Solved papers for JEE Main & Advanced JEE Main Paper Phase-I (Held on 07-1-2020 Evening)

done JEE Main Paper Phase-I (Held on 07-1-2020 Evening) Total Questions - 75

• question_answer1) A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is \[{{v}_{0}}=1400\] Hz and the velocity of sound in air 350 m/s. The speed of each tuning fork is close to:            [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\frac{1}{4}\,m/s\]
  done clear
  B)
    \[\frac{1}{2}\,m/s\]
  done clear
  C)
  \[1\,m/s\]         
  done clear
  D)
  \[\frac{1}{8}\,m/s\]
  done clear
  View Answer play_arrow

• question_answer2) The electric field of a plane electromagnetic wave is given by \[\vec{E}={{E}_{0}}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\,\cos \,(kz+\omega t)\] At t = 0, a positively charged particle is at the point \[(x,y,z)\,=\,\left( 0,0,\,\frac{\pi }{k} \right)\]. If its instantaneous velocity at (t = 0) is\[{{v}_{0}}\,\hat{k},\], the force acting on it due to the wave is: [JEE MAIN Held on 07-01-2020 Evening]
  A)
  Antiparallel to \[\frac{\hat{i}+\hat{j}}{\sqrt{2}}\]
  done clear
  B)
  Zero
  done clear
  C)
  Parallel to \[\frac{\hat{i}+\hat{j}}{\sqrt{2}}\]
  done clear
  D)
  Parallel to \[\hat{k}\]
  done clear
  View Answer play_arrow

• question_answer3) In a Young's double slit experiment, the separation between the slits is 0.15 mm. In the experiment, a source of light of wavelength 589 nm is used and the interference pattern is observed on a screen kept 1.5 m away. The separation between the successive bright fringes on the screen is: [JEE MAIN Held on 07-01-2020 Evening]
  A)
  3.9 mm
  done clear
  B)
  6.9 mm
  done clear
  C)
  5.9 mm
  done clear
  D)
  4.9 mm
  done clear
  View Answer play_arrow

• question_answer4) Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, \[{{T}_{1}}\]and \[{{T}_{2}}\]. The temperature of the hot reservoir of the first engine is \[{{T}_{1}}\] and the temperature of the cold reservoir of the second engine is\[{{T}_{2}}\]. \[T\] is temperature of the sink of first engine which is also the source for the second engine. How is \[T\] related to \[{{T}_{1}}\] and\[{{T}_{2}}\], if both the engines perform equal amount of work?  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[T=\frac{{{T}_{1}}+{{T}_{2}}}{2}\]
  done clear
  B)
  \[T=\sqrt{{{T}_{1}}{{T}_{2}}}\]
  done clear
  C)
  \[T=\frac{2{{T}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}\]    
  done clear
  D)
  \[T=0\]
  done clear
  View Answer play_arrow

• question_answer5) An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is:                                  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\frac{81}{256}\]      
  done clear
  B)
  \[\frac{9}{16}\]
  done clear
  C)
  \[\frac{3}{4}\]            
  done clear
  D)
  \[\frac{\sqrt{3}}{2}\]
  done clear
  View Answer play_arrow

• question_answer6) An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vacuum)                                                                 [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\frac{1}{c}{{\left( \frac{E}{2m} \right)}^{\frac{1}{2}}}\]
  done clear
  B)
  \[{{\left( \frac{E}{2m} \right)}^{\frac{1}{2}}}\]
  done clear
  C)
  \[c\,{{(2mE)}^{\frac{1}{2}}}\]      
  done clear
  D)
  \[\frac{1}{c}{{\left( \frac{2E}{m} \right)}^{\frac{1}{2}}}\]
  done clear
  View Answer play_arrow

• question_answer7) Mass per unit area of a circular disc of radius a depends on the distance r from its centre as\[\sigma \,(r)=A+Br\]. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is: [JEE MAIN Held on 07-01-2020 Evening]
  A)
   \[2\pi {{a}^{4}}\,\left( \frac{A}{4}+\frac{B}{5} \right)\]
  done clear
  B)
  \[\pi {{a}^{4}}\,\left( \frac{A}{4}+\frac{aB}{5} \right)\]
  done clear
  C)
  \[2\pi {{a}^{4}}\,\left( \frac{A}{4}+\frac{aB}{5} \right)\]
  done clear
  D)
  \[2\pi {{a}^{4}}\,\left( \frac{aA}{4}+\frac{B}{5} \right)\]
  done clear
  View Answer play_arrow

• question_answer8) A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of \[45{}^\circ \] with the vertical. Then F equals: (Take \[g=10\text{ }m{{s}^{2}}\] and the rope to be massless) [JEE MAIN Held on 07-01-2020 Evening]
  A)
  75 N
  done clear
  B)
  70 N
  done clear
  C)
  90 N
  done clear
  D)
  100 N
  done clear
  View Answer play_arrow

