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JEE Main 25 July 2021 Shift 2 Question Paper with Answers

25 July 2021 · July session · 89 questions

89 of the 90 questions from the JEE Main 25 July 2021 Shift 2 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

1 question is 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
30
Chemistry
29
Mathematics
30

Physics — JEE Main 25 July 2021 Shift 2

Q1·PhysicsSingle correct
A ray of light entering from air into a denser medium of refractive index 43\frac{4}{3}34​, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle θ\thetaθ should be equal to :
  1. (A)sin⁡−154\sin^{-1}\frac{\sqrt{5}}{4}sin−145​​
  2. (B)sin⁡−173\sin^{-1}\frac{\sqrt{7}}{3}sin−137​​
  3. (C)sin⁡−174\sin^{-1}\frac{\sqrt{7}}{4}sin−147​​
  4. (D)sin⁡−153\sin^{-1}\frac{\sqrt{5}}{3}sin−135​​

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
In the given potentiometer circuit arrangement, the balancing length AC is measured to be 250 cm. When the galvanometer connection is shifted from point (1)(1)(1) to point (2)(2)(2) in the given diagram, the balancing length becomes 400 cm. The ratio of the emf of two cells, ε1ε2\frac{\varepsilon_1}{\varepsilon_2}ε2​ε1​​ is:
  1. (A)43\frac{4}{3}34​
  2. (B)85\frac{8}{5}58​
  3. (C)32\frac{3}{2}23​
  4. (D)53\frac{5}{3}35​

Correct answer: (D)

Step-by-step solution →
Q3·PhysicsSingle correct
A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around : (takes the value of g as 10 m /s2^22)
  1. (A)250 m
  2. (B)300 m
  3. (C)200 m
  4. (D)125 m

Correct answer: (D)

Step-by-step solution →
Q4·PhysicsSingle correct
An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :
  1. (A)v2c\frac{v}{2c}2cv​
  2. (B)2cv\frac{2c}{v}v2c​
  3. (C)v3c\frac{v}{3c}3cv​
  4. (D)3cv\frac{3c}{v}v3c​

Correct answer: (A)

Step-by-step solution →
Q5·PhysicsSingle correct
Two vectors X⃗\vec{X}X and Y⃗\vec{Y}Y have equal magnitude. The magnitude of (X⃗−Y⃗)\left(\vec{X}-\vec{Y}\right)(X−Y) is n times the magnitude of (X⃗+Y⃗)\left(\vec{X}+\vec{Y}\right)(X+Y). The angle between X⃗\vec{X}X and Y⃗\vec{Y}Y is :
  1. (A)cos⁡−1(n2+1n2−1)\cos^{-1}\left(\frac{n^2+1}{n^2-1}\right)cos−1(n2−1n2+1​)
  2. (B)cos⁡−1(−n2−1n2−1)\cos^{-1}\left(\frac{-n^2-1}{n^2-1}\right)cos−1(n2−1−n2−1​)
  3. (C)cos⁡−1(n2−1−n2−1)\cos^{-1}\left(\frac{n^2-1}{-n^2-1}\right)cos−1(−n2−1n2−1​)
  4. (D)cos⁡−1(n2+1−n2−1)\cos^{-1}\left(\frac{n^2+1}{-n^2-1}\right)cos−1(−n2−1n2+1​)

Correct answer: (C)

Step-by-step solution →
Q6·PhysicsSingle correct
Two ideal electric dipoles A and B, having their dipole moment p1p_1p1​ and p2p_2p2​ respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37∘37^\circ37∘ with the axis. The ratio of the dipole moment of A and B, p1p2\frac{p_1}{p_2}p2​p1​​ is : (take sin⁡37∘=35\sin 37^\circ = \frac{3}{5}sin37∘=53​)
  1. (A)38\frac{3}{8}83​
  2. (B)32\frac{3}{2}23​
  3. (C)43\frac{4}{3}34​
  4. (D)23\frac{2}{3}32​

Correct answer: (D)

Step-by-step solution →
Q7·PhysicsSingle correct
A 10 Ω10\,\Omega10Ω resistance is connected across 220 V −-− 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is :
  1. (A)2.5 ms
  2. (B)4.5 ms
  3. (C)3.0 ms
  4. (D)1.5 ms

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
The relation between time t and distance x for a moving body is given as t=mx2+nxt = mx^2 + nxt=mx2+nx, where m and n are constants. The retardation of the motion is : (Where v stands for velocity)
  1. (A)2n2v22n^2v^22n2v2
  2. (B)2mnv32mnv^32mnv3
  3. (C)2mv32mv^32mv3
  4. (D)2nv32nv^32nv3

Correct answer: (C)

Step-by-step solution →
Q9·PhysicsSingle correct
A prism of refractive index μ\muμ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index value of A is :
  1. (A)2cos⁡−1(μ2)2\cos^{-1}\left(\frac{\mu}{2}\right)2cos−1(2μ​)
  2. (B)cos⁡−1(μ2)\cos^{-1}\left(\frac{\mu}{2}\right)cos−1(2μ​)
  3. (C)sin⁡−1(μ2)\sin^{-1}\left(\frac{\mu}{2}\right)sin−1(2μ​)
  4. (D)sin⁡−1(μ−12)\sin^{-1}\left(\sqrt{\frac{\mu-1}{2}}\right)sin−1(2μ−1​​)

