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JEE Main 26 February 2021 Shift 1 Question Paper with Answers

26 February 2021 · February session · 85 questions

85 of the 90 questions from the JEE Main 26 February 2021 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

5 questions are held back from this paper while we re-check the transcription or the answer key. We would rather show you nothing than show you an answer we are not confident is right.

Physics
29
Chemistry
27
Mathematics
29

Physics — JEE Main 26 February 2021 Shift 1

Q1·PhysicsSingle correct
If λ1_11​ and λ2_22​ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of λ1_11​ : λ2_22​ is :
  1. (A)1 : 3
  2. (B)1 : 9
  3. (C)7 : 135
  4. (D)7 : 108

Correct answer: (C)

Step-by-step solution →
Q2·PhysicsSingle correct
The temperature θ at the junction of two insulating sheets, having thermal resistances R1_11​ and R2_22​ as well as top and bottom temperatures θ1_11​ and θ2_22​ (as shown in figure) is given by :
  1. (A)θ1R2+θ2R1R1+R2\frac{\theta_1 R_2 + \theta_2 R_1}{R_1 + R_2}R1​+R2​θ1​R2​+θ2​R1​​
  2. (B)θ1R2−θ2R1R2−R1\frac{\theta_1 R_2 - \theta_2 R_1}{R_2 - R_1}R2​−R1​θ1​R2​−θ2​R1​​
  3. (C)θ2R2−θ1R1R2−R1\frac{\theta_2 R_2 - \theta_1 R_1}{R_2 - R_1}R2​−R1​θ2​R2​−θ1​R1​​
  4. (D)θ1R1+θ2R2R1+R2\frac{\theta_1 R_1 + \theta_2 R_2}{R_1 + R_2}R1​+R2​θ1​R1​+θ2​R2​​

Correct answer: (A)

Step-by-step solution →
Q3·PhysicsSingle correct
In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :
  1. (A)0.75 mm
  2. (B)0.50 mm
  3. (C)1 mm
  4. (D)0.25 mm

Correct answer: (D)

Step-by-step solution →
Q4·PhysicsSingle correct
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : An electron microscope can achieve better resolving power than an optical microscope. Reason R : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)A is true but R is false.
  2. (B)Both A and R are true but R is NOT the correct explanation of A.
  3. (C)Both A and R are true and R is the correct explanation of A.
  4. (D)A is false but R is true.

Correct answer: (C)

Step-by-step solution →
Q5·PhysicsSingle correct
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
  1. (A)45\frac{4}{5}54​ma2^{2}2
  2. (B)85\frac{8}{5}58​ma2^{2}2 + mb2^{2}2
  3. (C)45\frac{4}{5}54​ma2^{2}2 + 2mb2^{2}2
  4. (D)85\frac{8}{5}58​ma2^{2}2 + 2mb2^{2}2

Correct answer: (D)

Step-by-step solution →
Q6·PhysicsSingle correct
The normal density of a material is ρ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :
  1. (A)ρKP\frac{\rho K}{P}PρK​
  2. (B)KρP\frac{K}{\rho P}ρPK​
  3. (C)PKρ\frac{PK}{\rho}ρPK​
  4. (D)ρPK\frac{\rho P}{K}KρP​

Correct answer: (D)

Step-by-step solution →
Q7·PhysicsSingle correct
LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is 1.9 eV. Calculate the wavelength of light emitted and its colour. [h=6.63×10−34^{-34}−34 Js and c=3×108^{8}8 ms−1^{-1}−1]
  1. (A)654 nm and red colour
  2. (B)1046 nm and blue colour
  3. (C)1046 nm and red colour
  4. (D)654 nm and orange colour

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
Five equal resistances are connected in a network as shown in figure. The net resistance between the points A and B is :
  1. (A)3R2\frac{3R}{2}23R​
  2. (B)R2\frac{R}{2}2R​
  3. (C)R
  4. (D)2R

Correct answer: (C)

Step-by-step solution →
Q9·PhysicsSingle correct
Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If 8\sqrt{8}8​R is the distance between the centres of a ring (of mass 'm') and a sphere (mass 'M') where both have equal radius 'R'.
  1. (A)89⋅GmMR\frac{\sqrt{8}}{9}\cdot\frac{GmM}{R}98​​⋅RGmM​
  2. (B)827⋅GmMR2\frac{\sqrt{8}}{27}\cdot\frac{GmM}{R^{2}}278​​⋅R2GmM​
  3. (C)223⋅GMmR2\frac{2\sqrt{2}}{3}\cdot\frac{GMm}{R^{2}}322​​⋅R2GMm​
  4. (D)138⋅GMmR2\frac{1}{3\sqrt{8}}\cdot\frac{GMm}{R^{2}}38​1​⋅R2GMm​

Correct answer: (B)

Step-by-step solution →
Q10·PhysicsSingle correct
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :
  1. (A)2πRg\sqrt{\frac{R}{g}}gR​​
  2. (B)12πgR\frac{1}{2\pi}\sqrt{\frac{g}{R}}2π1​Rg​​
  3. (C)2πRg\frac{2\pi R}{g}g2πR​
  4. (D)g2πR\frac{g}{2\pi R}2πRg​