• question_answer9) A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is \[{{f}_{l}}\], then the ratio \[\frac{{{f}_{l}}}{f}\]is closest to the integer [JEE MAIN Held on 07-01-2020 Evening]
  A)
  17
  done clear
  B)
  1
  done clear
  C)
  5         
  done clear
  D)
  9
  done clear
  View Answer play_arrow

• question_answer10) A box weighs 196 N on a spring balance at the North Pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take \[g=10\text{ }m{{s}^{2}}\]at the north pole and the radius of the earth = 6400 km)                                                                                  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  194.66 N        
  done clear
  B)
  195.66 N
  done clear
  C)
  195.32 N        
  done clear
  D)
  194.32 N
  done clear
  View Answer play_arrow

• question_answer11) An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator \[(g=10\text{ }m/{{s}^{2}})\]must be at least  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  56300 W                     
  done clear
  B)
  66000 W
  done clear
  C)
  48000 W         
  done clear
  D)
  62360 W
  done clear
  View Answer play_arrow

• question_answer12) In a building there are 15 bulbs of 45 W, 15 bulbs of 100 W, 15 small fans of 10 W and 2 heaters of 1 kW. The voltage of electric main is 220 V. The minimum fuse capacity (rated value) of the building will be [JEE MAIN Held on 07-01-2020 Evening]
  A)
  15 A    
  done clear
  B)
  10 A
  done clear
  C)
  20 A
  done clear
  D)
  25 A
  done clear
  View Answer play_arrow

• question_answer13) Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from \[{{\tau }_{1}}\] to\[{{\tau }_{2}}\]. If \[\frac{{{C}_{P}}}{{{C}_{v}}}=\gamma \]for this gas then a good estimate for \[\frac{{{\tau }_{2}}}{{{\tau }_{1}}}\]is given by                                                               [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[{{\left( \frac{1}{2} \right)}^{\frac{\gamma +1}{2}}}\]  
  done clear
  B)
  \[{{\left( \frac{1}{2} \right)}^{\gamma }}\]
  done clear
  C)
  \[2\]                 
  done clear
  D)
  \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer14) An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and \[5\,\Omega \]resistor. The ratio of the currents a time \[t=\,\,\infty \] and at \[t=40\]s is close to (Take\[{{e}^{2}}=7.389\]) [JEE MAIN Held on 07-01-2020 Evening]
  A)
  1.06    
  done clear
  B)
  1.15
  done clear
  C)
  1.46
  done clear
  D)
  0.84
  done clear
  View Answer play_arrow

• question_answer15)   A particle of mass m and charge q has an initial velocity \[\vec{v}={{v}_{0}}\hat{j}\]. If an electric field \[\vec{E}={{E}_{0}}\hat{i}\] and magnetic field \[\vec{B}={{B}_{0}}\hat{i}\]act on the particle, its speed will double after a time: [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\frac{3\,m{{v}_{0}}}{q{{E}_{0}}}\]
  done clear
  B)
    \[\frac{\sqrt{3\,}m{{v}_{0}}}{q{{E}_{0}}}\]
  done clear
  C)
  \[\frac{2\,m{{v}_{0}}}{q{{E}_{0}}}\]       
  done clear
  D)
  \[\frac{\sqrt{2}\,m{{v}_{0}}}{q{{E}_{0}}}\]
  done clear
  View Answer play_arrow

• question_answer16) In the figure, potential difference between A and B is : [JEE MAIN Held on 07-01-2020 Evening]
  A)
  Zero    
  done clear
  B)
  5 V
  done clear
  C)
  10 V    
  done clear
  D)
  15 V
  done clear
  View Answer play_arrow

• question_answer17) The activity of a radioactive sample falls from \[700\text{ }{{s}^{\,1}}\]to \[500\text{ }{{s}^{\,1}}\] in 30 minutes. Its half-life is close to [JEE MAIN Held on 07-01-2020 Evening]
  A)
  66 min            
  done clear
  B)
  52 min
  done clear
  C)
  62 min
  done clear
  D)
  72 min
  done clear
  View Answer play_arrow

• question_answer18) The figure gives experimentally measured B vs. H variation in a ferromagnetic material. The retentivity, co-ercivity and saturation, respectively, of the material are [JEE MAIN Held on 07-01-2020 Evening]
  A)
  1.0 T, 50 A/m and 1.5 T
  done clear
  B)
  1.5 T, 50 A/m and 1.0 T
  done clear
  C)
  1.5 T, 50 A/m and 1.0 T
  done clear
  D)
  150 A/m, 1.0 T and 1.5 T
  done clear
  View Answer play_arrow

