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JEE Main 22 July 2021 Shift 2 Question Paper with Answers

22 July 2021 · July session · 88 questions

88 of the 90 questions from the JEE Main 22 July 2021 Shift 2 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 22 July 2021 Shift 2

Q1·PhysicsSingle correct
A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to earth reach height h is ________ s.
  1. (A)2Reg[(1+hRe)3/2−1]\sqrt{\frac{2R_e}{g}}\left[\left(1+\frac{h}{R_e}\right)^{3/2}-1\right]g2Re​​​[(1+Re​h​)3/2−1]
  2. (B)132Reg[(1+hRe)3/2−1]\frac{1}{3}\sqrt{\frac{2R_e}{g}}\left[\left(1+\frac{h}{R_e}\right)^{3/2}-1\right]31​g2Re​​​[(1+Re​h​)3/2−1]
  3. (C)13Re2g[(1+hRe)3/2−1]\frac{1}{3}\sqrt{\frac{R_e}{2g}}\left[\left(1+\frac{h}{R_e}\right)^{3/2}-1\right]31​2gRe​​​[(1+Re​h​)3/2−1]
  4. (D)Re2g[(1+hRe)3/2−1]\sqrt{\frac{R_e}{2g}}\left[\left(1+\frac{h}{R_e}\right)^{3/2}-1\right]2gRe​​​[(1+Re​h​)3/2−1]

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
An electron of mass mem_eme​ and a proton of mass mpm_pmp​ are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is :
  1. (A)mpme\frac{m_p}{m_e}me​mp​​
  2. (B)1
  3. (C)memp\frac{m_e}{m_p}mp​me​​
  4. (D)mpme\sqrt{\frac{m_p}{m_e}}me​mp​​​

Correct answer: (D)

Step-by-step solution →
Q3·PhysicsSingle correct
What will be the projection of vector A⃗=i^+j^+k^\vec{A}=\hat{i}+\hat{j}+\hat{k}A=i^+j^​+k^ on vector B⃗=i^+j^\vec{B}=\hat{i}+\hat{j}B=i^+j^​ ?
  1. (A)2(i^+j^+k^)2\left(\hat{i}+\hat{j}+\hat{k}\right)2(i^+j^​+k^)
  2. (B)2(i^+j^)\sqrt{2}\left(\hat{i}+\hat{j}\right)2​(i^+j^​)
  3. (C)(i^+j^)\left(\hat{i}+\hat{j}\right)(i^+j^​)
  4. (D)2(i^+j^+k^)\sqrt{2}\left(\hat{i}+\hat{j}+\hat{k}\right)2​(i^+j^​+k^)

Correct answer: (C)

Step-by-step solution →
Q4·PhysicsSingle correct
A ray of light passes from a denser medium to a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of 90° with each other. The angle of reflection and refraction are respectively r and r′. The critical angle is given by :
  1. (A)sin⁡−1(cot⁡r)\sin^{-1}(\cot r)sin−1(cotr)
  2. (B)tan⁡−1(sin⁡i)\tan^{-1}(\sin i)tan−1(sini)
  3. (C)sin⁡−1(tan⁡r′)\sin^{-1}(\tan r')sin−1(tanr′)
  4. (D)sin⁡−1(tan⁡r)\sin^{-1}(\tan r)sin−1(tanr)

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
A nucleus with number 184 initially at rest emits an α−\alpha-α−particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the α−\alpha-α−particle.
  1. (A)5.5 MeV
  2. (B)5.38 MeV
  3. (C)5.0 MeV
  4. (D)0.12 MeV

Correct answer: (B)

Step-by-step solution →
Q6·PhysicsSingle correct
Intensity of sunlight is observed as 0.092 Wm−2^{-2}−2 at a point in free space. What will be the peak value of magnetic field at that point? (ε0=8.85×10−12 C2 N−1 m−2)\left(\varepsilon_0=8.85\times10^{-12}\,\mathrm{C^2\,N^{-1}\,m^{-2}}\right)(ε0​=8.85×10−12C2N−1m−2)
  1. (A)5.88 T
  2. (B)1.96×10−81.96\times10^{-8}1.96×10−8 T
  3. (C)8.31 T
  4. (D)2.77×10−82.77\times10^{-8}2.77×10−8 T

Correct answer: (D)

Step-by-step solution →
Q7·PhysicsSingle correct
In a circuit consisting of a capacitance and a generator with alternating emf Eg=Eg0sin⁡ωtE_g=E_{g_0}\sin\omega tEg​=Eg0​​sinωt, VCV_CVC​ and ICI_CIC​ are the voltage and current. Correct phase diagram for such circuit is :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q8·PhysicsSingle correct
Consider a situation in which reverse biased current of a particular P−NP-NP−N junction increase when it is exposed to a light of wavelength ≤ 621 nm. During this process, enhancement in carrier concentration takes place due to generation of hole −-− electron pairs. The value of band gap is nearly.
  1. (A)1 eV
  2. (B)4 eV
  3. (C)0.5 eV
  4. (D)2 eV

Correct answer: (D)

Step-by-step solution →
Q9·PhysicsSingle correct
A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take g=9.8 ms−2)\left(\text{take } g=9.8\,\mathrm{ms^{-2}}\right)(take g=9.8ms−2)
  1. (A)−627.2-627.2−627.2 J
  2. (B)−62720.0-62720.0−62720.0 J
  3. (C)+627.2+627.2+627.2 J
  4. (D)784.0 J

Correct answer: (A)

Step-by-step solution →
Q10·PhysicsSingle correct
Match List −-− I with List −-− II : Choose the correct answer from the options given below :
List-IList-II
a.ωL>1ωC\omega L>\frac{1}{\omega C}ωL>ωC1​i.Current is in phase with emf
b.ωL=1ωC\omega L=\frac{1}{\omega C}ωL=ωC1​ii.Current lags behind the applied emf
c.ωL<1ωC\omega L<\frac{1}{\omega C}ωL<ωC1​iii.Maximum current occurs
d.Resonant frequencyiv.Current leads the emf
  1. (A)(a) −-−(iv); (b) −-−(iii); (c) −-−(ii); (d) −-−(i)
  2. (B)(a) −-−(ii); (b) −-−(i); (c) −-−(iv); (d) −-−(iii)
  3. (C)(a) −-−(iii); (b) −-−(i); (c) −-−(iv); (d) −-−(ii)
  4. (D)(a) −-−(ii); (b) −-−(i); (c) −-−(iii); (d) −-−(iv)