Correct answer: (A)

Step-by-step solution →
Q11·PhysicsSingle correct
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = 32\frac{\sqrt{3}}{2}23​​L .
  1. (A)Q23πε0L2\frac{Q}{2\sqrt{3}\pi\varepsilon_0 L^{2}}23​πε0​L2Q​
  2. (B)3Q4πε0L2\frac{\sqrt{3}Q}{4\pi\varepsilon_0 L^{2}}4πε0​L23​Q​
  3. (C)Q3πε0L2\frac{Q}{3\pi\varepsilon_0 L^{2}}3πε0​L2Q​
  4. (D)Q4πε0L2\frac{Q}{4\pi\varepsilon_0 L^{2}}4πε0​L2Q​

Correct answer: (A)

Step-by-step solution →
Q12·PhysicsSingle correct
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m<<M, body 'Q' will have a maximum speed equal to '2u' after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:
  1. (A)A is correct but R is not correct.
  2. (B)Both A and R are correct but R is NOT the correct explanation of A.
  3. (C)A is not correct but R is correct.
  4. (D)Both A and R are correct and R is the correct explanation of A.

Correct answer: (D)

Step-by-step solution →
Q13·PhysicsSingle correct
A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value |f| = 40 cm. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may conclude from the information :
  1. (A)Image is real, same side of concave mirror.
  2. (B)Image is virtual, opposite side of convex mirror.
  3. (C)Image is virtual, opposite side of concave mirror.
  4. (D)Image is real, same side of convex mirror.

Correct answer: (B)

Step-by-step solution →
Q14·PhysicsSingle correct
A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R3^{3}3. Its time period of revolution will be given by :
  1. (A)T ∝ R52R^{\frac{5}{2}}R25​
  2. (B)T ∝ R2R^{2}R2
  3. (C)T ∝ R43R^{\frac{4}{3}}R34​
  4. (D)T ∝ R32R^{\frac{3}{2}}R23​

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be :
  1. (A)2TrJ\frac{2T}{rJ}rJ2T​
  2. (B)3TrJ\frac{3T}{rJ}rJ3T​
  3. (C)2TJ(1r−1R)\frac{2T}{J}\left(\frac{1}{r}-\frac{1}{R}\right)J2T​(r1​−R1​)
  4. (D)3TJ(1r−1R)\frac{3T}{J}\left(\frac{1}{r}-\frac{1}{R}\right)J3T​(r1​−R1​)

Correct answer: (D)

Step-by-step solution →
Q16·PhysicsSingle correct
A planet revolving in elliptical orbit has : A. a constant velocity of revolution. B. has the least velocity when it is nearest to the sun. C. its areal velocity is directly proportional to its velocity. D. areal velocity is inversely proportional to its velocity. E. to follow a trajectory such that the areal velocity is constant. Choose the correct answer from the options given below :
  1. (A)A only
  2. (B)E only
  3. (C)D only
  4. (D)C only

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
An alternating current is given by the equation i=i1_{1}1​sinωt + i2_{2}2​cosωt. The rms current will be :
  1. (A)12(i12+i22)12\frac{1}{2}\left(i_{1}^{2} + i_{2}^{2}\right)^{\frac{1}{2}}21​(i12​+i22​)21​
  2. (B)12(i12+i22)12\frac{1}{\sqrt{2}}\left(i_{1}^{2} + i_{2}^{2}\right)^{\frac{1}{2}}2​1​(i12​+i22​)21​
  3. (C)12(i1+i2)2\frac{1}{\sqrt{2}}\left(i_{1} + i_{2}\right)^{2}2​1​(i1​+i2​)2
  4. (D)12(i1+i2)\frac{1}{\sqrt{2}}\left(i_{1} + i_{2}\right)2​1​(i1​+i2​)

Correct answer: (B)

Step-by-step solution →
Q18·PhysicsSingle correct
If two similar springs each of spring constant K1_{1}1​ are joined in series, the new spring constant and time period would be changed by a factor :
  1. (A)12\frac{1}{2}21​, 2\sqrt{2}2​
  2. (B)14\frac{1}{4}41​, 222\sqrt{2}22​
  3. (C)12\frac{1}{2}21​, 222\sqrt{2}22​
  4. (D)14\frac{1}{4}41​, 2\sqrt{2}2​

Correct answer: (A)

Step-by-step solution →
Q19·PhysicsSingle correct
In a typical combustion engine the workdone by a gas molecule is given by W=α2βe−βx2kTW = \alpha^{2}\beta e^{\frac{-\beta x^{2}}{kT}}W=α2βekT−βx2​, where x is the displacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be :
  1. (A)[M0 L T0][M^{0}\,L\,T^{0}][M0LT0]
  2. (B)[M2 L T−2][M^{2}\,L\,T^{-2}][M2LT−2]
  3. (C)[M L T−2][M\,L\,T^{-2}][MLT−2]
  4. (D)[M L T−1][M\,L\,T^{-1}][MLT−1]