• question_answer19) A planar loop of wire rotates in a uniform magnetic field. Initially, at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at [JEE MAIN Held on 07-01-2020 Evening]
  A)
  2.5 s and 7.5 s
  done clear
  B)
  5.0 s and 7.5 s
  done clear
  C)
  2.5 s and 5.0 s
  done clear
  D)
  5.0 s and 10.0 s
  done clear
  View Answer play_arrow

• question_answer20) The dimension of \[\frac{{{B}^{2}}}{2{{\mu }_{0}}},\] where B is magnetic field and \[{{\mu }_{0}}\] is the magnetic permeability of vaccum, is [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[M{{L}^{1}}\text{ }{{T}^{\,2}}\]
  done clear
  B)
  \[M{{L}^{2}}\text{ }{{T}^{\,\,2}}\]
  done clear
  C)
  \[M{{L}^{2}}\text{ }{{T}^{\,\,1}}\]
  done clear
  D)
  \[ML{{T}^{\,2}}\]
  done clear
  View Answer play_arrow

• question_answer21) Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is\[\mu =0.4,\] the maximum possible value of \[100\times \frac{b}{a}\] for box not to topple before moving is _________. [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer22) A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) _________. [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer23) The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of \[10\,\Omega \]  is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the cell is \[\frac{N}{10}\,\Omega \], where N is an integer then value of N is _________. [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer24) The sum of two forces \[\vec{P}\] and \[\vec{Q}\] is \[\vec{R}\] such that\[\left| {\vec{R}} \right|=\left| {\vec{P}} \right|\]. The angle \[\theta \] (in degrees) that the resultant of \[2\vec{P}\]and  \[\vec{Q}\] will make with \[\vec{Q}\]is_________. [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer25) M grams of steam at \[100{}^\circ C\] is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produces liquid water at \[40{}^\circ C\] [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g], the value of M is _________.  [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer26) 

  In the following reactions, products and (B), respectively, are

  \[\underset{(hot\,\,and\,\,conc.)}{\mathop{NaOH}}\,+C{{l}_{2}}\to \,(A)+\,side\,products\]

  \[\underset{(dry)}{\mathop{Ca(OH)}}\,+C{{l}_{2}}\to \,(B)+\,side\,products\]

  [JEE MAIN Held on 07-01-2020 Evening]

  A)
  \[NaOCl\] and \[Ca{{(OCl)}_{2}}\]
  done clear
  B)
  \[NaCl{{O}_{3}}\]and \[Ca{{(Cl{{O}_{3}})}_{2}}\]
  done clear
  C)
  \[NaOCl\] and \[Ca{{(Cl{{O}_{3}})}_{2}}\]
  done clear
  D)
  \[NaCl{{O}_{3}}\]and \[Ca{{(OCl)}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer27) 

  For the reaction

  \[2{{H}_{2}}(g)\,+2NO(g)\,\to \,{{N}_{2}}(g)+2{{H}_{2}}O(g)\]

  the observed rate expression is,

  rate = \[~{{k}_{f}}{{[NO]}^{2}}\,[{{H}_{2}}]\].

  The rate expression for the reverse reaction is:

  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[{{k}_{b}}[{{N}_{2}}]\,{{[{{H}_{2}}O]}^{2}}/[NO]\]          
  done clear
  B)
  \[~{{k}_{b}}\,[{{N}_{2}}]\,[{{H}_{2}}O]\]
  done clear
  C)
  \[~{{k}_{b}}\,[{{N}_{2}}]\,{{[{{H}_{2}}O]}^{2}}\]
  done clear
  D)
  \[{{k}_{b}}[{{N}_{2}}]{{[{{H}_{2}}O]}_{2}}/[{{H}_{2}}]\]
  done clear
  View Answer play_arrow

• question_answer28)  

  Among the statements (a)-(d), the incorrect ones are

  Octahedral Co(III) complexes with strong field ligands have very high magnetic moments

  When\[{{\Delta }_{0}}<P,\]the d-electron configuration of Co(III) in an octahedral complex is \[t_{eg}^{4}\,e_{g}^{2}\]

  Wavelength of light absorbed by \[[Co{{(en)}_{3}}]{{\,}^{3+}}\]is lower than that of \[[Co{{F}_{6}}]{{\,}^{3-}}\]

  If the \[{{\Delta }_{0}}\]  for an octahedral complex of Co(III) is \[18,000,\,c{{m}^{1}}\] the\[{{\Delta }_{t}}\] for its tetrahedral complex with the same ligand will be \[16,000\text{ }c{{m}^{1}}\]

  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  (c) and (d) only
  done clear
  B)
  (a) and (d) only
  done clear
  C)
  (a) and (b) only
  done clear
  D)
  (b) and (c) only
  done clear
  View Answer play_arrow

• question_answer29) 

  Consider the following reactions                                    [JEE MAIN Held on 07-01-2020 Evening]

  Which of these reactions are possible?