Correct answer: (B)

Step-by-step solution →
Q11·PhysicsSingle correct
T0T_0T0​ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to 116\frac{1}{16}161​ times of its initial value, the modified time period is :
  1. (A)T0T_0T0​
  2. (B)8π T08\pi\,T_08πT0​
  3. (C)4 T04\,T_04T0​
  4. (D)14T0\frac{1}{4}T_041​T0​

Correct answer: (D)

Step-by-step solution →
Q12·PhysicsSingle correct
Statement I : The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet. Statement II : At high temperature, the domain wall area of a ferromagnetic substance increases. 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 true but Statement II is false
  3. (C)Statement I is false but Statement II is true
  4. (D)Both Statement I and Statement II are true

Correct answer: (B)

Step-by-step solution →
Q13·PhysicsSingle correct
A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms−1^{-1}−1, the impulse imparted to the gun velocity of recoil of gun are :
  1. (A)0.4 kg ms−1^{-1}−1, 0.1 ms−1^{-1}−1
  2. (B)0.2 kg ms−1^{-1}−1, 0.05 ms−1^{-1}−1
  3. (C)0.4 kg ms−1^{-1}−1, 0.05 ms−1^{-1}−1
  4. (D)0.2 kg ms−1^{-1}−1, 0.1 ms−1^{-1}−1

Correct answer: (B)

Step-by-step solution →
Q14·PhysicsSingle correct
What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of 150 km? The average population density around the tower is 200 / km2^22 and the value of Re=6.5×106R_e=6.5\times10^6Re​=6.5×106 m.
  1. (A)Height = 1800 m; Population Covered = 1413×1081413\times10^81413×108
  2. (B)Height = 1241 m; Population Covered = 7×1057\times10^57×105
  3. (C)Height = 1600 m; Population Covered = 2×1052\times10^52×105
  4. (D)Height = 1731 m; Population Covered = 1413×1051413\times10^51413×105

Correct answer: (D)

Step-by-step solution →
Q15·PhysicsSingle correct
Choose the correct option :
  1. (A)True dip is not mathematically related to apparent dip.
  2. (B)True dip is always greater than the apparent dip.
  3. (C)True dip is always equal to apparent dip.
  4. (D)True dip is less than the apparent dip.

Correct answer: (D)

Step-by-step solution →
Q16·PhysicsSingle correct
The motion of a mass on a spring, with spring constant K is as shown in figure. The equation of motion is given by x(t)=Asin⁡ωt+Bcos⁡ωtx(t)=A\sin\omega t+B\cos\omega tx(t)=Asinωt+Bcosωt with ω=Km\omega=\sqrt{\frac{K}{m}}ω=mK​​. Suppose that at time t = 0, the position of mass is x(0)x(0)x(0) and velocity υ(0)\upsilon(0)υ(0), then its displacement can also be represented as x(t)=Ccos⁡(ωt−ϕ)x(t)=C\cos(\omega t-\phi)x(t)=Ccos(ωt−ϕ), where C and ϕ\phiϕ are :
  1. (A)C=υ(0)2ω2+x(0)2, ϕ=tan⁡−1(x(0)ωυ(0))C=\sqrt{\frac{\upsilon(0)^2}{\omega^2}+x(0)^2},\ \phi=\tan^{-1}\left(\frac{x(0)\omega}{\upsilon(0)}\right)C=ω2υ(0)2​+x(0)2​, ϕ=tan−1(υ(0)x(0)ω​)
  2. (B)C=2υ(0)2ω2+x(0)2, ϕ=tan⁡−1(x(0)ω2υ(0))C=\sqrt{\frac{2\upsilon(0)^2}{\omega^2}+x(0)^2},\ \phi=\tan^{-1}\left(\frac{x(0)\omega}{2\upsilon(0)}\right)C=ω22υ(0)2​+x(0)2​, ϕ=tan−1(2υ(0)x(0)ω​)
  3. (C)C=υ(0)2ω2+x(0)2, ϕ=tan⁡−1(υ(0)x(0)ω)C=\sqrt{\frac{\upsilon(0)^2}{\omega^2}+x(0)^2},\ \phi=\tan^{-1}\left(\frac{\upsilon(0)}{x(0)\omega}\right)C=ω2υ(0)2​+x(0)2​, ϕ=tan−1(x(0)ωυ(0)​)
  4. (D)C=2υ(0)2ω2+x(0)2, ϕ=tan⁡−1(υ(0)x(0)ω)C=\sqrt{\frac{2\upsilon(0)^2}{\omega^2}+x(0)^2},\ \phi=\tan^{-1}\left(\frac{\upsilon(0)}{x(0)\omega}\right)C=ω22υ(0)2​+x(0)2​, ϕ=tan−1(x(0)ωυ(0)​)

Correct answer: (C)

Step-by-step solution →
Q17·PhysicsSingle correct
What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T ?
  1. (A)32kBT\frac{3}{2}k_B T23​kB​T
  2. (B)12kBT\frac{1}{2}k_B T21​kB​T
  3. (C)kBTk_B TkB​T
  4. (D)23kBT\frac{2}{3}k_B T32​kB​T

Correct answer: (A)

Step-by-step solution →
Q18·PhysicsSingle correct
Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is :
  1. (A)The ring has the greatest and the cylinder has the least velocity of the centre of mass at the bottom of the inclined plane.
  2. (B)The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.
  3. (C)The cylinder has the greatest and the sphere has the least velocity of the centre of mass at the bottom of the inclined plane.
  4. (D)All of them will have same velocity.