Correct answer: (A)

Step-by-step solution →
Q20·PhysicsNumerical
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y=−0.21sin(x+30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x × 10−2^{-2}−2 N. Value of x is ____________. (Round-off to the nearest integer)

Correct answer: 1215

Step-by-step solution →
Q21·PhysicsNumerical
A radiation is emitted by 1000 W bulb and it generates an electric field and magnetic field at P, placed at a distance of 2m. The efficiency of the bulb is 1.25%. The value of peak electric field at P is x × 10−1^{-1}−1 V/m. Value of x is ____________. (Rounded-off to the nearest integer) [Take ε0_{0}0​ = 8.85×10−12^{-12}−12 C2^{2}2 N−1^{-1}−1 m−2^{-2}−2 , c=3×108^{8}8 ms−1^{-1}−1]

Correct answer: 137

Step-by-step solution →
Q22·PhysicsNumerical
The circuit contains two diodes each with a forward resistance of 50Ω and with infinite reverse resistance. If the battery voltage is 6 V, the current through the 120 Ω resistance is ___________ mA.

Correct answer: 20

Step-by-step solution →
Q23·PhysicsNumerical
As shown in the figure, a block of mass 3\sqrt{3}3​ kg is kept on a horizontal rough surface of coefficient of friction 133\frac{1}{3\sqrt{3}}33​1​. The critical force to be applied on the vertical surface as shown at an angle 60° with horizontal such that it does not move, will be 3x. The value of x will be ________. [g=10m/s2^{2}2; sin 60°=32\frac{\sqrt{3}}{2}23​​ ; cos 60°=12\frac{1}{2}21​]

Correct answer: 3.33

Step-by-step solution →
Q24·PhysicsNumerical
In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be ____________.

Correct answer: 282.84

Step-by-step solution →
Q25·PhysicsNumerical
In an electrical circuit, a battery is connected to pass 20 C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15 V. The work done by the battery is ____________ J.

Correct answer: 300

Step-by-step solution →
Q26·PhysicsNumerical
A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is x × 10−1^{-1}−1 atm. Value of x is _________.

Correct answer: 25

Step-by-step solution →
Q27·PhysicsNumerical
A boy pushes a box of mass 2kg with a force F⃗=(20i^+10j^)\vec{F} = \left(20\hat{i} + 10\hat{j}\right)F=(20i^+10j^​) N on a frictionless surface. If the box was initially at rest, then ____________m is displacement along the x-axis after 10 s.

Correct answer: 500

Step-by-step solution →
Q28·PhysicsNumerical
The maximum and minimum amplitude of an amplitude modulated wave is 16 V and 8 V respectively. The modulation index for this amplitude modulated wave is x ×10−2^{-2}−2. The value of x is _________.

Correct answer: 33

Step-by-step solution →
Q29·PhysicsNumerical
A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of 1.8 m/s2^{2}2 will be ____________ N. [g =10m/s2^{2}2]

Correct answer: 492

Step-by-step solution →

Chemistry — JEE Main 26 February 2021 Shift 1

Q30·ChemistrySingle correct
A (C4_44​H8_88​Cl2_22​) →373 KHydrolysis\xrightarrow[\text{373 K}]{\text{Hydrolysis}}Hydrolysis373 K​ B (C4_44​H8_88​O) B reacts with Hydroxyl amine but does not give Tollen's test. Identify A and B.
  1. (A)1, 1-Dichlorobutane and 2-Butanone
  2. (B)2, 2- Dichlorobutane and Butan-2-one
  3. (C)2, 2- Dichlorobutane and Butanal
  4. (D)1, 1- Dichlorobutane and Butanal

Correct answer: (B)

Step-by-step solution →
Q31·ChemistrySingle correct
Match List-I with List-II. List –I (Ore) (a) Kernite (b) Cassiterite (c) Calamine (d) Cryolite List-II (Element Present) (i) Tin (ii) Boron (iii) Fluorine (iv) Zinc Choose the most appropriate answer from the option given below :
  1. (A)(a) – (ii), (b) – (iv), (c) – (i), (d) – (iii)
  2. (B)(a) – (ii), (b) – (i), (c) – (iv), (d) – (iii)
  3. (C)(a) – (i), (b) – (iii), (c) – (iv), (d) – (ii)
  4. (D)(a) – (iii), (b) – (i), (c) – (ii), (d) – (iv)

Correct answer: (B)

Step-by-step solution →
Q32·ChemistrySingle correct
For the given reaction : What is 'A' ?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q33·ChemistrySingle correct
The orbital having two radial as well as two angular nodes is
  1. (A)5d
  2. (B)4f
  3. (C)3p
  4. (D)4d

Correct answer: (A)

Step-by-step solution →
Q34·ChemistrySingle correct
Given below are two statement : Statement I : o-Nitrophenol is steam volatile due to intramolecular hydrogen bonding Statement II : o-Nitrophenol has high melting point due to hydrogen bonding. In the light of the above statements, choose the most appropriate answer from the options given below :
  1. (A)Both Statement I and Statement II are false
  2. (B)Statement I is false but Statement II is true
  3. (C)Both Statement I and Statement II are true
  4. (D)Statement I is true but Statement II is false

