View Answer
12) At a given instant, say\[t=0\], two radioactive substances A and B have equal activities. The ratio \[\frac{{{R}_{B}}}{{{R}_{A}}}\] of their activities after time t itself decays with time t as \[{{e}^{-3t}}\]. If the half-life of A is ln2, the half-life of B is- [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{In\,2}{4}\]

B)

\[4\ln 2\]

C)

2ln2

D)

            \[\frac{In\,2}{2}\]

View Answer
13) Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror \[\left( {{M}_{1}} \right)\] and parallel to the second mirror \[({{M}_{2}})\] is finally reflected from the second mirror \[({{M}_{2}})\] parallel to the first mirror\[\left( {{M}_{1}} \right)\]. The angle between the two mirrors will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[60{}^\circ \]

B)

\[75{}^\circ \]

C)

\[45{}^\circ \]

D)

            \[90{}^\circ \]

View Answer
14)             [a] In the given circuit the internal resistance of the 18 V cell is negligible. If \[{{R}_{1}}\,\,=\,\,400\,\Omega \], \[{{R}_{3}}=100\text{ }\Omega \] and \[{{R}_{4}}=500\Omega \]and the reading of an ideal voltmeter across \[{{R}_{4}}\] is 5 V, then the value of \[{{R}_{2}}\] will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[550\text{ }\Omega \]

B)

\[450\text{ }\Omega \]

C)

\[230\,\,\Omega \]

D)

            \[300\,\,\Omega \]

View Answer
15) Charge is distributed within a sphere of radius R with a volume charge density\[\rho (r)=\frac{A}{{{r}^{2}}}{{e}^{{}^{-2r}/{}_{a}}}\], where A and a are constants. If Q is the total charge of this charge distribution, the radius R is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{a}{2}\,\log \,\left( 1-\frac{Q}{2\,\pi \,a\,A} \right)\]

B)

\[\frac{a}{2}\,\log \,\left( 1-\frac{1}{\frac{Q}{2\,\pi \,a\,A}} \right)\]

C)

\[a\,\,\log \,\,\left( \frac{1}{1-\frac{Q}{2\,\pi \,a\,A}} \right)\]

D)

\[a\,\,\log \,\,\left( 1-\frac{Q}{2\,\pi \,a\,A} \right)\]

View Answer
16) Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\sqrt{\frac{Gh}{{{c}^{5}}}}\]

B)

              \[\sqrt{\frac{h{{c}^{5}}}{G}}\]

C)

\[\sqrt{\frac{Gh}{{{c}^{3}}}}\]

D)

            \[\sqrt{\frac{{{c}^{3}}}{Gh}}\]

View Answer
17) In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed 'v' more than that of car B. Both the cars start, from rest and travel with constant acceleration \[{{a}_{1}}\text{ }and\text{ }{{a}_{2}}\] respectively. Then 'v' is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\sqrt{{{a}_{1}}\,{{a}_{2}}}\,\,t\]

B)

\[\frac{2{{a}_{1}}{{a}_{2}}}{{{a}_{1}}+{{a}_{2}}}\,\,t\]

C)

\[\frac{{{a}_{1}}+{{a}_{2}}}{2}\,\,t\]

D)

\[\sqrt{2{{a}_{1}}{{a}_{2}}}\,\,t\]

View Answer
18) A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of \[45{}^\circ \] at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is \[\left( g=10\text{ }m{{s}^{-}}^{2} \right)\] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

100 N

B)

70 N

C)

140 N

D)

            200 N

View Answer
19) The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

5.725 mm

B)

5.950 mm

C)

5.755 mm

D)

            5.740 mm

View Answer
20) A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A and its efficiency is \[90%\], the output current would be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

45 A

B)

35 A

C)

25 A

D)

            50 A

View Answer
21) A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature\[27{}^\circ C\]. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take\[\,R=8.3\] J/K mole] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

10 kJ

B)

                                      0.9 KJ

C)

14 kJ

D)

            6 kJ

View Answer
22) The position co-ordinates of a particle moving in a 3-D coordinate system is given by             \[~x=a\text{ }cos\omega t\]             \[y=a\text{ }sin\omega t\]       and \[z=a\omega t\] The speed of the particle is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[a\omega \]

B)

                          \[\sqrt{3}\,a\omega \]

C)

\[\sqrt{2}\,a\omega \]