Correct answer: (A)

Step-by-step solution →
Q10·PhysicsSingle correct
Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :
  1. (A)2 W
  2. (B)W
  3. (C)2\sqrt{2}2​ W
  4. (D)2132^{\frac{1}{3}}231​ W

Correct answer: (D)

Step-by-step solution →
Q11·PhysicsSingle correct
A force F⃗=(40i^+10j^)\vec{F} = \left(40\hat{i} + 10\hat{j}\right)F=(40i^+10j^​) N acts on a body of mass 5 kg. If the body starts from rest, its position vector r⃗\vec{r}r at time t === 10 s, will be :
  1. (A)(100i^+100j^)\left(100\hat{i} + 100\hat{j}\right)(100i^+100j^​) m
  2. (B)(400i^+100j^)\left(400\hat{i} + 100\hat{j}\right)(400i^+100j^​) m
  3. (C)(400i^+400j^)\left(400\hat{i} + 400\hat{j}\right)(400i^+400j^​) m
  4. (D)(100i^+400j^)\left(100\hat{i} + 400\hat{j}\right)(100i^+400j^​) m

Correct answer: (B)

Step-by-step solution →
Q12·Physics·Magnetic Field of CurrentSingle correct
Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :
  1. (A)3 : 1
  2. (B)2 : 3
  3. (C)4 : 3
  4. (D)1 : 4

Correct answer: (C)

Step-by-step solution →
Q13·PhysicsSingle correct
If qfq_fqf​ is the free charge on the capacitor plates and qbq_bqb​ is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge qbq_bqb​ can be expressed as :
  1. (A)qb=qf(1+1k)q_b = q_f\left(1 + \frac{1}{\sqrt{k}}\right)qb​=qf​(1+k​1​)
  2. (B)qb=qf(1−1k)q_b = q_f\left(1 - \frac{1}{\sqrt{k}}\right)qb​=qf​(1−k​1​)
  3. (C)qb=qf(1−1k)q_b = q_f\left(1 - \frac{1}{k}\right)qb​=qf​(1−k1​)
  4. (D)qb=qf(1+1k)q_b = q_f\left(1 + \frac{1}{k}\right)qb​=qf​(1+k1​)

Correct answer: (C)

Step-by-step solution →
Q14·PhysicsSingle correct
Two spherical soap bubbles of radii r1r_1r1​ and r2r_2r2​ in vacuum combine under isothermal conditions. The resulting bubble has radius equal to :
  1. (A)r1r2\sqrt{r_1 r_2}r1​r2​​
  2. (B)r12+r22\sqrt{r_1^2 + r_2^2}r12​+r22​​
  3. (C)r1r2r1+r2\frac{r_1 r_2}{r_1 + r_2}r1​+r2​r1​r2​​
  4. (D)r1+r22\frac{r_1 + r_2}{2}2r1​+r2​​

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
A heat engine has an efficiency of 16\frac{1}{6}61​. When the temperature of sink is reduced by 62∘62^\circ62∘ C, its efficiency get doubled. The temperature of the source is :
  1. (A)124∘^\circ∘C
  2. (B)99∘^\circ∘C
  3. (C)37∘^\circ∘C
  4. (D)62∘^\circ∘C

Correct answer: (B)

Step-by-step solution →
Q16·PhysicsSingle correct
The instantaneous velocity of a particle moving in a straight line is given as v=αt+βt2v = \alpha t + \beta t^2v=αt+βt2, where α\alphaα and β\betaβ are constants. The distance travelled by the particle between 1s and 2s is :
  1. (A)α2+β3\frac{\alpha}{2} + \frac{\beta}{3}2α​+3β​
  2. (B)32α+73β\frac{3}{2}\alpha + \frac{7}{3}\beta23​α+37​β
  3. (C)32α+72β\frac{3}{2}\alpha + \frac{7}{2}\beta23​α+27​β
  4. (D)3α+7β3\alpha + 7\beta3α+7β

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt The dimensional formula of ADB\frac{AD}{B}BAD​ is :
  1. (A)[M2L2T−3]\left[\mathrm{M}^2\mathrm{L}^2\mathrm{T}^{-3}\right][M2L2T−3]
  2. (B)[M1L1T−2]\left[\mathrm{M}^1\mathrm{L}^1\mathrm{T}^{-2}\right][M1L1T−2]
  3. (C)[ML2T−3]\left[\mathrm{M}\mathrm{L}^2\mathrm{T}^{-3}\right][ML2T−3]
  4. (D)[M0LT−1]\left[\mathrm{M}^0\mathrm{L}\mathrm{T}^{-1}\right][M0LT−1]

Correct answer: (C)

Step-by-step solution →
Q18·PhysicsSingle correct
When radiation of wavelength λ\lambdaλ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelength of the metal is:
  1. (A)6λ6\lambda6λ
  2. (B)8λ8\lambda8λ
  3. (C)2λ2\lambda2λ
  4. (D)4λ4\lambda4λ

Correct answer: (D)

Step-by-step solution →
Q19·PhysicsSingle correct
The given potentiometer has its wire of resistance 10 Ω10\,\Omega10Ω. When the sliding contact is in the middle of the potentiometer wire, the potential drop across 2 Ω2\,\Omega2Ω resistor is :
  1. (A)4011\frac{40}{11}1140​ V
  2. (B)10 V
  3. (C)409\frac{40}{9}940​ V
  4. (D)5 V

