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JEE Main 24 February 2021 Shift 1 Question Paper with Answers

24 February 2021 · February session · 88 questions

88 of the 90 questions from the JEE Main 24 February 2021 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

2 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
30
Chemistry
29
Mathematics
29

Physics — JEE Main 24 February 2021 Shift 1

Q1·PhysicsSingle correct
Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be -
  1. (A)(1+22)G2\frac{\sqrt{(1+2\sqrt{2})G}}{2}2(1+22​)G​​
  2. (B)G(1+22)\sqrt{G(1+2\sqrt{2})}G(1+22​)​
  3. (C)G2(22−1)\sqrt{\frac{G}{2}\left(2\sqrt{2}-1\right)}2G​(22​−1)​
  4. (D)G2(1+22)\sqrt{\frac{G}{2}\left(1+2\sqrt{2}\right)}2G​(1+22​)​

Correct answer: (A)

Step-by-step solution →
Q2·PhysicsSingle correct
Consider two satellites S1S_1S1​ and S2S_2S2​ with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits.The ratio of angular velocity of satellite S1S_1S1​ to the angular velocity of satellite S2S_2S2​ is -
  1. (A)8 : 1
  2. (B)1 : 8
  3. (C)2 : 1
  4. (D)1 : 4

Correct answer: (A)

Step-by-step solution →
Q3·PhysicsSingle correct
n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes – A→\rightarrow→B : Isothermal expansion at temperature T so that the volume is doubled from V1V_1V1​ to V2=2V1V_2 = 2V_1V2​=2V1​ and pressure changes from P1P_1P1​ to P2P_2P2​. B →\rightarrow→ C : Isobaric compression at pressure P2P_2P2​ to initial volume V1V_1V1​. C →\rightarrow→ A : Isochoric change leading to change of pressure from P2P_2P2​ to P1P_1P1​. Total workdone in the complete cycle ABCA is –
  1. (A)0
  2. (B)nRT(ln⁡2+12)nRT\left(\ln 2 + \frac{1}{2}\right)nRT(ln2+21​)
  3. (C)nRTln⁡2nRT\ln 2nRTln2
  4. (D)nRT(ln⁡2−12)nRT\left(\ln 2 - \frac{1}{2}\right)nRT(ln2−21​)

Correct answer: (D)

Step-by-step solution →
Q4·PhysicsSingle correct
Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities capacities in the two cases will be -
  1. (A)2 : 1
  2. (B)1 : 4
  3. (C)4 : 1
  4. (D)1 : 2

Correct answer: (B)

Step-by-step solution →
Q5·PhysicsSingle correct
A cell E1E_1E1​ of emf 6V and internal resistance 2Ω\OmegaΩ is connected with another cell E2E_2E2​ of emf 4V and internal resistance 8Ω\OmegaΩ (as shown in the figure). The potential difference across points X and Y is –
  1. (A)3.6V
  2. (B)10.0V
  3. (C)5.6V
  4. (D)2.0V

Correct answer: (C)

Step-by-step solution →
Q6·PhysicsSingle correct
If Y,K and η\etaη are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.
  1. (A)K=Yη9η−3YK = \frac{Y\eta}{9\eta - 3Y}K=9η−3YYη​ N/m2^22
  2. (B)η=3YK9K+Y\eta = \frac{3YK}{9K + Y}η=9K+Y3YK​ N/m2^22
  3. (C)Y=9Kη3K−ηY = \frac{9K\eta}{3K - \eta}Y=3K−η9Kη​ N/m2^22
  4. (D)Y=9Kη2η+3KY = \frac{9K\eta}{2\eta + 3K}Y=2η+3K9Kη​ N/m2^22

Correct answer: (A)

Step-by-step solution →
Q7·PhysicsSingle correct
Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is -
  1. (A)2πd33Gm2\pi\sqrt{\frac{d^3}{3Gm}}2π3Gmd3​​
  2. (B)12π3Gmd3\frac{1}{2\pi}\sqrt{\frac{3Gm}{d^3}}2π1​d33Gm​​
  3. (C)12πd33Gm\frac{1}{2\pi}\sqrt{\frac{d^3}{3Gm}}2π1​3Gmd3​​
  4. (D)2π3Gmd32\pi\sqrt{\frac{3Gm}{d^3}}2πd33Gm​​

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph ?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q9·PhysicsSingle correct
Given below are two statements : Statement – I: Two photons having equal linear momenta have equal wavelengths. Statement-II: If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease. In the light of the above statements, choose the correct answer from the options given below.
  1. (A)Statemnet-I is false but Statement-II is true
  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 true but Statement-II is false

Correct answer: (D)

Step-by-step solution →
Q10·PhysicsSingle correct
A current through a wire depends on time as i=α0t+βt2i = \alpha_0 t + \beta t^2i=α0​t+βt2 where α0\alpha_0α0​ = 20 A/s and β\betaβ = 8 As−2^{-2}−2. Find the charge crossed through a section of the wire in 15 s.
  1. (A)2100 C
  2. (B)260 C
  3. (C)2250 C
  4. (D)11250 C

Correct answer: (D)

Step-by-step solution →
Q11·PhysicsSingle correct
match List I with List II List-I (a) Isothermal (b) Isochoric (c) Adiabatic (d) Isobaric List-II (i) Pressure constant (ii) Temperature constant (iii) Volume constant (iv) Heat content is constant Choose the correct answer from the options given below –
  1. (A)(a) – (ii), (b) – (iv), (c) – (iii), (d) – (i)
  2. (B)(a) – (ii), (b) – (iii), (c) – (iv), (d) – (i)
  3. (C)(a) – (i), (b) – (iii), (c) – (ii), (d) – (iv)
  4. (D)(a) – (iii), (b) – (ii), (c) – (i), (d) – (iv)

Correct answer: (B)

Step-by-step solution →
Q12·PhysicsSingle correct
In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A,B,C,D and E. The transitions A,B and C respectively represents –
  1. (A)The series limit of Lyman series, third member of balmer series and second member of paschen series
  2. (B)The first member of the Lyman series, third member of Balmer series and second member of paschen series
  3. (C)The ionization potential of hydrogen, second member of Balmer series and third member of Paschen series
  4. (D)The series limit of Lyman series, second memebr of Balmer series and second member of Paschen series.