D)

            \[2\,a\omega \]

View Answer
23) A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about\[x=0\]. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{A}{2\sqrt{2}}\]

B)

\[\frac{A}{\sqrt{2}}\]

C)

\[\frac{A}{2}\]

D)

            A

View Answer
24) The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth \[=6.4\times {{10}^{3}}km\]) is \[{{E}_{1}}\] and kinetic energy required for the satellite to be in a circular orbit at this height is \[{{E}_{2}}\]. The value of h for which \[{{E}_{1}}\] and \[{{E}_{2}}\] are equal, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[3.2\times {{10}^{3}}\text{ }km\]

B)

\[1.6\times {{10}^{3}}km\]

C)

\[1.28\times {{10}^{4}}km\]

D)

\[6.4\times {{10}^{3}}km\]

View Answer
25) A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at n speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

753 Hz

B)

666 Hz

C)

500 Hz

D)

            333 Hz

View Answer
26) A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron \[=1.6\,\times \,{{10}^{-19}}C\]) [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[1.6\times {{10}^{-19}}kg\]

B)

\[1.6\times {{10}^{-27}}\text{ }kg\]

C)

\[9.1\times {{10}^{-}}^{31}kg\]

D)

            \[2.0\times {{10}^{-}}^{24}kg\]

View Answer
27) A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of \[30{}^\circ \]from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad \[{{s}^{-1}}\]) will be (\[g=10\text{ }m{{s}^{-2}}\]) [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\sqrt{\frac{30}{2}}\]

B)

\[\frac{\sqrt{20}}{3}\]

C)

\[\frac{\sqrt{30}}{2}\]

D)

            \[\sqrt{30}\]

View Answer
28) The energy associated with electric field is (\[{{U}_{E}}\]) and with magnetic field is (\[{{U}_{B}}\]) for an electromagnetic wave in free space. Then: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[{{U}_{E}}<{{U}_{B}}\]

B)

\[{{U}_{E}}=\,\frac{{{U}_{B}}}{2}\]

C)

\[{{U}_{E}}={{U}_{B}}\]

D)

            \[{{U}_{E}}>{{U}_{B}}\]

View Answer
29) Two point charges \[{{q}_{1}}\,(\sqrt{10}\,\mu C)\]and \[{{q}_{2}}(-25\,\,\mu C)\] are placed on the x-axis at \[x=1\,m\] and \[x=4\,m\]respectively. The electric field (in V/m) at a point \[y=3\]m on y-axis is, [take\[\frac{1}{4\pi {{\in }_{0}}}\,\,=\,\,9\,\times {{10}^{9}}\,N{{m}^{2}}{{C}^{-}}^{2}\]] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[(-81\widehat{i}\,\,+\,\,81\widehat{j})\,\,\times \,{{10}^{2}}\]

B)

\[(81\widehat{i}-81\widehat{j})\times {{10}^{2}}\]

C)

\[(63\widehat{i}\,\,-\,\,27\widehat{j})\,\,\times \,{{10}^{2}}\]

D)

\[(-63\widehat{i}+27\widehat{j})\times {{10}^{2}}\]

View Answer
30) Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of \[{{V}_{0}}\] changes by: (assume that the Ge diode has large breakdown voltage) [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

0.4 V

B)

                                      0.6 V

C)

0.8 V

D)

            0.2 V

View Answer

31) Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?

[A] An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum.

[B] For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number.

[C] According to wave mechanics, the ground state angular momentum is equal to\[\frac{h}{2\pi }\].

[D] The plot of \[\psi \,Vs\,\,r\]for various azimuthal quantum numbers, shows peak shifting towards higher r value.

[JEE Main Online Paper (Held On 09-Jan-2019 Evening]

[B], [C]

[A], [D]

[A], [B]

[A], [C]

View Answer

32) A solution containing 62 g ethylene glycol in 250 g water is cooled to\[-10{}^\circ C\]. If \[{{K}_{f}}\] for water is \[1.86\text{ }K\text{ }kg\text{ }mo{{l}^{-1}}\], the amount of water (in g) separated as ice is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

32

B)

16

C)

64

D)

48

View Answer
33) For coagulation of arsenious sulphide sol which one of the following salt solution will be most effective? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[AlC{{l}_{3}}\]

B)

\[NaCl\]

