JEE Main 2021 Answer Key (Out), Papers, Solution – Get Keys Here

Q.1 A circle center = (-15, 0) and radius = 15/2. Chord to the circle passes through (-30, 0) & tangent to y² = 30x. Length of the chord = ?

Answer. 15/√5

Q.2 If ln (x+y) = 4xy, find d²y/ dx² at x = 0.

Answer. 40

Q.3 If the sum of distances of point P from (0,0) (0, 1) (1, 0) (1,1) = 18. Locus is at the circle of the diameter. Find d².

Answer. 16

Q.4 Frequency changes from 280 to 400nm. Work function = 2.5eV. Then find the change in the stopping potential.

Answer. 1.32eV

Q.5 3m long chain on a table. Mass of chain is 3 kg. 2m on the table…if it slips find the kinetic energy.

Answer. 40 J

Q.6 Number of compounds which have a greater freezing point of 0.1M enthanol.

Answer. 0

Q.7 How many electrons are present in 4f orbital of Gd²⁺.

Answer. 7 outermost configuration is 4f*7 5d*1

Q.8 S1: Frenkel defect is shown as interstitial as well as vacancy defect.
S2: In Frenkel defect, solids show colour due to F-center.

Answer. Both S1 & S2 are incorrect

Q.9 Interhalogen compound AB₃ has a T-shaped structure, home many lone pairs are present on A?

Answer. 2

Q.10 For the Hydrogen like atom, the transition from n=3 to n=1, frequency is 192 x 10¹⁵. Then find the frequency when transition takes place from n=2 to n=1.

Answer. 162 x 10¹⁵

Q.11 At the same temperature rms speed of Hydrogen, oxygen and carbon dioxide be V_H2, V_O2, V_CO2

Answer. V_H2 > V_O2 > V_CO2

Q.12 Formula for Hydroxyapatite

Answer. Ca₅(PO₄)₃

Q.13 If ln (x+y) = 4xy, find d²y/ dx² at x = 0.

Answer. 40

Q. 14 The ratio of water molecules of potash alum to Mohr’s salt is

Answer. 4

Q.15 Car A overtakes car B with relative velocity of 40 ms^-1. With what velocity car A appearing in the mirror (f = 10 cm) of car N 1.9m far from it.

Answer. 0.1ms^-1

Q.16 Ellipse: x²/8 + y²/4 = 1 tangent at P(2nd quard) ⊥ to x+dy=0 eccentricity = e. SS’ is foci. Find (5-e²)* ΔSPS’.

Answer. 12

Q.17 Find ∑ r² . ²⁰C_r.

Answer. 210 x 2¹⁹

Q.18 Which of the following will dissolve in water and give colour?
1.) Cu₂Cl₂
2.) CuCl₂
3.) AgBr
4.) ZnCl₂

Answer. CuCl₂

Q.19 On heating novolac with formaldehyde which of the following polymers will form.

Answer. Bakelite

Q.20 Mean & standard deviation of 20 observations are 10 & 2.5. It is observed that one entry was taken 25 instead of 35. Find correct mean & variance.

Answer. 10.5, 26

Q.21 a + ar + ar² + …… ^∞ = 15
a² + (ar)² + (ar²)² + ……. ^∞ = 150. Find ar² + ar⁴ + ar⁶ + ……^∞

Answer. 1/2

Q.22 S1: Ellingham diagram is used to check which metal to be reduced by which compound.
S2: In Ellingham diag as we move from left to right ΔS increases.

Answer. S1 is incorrect but S2 is correct.

Q.23 S1: Methyl orange is a suitable indicator for titration of strong acid and weak base.
S2: Phenolphthalein is not a suitable indicator for titration of acetic acid and NaOH.

Answer. S1 is correct but S2 is incorrect.

Q.24 Find the dimensions of p in the formula p = E L M^-5G^-2, where E = Energy, M = Angular Momentum, M = Mass, G = Gravitational Constant

Answer. M⁰L⁰T⁰

Q.25 ((cos^2(x)+cos^4(x))/(sin^2(x)+sin^4(x)))

Q.26 Reaction of phenol with Br₂ and H₂O gives A reaction and reaction of phenol with Br₂ and CS₂ at less than 5^oC gives B. Find the products A and B.