  A)
  [b] and [d]      
  done clear
  B)
  [a] and [d]
  done clear
  C)
  [a] and [b]      
  done clear
  D)
  [b], [c] and [d]
  done clear
  View Answer play_arrow

• question_answer30) For the following reactions where, \[{{k}_{s}}\] and \[{{k}_{e}}\], are, respectively, the rate constants for substitution and elimination, and \[\mu =\frac{{{k}_{s}}}{{{k}_{e}}}\]the correct option is _________ .  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[{{\mu }_{B}}>{{\mu }_{A}}\] and \[{{k}_{e}}(A)>{{k}_{e}}(B)\]
  done clear
  B)
  \[{{\mu }_{A}}>{{\mu }_{B}}\] and \[{{k}_{e}}(A)>{{k}_{e}}(B)\]
  done clear
  C)
  \[{{\mu }_{B}}>{{\mu }_{A}}\] and \[{{k}_{e}}(A)>{{k}_{e}}(B)\]
  done clear
  D)
  \[{{\mu }_{A}}>{{\mu }_{B}}\] and \[{{k}_{e}}(A)>{{k}_{e}}(B)\]
  done clear
  View Answer play_arrow

• question_answer31) A chromatography column, packed with silica gel as stationary phase, was used to separate a mixture of compounds consisting of (A) benzanilide (B) aniline and (C) acetophenone. When the column is eluted with a mixture of solvents, hexane : ethyl acetate (20 : 80), the sequence of obtained compounds is                     [JEE MAIN Held on 07-01-2020 Evening]
  A)
  (A), (B) and (C)
  done clear
  B)
  (C), (A) and (B)
  done clear
  C)
  (B), (C) and (A)
  done clear
  D)
  (B), (A) and (C)
  done clear
  View Answer play_arrow

• question_answer32) The number of possible optical isomers for the complexes \[M{{A}_{2}}{{B}_{2}}\] with \[s{{p}^{3}}\] and \[ds{{p}^{2}}\]hybridized metal atom, respectively, is Note: A and B are unidentate neutral and unidentate monoanionic ligands, respectively. [JEE MAIN Held on 07-01-2020 Evening]
  A)
  2 and 2
  done clear
  B)
  0 and 2
  done clear
  C)
  0 and 1
  done clear
  D)
  0 and 0
  done clear
  View Answer play_arrow

• question_answer33) Which of the following statements is correct?                  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  Gluconic acid is a dicarboxylic acid
  done clear
  B)
  Gluconic acid can form cyclic (acetal/ hemiacetal) structure
  done clear
  C)
  Gluconic acid is a partial oxidation product of glucose
  done clear
  D)
  Gluconic acid is obtained by oxidation of glucose with \[HN{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer34) The bond order and the magnetic characteristics of CN- are [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[2\frac{1}{2}\], paramagnetic          
  done clear
  B)
  3, diamagnetic
  done clear
  C)
  \[2\frac{1}{2}\], diamagnetic
  done clear
  D)
  3, paramagnetic
  done clear
  View Answer play_arrow

• question_answer35) 

  Among statements (A)-(D) the correct ones are:

  (A) Decomposition of hydrogen peroxide gives dioxygen.

  (B) Like hydrogen peroxide, compounds, such as \[KCl{{O}_{3}},Pb\,{{(N{{O}_{3}})}_{2}}\] and \[NaN{{O}_{3}}\]when heated liberate dioxygen.

  (C) 2-Ethylanthraquinone is useful for the industrial preparation of hydrogen peroxide.

  (D) Hydrogen peroxide is used for the manufacture of sodium perborate.

  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  (A) and (C) only
  done clear
  B)
  (A), (B) and (C) only
  done clear
  C)
  (A), (B), (C) and (D)
  done clear
  D)
  (A), (C) and (D) only
  done clear
  View Answer play_arrow

• question_answer36) Two open beakers one containing a solvent and the other containing a mixture of that solvent with a nonvolatile solute are together sealed in a container. Over time: [JEE MAIN Held on 07-01-2020 Evening]
  A)
  The volume of the solution and the solvent does not change
  done clear
  B)
  The volume of the solution increases and the volume of the solvent decreases
  done clear
  C)
  The volume of the solution does not change and the volume of the solvent decreases
  done clear
  D)
  The volume of the solution decreases and the volume of the solvent increases.
  done clear
  View Answer play_arrow