C)

\[N{{a}_{3}}P{{O}_{4}}~~~~~~~~\]

D)

\[BaC{{l}_{2}}\]

View Answer
34)             In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[NO\,\,\to \,\,N{{O}^{+}}\]

B)

            \[{{O}_{2}}\to {{O}_{{{2}^{+}}}}\]

C)

\[{{N}_{2}}\,\,\to \,\,{{N}_{{{2}^{+}}}}\]

D)

            \[{{O}_{2}}\,\,\to \,\,{{O}_{{{2}^{2-}}}}\]

View Answer
35) The complex that has highest crystal field splitting energy \[(\Delta )\], is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[{{K}_{3}}\left[ Co{{\left( CN \right)}_{6}} \right]\]

B)

\[{{K}_{2}}\left[ CoC{{l}_{4}} \right]\]

C)

\[\left[ Co{{\left( N{{H}_{3}} \right)}_{5}}Cl \right]\text{ }C{{l}_{2}}\]

D)

\[\left[ Co{{\left( N{{H}_{3}} \right)}_{5}}\left( {{H}_{2}}O \right)C{{l}_{3}} \right]\]

View Answer
36) For the following reaction, the mass of water produced from 4.45 g of \[{{C}_{57}}{{H}_{110}}{{O}_{6}}\] is: \[2{{C}_{57}}{{H}_{110}}{{O}_{6}}(s)+163{{O}_{2}}(g)\to 114C{{O}_{2}}(g)+110{{H}_{2}}O(\ell )\] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

445 g

B)

490 g

C)

495g

D)

890 g

View Answer
37) If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for the reaction \[Zn(s)+C{{u}^{2+}}(aq)\,\,\,\rightleftharpoons \,\,Z{{n}^{2+}}(aq)+Cu\,(s)\] At 300 K is approximately \[\left( R=8J{{K}^{-}}^{1}mo{{l}^{-1}},\text{ }F\,\,=\,\,96000\text{ }C\text{ }mo{{l}^{-1}} \right)\] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[{{e}^{160}}\]

B)

\[{{e}^{-160}}\]

C)

\[{{e}^{-80}}\]

D)

            \[{{e}^{320}}\]

View Answer
38) The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is: (Specific heat of water liquid and water vapour are \[4.2\text{ }kJ\text{ }{{K}^{-1}}\,k{{g}^{-}}^{1}\] and \[2.0\text{ }kJ\text{ }{{K}^{-1}}\,k{{g}^{-}}^{1}\]heat of liquid fusion and vapourisation of water are \[334\text{ }kJ\text{ }k{{g}^{-1}}\] and \[2491\text{ }kJ\text{ }k{{g}^{-1}}\], respectively), \[(log\text{ }273\,\,\,=\,\,2.436\], \[log\text{ }373=2.572,\text{ }log\text{ }383\,\,\text{=}\,\,2.583)\] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[2.64\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\]

B)

\[9.26\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\]

C)

\[7.90\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}~\]

D)

\[8.49\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\]

View Answer
39) For the reaction, \[2A\,\,+\,\,B\,\,\to \] products, when the concentrations of A and B both were doubled, the rate of the reaction increased from \[0.3\text{ }mol\text{ }{{L}^{-1}}{{s}^{-}}^{1}\] to\[2.4\text{ }mol\text{ }{{L}^{-1}}{{s}^{-}}^{1}\]. When the concentration of A alone is doubled, the rate increased from \[0.3\text{ }mol\text{ }{{L}^{-}}^{1}\,{{s}^{-}}^{1}\] to\[0.6\text{ }mol\,\,L{{\,}^{-}}^{1}s{{\,}^{-1}}\]. Which one of the following statements is correct? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

Order of the reaction with respect to A is 2.

B)

Total order of the reaction is 4.

C)

Order of the reaction with respect to B is 1.

D)

Order of the reaction with respect to B is 2.