JEE Main 2021 Final Answer Key (Official) for third phase has been released on 5th August 2021. Click here to view answer key.

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JEE Main 2021 Institutional Answer Key for April session has been released for  Day 4 (Shift 1 & 2). Check below for the institutional answer key.

Institutional Answer Key by Resonance:

JEE Main 2021 Final Answer Key for March session has been released on 24th March 2021. Click here to view answer keys.

JEE Main 2021 Institutional Answer Key for March session exam has been released. Official answer key is releasing soon. Check answer key from below.

JEE Main 2021 Final Answer Key for February session (Paper 2) has been released on 18th March 2021. Click here to view answer key.

Institutional Answer Key by Reliable Kota:

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Memory Based Answer Key (16th March- Shift 1)

Q. 1: A magnetized steel wire magnetic moment M₁. If the wire is bent to form a semi-circular arc. What will be the new magnetic moment?

Answer: 2m/π

Q.2: Separation of sulphur & oxide are done by what method?

Answer: Froth floatation

Q.3: The middle term in the expression (x² +1/n² + 2)ⁿ is?

Answer: (2n)! /(n!)²

Q.4: Which hydride of group 15 has most reducing power?

Answer: Bi

Q.5: Which is a natural polymer?

Answer: Pectin

Q.6: What is the name of vitamin B12?

Answer: Cyclocobalamine

Q.7: A particle is moving along x-axis. x = A + Bsinωt, SHM. Find amplitude.

Answer: B

Q.8: Total volume of container is V, 16g O₂, 44g CO₂, 28g N₂. Find pressure.

Answer: 5RT/2V

Q.9: Number of divisors of the form (4n+2), of the integer 240 is?

Answer: 20

Q.10: Ozone is responsible for ?

Answer: Oxidizing smog

Q. 1: The minimum number of times a fair coin need to be tossed so that probability of getting at least two head is at least 0.96 is…?

Answer: 8

Q.2: Find the equation of normal to the curve x² = 4y which passes through the point (1,2)?

Answer: x+y=3

Q.3: If A+B+C=180° then find tanA+tanB+tanC=?

Answer: tanA tanB tanC

Q.4: Who was the designer of World Trade Center?

Answer: Minoru Yamasaki, Emery Roth

Q.5: Area of triangle formed by the complex number z, iz and z+iz is?

Answer: 1/2ΙzΙ²

Q.6: The DE representing the family of curve Y² (2c+x²⁰²¹) where c is the positive parameter is of?

Answer: Order 1

Q.7: If z₁ and z₂ unimodular complex number that satisfy z₁² + z₂² = 4 then (z_{1 +} z₁)² (z_{2 +} z₂)² is equal to?

Answer: 12

Q.8: Given x=cy+bx, y=az+cx, z=bx+ay, where x, y and z are not all zero then a² + b² + c² = 2ab is equal to?

Answer: 1

Q.9: Number of divisors of the form (4n+2), of the integer 240 is?

Answer: 20

Q.10: The locus of the midpoint of the chord of the circle x²+y=4 which substance a right angle at the origin is?

Answer: x²+y²=2

Q.11: The point on the curve Y² + 3x= 12y, when the tangent is vertical, is (are)?

Q.12: If B and C are square matrix of order n, and if A=B+C and BC=CB and C²=0, then for any positive integer P, AP+1=Bk[B+(P+1)C]

Answer: P

Q.13: The area bounded by the curve y=√x. 2y+3 =x, and x-axis in the first quadrant is?

Answer: 9 sq units

Q.14: If f:(1,∞)–> (2,∞) is given by f(n)=n+1, the f-1(n) equals to?

Answer: x+√x2-4/2

Q.15: If 0< P(A) < 1, 0< P(B) < 1 and P (A⋃B) = P (A) + P(B) – P(A) P(B), then select the appropriate answer.

Answer: P(A/B) = P(A)

Q.16: If x > 1, y > 1, z > 1 are in GP, then 1 /1+lnx, 1 /1+lny, 1 /1+lnz are in _______

Answer: HP

Q.17: If z₁ and z₂ are two non-zero complex number such that |z₁ + z₂| = |z₁| + |z₂|, then argz₁ – argz₂ is equal to?