Correct answer: (B)

Step-by-step solution →
Q19·PhysicsSingle correct
A Copper(Cu) rod of length 25 cm and cross −-− sectional area 3 mm2^22 is joined with a similar aluminium(Al) rod as shown in figure. Find the resistance of the combination between the ends A and B. (Take Resistivity of Copper = 1.7×10−8 Ωm1.7\times10^{-8}\,\Omega m1.7×10−8Ωm Resistivity of Aluminium = 2.6×10−8 Ωm2.6\times10^{-8}\,\Omega m2.6×10−8Ωm )
  1. (A)0.858 mΩ
  2. (B)0.0858 mΩ
  3. (C)1.420 mΩ
  4. (D)2.170 mΩ

Correct answer: (A)

Step-by-step solution →
Q20·PhysicsSingle correct
An electric dipole is placed on x −-− axis in proximity to a line charge of linear density 3.0×10−63.0\times10^{-6}3.0×10−6 C / m. Line charge is placed on z −-−axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4 N is exerted on the dipole, find out the amount of positive charge of the dipole.
  1. (A)0.485 mC
  2. (B)8.8 μC
  3. (C)815.1 nC
  4. (D)4.44 μC

Correct answer: (D)

Step-by-step solution →
Q21·PhysicsNumerical
The position of the centre of mass of a uniform semi − circular wire of radius 'R' placed in x − y plane with its centre at the origin and the line joining its ends as x-axis is given by (0,xRπ)\left(0, \frac{xR}{\pi}\right)(0,πxR​). Then, the value of |x| is ________.

Correct answer: 2

Step-by-step solution →
Q22·Physics·Electric Field and Coulomb's LawNumerical
The total charge enclosed in an incremental volume of 2×10−9 m32 \times 10^{-9}\,\mathrm{m^3}2×10−9m3 located at the origin is ________ nC, if electric flux density of its field is found as D=e−xsin⁡y i^−e−xcos⁡y j^+2z k^D = e^{-x}\sin y\,\hat{i} - e^{-x}\cos y\,\hat{j} + 2z\,\hat{k}D=e−xsinyi^−e−xcosyj^​+2zk^ C/m2^22.

Correct answer: 4

Step-by-step solution →
Q23·PhysicsNumerical
A ray of light passing through a prism (μ=3)\left(\mu = \sqrt{3}\right)(μ=3​) surface minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ________ (in degrees).

Correct answer: 60

Step-by-step solution →
Q24·PhysicsNumerical
The centre of a wheel rolling on a plane surface moves with a speed υ0\upsilon_0υ0​. A particle on the rim of the wheel at the same level as the centre will be moving at a speed x υ0\sqrt{x}\,\upsilon_0x​υ0​. Then the value of x is ________.

Correct answer: 2

Step-by-step solution →
Q25·PhysicsNumerical
Three students S1,S2S_1, S_2S1​,S2​ and S3S_3S3​ perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table. Student No. | Length of Pendulum (cm) | No. of oscillations (n) | Total for n oscillations | Time period (s) 1 | 64.0 | 8 | 128.0 | 16.0 2 | 64.0 | 4 | 64.0 | 16.0 3 | 20.0 | 4 | 36.0 | 9.0 (Least count of length = 0.1 cm least count for time = 0.1 s) If E1E_1E1​, E2E_2E2​ and E3E_3E3​ are the percentage errors 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no. ________.

Correct answer: 1

Step-by-step solution →
Q26·PhysicsNumerical
In 5 minutes, a body cools from 75°C to 65°C at room temperature of 25°C. The temperature of body at the end of next 5 minutes is ________ °C.

Correct answer: 57

Step-by-step solution →
Q27·PhysicsNumerical
The area of cross − section of a railway track is 0.01 m20.01\,\mathrm{m^2}0.01m2. The temperature variation is 10°C, Coefficient of liner expansion of material of track is 10−510^{-5}10−5 / °C. The energy stored per meter in the track is ________ J/m. (Young's modulus of material of track is 1011 Nm−210^{11}\,\mathrm{Nm^{-2}}1011Nm−2)

Correct answer: 5

Step-by-step solution →
Q28·PhysicsNumerical
In an electric circuit, a cell of certain emf provides a potential difference of 1.25 V across a load resistance of 5 Ω. However, it provides a potential difference of 1 V across a load resistance of 2 Ω. The emf of the cell is given by x10\frac{x}{10}10x​ V. Then the value of x is ________.

Correct answer: 15

Step-by-step solution →
Q29·PhysicsNumerical
In a given circuit diagram, a 5 V zener diode along with a series resistance is connected across a 50 V power supply. The minimum value of the resistance required, if the maximum zener current is 90 mA be ________ Ω.

Correct answer: 500

Step-by-step solution →
Q30·PhysicsNumerical
Three particles P,Q and R are moving along the vectors A⃗=i^+j^\vec{A} = \hat{i} + \hat{j}A=i^+j^​, B⃗=j^+k^\vec{B} = \hat{j} + \hat{k}B=j^​+k^ and C⃗=−i^+j^\vec{C} = -\hat{i} + \hat{j}C=−i^+j^​ respectively. They strike on point and start to move in different directions. Now particle P is moving normal to the plane which contains vector A⃗\vec{A}A and B⃗\vec{B}B. Similarly particle Q is moving normal to the plane which contains vector A⃗\vec{A}A and C⃗\vec{C}C. The angle between the direction of motion of P and Q cos⁡−1(1x)\cos^{-1}\left(\frac{1}{\sqrt{x}}\right)cos−1(x​1​). Then the value of x is ________.

Correct answer: 3

Step-by-step solution →

Chemistry — JEE Main 22 July 2021 Shift 2

Q31·ChemistrySingle correct
Which one of the following compounds will provide a tertiary alcohol on reaction with excess of CH3MgBrCH_3MgBrCH3​MgBr followed by hydrolysis?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q32·ChemistrySingle correct
When silver nitrate solution is added to potassium iodide solution then the sol produced is:
  1. (A)AgI/I⁻
  2. (B)AgNO3/NO3−AgNO_3/NO_3^-AgNO3​/NO3−​
  3. (C)KI/NO3−KI/NO_3^-KI/NO3−​
  4. (D)AgI/Ag+AgI/Ag^+AgI/Ag+

Correct answer: (A)

Step-by-step solution →
Q33·ChemistrySingle correct
Isotope(s) of hydrogen which emits low energy β−\beta^-β− particles with t12t_{\frac{1}{2}}t21​​ value > 12 years is / are:
  1. (A)Protium
  2. (B)Tritium
  3. (C)Deuterium
  4. (D)Deuterium and Tritium

Correct answer: (B)

Step-by-step solution →
Q34·ChemistrySingle correct
Which one of the following 0.06 M aqueous solutions has lowest freezing point ?
  1. (A)KI
  2. (B)C6H12O6C_6H_{12}O_6C6​H12​O6​
  3. (C)K2SO4K_2SO_4K2​SO4​
  4. (D)Al2(SO4)3Al_2(SO_4)_3Al2​(SO4​)3​