Correct answer: (A)

Step-by-step solution →
Q13·PhysicsSingle correct
The focal length f is related to the radius of curvature r of the spherical convex mirror by -
  1. (A)f=rf = rf=r
  2. (B)f=−12rf = -\frac{1}{2}rf=−21​r
  3. (C)f=+12rf = +\frac{1}{2}rf=+21​r
  4. (D)f=−rf = -rf=−r

Correct answer: (C)

Step-by-step solution →
Q14·PhysicsSingle correct
Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as – I1I_1I1​ = M.I. of thin circular ring about its diameter, I2I_2I2​ = M.I. of circular disc about an axis perpendicular to disc and going through the centre, I3I_3I3​ = M.I. of solid cylinder about its axis and I4I_4I4​ = M.I. of solid sphere about its diameter. Then :-
  1. (A)I1=I2=I3<I4I_1 = I_2 = I_3 < I_4I1​=I2​=I3​<I4​
  2. (B)I1+I2=I3+52I4I_1 + I_2 = I_3 + \frac{5}{2}I_4I1​+I2​=I3​+25​I4​
  3. (C)I1+I3<I2+I4I_1 + I_3 < I_2 + I_4I1​+I3​<I2​+I4​
  4. (D)I1=I2=I3>I4I_1 = I_2 = I_3 > I_4I1​=I2​=I3​>I4​

Correct answer: (D)

Step-by-step solution →
Q15·PhysicsSingle correct
The workdone by a gas molecule in an isolated system is given by, W=αβ2e−x2αkTW = \alpha\beta^2 e^{-\frac{x^2}{\alpha kT}}W=αβ2e−αkTx2​ , where x is the displacement, k is the Boltzmann constant and T is the temperature.α\alphaα and β\betaβ are constants. Then the dimensions of β\betaβ will be -
  1. (A)[M0LT0][M^0LT^0][M0LT0]
  2. (B)[M2LT2][M^2LT^2][M2LT2]
  3. (C)[MLT−2][MLT^{-2}][MLT−2]
  4. (D)[ML2T−2][ML^2T^{-2}][ML2T−2]

Correct answer: (C)

Step-by-step solution →
Q16·PhysicsSingle correct
If an emitter current is changed by 4mA, the collector current changes by 3.5 mA.The value of β\betaβ will be -
  1. (A)7
  2. (B)0.875
  3. (C)0.5
  4. (D)3.5

Correct answer: (A)

Step-by-step solution →
Q17·PhysicsSingle correct
In a Young's double slit experiment, the width ofthe one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.
  1. (A)4 : 1
  2. (B)2 : 1
  3. (C)3 : 1
  4. (D)1 : 4

Correct answer: (A)

Step-by-step solution →
Q18·PhysicsSingle correct
In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillation will be -
  1. (A)AMM+mA\sqrt{\frac{M}{M+m}}AM+mM​​
  2. (B)AMM−mA\sqrt{\frac{M}{M-m}}AM−mM​​
  3. (C)AM−mMA\sqrt{\frac{M-m}{M}}AMM−m​​
  4. (D)AM+mMA\sqrt{\frac{M+m}{M}}AMM+m​​

Correct answer: (A)

Step-by-step solution →
Q19·PhysicsSingle correct
A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is –Q. The electric field at the centre of cube is :
  1. (A)2Q33πε0a2(x^+y^+z^)\frac{2Q}{3\sqrt{3}\pi\varepsilon_0 a^2}\left(\hat{x}+\hat{y}+\hat{z}\right)33​πε0​a22Q​(x^+y^​+z^)
  2. (B)Q33πε0a2(x^+y^+z^)\frac{Q}{3\sqrt{3}\pi\varepsilon_0 a^2}\left(\hat{x}+\hat{y}+\hat{z}\right)33​πε0​a2Q​(x^+y^​+z^)
  3. (C)−2Q33πε0a2(x^+y^+z^)\frac{-2Q}{3\sqrt{3}\pi\varepsilon_0 a^2}\left(\hat{x}+\hat{y}+\hat{z}\right)33​πε0​a2−2Q​(x^+y^​+z^)
  4. (D)−Q33πε0a2(x^+y^+z^)\frac{-Q}{3\sqrt{3}\pi\varepsilon_0 a^2}\left(\hat{x}+\hat{y}+\hat{z}\right)33​πε0​a2−Q​(x^+y^​+z^)

Correct answer: (C)

Step-by-step solution →
Q20·PhysicsSingle correct
Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is 'α\alphaα'. The metal sheet is heated uniformly, by a small temperature Δ\DeltaΔT, so that its new temeprature is T+Δ\DeltaΔT. Calculate theincrease in the volume of the metal box-
  1. (A)43πa3αΔT\frac{4}{3}\pi a^3\alpha\Delta T34​πa3αΔT
  2. (B)4πa3αΔT4\pi a^3\alpha\Delta T4πa3αΔT
  3. (C)3a3αΔT3a^3\alpha\Delta T3a3αΔT
  4. (D)4a3αΔT4a^3\alpha\Delta T4a3αΔT

Correct answer: (C)

Step-by-step solution →
Q21·PhysicsNumerical
A resonance circuit having inductance and resistance 2×10−42 \times 10^{-4}2×10−4 H and 6.28 Ω\OmegaΩ respectively oscillates at 10 MHz frequency. The value of quality factor of this resonator is__________. [π\piπ = 3.14]

Correct answer: 2000

Step-by-step solution →
Q22·PhysicsNumerical
A ball with a speed of 9 m/s collides with another identical ball at rest. After thecollision, the direction of each ball makes an angle of 30° with the original direction. The ratio of velocities of the balls after collision is x : y, where x is ___________.

Correct answer: 1

Step-by-step solution →
Q23·PhysicsNumerical
An audio signal υm\upsilon_mυm​ = 20sin2π\piπ(1500t) amplitude modulates a carrier υc\upsilon_cυc​ =80 sin 2π\piπ (100,000t). The value of percent modulation is __________.