View Answer
40) The major product obtained in the following reaction is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

View Answer
41) The increasing basicity order of the following compounds is:

[a]

[b]

[c]

[d]

[JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

[a] <[b] < [c] < [d]

B)

[d] < [c] < [b] < [a]

C)

[d] < [c] < [a] < [b]

D)

[a] < [b] < [d] < [c]

View Answer
42) Homoleptic octahedral complexes of a metal ion \[{{M}^{3+}}\] with three monodentate ligands \[{{L}_{1}},\text{ }{{L}_{2}}and\text{ }{{L}_{3}}\] absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is- [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[{{L}_{3}}<{{L}_{2}}<{{L}_{1}}\]

B)

\[{{L}_{3}}<{{L}_{1}}<{{L}_{2}}\]

C)

\[{{L}_{1}}<{{L}_{2}}<{{L}_{3}}\]

D)

\[{{L}_{2}}<{{L}_{1}}<{{L}_{3}}\]

View Answer
43) When the first electron gain enthalpy \[\left( {{\Delta }_{eg}}H \right)\] of oxygen is \[-141\text{ }kJ/mol\], Its second electron gain enthalpy is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

a positive value

B)

a more negative value than the first

C)

almost the same as that of the first

D)

negative, but less negative than the first

View Answer

44) Consider the following reversible chemical reactions:

\[{{A}_{2}}(g)\,\,+\,\,{{B}_{2}}\,(g)\,\,\,\,\,2AB\,(g)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.......\,(1)\]

\[6AB\,(g)\,\,\,\,\,3{{A}_{2}}\,(g)\,\,+3{{B}_{2}}\,(g)\,\,\,\,\,\,\,\,\,\,\,\,\,.......\,\,(2)\]

The relation between \[{{K}_{1}}\,\,\,and\,\,\,{{K}_{2}}\] is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

\[{{K}_{2}}={{K}_{1}}^{-3}\]

\[{{K}_{1}}{{K}_{2}}\,\,=\,\,\frac{1}{3}\]

\[{{K}_{1}}{{K}_{2}}\,\,=\,\,3\]

\[{{K}_{2}}={{K}_{1}}^{3}\]

View Answer

45) Good reducing nature of \[{{H}_{3}}P{{O}_{2}}\] attributed to the presence of: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

One \[P-H\] bond

B)

Two \[P-OH\] bonds

C)

One \[P-OH\] bond

D)

Two \[P-H\]bonds

View Answer
46) The tests performed on compound X and their inferences are:

Test Inference

[A] 2, 4-DNP test Coloured Precipitate

[B] Iodoform test Yellow Precipitate

[C] Azo-dye test No dye precipitate

Compound ?X? is- [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

View Answer
47) The pH rain water, is approximately: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

5.6

B)

6.5

C)

7.5

D)

            7.0

View Answer
48) Which of the following compounds is not aromatic? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

View Answer
49) The correct statement regarding the given Ellingham diagram is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

Coke cannot be used for the extraction of Cu from \[C{{u}_{2}}O\]

B)

At\[500{}^\circ C\], coke can be used for the extraction of Zn from \[ZnO\]

C)

At\[1400{}^\circ C\], Al can be used for the extraction of Zn from \[ZnO\]

D)

At \[800{}^\circ C\] Cu can be used for the extraction of Zn from \[ZnO\]

View Answer
50) The temporary hardness of water is due to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[N{{a}_{2}}S{{O}_{4}}\]

B)

\[CaC{{l}_{2}}\]

C)

\[NaCI\]

D)

\[Ca{{\left( HC{{O}_{3}} \right)}_{2}}_{~}~~~~~~~~~\]

View Answer
51) The major product of the following reaction is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

View Answer
52) The products formed in the reaction of cumene with \[{{O}_{2}}\] followed by treatment with dil. HCl are: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

View Answer
53) At\[100{}^\circ C\], copper (Cu) has FCC unit cell structure with cell edge length of x \[\overset{o}{\mathop{A}}\,\]. What is the approximate density of Cu (in\[g\text{ }c{{m}^{-}}^{3}\]) at this temperature? [Atomic Mass of \[Cu\,\,=\,\,63.55\,u\]] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{422}{{{x}^{3}}}\]

B)

\[\frac{205}{{{x}^{3}}}\]

C)

\[\frac{211}{{{x}^{3}}}\]

D)

\[\frac{105}{{{x}^{3}}}\]

View Answer
54) The transition element that has lowest enthalpy of atomization, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

Zn

B)

Fe

C)

Cu

D)

            V

View Answer
55) Which of the following conditions in drinking water causes methemoglobinemia? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

> 50 ppm of nitrate

B)

> 50 ppm of chloride

C)

> 50 ppm of lead

D)

> 100 ppm of sulphate

View Answer
56) The major product formed in the following reaction is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