Correct answer: (C)

Step-by-step solution →
Q20·PhysicsSingle correct
In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.
  1. (A)12\frac{1}{2}21​
  2. (B)34\frac{3}{4}43​
  3. (C)13\frac{1}{3}31​
  4. (D)14\frac{1}{4}41​

Correct answer: (B)

Step-by-step solution →
Q21·PhysicsNumerical
From the given data, the amount of energy required to break the nucleus of aluminium 1327Al^{27}_{13}\text{Al}1327​Al is ________ x×10−3x \times 10^{-3}x×10−3 J. Mass of neutron = 1.00866u Mass of proton = 1.00726 u Mass of Aluminium nucleus = 27.18846 u (Assume 1 u corresponds to x J of energy) (Round off to the nearest integer)

Correct answer: 27

Step-by-step solution →
Q22·PhysicsNumerical
A force of F=(5y+20)j^F = (5y + 20)\hat{j}F=(5y+20)j^​ N acts on a particle. The work done by this force when the particle is moved from y = 0m to y = 10m is ________ J.

Correct answer: 450

Step-by-step solution →
Q23·PhysicsNumerical
A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10s is ________ π×10−1\pi \times 10^{-1}π×10−1 Nm.

Correct answer: 4

Step-by-step solution →
Q24·PhysicsNumerical
A 16 Ω16\,\Omega16Ω wire is bend to form a square loop. A 9V supply having internal resistance of 1 Ω1\,\Omega1Ω is connected across one of its sides. The potential drop across the diagonals of the square loop is ________ ×10−1\times 10^{-1}×10−1 V.

Correct answer: 45

Step-by-step solution →
Q25·PhysicsNumerical
Two circuits are shown in the figure (a) & (b). At a frequency of ________ rad /s the average power dissipated in one cycle will be same in both the circuits.

Correct answer: 500

Step-by-step solution →
Q26·PhysicsNumerical
A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular arc of radius 30cm. The value of B is ________ ×10−7\times 10^{-7}×10−7 T. Given hc = 20×10−2620 \times 10^{-26}20×10−26 J − m, mass of electron = 9×10−319 \times 10^{-31}9×10−31 kg

Correct answer: 125

Step-by-step solution →
Q27·PhysicsNumerical
A message single of frequency 20 kHz and peak voltage of 20 volt is used to modulate a carrier wave of frequency 1 MHz and peak voltage of 20 volt. The modulation index will be ________.

Correct answer: 1

Step-by-step solution →
Q28·PhysicsNumerical
A system consists of two types of gas molecules A and B having same number density 2×10252 \times 10^{25}2×1025 / m³. The diameter of A and B are 10 Å and 5 Å respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is ________ ×10−2\times 10^{-2}×10−2.

Correct answer: 25

Step-by-step solution →
Q29·PhysicsNumerical
In a semiconductor, the number density of intrinsic charge carriers at 27°C is 1.5×10161.5 \times 10^{16}1.5×1016 / m³. If the semiconductor is doped with impurity atom, the hole density increases to 4.5×10224.5 \times 10^{22}4.5×1022 / m³. The electron density in the doped semiconductor is ________ ×109\times 10^{9}×109 / m³.

Correct answer: 5

Step-by-step solution →
Q30·PhysicsNumerical
The nuclear activity of a radioactive element becomes (18)th\left(\frac{1}{8}\right)^{\text{th}}(81​)th of its initial value in 30 years. The half –life of radioactive element is ________ years.

Correct answer: 10

Step-by-step solution →

Chemistry — JEE Main 25 July 2021 Shift 2

Q31·ChemistrySingle correct
Given below are two statements: Statement I : Chlorofluoro carbons breakdown by radiation in the visible energy region and release chlorine gas in the atmosphere which then reacts with stratospheric ozone. Statement II : Atmospheric ozone reacts with nitric oxide to give nitrogen and oxygen gases, which add to the atmosphere. For the above statements choose the correct answer from the options given below:
  1. (A)Statement I is incorrect but Statement II is true
  2. (B)Both Statement I and II are correct
  3. (C)Both Statement I and II are false
  4. (D)Statement I is correct but Statement II is false

Correct answer: (C)

Step-by-step solution →
Q32·ChemistrySingle correct
Maleic anhydride can be prepared by:
  1. (A)Heating cis-but-2-enedioic acid
  2. (B)Treating cis-but-2-enedioic acid with alcohol and acid
  3. (C)Heating trans- but-2- enedioic acid
  4. (D)Treating trans-but-2-enedioic acid with alcohol and acid

Correct answer: (A)

Step-by-step solution →
Q33·ChemistrySingle correct
The ionic radii of F−F^{-}F− and O2−O^{2-}O2− respectively are 1.33 Å and 1.4 Å, while the covalent radius of N is 0.74 Å. The correct statement for the ionic radius of N3−N^{3-}N3− from the following is:
  1. (A)It is smaller than O2−O^{2-}O2− and F−F^{-}F−, but bigger than of N
  2. (B)It is bigger than F−F^{-}F− and N, but smaller than of O2−O^{2-}O2−
  3. (C)It is smaller than F−F^{-}F− and N
  4. (D)It is bigger than O2−O^{2-}O2− and F−F^{-}F−

Correct answer: (D)