Correct answer: (D)

Step-by-step solution →
Q35·ChemistrySingle correct
An amine on reaction with benzenesulphonyl chloride produces a compound insoluble in alkaline solution. This amine can be prepared by ammonolysis of ethyl chloride. The correct structure of amine is :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q36·ChemistrySingle correct
For the given reaction : What is 'A'
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q37·ChemistrySingle correct
Statement about heavy water are given below A. Heavy water is used in exchange reactions for the study of reaction mechanisms B. Heavy water is prepared by exhaustive electrolysis of water C. Heavy water has higher boiling point than ordinary water D. Viscosity of H2_22​O is greater than D2_22​O
  1. (A)A and B only
  2. (B)A and D only
  3. (C)A, B and C only
  4. (D)A and C only

Correct answer: (C)

Step-by-step solution →
Q38·ChemistrySingle correct
Which of the following is 'a' FALSE statement ?
  1. (A)Carius tube used in the estimation of sulphur in an organic compound
  2. (B)Kjedahl's method is used for the estimation of nitrogen in an organic compound
  3. (C)Phosphoric acid produced on oxidation of phosphorus present in an organic compound is precipitated as Mg2_22​P2_22​O7_77​ by adding magnesia mixture
  4. (D)Carius method is used for the estimation of nitrogen in an organic compound

Correct answer: (D)

Step-by-step solution →
Q39·ChemistrySingle correct
Given below are two statements : Statement I : A mixture of chloroform and aniline can be separated by simple distillation Statement II : When separating aniline from a mixture of aniline and water by steam distillation aniline boils below its boiling point In the light of the above statements, choose the most appropriate answer from the options given below
  1. (A)Statement I is true, statement II is false
  2. (B)Both Statement I and Statement II are true
  3. (C)Both Statement I and Statement II are false
  4. (D)Statement I is false, Statement II is true

Correct answer: (B)

Step-by-step solution →
Q40·ChemistrySingle correct
On treating a compound with warm dil. H2_22​SO4_44​, gas X is evolved which turns K2_22​Cr2_22​O7_77​ paper acidified with dil. H2_22​SO4_44​ to a green compound Y. X and Y respectively are :
  1. (A)X = SO2_22​, Y = Cr2_22​(SO4_44​)3_33​
  2. (B)X = SO2_22​, Y = Cr2_22​O3_33​
  3. (C)X = SO3_33​, Y = Cr2_22​O3_33​
  4. (D)X = SO3_33​, Y = Cr2_22​(SO4_44​)3_33​

Correct answer: (A)

Step-by-step solution →
Q41·ChemistrySingle correct
Find A, B and C in the following reaction : NH3_33​ + A + CO2_22​ → (NH4_44​)2_22​CO3_33​ (NH4_44​)2_22​CO3_33​ + H2_22​O + B → NH4_44​HCO3_33​ NH4_44​HCO3_33​ + NaCl → NH4_44​Cl + C
  1. (A)A – H2_22​O ; B – CO2_22​ ; C – NaHCO3_33​
  2. (B)A – H2_22​O ; B – O2_22​ ; C – Na2_22​CO3_33​
  3. (C)A – O2_22​ ; B – CO2_22​ ; C – Na2_22​CO3_33​
  4. (D)A – H2_22​O ; B – O2_22​ ; C – NaHCO3_33​

Correct answer: (A)

Step-by-step solution →
Q42·ChemistrySingle correct
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Dipole-dipole interactions are the only non-covalent interactions, resulting in hydrogen bond formation Reason R : Fluorine is the most electronegative element and hydrogen bonds in HF are symmetrical In the light of the above statements, choose the most appropriate answer from the options given below :
  1. (A)A is false but R is true
  2. (B)Both A and R are true and R is the correct explanation of A
  3. (C)A is true but R is false
  4. (D)Both A and R are true and R is not the correct explanation of A

Correct answer: (C)

Step-by-step solution →
Q43·ChemistrySingle correct
Match List-I with List-II. List –I : Electronic configuration of elements List-II : Δi_ii​H in kJ mol−1^{-1}−1 (a) 1s2^222s2^22 — (i) 801 (b) 1s2^222s2^222p4^44 — (ii) 899 (c) 1s2^222s2^222p3^33 — (iii) 1314 (d) 1s2^222s2^222p1^11 — (iv) 1402
  1. (A)(a) – (ii), (b) – (iii), (c) – (iv), (d) – (i)
  2. (B)(a) – (iv), (b) – (i), (c) – (ii), (d) – (iii)
  3. (C)(a) – (i), (b) – (iv), (c) – (iii), (d) – (ii)
  4. (D)(a) – (i), (b) – (iii), (c) – (iv), (d) – (ii)

Correct answer: (A)