View Answer
57) The correct match between Item-I and Item-II is:

Item-I Item-II

[A] Benzaldehyde (P) Mobile phase

[B] Alumina (Q) Adorbent

[C] Acetonitrile (R) Adsorbate

[JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

[A] \[\to \] (Q); [B] \[\to \] (P); [C] \[\to \] (R)

B)

[A] \[\to \] (Q); [B] \[\to \] (R); [C] \[\to \] (P)

C)

[A] \[\to \] (P); [B] \[\to \] (R); [C] \[\to \] (Q)

D)

[A] \[\to \] (R); [B] \[\to \] (Q); [C] \[\to \] (P)

View Answer
58) The metal that forms nitride by reacting directly with N2 of air, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

Li

B)

Cs

C)

K

D)

            Rb

View Answer
59) The major product of the following reaction is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

View Answer
60) The correct sequence of amino acids present in the tripetide given below is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

Val - Ser - Thr

B)

Thr - Ser - Vnl

C)

Thr - Ser - Leu

D)

            Leu - Ser - Thr

View Answer
61) Let \[{{z}_{0}}\] be a root of the quadratic equation, \[{{x}^{2}}+x+1=0\]. If \[z=3+6i\,{{z}_{0}}^{81}-\,3i\,{{z}_{0}}^{93}\], then arg z is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{\pi }{6}\,\]

B)

                                                  \[\frac{\pi }{3}\,\]

C)

              0

D)

              \[\frac{\pi }{4}\,\]

View Answer
62) Let f: \[\left[ 0,\text{ }1 \right]\,\,\to \,\,R\] be such that\[f\left( xy \right)=f\left( x \right).f\left( y \right)\], for all \[x,\,\,y\,\,\in \,\,\,[0,\,\,\,1]\] and\[f(0)\,\,\ne \,\,0\]. If \[y\,\,=\,\,y(x)\]satisfies the differential equation, \[\frac{dy}{dx}\,\,=\,\,f(x)\,\]with \[y\left( 0 \right)\,\,=\,\,1\], then \[y\left( \frac{1}{4} \right)+y\left( \frac{3}{4} \right)\]is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

2

B)

                          3

C)

              5

D)

              4

View Answer
63) The coefficient of \[{{t}^{4}}\] in the expansion of \[{{\left( \frac{1-{{t}^{6}}}{1-t} \right)}^{3}}\] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

15

B)

              10

C)

              14

D)

              12

View Answer
64) Let \[\overrightarrow{a}=\widehat{i}+\widehat{j}\,\,+\sqrt{2}\widehat{k},\,\,\,\overrightarrow{b}={{b}_{1}}\widehat{i}\,\,+\,{{b}_{2}}\widehat{j}\,\,+\,\,\sqrt{2}\widehat{k}\]and \[\overrightarrow{c}=5\widehat{i}\,\,+\,\,\widehat{j}\,\,+\,\,\sqrt{2}\widehat{k}\] be three vectors such that the projection vector of \[\overrightarrow{b}\] on \[\overrightarrow{a}\] is \[\overrightarrow{a}\]. If \[\overrightarrow{a}\,\,+\,\,\overrightarrow{b}\] is perpendicular to \[\overrightarrow{c}\], then \[\left| \overrightarrow{b} \right|\] is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

4

B)

              \[\sqrt{22}\]

C)

              6

D)

              \[\sqrt{32}\]

View Answer
65) If \[f\left( x \right)\,\,=\,\int{\frac{5{{x}^{8}}+7{{x}^{6}}}{{{({{x}^{2}}+1+2{{x}^{7}})}^{2}}}}\,\,dx\,,\,\,\,(x\,\,\ge \,\,0)\,\], and \[f\left( 0 \right)\,\,\,=\,\,0\], then the value of f(1) is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[-\frac{1}{2}\]

B)

              \[-\frac{1}{4}\]

C)

              \[\frac{1}{4}\]

D)

              \[\frac{1}{2}\]

View Answer
66) If \[x\,\,=\,\,3\text{ }tan\text{ }t\] and \[y\,\,=\,\,3\text{ }sec\text{ }t\], then the value of \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] at \[t=\frac{\pi }{4}\]is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{3}{2\sqrt{2}}\]

B)

              \[\frac{1}{6}\]

C)

              \[\frac{1}{6\sqrt{2}}\]