Step-by-step solution →
Q34·ChemistrySingle correct
The spin only magnetic moments (in BM) for free Ti3+,V2+Ti^{3+}, V^{2+}Ti3+,V2+ and Sc3+Sc^{3+}Sc3+ ions respectively are (At. No. Sc: 21; Ti:22; V:23)
  1. (A)1.73,0,3.87
  2. (B)0,3.87,1.73
  3. (C)3.87,1.73,0
  4. (D)1.73, 3.87,0

Correct answer: (D)

Step-by-step solution →
Q35·ChemistrySingle correct
Which one of the following metal complexes is most stable?
  1. (A)[Co(en)2(NH3)2]Cl2\left[Co(en)_2(NH_3)_2\right]Cl_2[Co(en)2​(NH3​)2​]Cl2​
  2. (B)[Co(NH3)6]Cl2\left[Co(NH_3)_6\right]Cl_2[Co(NH3​)6​]Cl2​
  3. (C)[Co(en)3]Cl2\left[Co(en)_3\right]Cl_2[Co(en)3​]Cl2​
  4. (D)[Co(en)(NH3)4]Cl2\left[Co(en)(NH_3)_4\right]Cl_2[Co(en)(NH3​)4​]Cl2​

Correct answer: (C)

Step-by-step solution →
Q36·ChemistrySingle correct
Match List – I with List – II: List – I Elements (a) Li (b) Na (c) K (d) Cs List – II Properties (i) Poor water solubility of I−I^-I− salt (ii) Most abundant element in cell fluid (iii) Bicarbonate salt used in fire extinguisher (iv) Carbonate salt decomposes easily on heating Choose the correct answer from the options given below:
  1. (A)(a) – (iv), (b) – (ii), (c) – (iii), (d) – (i)
  2. (B)(a) – (i), (b) –(ii), (c) – (iii), (d) – (iv)
  3. (C)(a) –(i), (b) – (iii), (c) – (ii), (d) – (iv)
  4. (D)(a) – (iv), (b) –(iii), (c) –(ii), (d) –(i)

Correct answer: (D)

Step-by-step solution →
Q37·ChemistrySingle correct
In the following the correct bond order sequence is:
  1. (A)O2>O2−>O22−>O2+O_2 > O_2^- > O_2^{2-} > O_2^+O2​>O2−​>O22−​>O2+​
  2. (B)O2+>O2>O2−>O22−O_2^+ > O_2 > O_2^- > O_2^{2-}O2+​>O2​>O2−​>O22−​
  3. (C)O22−>O2+>O2−>O2O_2^{2-} > O_2^+ > O_2^- > O_2O22−​>O2+​>O2−​>O2​
  4. (D)O2+>O2−>O22−>O2O_2^+ > O_2^- > O_2^{2-} > O_2O2+​>O2−​>O22−​>O2​

Correct answer: (B)

Step-by-step solution →
Q38·ChemistrySingle correct
Match List – I with List – II: Choose the most appropriate answer from the option given below:
List-I (Example of Colloids)List-II (Classification)
a.Cheesei.dispersion of liquid in liquid
b.Pumice stoneii.dispersion of liquid in gas
c.Hair creamiii.dispersion of gas in solid
d.Cloudiv.dispersion of liquid in solid
  1. (A)(a) – (iii), (b) –(iv), (c) –(i), (d) –(ii)
  2. (B)(a) –(iv), (b) –(iii), (c) –(ii), (d) – (i)
  3. (C)(a) –(iv), (b) –(iii), (c) –(i), (d) –(ii)
  4. (D)(a) –(iv), (b) –(i), (c) –(iii), (d) –(ii)

Correct answer: (C)

Step-by-step solution →
Q39·ChemistrySingle correct
[where Et ⇒ C2H5C_2H_5C2​H5​, t − Bu ⇒ (CH3)3C(CH_3)_3C(CH3​)3​C −] Consider the above reaction sequence, product "A" and product "B" formed respectively are:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q40·Chemistry·Electronic Effects and StabilitySingle correct
Which among the following is the strongest acid?
  1. (A)CH3CH2CH2CH3CH_3CH_2CH_2CH_3CH3​CH2​CH2​CH3​
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q41·ChemistrySingle correct
Which one of the following is correct structure for cytosine?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q42·ChemistrySingle correct
Identify the species having one π-bond and maximum number of canonical forms from the following:
  1. (A)SO2SO_2SO2​
  2. (B)CO32−CO_3^{2-}CO32−​
  3. (C)O2O_2O2​
  4. (D)SO3SO_3SO3​

Correct answer: (B)

Step-by-step solution →
Q43·ChemistrySingle correct
A biodegradable polyamide can be made from:
  1. (A)Glycine and aminocaproic acid
  2. (B)Hexamethylene diamine and adipic acid
  3. (C)Glycine and isoprene
  4. (D)Styrene and caproic acid

Correct answer: (A)

Step-by-step solution →
Q44·ChemistrySingle correct
Match List – I with List – II: Choose the correct answer from the options given below:
List-IList-II
a.Concentration of Ag orei.Reverberatory furnace
b.Blast furnaceii.Pig iron
c.Blister copperiii.Leaching with dilute NaCN solution
d.Froth floatation methodiv.Sulfide ores
  1. (A)(a) –(iii), (b) –(ii), (c) –(i), (d) –(iv)
  2. (B)(a) –(iii), (b) – (iv), (c) –(i), (d) – (ii)
  3. (C)(a) – (iv), (b) – (i), (c) – (iii), (d) – (ii)
  4. (D)(a) –(iv), (b) – (iii), (c) – (ii), (d) –(i)