Step-by-step solution →
Q44·ChemistrySingle correct
Which one of the following lanthanoids does not form MO2_22​ ? [M is lanthanoid metal]
  1. (A)Nd
  2. (B)Yb
  3. (C)Dy
  4. (D)Pr

Correct answer: (B)

Step-by-step solution →
Q45·ChemistrySingle correct
Identify the major products A and B respectively in the following reaction of phenol :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q46·ChemistrySingle correct
The structure of Neoprene is :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q47·ChemistrySingle correct
Compound A used as a strong oxidizing agent is amphoteric in nature. It is the part of lead storage batteries. Compound A is :
  1. (A)Pb3_33​O4_44​
  2. (B)PbO2_22​
  3. (C)PbSO4_44​
  4. (D)PbO

Correct answer: (B)

Step-by-step solution →
Q48·ChemistryNumerical
Consider the following reaction MnO4−_4^{-}4−​ + 8H+^++ + 5e−^-− → Mn+2^{+2}+2 + 4H2_22​O, E° = 1.51 V. The quantity of electricity required in Faraday to reduce five moles of MnO4−_4^{-}4−​ is_____.

Correct answer: 25

Step-by-step solution →
Q49·ChemistryNumerical
3.12 g of oxygen is adsorbed on 1.2 g of platinum metal. The value of oxygen adsorbed per gram of the adsorbent at 1 atm and 300 K in L is ________. [R = 0.0821 L atm K−1^{-1}−1 mol−1^{-1}−1]

Correct answer: 2

Step-by-step solution →
Q50·ChemistryNumerical
The number of significant figures in 50000.020 × 10−3^{-3}−3 is _______.

Correct answer: 7

Step-by-step solution →
Q51·ChemistryNumerical
Number of bridging CO ligands in [Mn2_22​(CO)10_{10}10​] is _____.

Correct answer: 0

Step-by-step solution →
Q52·ChemistryNumerical
For a chemical reaction A + B ⇌ C + D (Δr_rr​H⊖^{\ominus}⊖ = 80 kJ mol−1^{-1}−1) the entropy change Δr_rr​S⊖^{\ominus}⊖ depends on the temperature T (in K) as Δr_rr​S⊖^{\ominus}⊖ = 2T (J K−1^{-1}−1 mol−1^{-1}−1). Minimum temperature at which it will become spontaneous is _________K.

Correct answer: 200

Step-by-step solution →
Q53·ChemistryNumerical
An exothermic reaction X → Y has an activation energy 30 kJ mol−1^{-1}−1. If energy change ΔE during the reaction is −20 kJ, then the activation energy for the reverse reaction in kJ is _______.

Correct answer: 50

Step-by-step solution →
Q54·ChemistryNumerical
A certain gas obeys P(Vm_mm​ − b) = RT. The value of (∂Z∂P)T\left(\frac{\partial Z}{\partial P}\right)_{T}(∂P∂Z​)T​ is xbRT\frac{xb}{RT}RTxb​ . The value of x is _______ .

Correct answer: 1

Step-by-step solution →
Q55·ChemistryNumerical
A homogeneous ideal gaseous reaction AB2(g)_{2(g)}2(g)​ ⇌ A(g)_{(g)}(g)​ + 2B(g)_{(g)}(g)​ is carried out in a 25 litre flask at 27°C. The initial amount of AB2_22​ was 1 mole and the equilibrium pressure was 1.9 atm. The value of Kp_pp​ is x × 10−2^{-2}−2. The value of x is ________. [R = 0.08206 dm3^33 atm K−1^{-1}−1 mol−1^{-1}−1]

Correct answer: 74

Step-by-step solution →
Q56·ChemistryNumerical
Dichromate ion is treated with base, the oxidation number of Cr in the product formed is :

Correct answer: 6

Step-by-step solution →

Mathematics — JEE Main 26 February 2021 Shift 1

Q57·MathematicsSingle correct
The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only is
  1. (A)77
  2. (B)42
  3. (C)35
  4. (D)82

Correct answer: (A)

Step-by-step solution →
Q58·MathematicsSingle correct
The maximum value of the term independent of ‘t’ in the expansion of (tx15+(1−x)110t)10\left( tx^{\frac{1}{5}} + \frac{(1-x)^{\frac{1}{10}}}{t} \right)^{10}(tx51​+t(1−x)101​​)10 where x ∈ (0,1) is:
  1. (A)10!3(5!)2\frac{10!}{\sqrt{3}(5!)^{2}}3​(5!)210!​
  2. (B)2.10!3(5!)2\frac{2.10!}{3(5!)^{2}}3(5!)22.10!​
  3. (C)10!3(5!)2\frac{10!}{3(5!)^{2}}3(5!)210!​
  4. (D)2.10!33(5!)2\frac{2.10!}{3\sqrt{3}(5!)^{2}}33​(5!)22.10!​

Correct answer: (D)

Step-by-step solution →
Q59·MathematicsSingle correct
The value of ∑n=1100∫n−1nex−[x]dx\sum_{n=1}^{100} \int_{n-1}^{n} e^{x-[x]}dx∑n=1100​∫n−1n​ex−[x]dx, where [x] is the greatest integer ≤ x, is:
  1. (A)100 (e–1)
  2. (B)100e
  3. (C)100(1-e)
  4. (D)100 (1 + e)