• question_answer37) The redox reaction among the following is:                  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  Reaction of \[[Co{{({{H}_{2}}O)}_{6}}]C{{l}_{3}}\]with \[AgN{{O}_{3}}\]
  done clear
  B)
  Formation of ozone from atmospheric oxygen in the presence of sunlight.
  done clear
  C)
  Combination of dinitrogen with dioxygen at 2000 K
  done clear
  D)
  Reaction of \[{{H}_{2}}S{{O}_{4}}\]with NaOH
  done clear
  View Answer play_arrow

• question_answer38) In the following reaction sequence:  the major product B is:     [JEE MAIN Held on 07-01-2020 Evening]
  A)
        
  done clear
  B)
   
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer39) Within each pair of elements F & Cl, S & Se, and Li & Na, respectively, the elements that release more energy upon an electron gain are:                                   [JEE MAIN Held on 07-01-2020 Evening]
  A)
  F, S and Li
  done clear
  B)
  F, Se and Na
  done clear
  C)
  Cl, S and Li
  done clear
  D)
  Cl, Se and Na
  done clear
  View Answer play_arrow

• question_answer40) Identify the correct labels of A, B and C in the following graph from the options given below: Root mean square speed\[({{V}_{rms}})\]; most probable speed\[({{V}_{mp}})\]; Average speed \[({{V}_{av}})\] [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[A{{V}_{av}};\text{ }B{{V}_{rms}};\text{ }C{{V}_{mp}}\]
  done clear
  B)
  \[A{{V}_{rms}};\text{ }B{{V}_{mp}};C{{V}_{av}}\]
  done clear
  C)
  \[A{{V}_{mp}};\text{ }B{{V}_{rms}};\text{ }C{{V}_{av}}\]
  done clear
  D)
  \[A{{V}_{mp}};\,B{{V}_{av}};\,C{{V}_{rms}}\]
  done clear
  View Answer play_arrow

• question_answer41) The correct order of stability for the following alkoxides is                     [JEE MAIN Held on 07-01-2020 Evening]
  A)
  (B) > (A) > (C)
  done clear
  B)
  (C) > (B) > (A)
  done clear
  C)
  (B) > (C) > (A)
  done clear
  D)
  (C) > (A) > (B)
  done clear
  View Answer play_arrow

• question_answer42) The equation that is incorrect is                                     [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[{{(\Lambda _{m}^{{}^\circ })}_{NaBr}}-(\Lambda _{m}^{{}^\circ }){{\,}_{NaCl}}={{(\Lambda _{m}^{{}^\circ })}_{kBr}}-{{(\Lambda _{m}^{{}^\circ })}_{KCl}}\]
  done clear
  B)
  \[{{(\Lambda _{m}^{{}^\circ })}_{{{H}_{2}}O}}={{(\Lambda _{m}^{{}^\circ })}_{\,HCl}}+{{(\Lambda _{m}^{{}^\circ })}_{NaO{{H}^{-}}}}{{(\Lambda _{m}^{{}^\circ })}_{NaCl}}\]
  done clear
  C)
  \[{{(\Lambda _{m}^{{}^\circ })}_{NaBr}}-(\Lambda _{m}^{{}^\circ }){{\,}_{NaI}}={{(\Lambda _{m}^{{}^\circ })}_{kBr}}-{{(\Lambda _{m}^{{}^\circ })}_{NaBr}}\]
  done clear
  D)
  \[{{(\Lambda _{m}^{{}^\circ })}_{KCl}}-(\Lambda _{m}^{{}^\circ }){{\,}_{NaCl}}={{(\Lambda _{m}^{{}^\circ })}_{kBr}}-{{(\Lambda _{m}^{{}^\circ })}_{NaBr}}\]
  done clear
  View Answer play_arrow

• question_answer43) In the following reaction sequence, structures of A and B, respectively will be  [JEE MAIN Held on 07-01-2020 Evening]
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer44) The refining method used when the metal and the impurities have low and high melting temperatures, respectively, is                                                                      [JEE MAIN Held on 07-01-2020 Evening]
  A)
  Zone refining
  done clear
  B)
  Vapour phase refining
  done clear
  C)
  Liquation
  done clear
  D)
  Distillation
  done clear
  View Answer play_arrow

• question_answer45) The ammonia \[(N{{H}_{3}})\]released on quantitative reaction of 0.6 g urea \[(N{{H}_{2}}CON{{H}_{2}})\]with sodium hydroxide (NaOH) can be neutralized by [JEE MAIN Held on 07-01-2020 Evening]
  A)
  200 ml of 0.4 N HCl
  done clear
  B)
  100 ml of 0.1 N HCl
  done clear
  C)
  200 ml of 0.2 N HCl
  done clear
  D)
  100 ml of 0.2 N HCl
  done clear
  View Answer play_arrow

• question_answer46) 

  Consider the following reactions:

  \[NaCl+{{K}_{2}}C{{r}_{2}}{{O}_{7}}+\underset{(Conc.)}{\mathop{{{H}_{2}}S{{O}_{4}}}}\,\to (A)+side\,products\]

  \[(A)+NaOH\to (B)+Side\,products\]

  \[(B)+\underset{(dilute)}{\mathop{{{H}_{2}}S{{O}_{4}}}}\,+{{H}_{2}}{{O}_{2}}\to \text{(}C\text{)}+Side\text{ }products\]

  The sum of the total number of atoms in one molecule each of (A), and is _____.