Answer: 0

Q. 1: A gas have three translation and two rotational degree of freedom. Find c∨p/ c∨v.

Answer: 7/5

Q. 2: Length of clock second hand 0.1 m what is the order of its angular velocity in radian per/ sec.

Answer: 10^∧-1

Q. 1: Which is not an essentials amino acids?

1. Valine
2. Tryosine
3. Leucine
4. Lysine

Answer: 2. Tryosine 

Q. 2: Water vapours and water in container are in equilibrium. Some amount of glucose is added to water. What happens to the rate of evaporations?

Answer: Decrease 

Q. 3: How many coordination sides are there in EDTA4- in integer type?

Answer: 4 

Q. 4: If the co- ordinates of two point A and B are (√7, 0) and (-√7, 0) respectively and P is any point on the curve 9x^∧2+16y^∧2=144. Then find AP+PB.

Answer: 8 

Q. 5: Given that these are 7 observations 2, 4, 10, 12, 14, x, y and their mean=8 and variance= 16. The Ι x-y Ι is:

1. 2
2. 4
3. 5
4. 6

Answer: 1. 2 

Q. 6: Which is not necessary Apparatus in acid base titration?

Answer: Bunsen burner 

Q. 7: A uniform current carrying ring of mass m and radius R is connected by a mass less string. A uniform magnetic field B0 exists in the region to keep the ring horizontal. The current in the ring is:

Q. 8: If the distance of the line 2x-y+3= 0 from 4x-2y+p=0 and 6x-3y+r=0 is respectively 1/√5 and 2√5.

Answer: P=(8,4) R(15,13)

Q. 9: Let λ ∈ R, the system of linear equation

2x₁-4x₂+λx₃=1

x₁-6x₂+x₃=2

λx₁-10x₂+4x₃=3

is 0 in constant. Find the value of λ

Answer: -4

Q. 10: Find the magnetics moment and electronic configuration of Gd3+(Z=64) is:

Q. 11: How many isomers possible for [Pt (en)²(NO2)2] compound?

Answer: 3 

Q. 12: If the point P on the curve 4x^∧2+5y^∧2-20 is the farthest from the point Q (0, -4) then find PQ^∧2

Answer: 36 

Q. 13: Find the product of the roots of equation 9x^∧2-18 ΙxΙ + 5=0

Answer: 25/ 81 

Q. 14: If the common tangent to the parabola y^∧2=4x and x^∧2=4y also touches the circle  x^∧2+y^∧2= c^∧2. Then find the value of c?

Q. 15: 2^∧10+2^∧9. 3^∧1,…..+2.3^∧10+ 3^∧10=A-2^∧11. Find A

Answer: 2.3^∧10

Q. 1: What is the role of the CaCo3 in the extraction of iron?

1. If decomposes to form CaCo3 which acts as a flux
2. It is used a reducing agent
3. For purification of iron
4. None of these

Q. 2: Which is the following is not a method of purification of colloid?

1. Dialysis
2. Peptization
3. Electrodialysis
4. Ultrafiltration

Answer: 2. Peptization 

Q. 3: A Balmer series lies in which region of the electromagnetic spectrom?

1. Ultraviolet
2. Infrared
3. Visible range
4. Microwave

Answer: 3. Visible range 

Q. 4: A circular disc of mass M and radius R rotating with the speed w and another disc of the same mass M and radius R/ 2 placed coaxially on first disc. After sometime, disc 2 also attain constant speed w∨2 . Find the loss of percentage in energy.

Answer: 20%

Q. 5: Two charges 4q and -q are kept on x-axis at (-d/2,0) and (d/2,0). Then a charge +q is is moved from the origin to x=d via semi circler path. Then find the charge in its energy.

Answer: 16kq/3d

Q. 6: In maltose structure which three groups are there?

Answer: Hemiacetal, acetal 

Q. 7: For the first order reaction/ 75% reaction complete in 90 min. For the same reaction 60% complete in what time?

Answer: 33 min 

Q. 8: Leat nitrate on heating gives A, A on cooling gives B, NO with B give C (blue solid). Find oxidation number of N in compound C.

1. +1
2. +2
3. +3
4. +4

Answer: 3. +3

Q. 9: Which is the following reacts with CHCl3+ KOH?

1. Adenine and uracil
2. Adenine and lysine
3. Adenine and thymine
4. Adenine and uracil

Answer: 3. Adenine and thymine 

Q. 10: It is given that AB=15 and CD=10. They are parallel rods on the ground. AC and BD meet hypothetically at P. Find distance of P from the ground.