D)

              \[\frac{1}{3\sqrt{2}}\]

View Answer
67) The sum of the following series \[1+6+\frac{9({{1}^{2}}+{{2}^{2}}+{{3}^{2}})}{7}\,\,+\,\,\frac{12({{1}^{2}}+{{2}^{2}}+{{3}^{2}}+{{4}^{2}})}{9}+\] \[\frac{15({{1}^{2}}+{{2}^{2}}+......\,\,+{{5}^{2}})}{11}\,+\,.....\]up to 15 terms, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

7830

B)

              7520

C)

              7820

D)

              7510

View Answer
68) Let a, b and c be the\[{{7}^{th}}\], \[{{11}^{th}}\] and \[{{13}^{th}}\] terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then \[\frac{a}{c}\] is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{7}{13}\]

B)

              2

C)

              4

D)

              \[\frac{1}{2}\]

View Answer
69) A hyperbola has its centre at the origin, passes through the point \[\left( 4,\text{ }2 \right)\] and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{3}{2}\]

B)

              \[\frac{2}{\sqrt{3}}\]

C)

              2

D)

              \[\sqrt{3}\]

View Answer
70) Let the equations of two sides of a triangle be \[3x-2y+6=0\] and\[4x+5y-20=0\]. If the orthocentre of this triangle is at \[\left( 1,\text{ }1 \right)\], then the equation of its third side is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[26x\,-\,122y\,-\,1675\,=\,0\]

B)

              \[26x\,+61y\,+\,1675\,=\,0\]

C)

              \[122y\,-\,\,26x\,-\,1675\,=\,0\]

D)

              \[122y\,+\,\,26x\,+\,1675\,=\,0\]

View Answer
71) A data consists of n observations: \[{{x}_{1}},\,\,{{x}_{2}},\,\,\,....,\,\,{{x}_{n}},\]. If \[\sum\limits_{i\,=\,1}^{n}{{{({{x}_{i}}+1)}^{2}}\,\,=\,\,9n}\] and \[\sum\limits_{i\,=\,1}^{n}{{{({{x}_{i}}-1)}^{2}}=5n}\]then the standard deviation of this data is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

2

B)

              4

C)

              3

D)

              1

View Answer
72) If \[0\,\,\le \,\,x\,<\,\,\frac{\pi }{2}\] , then the number of values of x for which \[\sin \,\,x-sin\text{ 2}x+sin\text{ }3x=0\] is [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

2

B)

              4

C)

              3

D)

              1

View Answer
73) If the tines \[x=ay+b,\]\[z=cy+d\]and \[x=a'z\,\,+b'\], \[y\,\,=\,\,c'z\,\,+d'\] are perpendicular then: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[cc'+a+a'=0\]

B)

              \[aa'+c+c'=0\]

C)

              \[bb'+cc'+1=0\]

D)

              \[ab'+bc'+1=0\]

View Answer
74) The equation of the plane containing the straight line \[\frac{x}{2}\,\,=\,\,\frac{y}{3}\,\,=\,\,\frac{z}{4}\]and perpendicular to the plane containing the straight lines \[\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\,\,and\,\,\frac{x}{4}=\frac{y}{2}=\frac{z}{3}\] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[3x+2y-3z\,\,=\,\,0\]

B)

              \[x+2y-2z\,\,=\,\,0\]

C)

              \[x-2y+z=0\]

D)

              \[~5x+2y-4z=0\]

View Answer
75) Let f be a differentiable function from, R to R such that\[\left| f(x)-f(y) \right|\,\,\le \,\,2\,\,{{\left| x-y \right|}^{3/2}}\], for all\[x,\,\,y\,\,\in \,\,\,R.\,\]. If \[f\left( 0 \right)=1\] then \[\int\limits_{0}^{1}{{{f}^{2}}\left( x \right)dx}\] is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

2

B)

                                                  \[\frac{1}{2}\]

C)

              0

D)

              1

View Answer
76) Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:

A)

32

B)

              36

C)

              9

D)

              18

View Answer
77) The area of the region \[A=\{(x,\,\,y):0\,\,\le \,\,y\,\,\le \,\,x|x|+1\,\,and\,\,-\,1\le x\le 1\}\]in sq. units, is : [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{4}{3}\]

B)

              \[\frac{1}{3}\]

C)

              \[\frac{2}{3}\]

D)