  [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer47) The flocculation value of HCl for arsenic sulphide sol. is\[30\text{ }m\text{ }mol\text{ }{{L}^{1}}\]. If \[{{H}_{2}}S{{O}_{4}}\]is used for the flocculation of arsenic sulphide, the amount, in grams, of \[{{H}_{2}}S{{O}_{4}}\] in 250 ml required for the above purpose is ______. (molecular mass of \[{{H}_{2}}S{{O}_{4}}\] = 98 g/mol) [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer48) The number of \[s{{p}^{2}}\] hybridised carbons present in "Aspartame" is ______. [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer49) 

  3 g of acetic acid is added to 250 mL of 0.1 M HCl and the solution made up to 500 mL. To 20 mL of this solution \[\frac{1}{2}\,mL\]of 5 M NaOH is added. The pH of the solution is_______.

  [Given: \[p{{K}_{a}}\] of acetic acid = 4.75, molar mass of acetic acid = 60 g/mol, log3 = 0.4771]

  Neglect any changes in volume.

  [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer50) The standard heat of formation \[({{\Delta }_{f}}H_{298}^{0})\] ethane (in kJ/mol), if the heat of combustion of ethane, hydrogen and graphite are -1560, -393.5 and -286 kJ/mol, respectively is_______.         [JEE MAIN Held on 07-01-2020 Evening]
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• question_answer51) The value of c in the Lagrange's mean value theorem for the function \[f(x)={{x}^{3}}4{{x}^{2}}+8x+11,\] when \[x\in [0,1]\]  is [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\frac{4-\sqrt{7}}{2}\]          
  done clear
  B)
  \[\frac{4-\sqrt{5}}{3}\]
  done clear
  C)
  \[\frac{2}{3}\]
  done clear
  D)
  \[\frac{\sqrt{7}-2}{3}\]
  done clear
  View Answer play_arrow

• question_answer52) Let y= y(x) be the solution curve of the differential equation, \[({{y}^{2}}-x)\frac{dx}{dx}=1,\] satisfying y(0) = 1. This curve intersects the x-axis at a point whose abscissa is [JEE MAIN Held on 07-01-2020 Evening]
  A)
  2 - e
  done clear
  B)
  2 + e
  done clear
  C)
  - e                   
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer53) Let y = y(x) be a function of x satisfying \[y\sqrt{1-{{x}^{2}}}=k-x\sqrt{1-{{y}^{2}}}\] where k is a constant and \[y\left( \frac{1}{2} \right)=-\frac{1}{4}.\]Then \[\frac{dy}{dx}\]at \[x=\frac{1}{2}\], is equal to [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[-\frac{\sqrt{5}}{2}\]
  done clear
  B)
  \[\frac{2}{\sqrt{5}}\]
  done clear
  C)
  \[\frac{\sqrt{5}}{2}\] 
  done clear
  D)
  \[-\frac{\sqrt{5}}{4}\]
  done clear
  View Answer play_arrow

• question_answer54) Let \[A=[{{a}_{ij}}]\] and \[B=[{{b}_{ij}}]\] be two \[3\times 3\] real matrices such that \[{{b}_{ij}}={{(3)}^{(i+j2)}}\,{{a}_{ji}},\]where i, j = 1, 2, 3. If the determinant of B is 81, then the determinant of A is         [JEE MAIN Held on 07-01-2020 Evening]
  A)
  1/9      
  done clear
  B)
  1/81
  done clear
  C)
  3                     
  done clear
  D)
  1/3
  done clear
  View Answer play_arrow

• question_answer55) Let \[\alpha \] and \[\beta \] be the roots of the equation \[{{x}^{2}}-x-1=0\].  If \[{{p}_{k}}={{(\alpha )}^{k}}+{{(\beta )}^{k}}\], \[k\ge 1,\]then which one of the following statements is not true? [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[{{p}_{3}}={{p}_{5}}{{p}_{4}}\]
  done clear
  B)
  \[({{p}_{1}}+{{p}_{2}}+{{p}_{3}}+{{p}_{4}}+{{p}_{5}})=26\]
  done clear
  C)
  \[{{p}_{5}}=11\]
  done clear
  D)
  \[{{p}_{5}}={{p}_{2}}\cdot {{p}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer56) Let A, B, C and D be four non-empty sets. The contrapositive statement of "If \[A\subseteq B\] and\[B\subseteq D\], then \[A\subseteq C\]" is                                                   [JEE MAIN Held on 07-01-2020 Evening]
  A)
  If \[AC\], then \[A\subseteq B\] and \[B\subseteq D\]
  done clear
  B)
  If \[AC\], then \[AB\] and \[B\subseteq D\]
  done clear
  C)
  If \[AC\], then \[AB\] or \[BD\]
  done clear
  D)
  If \[A\subseteq C\], then \[B\subset A\] or \[D\subset B\]
  done clear
  View Answer play_arrow