Correct answer: (A)

Step-by-step solution →
Q60·MathematicsSingle correct
The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t = 0. The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is 2000 after klog⁡e(65)\frac{k}{\log_{e}\left(\frac{6}{5}\right)}loge​(56​)k​ hours, then (klog⁡e2)2\left(\frac{k}{\log_{e} 2}\right)^{2}(loge​2k​)2 is equal to
  1. (A)4
  2. (B)2
  3. (C)16
  4. (D)8

Correct answer: (A)

Step-by-step solution →
Q61·MathematicsSingle correct
If a⃗\vec{a}a & b⃗\vec{b}b are perpendicular vactors, then a⃗×(a⃗×(a⃗×(a⃗×b⃗)))\vec{a} \times \left( \vec{a} \times \left( \vec{a} \times \left( \vec{a} \times \vec{b} \right) \right) \right)a×(a×(a×(a×b))) is equal to
  1. (A)12∣a⃗∣4 b⃗\frac{1}{2}\left|\vec{a}\right|^{4}\,\vec{b}21​∣a∣4b
  2. (B)a⃗×b⃗\vec{a} \times \vec{b}a×b
  3. (C)∣a⃗∣4 b⃗\left|\vec{a}\right|^{4}\,\vec{b}∣a∣4b
  4. (D)0⃗\vec{0}0

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
In an increasing, geometric series, the sum of the second and the sixth term is 252\frac{25}{2}225​ and the product of the third and fifth term is 25. Then, the sum of 4th4^{th}4th, 6th6^{th}6th and 8th8^{th}8th terms is equal to :
  1. (A)35
  2. (B)30
  3. (C)26
  4. (D)32

Correct answer: (A)

Step-by-step solution →
Q63·MathematicsSingle correct
Consider the three planes P1P_{1}P1​ : 3x + 15y + 21z = 9, P2P_{2}P2​ : x − 3y − z= 5, and P3P_{3}P3​ : 2x + 10 y + 14z = 5 Then, which one of the following is true?
  1. (A)P1P_{1}P1​ and P3P_{3}P3​ are parallel.
  2. (B)P2P_{2}P2​ and P3P_{3}P3​ are parallel.
  3. (C)P1P_{1}P1​ and P2P_{2}P2​ are parallel.
  4. (D)P1P_{1}P1​ , P2P_{2}P2​ and P3P_{3}P3​ all are parallel.

Correct answer: (A)

Step-by-step solution →
Q64·MathematicsSingle correct
The sum of the infinite series 1+23+732+1233+1734+2235+…1 + \frac{2}{3} + \frac{7}{3^{2}} + \frac{12}{3^{3}} + \frac{17}{3^{4}} + \frac{22}{3^{5}} + \ldots1+32​+327​+3312​+3417​+3522​+… is equal to
  1. (A)94\frac{9}{4}49​
  2. (B)154\frac{15}{4}415​
  3. (C)134\frac{13}{4}413​
  4. (D)114\frac{11}{4}411​

Correct answer: (C)

Step-by-step solution →
Q65·MathematicsSingle correct
The value of ∣(a+1)(a+2)a+21(a+2)(a+3)a+31(a+3)(a+4)a+41∣\begin{vmatrix} (a+1)(a+2) & a+2 & 1 \\ (a+2)(a+3) & a+3 & 1 \\ (a+3)(a+4) & a+4 & 1 \end{vmatrix}​(a+1)(a+2)(a+2)(a+3)(a+3)(a+4)​a+2a+3a+4​111​​ is
  1. (A)−2
  2. (B)(a+1) (a+2) (a+3)
  3. (C)0
  4. (D)(a+2) (a+3) (a+4)

Correct answer: (A)

Step-by-step solution →
Q66·MathematicsSingle correct
If sin⁡−1xa=cos⁡−1xb=tan⁡−1yc\frac{\sin^{-1}x}{a} = \frac{\cos^{-1}x}{b} = \frac{\tan^{-1}y}{c}asin−1x​=bcos−1x​=ctan−1y​ ; 0 < x < 1, then the value of cos⁡(πca+b)\cos\left(\frac{\pi c}{a+b}\right)cos(a+bπc​) is:
  1. (A)1−y22y\frac{1-y^{2}}{2y}2y1−y2​
  2. (B)1−y21+y2\frac{1-y^{2}}{1+y^{2}}1+y21−y2​
  3. (C)1−y21-y^{2}1−y2
  4. (D)1−y2yy\frac{1-y^{2}}{y\sqrt{y}}yy​1−y2​

Correct answer: (B)

Step-by-step solution →
Q67·MathematicsSingle correct
Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A2A^{2}A2 is 1, then the possible number of such matrices is:
  1. (A)6
  2. (B)1
  3. (C)4
  4. (D)12

Correct answer: (C)