Correct answer: 25

Step-by-step solution →
Q24·PhysicsNumerical
The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be ________ N. [g = 10 ms−2^{-2}−2]

Correct answer: 25

Step-by-step solution →
Q25·PhysicsNumerical
An inclined plane is bent in such a way that the vertical cross-section is given by y=x24y = \frac{x^2}{4}y=4x2​ where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction μ\muμ = 0.5, the maximum height in cm at which a stationary block will not slip downward is ______ cm.

Correct answer: 25

Step-by-step solution →
Q26·PhysicsNumerical
An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability bothare 2. Its velocity in this medium is ________ ×107\times 10^{7}×107 m/s.

Correct answer: 15

Step-by-step solution →
Q27·PhysicsNumerical
A hydraulic press can lift 100 kg when a mass ‘m’ is placed on the smaller piston. It can lift ________ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass ‘m’ on the smaller piston.

Correct answer: 25600

Step-by-step solution →
Q28·PhysicsNumerical
A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V (A.C.) on standard domestic A.C. supply. The number of turns of secondary coil are 24, then the number of turns of primary are ________.

Correct answer: 440

Step-by-step solution →
Q29·PhysicsNumerical
An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging fromthe analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by 30° in clockwise direction, the intensity of emerging light will be__________ Lumens.

Correct answer: 75

Step-by-step solution →
Q30·PhysicsNumerical
In connection with the circuit drawn below, the value of current flowing through 2kΩ\OmegaΩresistor is ________ ×10−4\times 10^{-4}×10−4 A.

Correct answer: 25

Step-by-step solution →

Chemistry — JEE Main 24 February 2021 Shift 1

Q31·ChemistrySingle correct
The gas released during anaerobic degradation of vegetation may lead to:
  1. (A)Global warming and cancer
  2. (B)Acid rain
  3. (C)Corrosion of metals
  4. (D)Ozone hole

Correct answer: (A)

Step-by-step solution →
Q32·ChemistrySingle correct
Out of the following, which type of interaction is responsible for the stabilisation α\alphaα−helix structure of proteins ?
  1. (A)Ionic bonding
  2. (B)Hydrogen bonding
  3. (C)vander Waals forces
  4. (D)Covalent bonding

Correct answer: (B)

Step-by-step solution →
Q33·ChemistrySingle correct
Which of the following are isostructural pairs ? (A) SO42−\mathrm{SO_4^{2-}}SO42−​ and CrO42−\mathrm{CrO_4^{2-}}CrO42−​ (B) SiCl4\mathrm{SiCl_4}SiCl4​ and TiCl4\mathrm{TiCl_4}TiCl4​ (c) NH3\mathrm{NH_3}NH3​ and NO3−\mathrm{NO_3^{-}}NO3−​ (D) BCl3\mathrm{BCl_3}BCl3​ and BrCl3\mathrm{BrCl_3}BrCl3​
  1. (A)A and C only
  2. (B)A and B only
  3. (C)B and C only
  4. (D)C and D only

Correct answer: (B)

Step-by-step solution →
Q34·ChemistrySingle correct
Identify products A and B.
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q35·ChemistrySingle correct
The electrode potential of M2+/M\mathrm{M^{2+}/M}M2+/M of 3d− series elements shows positive value for:
  1. (A)Zn
  2. (B)Co
  3. (C)Fe
  4. (D)Cu

Correct answer: (D)

Step-by-step solution →
Q36·ChemistrySingle correct
In the following reaction the reason why meta−nitro product also formed is:
  1. (A)Formation of anilinium ion
  2. (B)−NO2\mathrm{-NO_2}−NO2​ substitution always takes place at meta−position
  3. (C)low temperature
  4. (D)−NH2\mathrm{-NH_2}−NH2​ group is highly meta−directive

Correct answer: (A)

Step-by-step solution →
Q37·ChemistrySingle correct
(A) HOCl+H2O2→H3O++Cl−+O2\mathrm{HOCl + H_2O_2 \rightarrow H_3O^{+} + Cl^{-} + O_2}HOCl+H2​O2​→H3​O++Cl−+O2​ (B) I2+H2O2+2OH−→2I−+2H2O+O2\mathrm{I_2 + H_2O_2 + 2OH^{-} \rightarrow 2I^{-} + 2H_2O + O_2}I2​+H2​O2​+2OH−→2I−+2H2​O+O2​ Choose the correct option.
  1. (A)H2O2\mathrm{H_2O_2}H2​O2​ act as oxidizing and reducing agent respectively in equations (A) and (B).
  2. (B)H2O2\mathrm{H_2O_2}H2​O2​ acts as oxidizing agent in equations (A) and (B).
  3. (C)H2O2\mathrm{H_2O_2}H2​O2​ acts as reducing agent in equations (A) and (B).
  4. (D)H2O2\mathrm{H_2O_2}H2​O2​ acts as reducing and oxidising agent respectively in equation (A) and (B).

Correct answer: (C)

Step-by-step solution →
Q38·ChemistrySingle correct
Which of the following ore is concentrated using group 1 cyanide salt ?
  1. (A)Sphalerite
  2. (B)Siderite
  3. (C)Malachite
  4. (D)Calamine

Correct answer: (A)

Step-by-step solution →
Q39·ChemistrySingle correct
Which is the final product (major) 'A' in the given reaction?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q40·ChemistrySingle correct
What is the major product formed by HI on reaction with CH3−CH3CCH3−CH=CH2\mathrm{CH_3-\overset{CH_3}{\underset{H_3C}{C}}-CH=CH_2}CH3​−H3​CC​CH3​​−CH=CH2​ ?
  1. (A)CH3−CH3CCH3−CIH−CH3\mathrm{CH_3-\overset{CH_3}{\underset{H_3C}{C}}-\underset{I}{C}H-CH_3}CH3​−H3​CC​CH3​​−IC​H−CH3​
  2. (B)CH3−CH3CH−CIH−CH2−CH3\mathrm{CH_3-\underset{H_3C}{C}H-\underset{I}{C}H-CH_2-CH_3}CH3​−H3​CC​H−IC​H−CH2​−CH3​
  3. (C)CH3−CICH3−CCH3H−CH3\mathrm{CH_3-\overset{CH_3}{\underset{I}{C}}-\underset{CH_3}{C}H-CH_3}CH3​−IC​CH3​​−CH3​C​H−CH3​
  4. (D)CH3−CH3CCH3−CHH−CH2I\mathrm{CH_3-\overset{CH_3}{\underset{H_3C}{C}}-\underset{H}{C}H-CH_2I}CH3​−H3​CC​CH3​​−HC​H−CH2​I