Correct answer: (D)

Step-by-step solution →
Q35·ChemistrySingle correct
Match List − I with List − II : Choose the correct answer from the options given below :
List-I (Species)List-II (Hybrid Orbitals)
a.SF4SF_4SF4​i.sp3d2sp^3d^2sp3d2
b.IF5IF_5IF5​ii.d2sp3d^2sp^3d2sp3
c.NO2+NO_2^+NO2+​iii.sp3dsp^3dsp3d
d.NH4+NH_4^+NH4+​iv.sp3sp^3sp3
v.sp
  1. (A)(a) −(iii) , (b) −(i), (c) −(v) and (d) −(iv)
  2. (B)(a) −(ii), (b) −(i), (c) −(iv) and (d) −(v)
  3. (C)(a) −(i), (b) −(ii), (c) −(v) and (d) −(iii)
  4. (D)(a) −(iv), (b) −(iii), (c) −(ii) and (d) −(v)

Correct answer: (A)

Step-by-step solution →
Q36·Chemistry·Electronic Effects and StabilitySingle correct
Which one of the following compounds does not exhibit resonance?
  1. (A)CH3CH2CH2CONH2CH_{3}CH_{2}CH_{2}CONH_{2}CH3​CH2​CH2​CONH2​
  2. (B)CH3CH2CH=CHCH2NH2CH_{3}CH_{2}CH = CHCH_{2}NH_{2}CH3​CH2​CH=CHCH2​NH2​
  3. (C)CH3CH2OCH=CH2CH_{3}CH_{2}OCH = CH_{2}CH3​CH2​OCH=CH2​
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q37·ChemistrySingle correct
The set having ions which are coloured and paramagnetic both is :
  1. (A)Ni2+,Mn7+,Hg2+Ni^{2+},Mn^{7+},Hg^{2+}Ni2+,Mn7+,Hg2+
  2. (B)Cu+,Zn2+,Mn4+Cu^{+},Zn^{2+},Mn^{4+}Cu+,Zn2+,Mn4+
  3. (C)Sc3+,V5+,Ti4Sc^{3+},V^{5+},Ti^{4}Sc3+,V5+,Ti4
  4. (D)Cu2+,Cr3+,Sc+Cu^{2+},Cr^{3+},Sc^{+}Cu2+,Cr3+,Sc+

Correct answer: (D)

Step-by-step solution →
Q38·Chemistry·Alcohols and EthersSingle correct
An organic compound A (C6H6OC_{6}H_{6}OC6​H6​O) gives dark green colouration with ferric chloride. On treatment with CHCl3CHCl_{3}CHCl3​ and KOH, followed by acidification gives compound B. Compound B can also be obtained from compound C on reaction with pyridinium chlorochromate (PCC). Identify A, B and C.
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q39·ChemistrySingle correct
Given below are the statements about diborane. (a) Diborane is prepared by the oxidation of NaBH4NaBH_{4}NaBH4​ With I2I_{2}I2​. (b) Each boron atom is in sp2sp^{2}sp2 hybridized state. (c) Diborane has one bridged 3 centre − 2 − electron bond. (d) Diborane is a planar molecule. The option with correct statement(s) is :
  1. (A)(a) only
  2. (B)(c) only
  3. (C)(a) and (b) only
  4. (D)(c) and (d) only

Correct answer: (A)

Step-by-step solution →
Q40·ChemistrySingle correct
Match List − I with List − II : Choose the correct answer from the options given below :
List-IList-II
a.Chloroprenei.(drawn structure — see figure)
b.Neopreneii.(drawn structure — see figure)
c.Acrylonitrileiii.(drawn structure — see figure)
d.Isopreneiv.CH2CH_{2}CH2​ = CH - CN
  1. (A)(a) − (iii), (b) − (i), (c) − (iv), (d) − (ii)
  2. (B)(a) − (iii), (b) − (iv), (c) − (ii), (d) − (i)
  3. (C)(a) − (ii), (b) − (i), (c) − (iv), (d) − (iii)
  4. (D)(a) − (ii), (b) − (iii), (c) − (iv), (d) − (i)

Correct answer: (D)

Step-by-step solution →
Q41·ChemistrySingle correct
Which one of the following molecules does not show stereo isomerism ?
  1. (A)3 − Ethylhex − 3 − ene
  2. (B)3 − Methylhex − 1 − ene
  3. (C)3,4 − Dimethylhex − 3 − ene
  4. (D)4 − Methylhex − 1 − ene

Correct answer: (A)

Step-by-step solution →
Q42·ChemistrySingle correct
Sulphide ion is soft base and its ores are common for metals. (a) Pb (b) Al (c) Ag (d) Mg Choose the correct answer from the options given below :
  1. (A)(c) and (d) only
  2. (B)(a) and (c) only
  3. (C)(a) and (d) only
  4. (D)(a) and (b) only

Correct answer: (B)

Step-by-step solution →
Q43·ChemistrySingle correct
In the chemical reactions given above A and B respectively are:
  1. (A)CH3CH2OHCH_{3}CH_{2}OHCH3​CH2​OH and H3PO2H_{3}PO_{2}H3​PO2​
  2. (B)CH3CH2ClCH_{3}CH_{2}ClCH3​CH2​Cl and H3PO2H_{3}PO_{2}H3​PO2​
  3. (C)H3PO2H_{3}PO_{2}H3​PO2​ and CH3CH2OHCH_{3}CH_{2}OHCH3​CH2​OH
  4. (D)H3PO2H_{3}PO_{2}H3​PO2​ and CH3CH2ClCH_{3}CH_{2}ClCH3​CH2​Cl

Correct answer: (D)

Step-by-step solution →
Q44·ChemistrySingle correct
Match List − I with List − II : Choose the correct answer from the options given below :
List-I (Elements)List-II (Properties)
a.Bai.Organic solvent soluble compounds
b.Caii.Outer electronic configuration 6s26s^{2}6s2
c.Liiii.Oxalate insoluble in water
d.Naiv.Formation of very strong monoacidic base
  1. (A)(a) − (ii), (b) − (iii), (c) − (i) and (d) − (iv)
  2. (B)(a) − (iv), (b) − (i), (c) − (ii) and (d) − (iii)
  3. (C)(a) − (i), (b) − (iv), (iii) − (ii) and (d) − (iii)
  4. (D)(a) − (iii), (b) − (ii), (c) − (iv) and (d) − (i)