Step-by-step solution →
Q68·MathematicsSingle correct
The intersection of three lines x−y = 0, x + 2y = 3 and 2x + y = 6 is a:
  1. (A)Equilateral triangle
  2. (B)None of the above
  3. (C)Isosceles triangle
  4. (D)Right angled triangle

Correct answer: (C)

Step-by-step solution →
Q69·MathematicsSingle correct
The maximum slope of the curve y=12x4−5x3+18x2−19xy = \frac{1}{2}x^{4} - 5x^{3} + 18x^{2} - 19xy=21​x4−5x3+18x2−19x occurs at the point:
  1. (A)(2, 9)
  2. (B)(2,2)
  3. (C)(3,212)\left( 3, \frac{21}{2} \right)(3,221​)
  4. (D)(0, 0)

Correct answer: (B)

Step-by-step solution →
Q70·MathematicsSingle correct
Let f be any function defined on R and let it satisfy the condition : (∣f(x)−f(y)∣≤∣(x−y)2∣,∀(x,y)∈R(\left|f(x) - f(y)\right| \le \left|(x - y)^{2}\right|, \forall (x, y) \in R(∣f(x)−f(y)∣≤​(x−y)2​,∀(x,y)∈R If f(0) = 1, then:
  1. (A)f(x) < 0, ∀x ∈ R
  2. (B)f(x) can take any value in R
  3. (C)f(x) = 0, ∀ x ∈ R
  4. (D)f(x) >0, ∀ x ∈ R

Correct answer: (D)

Step-by-step solution →
Q71·MathematicsSingle correct
The value of ∫−π/2π/2cos⁡2x1+3xdx\int_{-\pi/2}^{\pi/2} \frac{\cos^{2}x}{1+3^{x}}dx∫−π/2π/2​1+3xcos2x​dx is:
  1. (A)2π
  2. (B)4π
  3. (C)π2\frac{\pi}{2}2π​
  4. (D)π4\frac{\pi}{4}4π​

Correct answer: (D)

Step-by-step solution →
Q72·MathematicsSingle correct
The value of lim⁡h→0{3 sin⁡(π6+h)−cos⁡(π6+h)3h(3 cos⁡h−sin⁡h)}\lim_{h \to 0}\left\{\frac{\sqrt{3}\,\sin\left(\frac{\pi}{6}+h\right)-\cos\left(\frac{\pi}{6}+h\right)}{\sqrt{3}h\left(\sqrt{3}\,\cos h-\sin h\right)}\right\}limh→0​{3​h(3​cosh−sinh)3​sin(6π​+h)−cos(6π​+h)​} is:
  1. (A)34\frac{3}{4}43​
  2. (B)23\frac{2}{\sqrt{3}}3​2​
  3. (C)43\frac{4}{3}34​
  4. (D)23\frac{2}{3}32​

Correct answer: (C)

Step-by-step solution →
Q73·MathematicsSingle correct
A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is :
  1. (A)15212\frac{15}{2^{12}}21215​
  2. (B)15213\frac{15}{2^{13}}21315​
  3. (C)15214\frac{15}{2^{14}}21415​
  4. (D)1528\frac{15}{2^{8}}2815​

Correct answer: (B)

Step-by-step solution →
Q74·MathematicsSingle correct
If (1,5,35), (7,5,5), (1, λ, 7) and (2λ, 1, 2) are coplanar, then the sum of all possible values of λ is:
  1. (A)−445-\frac{44}{5}−544​
  2. (B)395\frac{39}{5}539​
  3. (C)−395-\frac{39}{5}−539​
  4. (D)445\frac{44}{5}544​

Correct answer: (D)

Step-by-step solution →
Q75·MathematicsSingle correct
Let R = {P,Q)|P and Q are at the same distance from the origin} be a relation, then the equivalence class of (1,−1) is the set:
  1. (A)S={(x,y) ∣ x2+y2=1}S=\{(x,y)\,|\,x^{2}+y^{2}=1\}S={(x,y)∣x2+y2=1}
  2. (B)S={(x,y) ∣ x2+y2=4}S=\{(x,y)\,|\,x^{2}+y^{2}=4\}S={(x,y)∣x2+y2=4}
  3. (C)S={(x,y) ∣ x2+y2=2}S=\{(x,y)\,|\,x^{2}+y^{2}=\sqrt{2}\}S={(x,y)∣x2+y2=2​}
  4. (D)S={(x,y) ∣ x2+y2=2}S=\{(x,y)\,|\,x^{2}+y^{2}=2\}S={(x,y)∣x2+y2=2}

Correct answer: (D)

Step-by-step solution →
Q76·MathematicsSingle correct
In the circle given below, let OA = 1 unit, OB = 13 unit and PQ ⊥ OB. Then, the area of the triangle PQB (in square units) is:
  1. (A)26326\sqrt{3}263​
  2. (B)24224\sqrt{2}242​
  3. (C)24324\sqrt{3}243​
  4. (D)26226\sqrt{2}262​

Correct answer: (C)

Step-by-step solution →
Q77·MathematicsNumerical
The number of integral values of 'k' for which the equation 3sinx + 4cos x = k + 1 has a solution, k ∈ R is _______.