Correct answer: (C)

Step-by-step solution →
Q41·ChemistrySingle correct
Which of the following reagent is used for the following reaction ? CH3CH2CH3→  ?  CH3CH2CHO\mathrm{CH_3CH_2CH_3 \xrightarrow{\;?\;} CH_3CH_2CHO}CH3​CH2​CH3​?​CH3​CH2​CHO
  1. (A)Potassium permanganate
  2. (B)Molybdenum oxide
  3. (C)Copper at high temperature and pressure
  4. (D)Manganese acetate

Correct answer: (B)

Step-by-step solution →
Q42·ChemistrySingle correct
In Freundlich adsorption isotherm, slope of AB line is :
  1. (A)1n\frac{1}{n}n1​ with (1n=0 to 1)\left(\frac{1}{n} = 0 \text{ to } 1\right)(n1​=0 to 1)
  2. (B)log⁡1n\log \frac{1}{n}logn1​ with (n<1)(n<1)(n<1)
  3. (C)log⁡n\log nlogn with (n>1)(n>1)(n>1)
  4. (D)nnn with (n,0.1 to 0.5)(n, 0.1 \text{ to } 0.5)(n,0.1 to 0.5)

Correct answer: (A)

Step-by-step solution →
Q43·ChemistrySingle correct
The major components in “Gun Metal” are:
  1. (A)Al, Cu, Mg and Mn
  2. (B)Cu, Sn and Zn
  3. (C)Cu, Zn and Ni
  4. (D)Cu, Ni and Fe

Correct answer: (B)

Step-by-step solution →
Q44·ChemistrySingle correct
'A' and 'B' in the following reactions are :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q45·ChemistrySingle correct
Which of the following compound gives pink colour on reaction with phthalic anhydride in conc.H2SO4\mathrm{H_2SO_4}H2​SO4​ followed by treatment with NaOH ?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q46·ChemistrySingle correct
Consider the elements Mg, Al, S, P and Si, the correct increasing order of their first ionization enthalpy is:
  1. (A)Al < Mg < Si < S < P
  2. (B)Al < Mg < S < Si < P
  3. (C)Mg < Al < Si < S < P
  4. (D)Mg < Al < Si < P < S

Correct answer: (A)

Step-by-step solution →
Q47·ChemistrySingle correct
Given below are two statements : Statement I : Colourless cupric metaborate is reduced to cuprous metaborate in a luminous flame. Statement II : Cuprous metaborate is obtained by heating boric anhydride and copper sulphate in a non-luminous flame. In the light of the above statements, choose the most appropriate answer from the options given below.
  1. (A)Statement I is false but statement II is true.
  2. (B)Statement I is true but Statement II is false.
  3. (C)Both Statement I and Statement II are true.
  4. (D)Both Statement I and Statement II are false.

Correct answer: (D)

Step-by-step solution →
Q48·ChemistrySingle correct
Al2O3\mathrm{Al_2O_3}Al2​O3​ was leached with alkali to get X. The solution of X on passing of gas Y, forms Z. X, Y and Z respectively are :
  1. (A)X = Na[Al(OH)4]\mathrm{Na[Al(OH)_4]}Na[Al(OH)4​], Y=CO2\mathrm{CO_2}CO2​, Z = Al2O3.xH2O\mathrm{Al_2O_3.xH_2O}Al2​O3​.xH2​O
  2. (B)X=Na[Al(OH)4]\mathrm{Na[Al(OH)_4]}Na[Al(OH)4​], Y=SO2\mathrm{SO_2}SO2​, Z = Al2O3\mathrm{Al_2O_3}Al2​O3​
  3. (C)X=Al(OH)3\mathrm{Al(OH)_3}Al(OH)3​, Y=SO2\mathrm{SO_2}SO2​, Z = Al2O3.xH2O\mathrm{Al_2O_3.xH_2O}Al2​O3​.xH2​O
  4. (D)X = Al(OH)3\mathrm{Al(OH)_3}Al(OH)3​, Y=CO2\mathrm{CO_2}CO2​, Z= Al2O3\mathrm{Al_2O_3}Al2​O3​

Correct answer: (A)

Step-by-step solution →
Q49·ChemistrySingle correct
Match List I with List II. List I (Monomer Unit) (a) Caprolactum (b) 2-Chloro-1,3-butadiene (c) Isoprene (d) Acrylonitrile List II (Polymer) (i) Natural rubber (ii) Buna-N (iii) Nylon 6 (iv) Neoprene Choose the correct answer from the options given below :
  1. (A)(a) →\rightarrow→ (iii), (b) →\rightarrow→ (iv), (c) →\rightarrow→ (i), (d) →\rightarrow→ (ii)
  2. (B)(a) →\rightarrow→ (i), (b) →\rightarrow→ (ii), (c) →\rightarrow→ (iii), (d) →\rightarrow→ (iv)
  3. (C)(a) →\rightarrow→ (ii), (b) →\rightarrow→ (i), (c) →\rightarrow→ (iv), (d) →\rightarrow→ (iii)
  4. (D)(a) →\rightarrow→ (iv), (b) →\rightarrow→ (iii), (c) →\rightarrow→ (ii), (d) →\rightarrow→ (i)

Correct answer: (A)