Correct answer: (A)

Step-by-step solution →
Q45·ChemistrySingle correct
Which one of the following group − 15 hydride is the strongest reducing agent ?
  1. (A)AsH3AsH_{3}AsH3​
  2. (B)SbH3SbH_{3}SbH3​
  3. (C)BiH3BiH_{3}BiH3​
  4. (D)PH3PH_{3}PH3​

Correct answer: (C)

Step-by-step solution →
Q46·ChemistrySingle correct
Thiamine and pyridoxine are also known respectively as :
  1. (A)Vitamin B1B_{1}B1​ and Vitamin B6B_{6}B6​
  2. (B)Vitamin E and Vitamin B2B_{2}B2​
  3. (C)Vitamin B6B_{6}B6​ and Vitamin B2B_{2}B2​
  4. (D)Vitamin B2B_{2}B2​ and Vitamin E

Correct answer: (A)

Step-by-step solution →
Q47·ChemistrySingle correct
Which one of the following reactions does not occur?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q48·ChemistrySingle correct
Which one of the following statements for D.I. Mendeleeff, is incorrect?
  1. (A)At the time, he proposed periodic table of elements structure of atom was known.
  2. (B)Element with atomic number 101 is named after him.
  3. (C)He invented accurate barometer.
  4. (D)He authored the textbook − Principles of Chemistry.

Correct answer: (A)

Step-by-step solution →
Q49·ChemistrySingle correct
The water having more dissolved O2O_{2}O2​ is :
  1. (A)Water at 80° C
  2. (B)boiling water
  3. (C)polluted water
  4. (D)water at 4° C

Correct answer: (D)

Step-by-step solution →
Q50·ChemistrySingle correct
Which purification technique is used for high boiling organic liquid compound (decomposes near its boiling point) ?
  1. (A)Fractional distillation
  2. (B)Steam distillation
  3. (C)Simple distillation
  4. (D)Reduced pressure distillation

Correct answer: (D)

Step-by-step solution →
Q51·ChemistryNumerical
N2O5(g)→2NO2(g)+12O2(g)\mathrm{N_2O_{5(g)} \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}}N2​O5(g)​→2NO2(g)​+21​O2(g)​ In the above first order reaction the initial concentration of N2O5\mathrm{N_2O_5}N2​O5​ is 2.40×10−22.40 \times 10^{-2}2.40×10−2 mol L−1^{-1}−1 at 318K. The concentration of N2O5\mathrm{N_2O_5}N2​O5​ after 1 hours was 1.60×10−21.60 \times 10^{-2}1.60×10−2 mol L−1^{-1}−1. The rate constant of the reaction at 318K is _________ ×10−3\times 10^{-3}×10−3 min−1^{-1}−1. ( Nearest integer ) [Given : log3 = 0.477, log5 = 0.699 ]

Correct answer: 7

Step-by-step solution →
Q52·ChemistryNumerical
Number of electrons that Vanadium (Z=23)(Z = 23)(Z=23) has in p-orbitals is equal to ----------.

Correct answer: 12

Step-by-step solution →
Q53·ChemistryNumerical
If the standard molar enthalpy change for combustion of graphite powder is −2.48×102-2.48 \times 10^{2}−2.48×102 kJ mol−1^{-1}−1, the amount of heat generated on combustion of 1 g of graphite powder is __________ kJ. (Nearest integer)

Correct answer: 21

Step-by-step solution →
Q54·ChemistryNumerical
Value of KpK_pKp​ for the equilibrium reaction N2O4(g)⇌2NO2(g)\mathrm{N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}}N2​O4(g)​⇌2NO2(g)​ at 288 K is 47.9. The KcK_cKc​ for this reaction at same temperature is __________. (Nearest integer) (R = 0.083 L bar K−1^{-1}−1 mol−1^{-1}−1)

Correct answer: 2

Step-by-step solution →
Q55·ChemistryNumerical
A copper complex crystallizing in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing X-ray diffraction studies. The density of a copper complex is found to be 7.26 g cm−3^{-3}−3. The molar mass of copper complex is __________ g mol−1^{-1}−1. (Nearest integer) [Given : NAN_ANA​ = 6.022 ×1023\times 10^{23}×1023 mol−1^{-1}−1 ]

Correct answer: 101

Step-by-step solution →
Q56·ChemistryNumerical
The number of acyclic structural isomers (including geometrical isomers) for pentene is -.

Correct answer: 6

Step-by-step solution →
Q57·Chemistry·Redox Reactions and ElectrochemistryNumerical
Assume a cell with the following reaction Cu(s)+2Ag+(1×10−3 M)→Cu2+(0.250 M)+2Ag(s)\mathrm{Cu_{(s)} + 2Ag^+ \left(1 \times 10^{-3}\,M\right) \rightarrow Cu^{2+} \left(0.250\,M\right) + 2Ag_{(s)}}Cu(s)​+2Ag+(1×10−3M)→Cu2+(0.250M)+2Ag(s)​ Ecell⊖E_{\mathrm{cell}}^{\ominus}Ecell⊖​ = 2.97 V EcellE_{\mathrm{cell}}Ecell​ for the above reaction is _____________ V. (Nearest integer) [ Given : log 2.5 = 0.3979, T = 298K]

Correct answer: 3

Step-by-step solution →
Q58·ChemistryNumerical
Methylation of 10g of benzene give 9.2g of toluene. Calculate the percentage yield of toluene __________. (Nearest integer)

Correct answer: 78

Step-by-step solution →
Q59·ChemistryNumerical
If the concentration of glucose (C6H12O6)(\mathrm{C_6H_{12}O_6})(C6​H12​O6​) in blood is 0.72 g L−1^{-1}−1, the molarity of glucose in blood is __________ ×10−3\times 10^{-3}×10−3 M. (Nearest integer) (Given : Atomic mass of C = 12, H = 1, O = 16u )

Correct answer: 4

Step-by-step solution →

Mathematics — JEE Main 22 July 2021 Shift 2

Q60·MathematicsSingle correct
Let the circle S:36x2+36y2−108x+120y+C=0S : 36x^2 + 36y^2 - 108x + 120y + C = 0S:36x2+36y2−108x+120y+C=0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x−2y=4x - 2y = 4x−2y=4 and 2x−y=52x - y = 52x−y=5 lies inside the circle S, then :
  1. (A)81 < C < 156
  2. (B)100 < C < 165
  3. (C)100 < C < 156
  4. (D)259<C<133\frac{25}{9} < C < \frac{13}{3}925​<C<313​