Answer: -6 

Q. 11: Element with atomic number 101 and 104 belongs to the group respectively.

1. Actinoacids and gr 4
2.  gr 4 and gr 3
3. gr 4 and gr 5
4. None

Answer: 1. Actinoacids and gr 4 

Q. 12: If from point P (3,3) on the hyperbola as a normal is drawn which cuts x-axis at (9,0) on the hyperbola x2/a2-y2/b2 =1 then the value of (a2, e2) is:

Answer: (9/2, 3)

Q. 13: Which represents the correct order of ionic radii?

Answer: Mg2+<Na+<F-<O2 2-

Q. 14: 76% people read newspaper A and 63% read newspaper B then the probability of people who read both of the newspapers are?

Q. 15: A solution contains two volatile solvents of 1 mole of n- hexane and 3 mole of n- heptane. In this case, vapour pressure of the solution 550 mm Hg. If 1 mole of 1- Heptane if further added to solution. The vapour pressure increases by 10 mm Hg. Find out the pressure of pure n- Heptane solution?

Answer: 600 mm Hg 

Q.1: Thermal power plant cause

1. Acid rain
2. Ozone layer depletion
3. baby syndrome
4. eutrophication

Aswer: 1. Acid rain 

Q. 2: No. of P=o, P-oh, P-o-p bond is pyrophosphoric acid?

Q. 3: If a variable place in 3-0 space moves in such a way that the sum of its intercepts on the x and y-axis exceeds, the reciprocal of its intercept on the Z-axis is by 2, then all such plane will pass through  the point:

1. (1/2, 1/2, -1/2)
2. (1/2, 1/2, 1/2)
3. (1/2, -1/2, -1/2)
4. (1/2, -1/2, 1/2)

Answer: (1/2, 1/2, -1/2)

Q. 4: A bag is contain 6 red balls and 10 orange balls. 3 balls are drawn from it one by one randomly without replacement. if the third ball drawn is red, then the probably that the first two balls are green is:

1. 3/7
2. 9/149
3. 9/56
4. 3/8

Answer: 1. 3/7 

Q. 5: If the first term is 3 and sum of the first 25 terms is equal to the sum of the next 15 terms then find the common difference?

Q. 6: Let the data 4, 10, x, y, 27 be in increasing order. If the medium of data is 18 and its mean deviation about mean is 7.6, then the mean of this data is:

1. 7
2. 16
3. 16.5
4. 15.5

Answer: 1. 7 

Q. 7: Let the ellipse, x2/ a2, y2/ b2 = 1, if a > b pass through the point (2,3) and have eccentricity equal to 1/2, then the equation of normal to the ellipse to (2,3) is:

Q. 8: Gas released When Ay, Pt dissolved in Aqua region

1. NO
2. N2
3. N2O3
4. N2O5

Answer: 1. NO

Q. 9: Number of isomers including stereoisomers of simplest optically active alkene after hydrogenation H2/ Ni and monohalogenation with HX

Answer: 8

Q.10: Min bond length

1. NO2⁺
2. NO⁺
3. NO
4. NO^–

Q. 11: Find % w/w of H₂O in solution containing glucose with Xgluc =0.1

1. 20%
2. 47.3%
3. 25.3%
4. 27.4%

Answer: 2. 47.3%

Q. 12: Most basic amino acid is?

Answer: Cystein

Q. 13: A solution of 4% X and another solution having 12% Y (both soliton have same solvent). If molar mass X is A then molecular mass of Y is:

1. 3A
2. A
3. A/2
4. 2A

Answer: 1. 3A

Q. 14: If the centre of circle lies on x+y=2 and it touches the line x=3 and y=2, find the diameter of the circle?

Answer: 3

Q. 15: A dice is thrown twice. Sum of both the observation is a multiple of 4. Find the probability that 4 appeared at at least once?

Answer: 1/9

Q. 16: If the wavelength on incident radiation changes from 500nm to 200nm, then the maximum kinetic energy increases to three times. Find the work function?