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Q50·ChemistryNumerical
The stepwise formation of [Cu(NH3]2+\mathrm{[Cu(NH_3]^{2+}}[Cu(NH3​]2+ is given below: Cu2++NH3⇌K1[Cu(NH3)4]2+\mathrm{Cu^{2+}} + \mathrm{NH_3} \overset{K_1}{\rightleftharpoons} \mathrm{\left[Cu(NH_3)_4\right]^{2+}}Cu2++NH3​⇌K1​​[Cu(NH3​)4​]2+ [Cu(NH3)2]2++NH3⇌K2[Cu(NH3)2]2+\mathrm{\left[Cu(NH_3)_2\right]^{2+}} + \mathrm{NH_3} \overset{K_2}{\rightleftharpoons} \mathrm{\left[Cu(NH_3)_2\right]^{2+}}[Cu(NH3​)2​]2++NH3​⇌K2​​[Cu(NH3​)2​]2+ [Cu(NH3)2]2++NH3⇌K3[Cu(NH3)3]2+\mathrm{\left[Cu(NH_3)_2\right]^{2+}} + \mathrm{NH_3} \overset{K_3}{\rightleftharpoons} \mathrm{\left[Cu(NH_3)_3\right]^{2+}}[Cu(NH3​)2​]2++NH3​⇌K3​​[Cu(NH3​)3​]2+ [Cu(NH3)3]2++NH3⇌K4[Cu(NH3)4]2+\mathrm{\left[Cu(NH_3)_3\right]^{2+}} + \mathrm{NH_3} \overset{K_4}{\rightleftharpoons} \mathrm{\left[Cu(NH_3)_4\right]^{2+}}[Cu(NH3​)3​]2++NH3​⇌K4​​[Cu(NH3​)4​]2+ The value of stability constants K1\mathrm{K_1}K1​, K2\mathrm{K_2}K2​, K3\mathrm{K_3}K3​ and K4\mathrm{K_4}K4​ are 10410^4104, 1.58×1021.58 \times 10^21.58×102 , 5×1025 \times 10^25×102 and 10210^2102 respectively. The overall equilibrium constants for dissociation of [Cu(NH3)4]2+\mathrm{[Cu(NH_3)_4]^{2+}}[Cu(NH3​)4​]2+ is x×10−12x \times 10^{-12}x×10−12. The value of x is ________. (Rounded off to the nearest integer)

Correct answer: 1

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Q51·ChemistryNumerical
At 1990 K and 1 atrm pressure, there are equal number of Cl2\mathrm{Cl_2}Cl2​ molecules and Cl\mathrm{Cl}Cl atoms in the reaction mixture. The value of Kp\mathrm{K_p}Kp​ for the reaction Cl2(g)⇌2Cl(g)\mathrm{Cl_{2(g)}} \rightleftharpoons \mathrm{2Cl_{(g)}}Cl2(g)​⇌2Cl(g)​ under the above conditions is x×10−1x \times 10^{-1}x×10−1. The value of x is _________. (Rounded off to the nearest integer)

Correct answer: 5

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Q52·ChemistryNumerical
4.5 g of compound A (MW = 90) was used to make 250 mL of its aqueous solution. The molarity of the solution in M is x×10−1x \times 10^{-1}x×10−1. The value of x is _________. (Rounded off to the nearest integer)

Correct answer: 2

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Q53·ChemistryNumerical
The coordination number of an atom in a body-centered cubic structure is ________________. [Assume that the lattice is made up of atoms]

Correct answer: 8

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Q54·ChemistryNumerical
Number of amphoteric compounds among the following is __________. (A) BeO (B) BaO (C) Be(OH)2\mathrm{Be(OH)_2}Be(OH)2​ (D) Sr(OH)2\mathrm{Sr(OH)_2}Sr(OH)2​

Correct answer: 2

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Q55·ChemistryNumerical
When 9.45g of ClCH2COOH\mathrm{ClCH_2COOH}ClCH2​COOH is added to 500 mL of water, its freezing point drops by 0.5°C. The dissociation constant of ClCH2COOH\mathrm{ClCH_2COOH}ClCH2​COOH is x×10−3x \times 10^{-3}x×10−3. The value of x is ________. (Rounded off to the nearest integer) [Kf(H2O)=1.86 K kg mol−1][\mathrm{K_{f(H_2O)}} = 1.86\,\mathrm{K\,kg\,mol^{-1}}][Kf(H2​O)​=1.86Kkgmol−1]

Correct answer: 35

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Q56·ChemistryNumerical
A proton and a Li3+\mathrm{Li^{3+}}Li3+ nucleus are accelerated by the same potential. If λLi\lambda_{\mathrm{Li}}λLi​ and λp\lambda_{\mathrm{p}}λp​ denote the de Broglie wavelengths of Li3+\mathrm{Li^{3+}}Li3+ and proton respectively, then the value of λLiλp\dfrac{\lambda_{\mathrm{Li}}}{\lambda_{\mathrm{p}}}λp​λLi​​ is x×10−1x \times 10^{-1}x×10−1. The value of x is _________. [Rounded off to the nearest integer] [Mass of Li3+\mathrm{Li^{3+}}Li3+ = 8.3 mass of proton]

Correct answer: 2

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Q57·ChemistryNumerical
Gaseous cyclobutene isomerizes to butadiene in a first order process which has a 'k' value of 3.3×10−4 s−13.3 \times 10^{-4}\,\mathrm{s^{-1}}3.3×10−4s−1 at 153°C. The time in minutes it takes for the isomerization to proceed 40% to completion at this temperature is ________. (Rounded off to the nearest integer)

Correct answer: 26

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Q58·ChemistryNumerical
For the reaction A(g)→B(g)\mathrm{A_{(g)}} \rightarrow \mathrm{B_{(g)}}A(g)​→B(g)​, the value of the equilibrium constant at 300 K and 1 atm is equal to 100.0. The value of ΔrG\mathrm{\Delta_r G}Δr​G for the reaction at 300 K and 1 atm in J mol−1\mathrm{J\,mol^{-1}}Jmol−1 is −xR-xR−xR, where x is ______. (Rounded off to the nearest integer) [R=8.31 J mol−1K−1[\mathrm{R} = 8.31\,\mathrm{J\,mol^{-1}K^{-1}}[R=8.31Jmol−1K−1 and ln⁡10=2.3]\ln 10 = 2.3]ln10=2.3]