Correct answer: (C)

Step-by-step solution →
Q61·MathematicsSingle correct
If the shortest distance between the straight lines 3(x−1)=6(y−2)=2(z−1)3(x - 1) = 6(y - 2) = 2(z - 1)3(x−1)=6(y−2)=2(z−1) and 4(x−2)=2(y−λ)=(z−3)4(x - 2) = 2(y - \lambda) = (z - 3)4(x−2)=2(y−λ)=(z−3), λ∈R\lambda \in Rλ∈R is 138\frac{1}{\sqrt{38}}38​1​, then the integral value of λ\lambdaλ is equal to :
  1. (A)3
  2. (B)2
  3. (C)−1
  4. (D)5

Correct answer: (A)

Step-by-step solution →
Q62·MathematicsSingle correct
Let n denote the number of solutions of the equation z2+3zˉ=0z^2 + 3\bar{z} = 0z2+3zˉ=0, where z is a complex number. Then the value of ∑k=0∞1nk\sum_{k=0}^{\infty} \frac{1}{n^k}∑k=0∞​nk1​ is equal to :
  1. (A)1
  2. (B)2
  3. (C)32\frac{3}{2}23​
  4. (D)43\frac{4}{3}34​

Correct answer: (D)

Step-by-step solution →
Q63·MathematicsSingle correct
Let [x][x][x] denote the greatest integer less than or equal to x. Then, the values of x∈Rx \in Rx∈R satisfying the equation [ex]2+[ex+1]−3=0\left[e^x\right]^2 + \left[e^x + 1\right] - 3 = 0[ex]2+[ex+1]−3=0 lie in the interval :
  1. (A)[1,e)[1, e)[1,e)
  2. (B)[log⁡e2,log⁡e3)[\log_e 2, \log_e 3)[loge​2,loge​3)
  3. (C)[0,log⁡e2)[0, \log_e 2)[0,loge​2)
  4. (D)[0,1/ e)[0, 1/\,e)[0,1/e)

Correct answer: (C)

Step-by-step solution →
Q64·MathematicsSingle correct
Which of the following Boolean expressions is not a tautology?
  1. (A)(∼p⇒q)∨(∼q⇒p)(\sim p \Rightarrow q) \vee (\sim q \Rightarrow p)(∼p⇒q)∨(∼q⇒p)
  2. (B)(q⇒p)∨(∼q⇒p)(q \Rightarrow p) \vee (\sim q \Rightarrow p)(q⇒p)∨(∼q⇒p)
  3. (C)(p⇒∼q)∨(∼q⇒p)(p \Rightarrow \sim q) \vee (\sim q \Rightarrow p)(p⇒∼q)∨(∼q⇒p)
  4. (D)(p⇒q)∨(∼q⇒p)(p \Rightarrow q) \vee (\sim q \Rightarrow p)(p⇒q)∨(∼q⇒p)

Correct answer: (A)

Step-by-step solution →
Q65·MathematicsSingle correct
Let a line L : 2x+y=k2x + y = k2x+y=k, k>0k > 0k>0 be a tangent to the hyperbola x2−y2=3x^2 - y^2 = 3x2−y2=3. If L is also a tangent to the parabola y2=αxy^2 = \alpha xy2=αx, then α\alphaα is equal to :
  1. (A)242424
  2. (B)−24-24−24
  3. (C)−12-12−12
  4. (D)121212

Correct answer: (B)

Step-by-step solution →
Q66·MathematicsSingle correct
Let y=y(x)y = y(x)y=y(x) be the solution of the differential equation cosec⁡2x dy+2 dx=(1+ycos⁡2x)cosec⁡2x dx\cosec^2 x \, dy + 2 \, dx = (1 + y \cos 2x) \cosec^2 x \, dxcosec2xdy+2dx=(1+ycos2x)cosec2xdx, with y(π4)=0y\left(\dfrac{\pi}{4}\right) = 0y(4π​)=0. Then, the value of (y(0)+1)2\left(y(0) + 1\right)^2(y(0)+1)2 is equal to :
  1. (A)e1/2e^{1/2}e1/2
  2. (B)e−1/2e^{-1/2}e−1/2
  3. (C)e−1e^{-1}e−1
  4. (D)eee

Correct answer: (C)

Step-by-step solution →
Q67·MathematicsSingle correct
Let f:R→Rf : R \rightarrow Rf:R→R be defined as f(x)={−43x3+2x2+3x,x>03xex,x≤0f(x) = \begin{cases} -\dfrac{4}{3}x^3 + 2x^2 + 3x, & x > 0 \\ 3xe^{x}, & x \leq 0 \end{cases}f(x)=⎩⎨⎧​−34​x3+2x2+3x,3xex,​x>0x≤0​ Then f is increasing function in the interval.
  1. (A)(−12,2)\left(-\dfrac{1}{2}, 2\right)(−21​,2)
  2. (B)(−1,32)\left(-1, \dfrac{3}{2}\right)(−1,23​)
  3. (C)(−3,−1)(-3, -1)(−3,−1)
  4. (D)(0,2)(0, 2)(0,2)

Correct answer: (B)

Step-by-step solution →
Q68·MathematicsSingle correct
Let a vector a⃗\vec{a}a be coplanar with vectors b⃗=2i^+j^+k^\vec{b} = 2\hat{i} + \hat{j} + \hat{k}b=2i^+j^​+k^ and c⃗=i^−j^+k^\vec{c} = \hat{i} - \hat{j} + \hat{k}c=i^−j^​+k^. If a⃗\vec{a}a is perpendicular to d⃗=3i^+2j^+6k^\vec{d} = 3\hat{i} + 2\hat{j} + 6\hat{k}d=3i^+2j^​+6k^ and ∣a⃗∣=10\left|\vec{a}\right| = \sqrt{10}∣a∣=10​. Then a possible value of [a⃗b⃗c⃗]+[a⃗b⃗d⃗]+[a⃗c⃗d⃗]\left[\vec{a}\vec{b}\vec{c}\right] + \left[\vec{a}\vec{b}\vec{d}\right] + \left[\vec{a}\vec{c}\vec{d}\right][abc]+[abd]+[acd] is equal to :
  1. (A)−40-40−40
  2. (B)−38-38−38
  3. (C)−42-42−42
  4. (D)−29-29−29