Correct answer: (A)

Step-by-step solution →
Q45·ChemistrySingle correct
Consider the above reaction, the product "P" is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q46·ChemistrySingle correct
The correct decreasing order of densities of the following compounds is:
  1. (A)(C) > (B) > (A) > (D)
  2. (B)(A) > (B) > (C) > (D)
  3. (C)(D) > (C) > (B) > (A)
  4. (D)(C) > (D) > (A) > (B)

Correct answer: (C)

Step-by-step solution →
Q47·ChemistrySingle correct
What is the major product "P" of the following reaction?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q48·ChemistrySingle correct
Identify the process in which change in the oxidation state is five:
  1. (A)CrO42−CrO_4^{2-}CrO42−​ → Cr3+Cr^{3+}Cr3+
  2. (B)MnO4−MnO_4^-MnO4−​ → Mn2+Mn^{2+}Mn2+
  3. (C)Cr2O72−Cr_2O_7^{2-}Cr2​O72−​ → 2Cr3+2Cr^{3+}2Cr3+
  4. (D)C2O42−C_2O_4^{2-}C2​O42−​ → 2CO22CO_22CO2​

Correct answer: (B)

Step-by-step solution →
Q49·ChemistrySingle correct
A reaction of benzonitrile with one equivalent CH3MgBrCH_3MgBrCH3​MgBr followed by hydrolysis produces a yellow liquid "P". The compound "P" will give positive______.
  1. (A)Iodoform test
  2. (B)Schiff's test
  3. (C)Ninhydrin's test
  4. (D)Tollen's test

Correct answer: (A)

Step-by-step solution →
Q50·ChemistryNumerical
The number of significant figure in 0.00340 is______________.

Correct answer: 3

Step-by-step solution →
Q51·ChemistryNumerical
An LPG cylinder contains gas at a pressure of 300 kPa at 27∘C27^{\circ}C27∘C. The cylinder can withstand the pressure of 1.2×1061.2\times10^{6}1.2×106 Pa. The room in which the cylinder is kept catches fire. The minimum temperature at which the bursting of cylinder will take place is______ ∘C^{\circ}C∘C. (Nearest integer)

Correct answer: 927

Step-by-step solution →
Q52·ChemistryNumerical
An accelerated electron has speed of 5×1065\times10^{6}5×106 ms−1^{-1}−1 with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is x ×\times× 10−910^{-9}10−9 m . The value of x is________. (Nearest integer) [Use mass of electron = 9.1×10−319.1\times10^{-31}9.1×10−31 kg, h = 6.63×10−346.63\times10^{-34}6.63×10−34 Js, π\piπ=3.14]

Correct answer: 58

Step-by-step solution →
Q53·ChemistryNumerical
Number of electrons present in 4f orbital of Ho3+^{3+}3+ ion is____________________. (Given atomic number of Ho = 67)

Correct answer: 10

Step-by-step solution →
Q54·ChemistryNumerical
Consider the above chemical reaction. The total number of stereoisomers possible for product ‘P’ is___________.

Correct answer: 2

Step-by-step solution →
Q55·ChemistryNumerical
Assuming that Ba(OH)2_22​ is completely ionized in aqueous solution under the given conditions the concentration of H3_33​O+^{+}+ ions in 0.005 M aqueous solution of Ba(OH)2_22​ at 298 K is ___________ ×\times× 10−1210^{-12}10−12 mol L−1^{-1}−1. (nearest integer)

Correct answer: 1

Step-by-step solution →
Q56·ChemistryNumerical
For a chemical reaction A→B, it was found that concentration of B is increased by 0.2 mol L−1^{-1}−1 in 30 min. The average rate of the reaction is __________×10−1\times10^{-1}×10−1 mol L−1^{-1}−1 h−1^{-1}−1 . (in nearest integer)

Correct answer: 4

Step-by-step solution →
Q57·ChemistryNumerical
When 3.00 g of substance ‘X” is dissolved in 100 g of CCl4_44​, it raises the boiling point by 0.60K. The molar mass of the substance ‘X” is __________ g mol−1^{-1}−1. (nearest integer) [Given Kb_bb​ for CCl4_44​ is 5.0 K kg mol−1^{-1}−1]

Correct answer: 250

Step-by-step solution →
Q58·ChemistryNumerical
A system does 200 J of work and at the same time absorbs 150 J of heat. The magnitude of the change in internal energy is _________J. (Nearest integer)

Correct answer: 50

Step-by-step solution →
Q59·ChemistryNumerical
0.8 g of an organic compound was analysed by Kjeldahl’s method for the estimation of nitrogen. If the percentage of nitrogen in the compound was found to be 42%, then ___________ ml. of 1 M H2_22​SO4_44​ would have been neutralized by the ammonia evolved during the analysis.