Correct answer: 1380

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Q59·ChemistryNumerical
The reaction of sulphur in alkaline medium is given below: S8(s)+a OH−(aq)⟶b S2−(aq)+c S2O32−(aq)+d H2O(ℓ)\mathrm{S_{8(s)}} + a\,\mathrm{OH^-}_{(aq)} \longrightarrow b\,\mathrm{S^{2-}}_{(aq)} + c\,\mathrm{S_2O_3^{2-}}_{(aq)} + d\,\mathrm{H_2O}_{(\ell)}S8(s)​+aOH−(aq)​⟶bS2−(aq)​+cS2​O32−​(aq)​+dH2​O(ℓ)​ The values of 'a' is __________. (Integer answer)

Correct answer: 12

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Mathematics — JEE Main 24 February 2021 Shift 1

Q60·MathematicsSingle correct
The locus of the mid-point of the line segment joining the focus of the parabola y2=4axy^2=4axy2=4ax to a moving point of the parabola, is another parabola whose directrix is:.
  1. (A)x=ax = ax=a
  2. (B)x=0x = 0x=0
  3. (C)x=−a2x = -\frac{a}{2}x=−2a​
  4. (D)x=a2x = \frac{a}{2}x=2a​

Correct answer: (B)

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Q61·MathematicsSingle correct
A scientific committee is to formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is:
  1. (A)560
  2. (B)1050
  3. (C)1625
  4. (D)575

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
The equation of the plane passing through the point (1,2,−3)(1, 2, -3)(1,2,−3) and perpendicular to the planes 3x+y−2z=53x + y - 2z = 53x+y−2z=5 and 2x−5y−z=72x - 5y - z = 72x−5y−z=7, is:
  1. (A)3x−10y−2z+11=03x - 10y - 2z + 11 = 03x−10y−2z+11=0
  2. (B)6x−5y−2z−2=06x - 5y - 2z - 2 = 06x−5y−2z−2=0
  3. (C)11x+y+17z+38=011x + y + 17z + 38 = 011x+y+17z+38=0
  4. (D)6x−5y+2z+10=06x - 5y + 2z + 10 = 06x−5y+2z+10=0

Correct answer: (C)

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Q63·MathematicsSingle correct
A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 14\frac{1}{4}41​. Three stones A, B and C are placed at the points (1,1)(1, 1)(1,1), (2,2)(2, 2)(2,2) and (4,4)(4, 4)(4,4) respectively. Then which of these stones is/are on the path of the man?
  1. (A)B only
  2. (B)A only
  3. (C)All the three
  4. (D)C only

Correct answer: (A)

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Q64·MathematicsSingle correct
The statement among the following that is a tautology is:
  1. (A)A∧(A∨B)A \wedge (A \vee B)A∧(A∨B)
  2. (B)B→[A∧(A→B)]B \rightarrow \left[A \wedge (A \rightarrow B)\right]B→[A∧(A→B)]
  3. (C)A∨(A∧B)A \vee (A \wedge B)A∨(A∧B)
  4. (D)[A∧(A→B)]→B\left[A \wedge (A \rightarrow B)\right] \rightarrow B[A∧(A→B)]→B

Correct answer: (D)

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Q65·MathematicsSingle correct
Let f:R→Rf : R \rightarrow Rf:R→R be defined as f(x)=2x−1f(x) = 2x-1f(x)=2x−1 and g:R−{1}→Rg : R - \{1\} \rightarrow Rg:R−{1}→R be defined as g(x)=x−12x−1g(x) = \frac{x - \frac{1}{2}}{x - 1}g(x)=x−1x−21​​. Then the composition function f(g(x))f(g(x))f(g(x)) is :
  1. (A)both one-one and onto
  2. (B)onto but not one-one
  3. (C)neither one-one nor onto
  4. (D)one-one but not onto

Correct answer: (D)

Step-by-step solution →
Q66·MathematicsSingle correct
If f:R→Rf : R \rightarrow Rf:R→R is a function defined by f(x)=[x−1]cos⁡(2x−12)πf(x) = [x-1] \cos\left(\frac{2x - 1}{2}\right)\pif(x)=[x−1]cos(22x−1​)π, where [.][.][.] denotes the greatest integer function, then fff is :
  1. (A)discontinuous only at x=1x = 1x=1
  2. (B)discontinuous at all integral values of xxx except at x=1x = 1x=1
  3. (C)continuous only at x=1x = 1x=1
  4. (D)continuous for every real xxx

Correct answer: (D)

Step-by-step solution →
Q67·MathematicsSingle correct
The function f(x)=4x3−3x26−2sin⁡x+(2x−1)cos⁡xf(x) = \frac{4x^3 - 3x^2}{6} - 2\sin x + (2x - 1)\cos xf(x)=64x3−3x2​−2sinx+(2x−1)cosx :
  1. (A)increases in [12,∞)\left[\frac{1}{2}, \infty\right)[21​,∞)
  2. (B)decreases (−∞,12]\left(-\infty, \frac{1}{2}\right](−∞,21​]
  3. (C)increases in (−∞,12]\left(-\infty, \frac{1}{2}\right](−∞,21​]
  4. (D)decreases [12,∞)\left[\frac{1}{2}, \infty\right)[21​,∞)

Correct answer: (A)

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Q68·MathematicsSingle correct
The distance of the point (1,1,9)(1, 1, 9)(1,1,9) from the point of intersection of the line x−31=y−42=z−52\frac{x - 3}{1} = \frac{y - 4}{2} = \frac{z - 5}{2}1x−3​=2y−4​=2z−5​ and the plane x+y+z=17x + y + z = 17x+y+z=17 is:
  1. (A)38\sqrt{38}38​
  2. (B)19219\sqrt{2}192​
  3. (C)2192\sqrt{19}219​
  4. (D)383838

Correct answer: (A)

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Q69·MathematicsSingle correct
Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:
  1. (A)25
  2. (B)20320\sqrt{3}203​
  3. (C)30
  4. (D)25325\sqrt{3}253​