              2

View Answer
78) If the circles \[{{x}^{2}}+{{y}^{2}}-16x-20y+164={{r}^{2}}\]and \[{{\left( x-4 \right)}^{2}}+{{\left( y-7 \right)}^{2}}=36\] intersect at two distinct points, then [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[r\,\,>\,\,11\]

B)

              \[r\,\,=\,\,11\]

C)

              \[1\,\,<\,\,r\,\,<\,\,11\]

D)

              \[0\,\,<\,\,r\,\,<\,\,1\]

View Answer
79) An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[\frac{27}{49}\]

B)

              \[\frac{26}{49}\]

C)

              \[\frac{32}{49}\]

D)

              \[\frac{21}{49}\]

View Answer
80) If then A is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

invertible only if \[t=n\]

B)

              invertible for all \[t\,\,\in \,\,R\]

C)

              invertible only if \[t=\frac{\pi }{2}\]

D)

              not invertible for any \[t\text{ }\in \text{ }R\]

View Answer
81) The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

372

B)

              375

C)

              250

D)

              374

View Answer
82) If \[\int\limits_{0}^{\pi /3}{\frac{\tan \,\theta }{\sqrt{2\,k\,\,\sec \,\theta }}}\,d\,\theta \,\,=\,\,1-\frac{1}{\sqrt{2}}\,,\text{ }\left( k\,\,>\,\,0 \right)\], then the value of k is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

2

B)

              1

C)

              4

D)

              \[\frac{1}{2}\]

View Answer
83)             The number of all possible positive integral values of a for which the roots of the quadratic equation, \[6{{x}^{2}}-11x+\alpha =0\] are rational numbers is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

4

B)

              2

C)

              5

D)

              3

View Answer
84) The logical statement \[[\tilde{\ }\left( \tilde{\ }p\vee q \right)\vee (p\wedge r)]\,\,\wedge \,(\sim q\wedge r)\,\] is equivalent to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[(\sim p\wedge \sim q)\wedge r\]

B)

              \[(p\wedge \sim q)\vee r\]

C)

              \[\left( p\wedge r \right)\,\,\wedge \tilde{\ }\,q\]

D)

              \[\tilde{\ }p\wedge r\]

View Answer
85) If the system of linear equations

\[x-4y+7z=g\]

\[3y-5z=h\]

\[-2x+5y-9z=k\]

is consistent, then: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

\[g+2h+k=0\]

B)

              \[g+h+2k=0\]

C)

              \[g+h+k=0\]

D)

              \[2g+h+k=0\]

View Answer
86) If both the roots of the quadratic equation \[{{x}^{2}}-mx+4=0\] are real and distinct and they lie in the interval \[\left[ 1,\text{ }5 \right]\], then m lies in the interval: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

(4, 5)

B)

              (\[-5,\,\,-4\])

C)

              (3, 4)

D)

              (5, 6)

View Answer
87) If \[x=si{{n}^{-1}}\left( sin\text{ }10 \right)\] and \[y=co{{s}^{-1}}\,\,cos10)\], then \[y-x\] is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

0

B)

              \[7\,\pi \]

C)

              \[\pi \]

D)

              10

View Answer
88) Let \[A=\{x\text{ }\in \text{ }R:x\] is not a positive integer}. Define a function \[f:A\to R\] as \[f(x)\,\,=\,\,\frac{2x}{x-1}\], then f is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

not injective

B)

              surjective but not injective

C)

              injective but not surjective

D)

              neither injective nor surjective

View Answer
89) For each\[x\text{ }\in \text{ }R\], let [x] be the greatest integer less than or equal to x. Then\[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,\,\frac{x([x]+\left| x \right|)\,sin\,[x]}{\left| x \right|}\] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

1

B)

              0

C)

              \[sin\text{ }1\]

D)

              \[-sin\text{ }1\]

View Answer
90) Let A(\[4,\text{ }-4\]) and B(9, 6) be points on the parabola, \[{{y}^{2}}=4x\]. Let C be chosen on the arc AOB of the parabola, where 0 is the origin, such that the area of \[\Delta \,ACB\] is maximum. Then, the area (in sq. units) of \[\Delta \,ACB\], is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

32

B)

              \[31\frac{3}{4}\]

C)

              \[30\frac{1}{2}\]

D)

              \[31\frac{1}{4}\]

View Answer