• question_answer57) The area (in sq. units) of the region \[\{(x,\text{ }y)\in {{R}^{2}}|4{{x}^{2}}\le y\le 8x+12\}\] is [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\frac{128}{3}\]        
  done clear
  B)
  \[\frac{125}{3}\]
  done clear
  C)
  \[\frac{127}{3}\]        
  done clear
  D)
  \[\frac{124}{3}\]
  done clear
  View Answer play_arrow

• question_answer58) Let the tangents drawn from the origin to the circle, \[{{x}^{2}}+{{y}^{2}}8x4y+16=0\]touch it at the points A and B. The \[{{(AB)}^{2}}\]is equal to    [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\frac{64}{5}\]                      
  done clear
  B)
  \[\frac{52}{5}\]
  done clear
  C)
  \[\frac{56}{5}\]          
  done clear
  D)
  \[\frac{32}{5}\]
  done clear
  View Answer play_arrow

• question_answer59) Let \[{{a}_{1}},\,\,{{a}_{2}},\,\,{{a}_{3}}\text{ }...\]be a G.P. such that\[{{a}_{1}}<0\], \[{{a}_{1}}+{{a}_{2}}=4\]and\[{{a}_{3}}+{{a}_{4}}=16\]. If \[\sum\limits_{i=1}^{9}{{{a}_{i}}}=4\lambda \], then \[\lambda \] is equal to [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[-\,513\]         
  done clear
  B)
  \[-\,171\]
  done clear
  C)
  \[\frac{511}{3}\]        
  done clear
  D)
  \[171\]
  done clear
  View Answer play_arrow

• question_answer60) In a workshop, there are five machines and the probability of any one of them to be out of service on a day is \[\frac{1}{4}\]. If the probability that at most two machines will be out of service on the same day is \[{{\left( \frac{3}{4} \right)}^{3}}\]k, then k is equal to                     [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[4\]                 
  done clear
  B)
  \[\frac{17}{4}\]
  done clear
  C)
  \[\frac{17}{8}\]                      
  done clear
  D)
  \[\frac{17}{2}\]
  done clear
  View Answer play_arrow

• question_answer61) The number of ordered pairs (r, k) for which \[6\cdot {{\,}^{35}}{{C}_{r}}=({{k}^{2}}3)\,\cdot {{\,}^{36}}{{C}_{r}}_{+1},\]where k is an integer, is [JEE MAIN Held on 07-01-2020 Evening]
  A)
  3                     
  done clear
  B)
  6
  done clear
  C)
  2                     
  done clear
  D)
  4
  done clear
  View Answer play_arrow

• question_answer62) The locus of the mid-points of the perpendiculars drawn from points on the line, \[x=2y\]to the line \[x=y\] is [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[5x7y=0\]      
  done clear
  B)
  \[2x3y=0\]
  done clear
  C)
  \[3x2y=0\]      
  done clear
  D)
  \[7x5y=0\]
  done clear
  View Answer play_arrow

• question_answer63) Let f(x) be a polynomial of degree 5 such that \[x=\pm 1\] are its critical points. If \[\underset{x\to 0}{\mathop{\lim }}\,\left( 2+\frac{f(x)}{{{x}^{3}}} \right)=4\], then which one of the following is not true? [JEE MAIN Held on 07-01-2020 Evening]
  A)
  f is an odd function
  done clear
  B)
  x =1 is a point of minima and \[x=1\] is a point of maxima of f.
  done clear
  C)
  \[f\left( 1 \right)4f\left( 1 \right)=4\]
  done clear
  D)
  x =1 is a point of maxima and \[x=1\] is a point of minimum of f.
  done clear
  View Answer play_arrow

• question_answer64) If \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\] be respectively the smallest and the largest values of \[\theta \] in \[(0,2\pi )-\{\pi \}\] which satisfy the equation, \[2\,{{\cot }^{2}}\theta -\frac{5}{\sin \theta }+4=0\], then \[\int\limits_{{{\theta }_{1}}}^{{{\theta }_{2}}}{{{\cos }^{2}}\,3\theta \,d\theta },\] is equal to [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\frac{\pi }{3}+\frac{1}{6}\]          
  done clear
  B)
  \[\frac{\pi }{3}\]
  done clear
  C)
  \[\frac{2\pi }{3}\]                   
  done clear
  D)
  \[\frac{\pi }{9}\]
  done clear
  View Answer play_arrow