Correct answer: 11

Step-by-step solution →
Q78·MathematicsNumerical
Let m, n ∈ N and gcd (2, n) = 1. If 30(300)+29(301)+....+2(3028)+1(3029)=n⋅2m30\binom{30}{0}+29\binom{30}{1}+....+2\binom{30}{28}+1\binom{30}{29}=n\cdot 2^{m}30(030​)+29(130​)+....+2(2830​)+1(2930​)=n⋅2m, then n + m is equal to _______.

Correct answer: 45

Step-by-step solution →
Q79·MathematicsNumerical
If y = y(x) is the solution of the equation esin⁡ycos⁡y dydx+esin⁡ycos⁡x=cos⁡xe^{\sin y}\cos y\,\frac{dy}{dx}+e^{\sin y}\cos x=\cos xesinycosydxdy​+esinycosx=cosx, y(0) = 0 ; then 1+y(π6)+32y(π3)+12y(π4)1+y\left(\frac{\pi}{6}\right)+\frac{\sqrt{3}}{2}y\left(\frac{\pi}{3}\right)+\frac{1}{\sqrt{2}}y\left(\frac{\pi}{4}\right)1+y(6π​)+23​​y(3π​)+2​1​y(4π​) is equal to _______.

Correct answer: 1

Step-by-step solution →
Q80·MathematicsNumerical
The number of solutions of the equation log⁡4(x−1)=log⁡2(x−3)\log_{4}(x-1)=\log_{2}(x-3)log4​(x−1)=log2​(x−3) is _______.

Correct answer: 1

Step-by-step solution →
Q81·MathematicsNumerical
If 3(cos⁡2x)=(3−1)cos⁡x+1\sqrt{3}(\cos^{2}x)=(\sqrt{3}-1)\cos x+13​(cos2x)=(3​−1)cosx+1, the number of solutions of the given equation when x∈[0,π2]x \in \left[0,\frac{\pi}{2}\right]x∈[0,2π​] is _______.

Correct answer: 1

Step-by-step solution →
Q82·MathematicsNumerical
Let (λ, 2, 1) be a point on the plane which passes through the point (4, −2, 2). If the plane is perpendicular to the line joining the point (−2, −21, 29) and (−1, −16, 23), then (λ11)2−4λ11−4\left(\frac{\lambda}{11}\right)^{2}-\frac{4\lambda}{11}-4(11λ​)2−114λ​−4 is equal to _______.

Correct answer: 8

Step-by-step solution →
Q83·MathematicsNumerical
The difference betweeen degree and order of differential equation that represents the family of curves given by y2=a(x+a2)y^{2}=a\left(x+\frac{\sqrt{a}}{2}\right)y2=a(x+2a​​), a > 0 is _______.

Correct answer: 2

Step-by-step solution →
Q84·MathematicsNumerical
The sum of 162th162^{\text{th}}162th power of the roots of the equation x3−2x2+2x−1=0x^{3}-2x^{2}+2x-1=0x3−2x2+2x−1=0 is _______.

Correct answer: 3

Step-by-step solution →
Q85·MathematicsNumerical
The value of the integeral ∫0π∣sin⁡2x∣ dx\int_{0}^{\pi}\left|\sin 2x\right|\,dx∫0π​∣sin2x∣dx is _______

Correct answer: 2

Step-by-step solution →

Chapters tested in this paper

Open any chapter to practise every past-year question on that topic across all papers, and see how often it has actually appeared.

  • Properties of Solids and Liquids 172/186
  • Three Dimensional Geometry 176/186
  • Matrices and Determinants 180/186
  • Coordination Compounds 176/186
  • Sets, Relations and Functions 165/186
  • Current Electricity 160/186
  • Sequence and Series 164/186
  • p-Block Elements 164/186
  • Definite Integration 168/186
  • Rotational Motion 172/186
  • Redox Reactions and Electrochemistry 177/186
  • Geometrical Optics 172/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Probability 176/186
  • Permutations and Combinations 162/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Electromagnetic Waves 144/186
  • Chemical Bonding and Molecular Structure 151/186
  • Application of Derivatives 139/186
  • Limits and Continuity 149/186
  • d- and f-Block Elements 126/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Laws of Motion 130/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Hydrocarbons 126/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Circles 142/186
  • Dual Nature of Matter and Radiation 155/186
  • Amines 133/186
  • Quadratic Equations 148/186
  • Work, Energy and Power 132/186
  • Some Basic Concepts in Chemistry 129/186
  • Wave Optics 130/186
  • Kinetic Theory of Gases 135/186
  • Alcohols and Ethers 106/186
  • Purification and Characterisation of Organic Compounds 116/186
  • Oscillations 117/186
  • Alternating Currents 108/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Waves 109/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Isolation of Metals 106/186
  • Differentiability 91/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Inverse Trigonometric Functions 93/186
  • Hydrogen 81/186
  • Polymers 64/186
  • Principles of Qualitative Analysis 58/186
  • States of Matter: Gases and Liquids 52/186
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