Correct answer: (C)

Step-by-step solution →
Q69·MathematicsSingle correct
Let SnS_nSn​ denote the sum of the first n-terms of an arithmetic progression. If S10=530S_{10} = 530S10​=530, S5=140S_5 = 140S5​=140, then S20−S6S_{20} - S_6S20​−S6​ is equal to :
  1. (A)185218521852
  2. (B)184218421842
  3. (C)187218721872
  4. (D)186218621862

Correct answer: (D)

Step-by-step solution →
Q70·MathematicsSingle correct
Let f:R→Rf : R \rightarrow Rf:R→R be defined as f(x)={x3(1−cos⁡2x)2log⁡e(1+2xe−2x(1−xe−x)2),x≠0α,x=0f(x) = \begin{cases} \dfrac{x^{3}}{(1-\cos 2x)^{2}} \log_{e}\left(\dfrac{1+2xe^{-2x}}{\left(1-xe^{-x}\right)^{2}}\right) , & x \neq 0 \\ \alpha , & x = 0 \end{cases}f(x)=⎩⎨⎧​(1−cos2x)2x3​loge​((1−xe−x)21+2xe−2x​),α,​x=0x=0​ . If fff is continuous at x = 0, then α\alphaα is equal to :
  1. (A)0
  2. (B)1
  3. (C)2
  4. (D)3

Correct answer: (B)

Step-by-step solution →
Q71·MathematicsSingle correct
The number of solutions of sin⁡7x+cos⁡7x=1\sin^7 x + \cos^7 x = 1sin7x+cos7x=1, x∈[0,4π]x \in \left[0, 4\pi\right]x∈[0,4π] is equal to :
  1. (A)777
  2. (B)111111
  3. (C)555
  4. (D)999

Correct answer: (C)

Step-by-step solution →
Q72·MathematicsSingle correct
Let three vectors a⃗,b⃗\vec{a}, \vec{b}a,b and c⃗\vec{c}c be such that a⃗×b⃗=c⃗\vec{a} \times \vec{b} = \vec{c}a×b=c, b⃗×c⃗=a⃗\vec{b} \times \vec{c} = \vec{a}b×c=a and ∣a⃗∣=2\left|\vec{a}\right| = 2∣a∣=2. Then which one of the following is not true?
  1. (A)Projection of a⃗\vec{a}a on (b⃗×c⃗)\left(\vec{b} \times \vec{c}\right)(b×c) is 2
  2. (B)[a⃗b⃗c⃗]+[c⃗a⃗b⃗]=8\left[\vec{a}\vec{b}\vec{c}\right] + \left[\vec{c}\vec{a}\vec{b}\right] = 8[abc]+[cab]=8
  3. (C)∣3a⃗+b⃗−2c⃗∣2=51\left|3\vec{a} + \vec{b} - 2\vec{c}\right|^2 = 51​3a+b−2c​2=51
  4. (D)a⃗×((b⃗+c⃗)×(b⃗−c⃗))=0⃗\vec{a} \times \left(\left(\vec{b} + \vec{c}\right) \times \left(\vec{b} - \vec{c}\right)\right) = \vec{0}a×((b+c)×(b−c))=0

Correct answer: (C)

Step-by-step solution →
Q73·MathematicsSingle correct
Let L be the line of intersection of planes r⃗.(i^−j^+2k^)=2\vec{r}.\left(\hat{i} - \hat{j} + 2\hat{k}\right) = 2r.(i^−j^​+2k^)=2 and r⃗.(2i^+j^−k^)=2\vec{r}.\left(2\hat{i} + \hat{j} - \hat{k}\right) = 2r.(2i^+j^​−k^)=2. If P(α,β,γ)P(\alpha, \beta, \gamma)P(α,β,γ) is the foot of perpendicular on L from the point (1,2,0)(1, 2, 0)(1,2,0), then the value of 35(α+β+γ)35(\alpha + \beta + \gamma)35(α+β+γ) is equal to :
  1. (A)101101101
  2. (B)143143143
  3. (C)134134134
  4. (D)119119119

Correct answer: (D)

Step-by-step solution →
Q74·Mathematics·Matrices and DeterminantsSingle correct
Let A=∣aij∣A = \left|a_{ij}\right|A=∣aij​∣ be a real matrix of order 3 x 3, such that a11+ai2+ai3=1a_{11} + a_{i2} + a_{i3} = 1a11​+ai2​+ai3​=1, for i=1,2,3i = 1, 2, 3i=1,2,3. Then, the sum of all the entries of the matrix A3A^3A3 is equal to :
  1. (A)999
  2. (B)333
  3. (C)111
  4. (D)222

Correct answer: (B)

Step-by-step solution →
Q75·MathematicsSingle correct
If the domain of the function f(x)=cos⁡−1x2−x+1sin⁡−1(2x−12)f(x) = \dfrac{\cos^{-1}\sqrt{x^2 - x + 1}}{\sqrt{\sin^{-1}\left(\dfrac{2x - 1}{2}\right)}}f(x)=sin−1(22x−1​)​cos−1x2−x+1​​ is the interval (α,β]\left(\alpha, \beta\right](α,β], then α+β\alpha + \betaα+β is equal to :
  1. (A)111
  2. (B)12\dfrac{1}{2}21​
  3. (C)222
  4. (D)32\dfrac{3}{2}23​

Correct answer: (D)

Step-by-step solution →
Q76·Mathematics·Matrices and DeterminantsSingle correct
The values of λ\lambdaλ and μ\muμ such that the system of equations x+y+z=6x + y + z = 6x+y+z=6, 3x+5y+5z=263x + 5y + 5z = 263x+5y+5z=26, x+2y+λz=μx + 2y + \lambda z = \mux+2y+λz=μ has no solution, are :
  1. (A)λ=2,μ≠10\lambda = 2, \mu \neq 10λ=2,μ=10
  2. (B)λ=3,μ≠10\lambda = 3, \mu \neq 10λ=3,μ=10
  3. (C)λ=3,μ=5\lambda = 3, \mu = 5λ=3,μ=5
  4. (D)λ≠2,μ=10\lambda \neq 2, \mu = 10λ=2,μ=10

Correct answer: (A)