Correct answer: (D)

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Q70·MathematicsSingle correct
If the tangent to the curve y=x3y = x^3y=x3 at the point P(t,t3)P(t, t^3)P(t,t3) meets the curve again at QQQ, then the ordinate of the point which divides PQPQPQ internally in the ratio 1:21 : 21:2 is :
  1. (A)−2t3-2t^3−2t3
  2. (B)−t3-t^3−t3
  3. (C)000
  4. (D)2t32t^32t3

Correct answer: (A)

Step-by-step solution →
Q71·MathematicsSingle correct
The area (in sq. units) of the part of the circle x2+y2=36x^2+y^2=36x2+y2=36, which is outside the parabola y2=9xy^2=9xy2=9x, is :
  1. (A)24π+3324\pi + 3\sqrt{3}24π+33​
  2. (B)12π+3312\pi + 3\sqrt{3}12π+33​
  3. (C)12π−3312\pi - 3\sqrt{3}12π−33​
  4. (D)24π−3324\pi - 3\sqrt{3}24π−33​

Correct answer: (D)

Step-by-step solution →
Q72·MathematicsSingle correct
If ∫cos⁡x−sin⁡x8−sin⁡2xdx=asin⁡−1(sin⁡x+cos⁡xb)+c\int \frac{\cos x - \sin x}{\sqrt{8 - \sin 2x}} dx = a \sin^{-1}\left(\frac{\sin x + \cos x}{b}\right) + c∫8−sin2x​cosx−sinx​dx=asin−1(bsinx+cosx​)+c, where ccc is a constant of integration, then the ordered pair (a,b)(a, b)(a,b) is equal to :
  1. (A)(1,−3)(1, -3)(1,−3)
  2. (B)(1,3)(1, 3)(1,3)
  3. (C)(−1,3)(-1, 3)(−1,3)
  4. (D)(3,1)(3, 1)(3,1)

Correct answer: (B)

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Q73·MathematicsSingle correct
The population P=P(t)P = P(t)P=P(t) at time 't' of a certain species follows the differential equation dPdt=0.5P−450\frac{dP}{dt} = 0.5P - 450dtdP​=0.5P−450. If P(0)=850P(0) = 850P(0)=850, then the time at which population becomes zero is :
  1. (A)12log⁡e18\frac{1}{2}\log_e 1821​loge​18
  2. (B)2log⁡e182\log_e 182loge​18
  3. (C)log⁡e9\log_e 9loge​9
  4. (D)log⁡e18\log_e 18loge​18

Correct answer: (B)

Step-by-step solution →
Q74·MathematicsSingle correct
The value of −15C1+2.15C2−3.15C3+....−15.15C15+14C1+14C3+14C5+....+14C11-{}^{15}C_1 + 2.{}^{15}C_2 - 3.{}^{15}C_3 + .... -15.{}^{15}C_{15} + {}^{14}C_1 + {}^{14}C_3 + {}^{14}C_5 + ....+ {}^{14}C_{11}−15C1​+2.15C2​−3.15C3​+....−15.15C15​+14C1​+14C3​+14C5​+....+14C11​ is:
  1. (A)2142^{14}214
  2. (B)213−132^{13} - 13213−13
  3. (C)216−12^{16} - 1216−1
  4. (D)213−142^{13} - 14213−14

Correct answer: (D)

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Q75·MathematicsSingle correct
An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :
  1. (A)316\frac{3}{16}163​
  2. (B)12\frac{1}{2}21​
  3. (C)516\frac{5}{16}165​
  4. (D)132\frac{1}{32}321​

Correct answer: (B)

Step-by-step solution →
Q76·MathematicsSingle correct
Let p and q be two positive number such that p+q=2p + q = 2p+q=2 and p4+q4=272p^4 + q^4 = 272p4+q4=272. Then p and q are roots of the equation :
  1. (A)x2−2x+2=0x^2 - 2x + 2 = 0x2−2x+2=0
  2. (B)x2−2x+8=0x^2 - 2x + 8 = 0x2−2x+8=0
  3. (C)x2−2x+136=0x^2 - 2x + 136 = 0x2−2x+136=0
  4. (D)x2−2x+16=0x^2 - 2x + 16 = 0x2−2x+16=0

Correct answer: (D)

Step-by-step solution →
Q77·MathematicsSingle correct
If e(cos⁡2x+cos⁡4x+cos⁡6x+...∞)log⁡e2e^{\left(\cos^2 x + \cos^4 x + \cos^6 x + ...\infty\right)\log_e 2}e(cos2x+cos4x+cos6x+...∞)loge​2 satisfies the equation t2−9t+8=0t^2 - 9t + 8 = 0t2−9t+8=0, then the value of 2sin⁡xsin⁡x+3cos⁡x(0<x<π2)\frac{2\sin x}{\sin x + \sqrt{3}\cos x}\left(0 < x < \frac{\pi}{2}\right)sinx+3​cosx2sinx​(0<x<2π​) is :
  1. (A)32\frac{3}{2}23​
  2. (B)232\sqrt{3}23​
  3. (C)12\frac{1}{2}21​
  4. (D)3\sqrt{3}3​

Correct answer: (C)

Step-by-step solution →
Q78·MathematicsSingle correct
The system of linear equations 3x−2y−kz=103x - 2y - kz = 103x−2y−kz=10 2x−4y−2z=62x - 4y - 2z = 62x−4y−2z=6 x+2y−z=5mx + 2y - z = 5mx+2y−z=5m is inconsistent if :
  1. (A)k=3,m=45k = 3, m = \frac{4}{5}k=3,m=54​
  2. (B)k≠3,m∈Rk \neq 3, m \in Rk=3,m∈R
  3. (C)k≠3,m≠45k \neq 3, m \neq \frac{4}{5}k=3,m=54​
  4. (D)k=3,m≠45k = 3, m \neq \frac{4}{5}k=3,m=54​

Correct answer: (D)