Correct answer: 12

Step-by-step solution →

Mathematics — JEE Main 25 July 2021 Shift 2

Q60·MathematicsSingle correct
If [x] be the greatest integer less than or equal to x, then ∑n=8100[(−1)nn2]\sum_{n=8}^{100}\left[\frac{(-1)^n n}{2}\right]∑n=8100​[2(−1)nn​] is equal to :
  1. (A)4
  2. (B)-2
  3. (C)2
  4. (D)0

Correct answer: (A)

Step-by-step solution →
Q61·MathematicsSingle correct
The number of distinct real roots of ∣sin⁡xcos⁡xcos⁡xcos⁡xsin⁡xcos⁡xcos⁡xcos⁡xsin⁡x∣=0\begin{vmatrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \end{vmatrix} = 0​sinxcosxcosx​cosxsinxcosx​cosxcosxsinx​​=0 in the interval −π4≤x≤π4-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}−4π​≤x≤4π​ is:
  1. (A)2
  2. (B)4
  3. (C)1
  4. (D)3

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
Let a, b and c be distinct positive numbers. If the vectors ai^+aj^+ck^,i^+k^a\hat{i}+a\hat{j}+c\hat{k},\hat{i}+\hat{k}ai^+aj^​+ck^,i^+k^ and ci^+cj^+bk^c\hat{i}+c\hat{j}+b\hat{k}ci^+cj^​+bk^ are co-planar, then c is equal to :
  1. (A)21a+1b\frac{2}{\frac{1}{a}+\frac{1}{b}}a1​+b1​2​
  2. (B)a+b2\frac{a+b}{2}2a+b​
  3. (C)1a+1b\frac{1}{a}+\frac{1}{b}a1​+b1​
  4. (D)ab\sqrt{ab}ab​

Correct answer: (D)

Step-by-step solution →
Q63·MathematicsSingle correct
If a tangent to the ellipse x2+4y2=4x^{2}+4y^{2}=4x2+4y2=4 meets the tangents at the extremities of its major axis at B and C, then the circle with BC as diameter passes through the point :
  1. (A)(1,1)(1,1)(1,1)
  2. (B)(2,0)(\sqrt{2},0)(2​,0)
  3. (C)(3,0)(\sqrt{3},0)(3​,0)
  4. (D)(−1,1)(-1,1)(−1,1)

Correct answer: (C)

Step-by-step solution →
Q64·MathematicsSingle correct
If P=[10121]P=\begin{bmatrix} 1 & 0 \\ \frac{1}{2} & 1 \end{bmatrix}P=[121​​01​], then P50P^{50}P50 is :
  1. (A)[10251]\begin{bmatrix} 1 & 0 \\ 25 & 1 \end{bmatrix}[125​01​]
  2. (B)[12501]\begin{bmatrix} 1 & 25 \\ 0 & 1 \end{bmatrix}[10​251​]
  3. (C)[10501]\begin{bmatrix} 1 & 0 \\ 50 & 1 \end{bmatrix}[150​01​]
  4. (D)[15001]\begin{bmatrix} 1 & 50 \\ 0 & 1 \end{bmatrix}[10​501​]

Correct answer: (A)

Step-by-step solution →
Q65·MathematicsSingle correct
The sum of all those terms which are rational numbers in the expansion of (213+314)12\left(2^{\frac{1}{3}} + 3^{\frac{1}{4}}\right)^{12}(231​+341​)12 is :
  1. (A)89
  2. (B)35
  3. (C)27
  4. (D)43

Correct answer: (D)

Step-by-step solution →
Q66·MathematicsSingle correct
Let the equation of the pair of lines, y = px and y = qx, can be written as (y−px)(y−qx)=0\left( y - px \right)\left( y - qx \right) = 0(y−px)(y−qx)=0. Then the equation of the pair of the angle bisectors of the lines x2−4xy−5y2=0x^2 - 4xy - 5y^2 = 0x2−4xy−5y2=0 is :
  1. (A)x2−3xy+y2=0x^2 - 3xy + y^2 = 0x2−3xy+y2=0
  2. (B)x2+3xy−y2=0x^2 + 3xy - y^2 = 0x2+3xy−y2=0
  3. (C)x2−3xy−y2=0x^2 - 3xy - y^2 = 0x2−3xy−y2=0
  4. (D)x2+4xy−y2=0x^2 + 4xy - y^2 = 0x2+4xy−y2=0

Correct answer: (B)

Step-by-step solution →
Q67·MathematicsSingle correct
The number of real solutions of the equation, x2−∣x∣−12=0x^2 - \left|x\right| - 12 = 0x2−∣x∣−12=0 is :
  1. (A)1
  2. (B)4
  3. (C)3
  4. (D)2

Correct answer: (D)

Step-by-step solution →
Q68·MathematicsSingle correct
The lowest integer which is greater than (1+110100)10100\left(1 + \frac{1}{10^{100}}\right)^{10^{100}}(1+101001​)10100 is..........
  1. (A)3
  2. (B)2
  3. (C)4
  4. (D)1

Correct answer: (A)

Step-by-step solution →
Q69·MathematicsSingle correct
If ∣a⃗∣=2,∣b⃗∣=5\left|\vec{a}\right| = 2, \left|\vec{b}\right| = 5∣a∣=2,​b​=5 and ∣a⃗×b⃗∣=8\left|\vec{a} \times \vec{b}\right| = 8​a×b​=8, then ∣a⃗.b⃗∣\left|\vec{a} . \vec{b}\right|​a.b​ is equal to :
  1. (A)5
  2. (B)4
  3. (C)6
  4. (D)3

Correct answer: (C)