Step-by-step solution →
Q77·MathematicsSingle correct
Let E1:x2a2+y2b2=1E_1 : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1E1​:a2x2​+b2y2​=1, a>ba > ba>b. Let E2E_2E2​ be another ellipse such that it touches the end points of major axis of E1E_1E1​ and the foci of E2E_2E2​ are the end points of minor axis of E1E_1E1​. If E1E_1E1​ and E2E_2E2​ have same eccentricities, then its value is :
  1. (A)−1+52\dfrac{-1 + \sqrt{5}}{2}2−1+5​​
  2. (B)−1+32\dfrac{-1 + \sqrt{3}}{2}2−1+3​​
  3. (C)−1+82\dfrac{-1 + \sqrt{8}}{2}2−1+8​​
  4. (D)−1+62\dfrac{-1 + \sqrt{6}}{2}2−1+6​​

Correct answer: (A)

Step-by-step solution →
Q78·MathematicsSingle correct
Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 x 2 matrices. The probability that such formed matrices have all different entries and are non-singular, is :
  1. (A)2281\dfrac{22}{81}8122​
  2. (B)45162\dfrac{45}{162}16245​
  3. (C)43162\dfrac{43}{162}16243​
  4. (D)2381\dfrac{23}{81}8123​

Correct answer: (C)

Step-by-step solution →
Q79·MathematicsNumerical
Let A={0,1,2,3,4,5,6,7}A = \{0,1,2,3,4,5,6,7\}A={0,1,2,3,4,5,6,7}. Then the number of bijective functions f:A→Af : A \to Af:A→A such that f(1)+f(2)=3−f(3)f(1) + f(2) = 3 - f(3)f(1)+f(2)=3−f(3) is equal to...............

Correct answer: 720

Step-by-step solution →
Q80·MathematicsNumerical
Let f:R→Rf : R \rightarrow Rf:R→R be a function defined as f(x)={3(1−∣x∣2)if ∣x∣≤20if ∣x∣>2f(x) = \begin{cases} 3\left(1-\dfrac{|x|}{2}\right) & \text{if } |x| \leq 2 \\ 0 & \text{if } |x| > 2 \end{cases}f(x)=⎩⎨⎧​3(1−2∣x∣​)0​if ∣x∣≤2if ∣x∣>2​ Let g:R→Rg : R \rightarrow Rg:R→R be given by g(x)=f(x+2)−f(x−2)g(x) = f(x+2) - f(x-2)g(x)=f(x+2)−f(x−2). If n and m denote the number of points in R where g is the continuous and not differentiable, respectively, then n + m is equal to............

Correct answer: 4

Step-by-step solution →
Q81·MathematicsNumerical
Let y=y(x)y = y(x)y=y(x) be the solution of the differential equation ((x+2)ey+1x+2+(y+1))dx=(x+2)dy\left((x + 2)e^{\frac{y+1}{x+2}} + (y + 1)\right)dx = (x + 2)dy((x+2)ex+2y+1​+(y+1))dx=(x+2)dy, y(1)=1y(1) = 1y(1)=1. If the domain y=y(x)y = y(x)y=y(x) is an open interval (α,β)(\alpha, \beta)(α,β), then ∣α+β∣|\alpha + \beta|∣α+β∣ is equal to..........

Correct answer: 4

Step-by-step solution →
Q82·MathematicsNumerical
The number of elements in the set {n∈{1,2,3,....100}|(11)n>(10)n+(9)n}\left\{n \in \{1,2,3,.... 100\} \middle| (11)^n > (10)^n + (9)^n\right\}{n∈{1,2,3,....100}∣(11)n>(10)n+(9)n} is..........

Correct answer: 96

Step-by-step solution →
Q83·MathematicsNumerical
The area (in sq. units) of the region bounded by the curves x2+2y−1=0x^2 + 2y - 1 = 0x2+2y−1=0, y2+4x−4=0y^2 + 4x - 4 = 0y2+4x−4=0 and y2−4x−4=0y^2 - 4x - 4 = 0y2−4x−4=0, in the upper half plane is.........

Correct answer: 2

Step-by-step solution →
Q84·Mathematics·Matrices and DeterminantsNumerical
Let A=(010100001)A = \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix}A=​010​100​001​​. Then the number of 3 x 3 matrices B with entries from the set {1,2,3,4,5}\{1,2,3,4,5\}{1,2,3,4,5} and satisfying AB = BA is...........

Correct answer: 3125

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Q85·MathematicsNumerical
If the digits are not allowed to repeat in any number formed by using the digits 0,2,4,6,8, then the number of all numbers greater than 10,000 is equal to........

Correct answer: 96

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Q86·MathematicsNumerical
The sum of all the elements in the set {n∈{1,2,.......,100}|H.C.F. of n and 2040 is 1}\left\{n \in \{1,2,.......,100\} \middle| \text{H.C.F. of n and 2040 is 1}\right\}{n∈{1,2,.......,100}∣H.C.F. of n and 2040 is 1} is equal to...........

Correct answer: 1251

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Q87·MathematicsNumerical
If the constant term, in binomial expansion of (2xr+1x2)10\left(2x^{r} + \dfrac{1}{x^{2}}\right)^{10}(2xr+x21​)10 is 180, then r is equal to.......

Correct answer: 8

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Q88·MathematicsNumerical
Consider the following frequency distribution : Class : 0 – 6 6 – 12 12 – 18 18 – 24 24 – 30 Frequency : a b 12 9 5 If mean = 30922\frac{309}{22}22309​ and median = 14, then the value (a−b)2(a - b)^2(a−b)2 is equal to..................

Correct answer: 4

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
  • Sets, Relations and Functions 165/186
  • Current Electricity 160/186
  • Sequence and Series 164/186
  • p-Block Elements 164/186
  • 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
  • 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
  • Electronic Devices 145/186
  • Circles 142/186
  • Dual Nature of Matter and Radiation 155/186
  • Amines 133/186
  • Work, Energy and Power 132/186
  • Some Basic Concepts in Chemistry 129/186
  • Area Under Curves 139/186
  • 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
  • Nuclei 116/186
  • 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
  • Inverse Trigonometric Functions 93/186
  • Hydrogen 81/186
  • Electronic Effects and Stability 74/186
  • Hyperbola 77/186
  • Experimental Skills 68/186
  • Polymers 64/186
  • Solid State 63/186
  • Diazonium Salts and Reactions 53/186
  • Magnetism and Matter 50/186
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