Answer: 0.62eV

Q. 17: Pressure inside soap bubble is 1.01 and 1.02 atmosphere. The ratio between their volume is:

1. 102:101
2. (102)3: (101)3
3. 8:1
4. 2:1

Answer: 3. 8:1 

Q. 18: A ballon contain He gas at ‘T’ get burst then it is:

1. Reversible isothermal
2. Irreversible isothermal
3. Reversible adiabatic
4. Irreversible adiabatic

Answer: 4. Irreversible adiabatic

Q. 19: Boiling point of water is 273k, then the boiling point of H2S is:

1. >373k
2. <373k
3. 373k
4. 373>x>300k

Answer: 2. <373k

Q. 20: Find the atomic number of unnilennium

1. 101
2. 107
3. 109
4. 119

Answer: 3. 109

Q. 21: How glycerol can be purified

1. Distillation under reduced pressure
2. Fractional distillation
3. Differential extraction
4. steam distillation

Answer: 1. Distillation under reduced pressure 

Q. 1: Which of the following is different sol?

1. butter
2. paints
3. gen stone
4. cake

Answer: 3. gen stone 

Q. 2: Find the length and the foot of perpendicular from the point of (1, 3/2,2) to the plane 2x-2y+4z+5=0.

Q. 3: Which property has different order wrt others?

1. Atomic radius
2. Electronegativity
3. Ionisation energy
4. Electrongain Enthalpy

Answer: 1. Atomic radius 

Q. 4: What is structure of Dettol?

Q. 5: If F=ma and mass (M) is defined as α and acceleration (a) is defied as β. The find the new SI unit of F.

Q. 6: F(x)=-(3/4)X2-8X3-42/5X2+105.  calculate local maxima and local minima.

Q. 1: A boy can throw a stone up to a maximum height of 10m. The maximum horizontal distance that the boy can throw the same stone will be-

1. 20m
2. 20?2m
3. 10m
4. 10?2m

Answer- 1. 20m

Q. 2: Where is Notre Dame Cathedral located?

Answer- Paris, France

Q. 3: An equation of plane parallel to the plane x-2y+2z-5 =0 and at a unit distance from the origin is-

1. x-2y+2z-5=0
2. x-2y+2z-3=0
3. x-2y+2z+1=0
4. x-2y+2z-1=0

Answer- 2. x-2y+2z-3=0

Q. 4: A Carnot engine whose efficiency is 40% takes in the heat from a source maintained at a temperature of 500 k. It is desired to have an engine of efficiency of 60%. Then the intake temperature from the same exhaust (sink) temperature must be-

1. 600 k
2. Efficiency of Carnot cannot be made larger than 50%
3. 1200 k
4. 750 k

Answer- 4. 750 k

Q. 5: If the line 2x=y=k passes through the point which divides the line segment joining the points (1,1) and (2,4) the ratio 3:2, then k equals-

1. 11/15
2. 29/5
3. 5
4. 6

Answer- 4. 6

Q. 6: Where does the president of USA lives?

Answer – The white house

Q. 7: A thin liquid film formed between a U- shaped wire and a light slider supports and weight of 1.5×10-2N. The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is-

Answer- 0.025

Q. 8: Where Bara Imambra is located?

Answer: Lucknow

Q. 9: Downing street is whose residence?

Answer: Downing Street is the residence of the prime minister of the United Kingdom (the lord of the treasury).

Q. 10: Where is Badrinath located?

Answer: Uttarakhand

Q. 11: Which colour represents equality?

Answer: White

Q. 12: Where is leaning tower located?

Answer: Italy 

Q. 13: What does shaft represent?

Q. 14: If pth, nth, rah terms of G.P. then p,q,r are in?

Q. 15: Given 30 observation then 10 observations are 1/2-d, other 10 observations are d and remaining 10 observations are 1/2+d, the variance is given 4/3

Q. 16: Draw a highway road diagram with car and truck in opposite directions

Q. 17: F (x+y)= f(x).f(y)x, y€N f(1)=2 then sigma k= 1 to 50 f(4+k)=

Q. 18: Free fall of an object in vacuum in the case of motion

Q. 19: Who designed IIM?

Answer: Luis Khan 

Q. 20: Which colour reflects the maximum light?

Q. 21: a1 a2 a3 a4 a5 are ap. sum of the term is equal to 30. product of the term is equal to 3840. find product of first and last term