• question_answer65) Let \[\vec{a},\text{ }\vec{b}\] and \[\vec{c}\] be three unit vectors such that \[\vec{a}+\vec{b}+\vec{c}=\vec{0}.\] If \[\lambda \,=\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}.\] and \[\vec{d}=\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}\] then the ordered pair, \[\left( \lambda ,\vec{d} \right)\] is equal to                                 [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\left( \frac{3}{2},3\vec{a}\times \vec{c} \right)\]    
  done clear
  B)
  \[\left( -\frac{3}{2},3\vec{c}\times \vec{b} \right)\]
  done clear
  C)
  \[\left( -\frac{3}{2},3\vec{a}\times \vec{b} \right)\]
  done clear
  D)
  \[\left( -\frac{3}{2},3\vec{b}\times \vec{c} \right)\]
  done clear
  View Answer play_arrow

• question_answer66) If \[3x+4y=12\sqrt{2}\]is a tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{9}=1\]for some \[a\in R\], then the distance between the foci of the ellipse is                                                             [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[2\sqrt{5}\]    
  done clear
  B)
  \[~2\sqrt{7}\]
  done clear
  C)
  \[4\]                 
  done clear
  D)
  \[2\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer67) If the sum of the first 40 terms of the series, \[3+4+8+9+13+14+18+19+\]... is (102)m, then m is equal to                                                                              [JEE MAIN Held on 07-01-2020 Evening]
  A)
  5                     
  done clear
  B)
  20
  done clear
  C)
  25       
  done clear
  D)
  10
  done clear
  View Answer play_arrow

• question_answer68) If \[\frac{3+i\sin \theta }{4-i\cos \theta },\,\theta \in [0,\,2\pi ]\], is a real number, then an argument of \[\sin \,\theta +\,i\cos \theta \] [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[\pi -{{\tan }^{-1}}\left( \frac{3}{4} \right)\]
  done clear
  B)
  \[\pi -{{\tan }^{-1}}\left( \frac{4}{3} \right)\]
  done clear
  C)
  \[-{{\tan }^{-1}}\left( \frac{3}{4} \right)\]  
  done clear
  D)
  \[{{\tan }^{-1}}\left( \frac{4}{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer69) The coefficient of \[{{x}^{7}}\] in the expression \[{{(1+x)}^{10}}+x{{(1+x)}^{9}}+{{x}^{2}}{{(1+x)}^{8}}+\text{ }\ldots \text{ }+\text{ }{{x}^{10}}\] is [JEE MAIN Held on 07-01-2020 Evening]
  A)
  120                 
  done clear
  B)
  330
  done clear
  C)
  420                 
  done clear
  D)
  210
  done clear
  View Answer play_arrow

• question_answer70) The value of \[\alpha \] for which \[4\alpha \int\limits_{-1}^{2}{{{e}^{-\,\alpha \left| x \right|}}}\] dx=5, is [JEE MAIN Held on 07-01-2020 Evening]
  A)
  \[{{\log }_{e}}\left( \frac{4}{3} \right)\]       
  done clear
  B)
  \[{{\log }_{e}}\left( \frac{3}{2} \right)\]
  done clear
  C)
  \[{{\log }_{e}}2\]      
  done clear
  D)
  \[{{\log }_{e}}\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer71) 

  If the system of linear equations,

  \[x+y+z=6\]

  \[x+2y+3z=10\]

  \[3x+2y+\lambda z=\mu \]

  has more than two solutions, then \[\mu -{{\lambda }^{2}}\] is equal to ____________.

  [JEE MAIN Held on 07-01-2020 Evening]
  View Answer play_arrow

• question_answer72) If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through \[(\alpha ,\text{ }7,\text{ }1)\]is \[\left( \frac{5}{3},\frac{7}{3},\frac{17}{3} \right),\]then \[\alpha \] is equal to ____________. [JEE MAIN Held on 07-01-2020 Evening]
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• question_answer73) If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to __________.                                               [JEE MAIN Held on 07-01-2020 Evening]
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• question_answer74) If the function f defined on \[\left( -\frac{1}{3},\frac{1}{3} \right)\] by   is continuous, then k is equal to _________.                  [JEE MAIN Held on 07-01-2020 Evening]
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• question_answer75) Let\[X=\{n\in N:1\,\,\le \,\,n\le 50\}\]. If \[A=\{n\in X:n\] is a multiple of 2} and \[B=n\in X:n\] is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________. [JEE MAIN Held on 07-01-2020 Evening]
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