Step-by-step solution →
Q70·MathematicsSingle correct
The value of cot⁡π24\cot\frac{\pi}{24}cot24π​ is :
  1. (A)2+3+2+6\sqrt{2} + \sqrt{3} + 2 + \sqrt{6}2​+3​+2+6​
  2. (B)32−3−63\sqrt{2} - \sqrt{3} - \sqrt{6}32​−3​−6​
  3. (C)2−3−2+6\sqrt{2} - \sqrt{3} - 2 + \sqrt{6}2​−3​−2+6​
  4. (D)2+3+2−6\sqrt{2} + \sqrt{3} + 2 - \sqrt{6}2​+3​+2−6​

Correct answer: (A)

Step-by-step solution →
Q71·MathematicsSingle correct
Let X be a random variable such that the probability function of a distribution is given by P(X=0)=12,P(X=j)=13j(j=1,2,3,.....,∞)P\left(X = 0\right) = \frac{1}{2}, P\left(X = j\right) = \frac{1}{3^j}\left(j = 1,2,3,.....,\infty\right)P(X=0)=21​,P(X=j)=3j1​(j=1,2,3,.....,∞). Then the mean of the distribution and P(X is positive and even) respectively are :
  1. (A)34\frac{3}{4}43​ and 19\frac{1}{9}91​
  2. (B)34\frac{3}{4}43​ and 116\frac{1}{16}161​
  3. (C)34\frac{3}{4}43​ and 18\frac{1}{8}81​
  4. (D)38\frac{3}{8}83​ and 18\frac{1}{8}81​

Correct answer: (C)

Step-by-step solution →
Q72·MathematicsSingle correct
Consider functions f:A→Bf : A \to Bf:A→B and g:B→C(A,B,C⊆R)g : B \to C\left(A,B,C \subseteq R\right)g:B→C(A,B,C⊆R) such that (gof)−1\left(gof\right)^{-1}(gof)−1 exists, then :
  1. (A)f and g both are onto
  2. (B)f is onto and g is one-one
  3. (C)f is one-one and g is onto
  4. (D)f and g both are one-one

Correct answer: (C)

Step-by-step solution →
Q73·MathematicsSingle correct
The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation 13.44\sqrt{13.44}13.44​, then the standard deviation of the second sample is :
  1. (A)4
  2. (B)6
  3. (C)5
  4. (D)8

Correct answer: (A)

Step-by-step solution →
Q74·MathematicsSingle correct
Let y=y(x)y = y\left(x\right)y=y(x) be the solution of the differential equation xdy=(y+x3cos⁡x)dxxdy = \left(y + x^3\cos x\right)dxxdy=(y+x3cosx)dx with y(π)=0y\left(\pi\right) = 0y(π)=0, then y(π2)y\left(\frac{\pi}{2}\right)y(2π​) is equal to :
  1. (A)π24−π2\frac{\pi^2}{4} - \frac{\pi}{2}4π2​−2π​
  2. (B)π24+π2\frac{\pi^2}{4} + \frac{\pi}{2}4π2​+2π​
  3. (C)π22−π4\frac{\pi^2}{2} - \frac{\pi}{4}2π2​−4π​
  4. (D)π22+π4\frac{\pi^2}{2} + \frac{\pi}{4}2π2​+4π​

Correct answer: (B)

Step-by-step solution →
Q75·MathematicsSingle correct
The value of the integral ∫−11log⁡(x+x2+1)dx\int_{-1}^{1} \log\left(x + \sqrt{x^2 + 1}\right)dx∫−11​log(x+x2+1​)dx is :
  1. (A)-1
  2. (B)1
  3. (C)2
  4. (D)0

Correct answer: (D)

Step-by-step solution →
Q76·MathematicsSingle correct
If the greatest value of the term independent of 'x' in the expansion of (xsin⁡α+acos⁡αx)10\left(x\sin\alpha + a\frac{\cos\alpha}{x}\right)^{10}(xsinα+axcosα​)10 is 10!(5!)2\frac{10!}{\left(5!\right)^2}(5!)210!​, then the value of 'a' is equal to :
  1. (A)-1
  2. (B)2
  3. (C)-2
  4. (D)1

Correct answer: (B)

Step-by-step solution →
Q77·MathematicsSingle correct
If f(x)={∫0x(5+∣1−t∣)dt,x>25x+1,x≤2f\left(x\right) = \begin{cases} \int\limits_{0}^{x} \left(5 + \left|1 - t\right|\right)dt, & x > 2 \\ 5x + 1, & x \leq 2 \end{cases}f(x)=⎩⎨⎧​0∫x​(5+∣1−t∣)dt,5x+1,​x>2x≤2​, then
  1. (A)f(x) is not continuous at x = 2
  2. (B)f(x) is not differentiable at x = 1
  3. (C)f(x) is continuous but not differentiable at x = 2
  4. (D)f(x) is everywhere differentiable

Correct answer: (C)

Step-by-step solution →
Q78·MathematicsSingle correct
If nPr=nPr+1{}^n P_r = {}^n P_{r+1}nPr​=nPr+1​ and nCr=nCr−1{}^n C_r = {}^n C_{r-1}nCr​=nCr−1​, then the value of r is equal to :
  1. (A)4
  2. (B)1
  3. (C)3
  4. (D)2

Correct answer: (D)

Step-by-step solution →
Q79·MathematicsSingle correct
Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following :
  1. (A)The match will not be played or weather is good and ground is not wet.
  2. (B)The match will not be played or weather is not good and ground is wet.
  3. (C)If the match will not be played, then either weather is not good or ground is wet.
  4. (D)The match will be played and weather is not good or ground is wet.