Step-by-step solution →
Q79·MathematicsNumerical
Let P=[3−1−220α3−50]P = \begin{bmatrix} 3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0 \end{bmatrix}P=​323​−10−5​−2α0​​, where α∈R\alpha \in Rα∈R. Suppose Q=[qij]Q = [q_{ij}]Q=[qij​] is a matrix satisfying PQ=kI3PQ = kI_3PQ=kI3​ for some non-zero k∈Rk \in Rk∈R. If q23=−k8q_{23} = -\frac{k}{8}q23​=−8k​ and ∣Q∣=k22|Q| = \frac{k^2}{2}∣Q∣=2k2​, then α2+k2\alpha^2 + k^2α2+k2 is equal to _______

Correct answer: 17

Step-by-step solution →
Q80·MathematicsNumerical
Let Bi(i=1,2,3)B_i(i = 1, 2, 3)Bi​(i=1,2,3) be three independent events in a sample space. The probability that only B1B_1B1​ occur is α\alphaα, only B2B_2B2​ occurs is β\betaβ and only B3B_3B3​ occurs is γ\gammaγ. Let p be the probability that none of the events BiB_iBi​ occurs and these 4 probabilities satisfy the equations (α−2β)p=αβ(\alpha - 2\beta)p = \alpha\beta(α−2β)p=αβ and (β−3γ)p=2βγ(\beta - 3\gamma)p = 2\beta\gamma(β−3γ)p=2βγ (All the probabilities are assumed to lie in the interval (0, 1)). Then P(B1)P(B3)\frac{P(B_1)}{P(B_3)}P(B3​)P(B1​)​ is equal to _____

Correct answer: 6

Step-by-step solution →
Q81·MathematicsNumerical
The minimum value of α\alphaα for which the equation 4sin⁡x+11−sin⁡x=α\frac{4}{\sin x} + \frac{1}{1 - \sin x} = \alphasinx4​+1−sinx1​=α has at least one solution in (0,π2)\left(0, \frac{\pi}{2}\right)(0,2π​) is ______

Correct answer: 9

Step-by-step solution →
Q82·MathematicsNumerical
If one of the diameters of the circle x2+y2−2x−6y+6=0x^2 + y^2 - 2x - 6y + 6 = 0x2+y2−2x−6y+6=0 is a chord of another circle ‘C’ whose center is at (2,1), then its radius is _______

Correct answer: 3

Step-by-step solution →
Q83·MathematicsNumerical
lim⁡x→∞tan⁡{∑r=1ntan⁡−1(11+r+r2)}\lim_{x \to \infty} \tan\left\{ \sum_{r=1}^{n} \tan^{-1}\left(\frac{1}{1 + r + r^2}\right) \right\}limx→∞​tan{∑r=1n​tan−1(1+r+r21​)} is equal to ______

Correct answer: 1

Step-by-step solution →
Q84·MathematicsNumerical
If ∫−aa(∣x∣+∣x−2∣)dx=22\int_{-a}^{a} \left(|x| + |x - 2|\right) dx = 22∫−aa​(∣x∣+∣x−2∣)dx=22 ,(a>2)(a > 2)(a>2) and [x] denotes the greatest integer ≤x\leq x≤x, then ∫a−a(x+[x])dx\int_{a}^{-a} \left(x + [x]\right) dx∫a−a​(x+[x])dx is equal to ______

Correct answer: 3

Step-by-step solution →
Q85·MathematicsNumerical
Let three vectors a⃗,b⃗\vec{a}, \vec{b}a,b and c⃗\vec{c}c be such that c⃗\vec{c}c is coplanar with a⃗\vec{a}a and b⃗\vec{b}b, a⃗⋅c⃗=7\vec{a} \cdot \vec{c} = 7a⋅c=7 and b⃗\vec{b}b is perpendicular to c⃗\vec{c}c, where a⃗=−i^+j^+k^\vec{a} = -\hat{i} + \hat{j} + \hat{k}a=−i^+j^​+k^ and b⃗=2i^+k^\vec{b} = 2\hat{i} + \hat{k}b=2i^+k^, then the value of 2∣a⃗+b⃗+c⃗∣22\left|\vec{a} + \vec{b} + \vec{c}\right|^22​a+b+c​2 is ________

Correct answer: 75

Step-by-step solution →
Q86·MathematicsNumerical
Let A={n∈N:n is a 3-digit number}A = \{n \in N : n \text{ is a 3-digit number}\}A={n∈N:n is a 3-digit number} B={9k+2:k∈N}B = \{9k + 2 : k \in N\}B={9k+2:k∈N} and C:{9k+ℓ:k∈N}C : \{9k + \ell : k \in N\}C:{9k+ℓ:k∈N} for some ℓ\ellℓ (0<ℓ<9)(0 < \ell < 9)(0<ℓ<9) If the sum of all the elements of the set A∩(B∪C)A \cap (B \cup C)A∩(B∪C) is 274×400274 \times 400274×400, then ℓ\ellℓ is equal to __

Correct answer: 5

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Q87·MathematicsNumerical
If the least and the largest real values of α\alphaα, for which the equation z+α∣z−1∣+2i=0z + \alpha|z - 1| + 2i = 0z+α∣z−1∣+2i=0 (z∈C and i=−1)\left(z \in C \text{ and } i = \sqrt{-1}\right)(z∈C and i=−1​) has a solution, are p and q respectively; then 4(p2+q2)4(p^2 + q^2)4(p2+q2) is equal to ____

Correct answer: 10

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Q88·MathematicsNumerical
Let M be any 3×33 \times 33×3 matrix with entries from the set {0,1,2}\{0, 1, 2\}{0,1,2}. The maximum number of such matrices, for which the sum of diagonal elements of MTMM^T MMTM is seven, is __

Correct answer: 540

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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
  • 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
  • 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
  • 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
  • Area Under Curves 139/186
  • Alcohols and Ethers 106/186
  • Oscillations 117/186
  • Alternating Currents 108/186
  • Straight Lines 114/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Parabola 101/186
  • Isolation of Metals 106/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Inverse Trigonometric Functions 93/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Indefinite Integration 66/186
  • Polymers 64/186
  • Solid State 63/186
  • Principles of Qualitative Analysis 58/186
  • Diazonium Salts and Reactions 53/186
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