Correct answer: (D)

Step-by-step solution →
Q80·MathematicsNumerical
Consider the function f(x)=P(x)sin⁡(x−2)f(x) = \dfrac{P(x)}{\sin(x-2)}f(x)=sin(x−2)P(x)​ , x≠2x \neq 2x=2 =7= 7=7 , x=2x = 2x=2 where P(x) is a polynomial such that P''(x) is always a constant and P(3) = 9. If (x) is continuous at x = 2, then P(5) is equal to.......

Correct answer: 39

Step-by-step solution →
Q81·MathematicsNumerical
If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a4+b4+c4a^{4} + b^{4} + c^{4}a4+b4+c4 is equal to.....

Correct answer: 13

Step-by-step solution →
Q82·MathematicsNumerical
If the co-efficients of x7x^{7}x7 and x8x^{8}x8 in the expansion of (2+x3)n\left(2 + \dfrac{x}{3}\right)^{n}(2+3x​)n are equal, then the value of n is equal to .........

Correct answer: 55

Step-by-step solution →
Q83·MathematicsNumerical
If the lines x−k1=y−22=z−33\dfrac{x-k}{1} = \dfrac{y-2}{2} = \dfrac{z-3}{3}1x−k​=2y−2​=3z−3​ and x+13=y+22=z+31\dfrac{x+1}{3} = \dfrac{y+2}{2} = \dfrac{z+3}{1}3x+1​=2y+2​=1z+3​ are co-planar, then the value of k is......

Correct answer: 1

Step-by-step solution →
Q84·MathematicsNumerical
If a rectangle is inscribed in an equilateral triangle of side length 222\sqrt{2}22​ as shown in the figure, then the square of the largest area of such a rectangle is .........

Correct answer: 3

Step-by-step solution →
Q85·MathematicsNumerical
If (a⃗+3b⃗)\left(\vec{a} + 3\vec{b}\right)(a+3b) is perpendicular to (7a⃗−5b⃗)\left(7\vec{a} - 5\vec{b}\right)(7a−5b) and (a⃗−4b⃗)\left(\vec{a} - 4\vec{b}\right)(a−4b) is perpendicular to (7a⃗−2b⃗)\left(7\vec{a} - 2\vec{b}\right)(7a−2b) , then the angle between a⃗\vec{a}a and b⃗\vec{b}b (in degrees) is.......

Correct answer: 60

Step-by-step solution →
Q86·MathematicsNumerical
Let n∈Nn \in Nn∈N and [x] denote the greatest integer less than or equal to x. If the sum of (n+1) terms nC0,3.nC1,5.nC2,7.nC3,.....^{n}C_{0}, 3.^{n}C_{1}, 5.^{n}C_{2}, 7.^{n}C_{3},.....nC0​,3.nC1​,5.nC2​,7.nC3​,..... is equal to 2100.1012^{100}.1012100.101, then 2[n−12]2\left[\dfrac{n-1}{2}\right]2[2n−1​] is equal to

Correct answer: 98

Step-by-step solution →
Q87·MathematicsNumerical
A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is...........

Correct answer: 4

Step-by-step solution →
Q88·MathematicsNumerical
Let a curve y=f(x)y = f(x)y=f(x) pass through the point (2,(log⁡e2)2)\left(2, \left(\log_{e}2\right)^{2}\right)(2,(loge​2)2) and have slope 2yxlog⁡ex\dfrac{2y}{x\log_{e}x}xloge​x2y​ for all positive real value of x. Then the value of f(e)f(e)f(e) is equal to..........

Correct answer: 1

Step-by-step solution →
Q89·MathematicsNumerical
The equation of a circle is Re(z2)+2(Im(z))2+2Re(z)=0Re\left(z^{2}\right) + 2\left(Im(z)\right)^{2} + 2Re(z) = 0Re(z2)+2(Im(z))2+2Re(z)=0, where z=x+iyz = x + iyz=x+iy. A line which passes through the center of the given circle and the vertex of the parabola, x2−6x−y+13=0x^{2} - 6x - y + 13 = 0x2−6x−y+13=0, has y-intercept equal to.........

Correct answer: 1

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
  • Definite Integration 168/186
  • Rotational Motion 172/186
  • Redox Reactions and Electrochemistry 177/186
  • Geometrical Optics 172/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Probability 176/186
  • Permutations and Combinations 162/186
  • Magnetic Field of Current 147/186
  • 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
  • Thermodynamics 154/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Solutions 158/186
  • 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
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • 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
  • Kinetic Theory of Gases 135/186
  • Purification and Characterisation of Organic Compounds 116/186
  • Oscillations 117/186
  • Alternating Currents 108/186
  • Nuclei 116/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Capacitors and Dielectrics 115/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Statistics 118/186
  • Ellipse 103/186
  • Isolation of Metals 106/186
  • Differentiability 91/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Environmental Chemistry 83/186
  • Electronic Effects and Stability 74/186
  • Polymers 64/186
  • Carboxylic Acids and Derivatives 54/186
  • Diazonium Salts and Reactions 53/186
  • States of Matter: Gases and Liquids 52/186
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