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JEE Main 31 August 2021 Shift 2 Question Paper with Answers

31 August 2021 · August session · 88 questions

88 of the 90 questions from the JEE Main 31 August 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
28
Mathematics
30

Physics — JEE Main 31 August 2021 Shift 2

Q1·PhysicsSingle correct
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50×10350 \times 10^350×103 kg, The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y=2.0×1011Y = 2.0 \times 10^{11}Y=2.0×1011 Pa, g=9.8g = 9.8g=9.8 m/s2^22]
  1. (A)3.60×10−83.60 \times 10^{-8}3.60×10−8
  2. (B)2.60×10−72.60 \times 10^{-7}2.60×10−7
  3. (C)1.87×10−31.87 \times 10^{-3}1.87×10−3
  4. (D)7.07×10−47.07 \times 10^{-4}7.07×10−4

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle is : (Assume that the current is flowing in the clockwise direction.)
  1. (A)3×10−73 \times 10^{-7}3×10−7 T, outside the plane of triangle
  2. (B)23×10−72\sqrt{3} \times 10^{-7}23​×10−7 T, outside the plane of triangle
  3. (C)23×10−52\sqrt{3} \times 10^{-5}23​×10−5 T, inside the plane of triangle
  4. (D)3×10−53 \times 10^{-5}3×10−5 T, inside the plane of triangle

Correct answer: (D)

Step-by-step solution →
Q3·PhysicsSingle correct
A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint ?
  1. (A)18.7518.7518.75 kgm2^22
  2. (B)1.905×1051.905 \times 10^51.905×105 kgm2^22
  3. (C)19.0519.0519.05 kgm2^22
  4. (D)1.875×1051.875 \times 10^51.875×105 kgm2^22

Correct answer: (C)

Step-by-step solution →
Q4·PhysicsSingle correct
Statement I : Two forces (P⃗+Q⃗)\left(\vec{P} + \vec{Q}\right)(P+Q​) and (P⃗−Q⃗)\left(\vec{P} - \vec{Q}\right)(P−Q​) where P⃗⊥Q⃗\vec{P} \perp \vec{Q}P⊥Q​, when act at an angle θ1\theta_1θ1​ to each other, the magnitude of their resultant is 3(P2+Q2)\sqrt{3(P^2 + Q^2)}3(P2+Q2)​, when they act at an angle θ2\theta_2θ2​, the magnitude of their resultant becomes 2(P2+Q2)\sqrt{2(P^2 + Q^2)}2(P2+Q2)​. This is possible only when θ1<θ2\theta_1 < \theta_2θ1​<θ2​. Statement II : In the situation given above. θ1=60∘\theta_1 = 60^\circθ1​=60∘ and θ2=90∘\theta_2 = 90^\circθ2​=90∘ 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)Both Statement-I and Statement-II are true
  3. (C)Statement-I is true but Statement-II is false
  4. (D)Both Statement-I and Statement-II are false.

Correct answer: (B)

Step-by-step solution →
Q5·PhysicsSingle correct
A free electron of 2.6 eV energy collides with a H+^++ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (h=6.6×10−34(h = 6.6 \times 10^{-34}(h=6.6×10−34 Js)))
  1. (A)1.45×10161.45 \times 10^{16}1.45×1016 MHz
  2. (B)0.19×10150.19 \times 10^{15}0.19×1015 MHz
  3. (C)1.45×1091.45 \times 10^{9}1.45×109 MHz
  4. (D)9.0×10279.0 \times 10^{27}9.0×1027 MHz

Correct answer: (C)

Step-by-step solution →
Q6·PhysicsSingle correct
Two thin metallic spherical shells of radii r1r_1r1​ and r2r_2r2​ (r1<r2)(r_1 < r_2)(r1​<r2​) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature θ1\theta_1θ1​ and the outer shell at temperature θ2(θ1<θ2)\theta_2 (\theta_1 < \theta_2)θ2​(θ1​<θ2​). The rate at which heat flows radially through the material is :-
  1. (A)4πKr1r2(θ2−θ1)r2−r1\frac{4\pi K r_1 r_2 (\theta_2 - \theta_1)}{r_2 - r_1}r2​−r1​4πKr1​r2​(θ2​−θ1​)​
  2. (B)πr1r2(θ2−θ1)r2−r1\frac{\pi r_1 r_2 (\theta_2 - \theta_1)}{r_2 - r_1}r2​−r1​πr1​r2​(θ2​−θ1​)​
  3. (C)K(θ2−θ1)r2−r1\frac{K(\theta_2 - \theta_1)}{r_2 - r_1}r2​−r1​K(θ2​−θ1​)​
  4. (D)K(θ2−θ1)(r2−r1)4πr1r2\frac{K(\theta_2 - \theta_1)(r_2 - r_1)}{4\pi r_1 r_2}4πr1​r2​K(θ2​−θ1​)(r2​−r1​)​

Correct answer: (A)

Step-by-step solution →
Q7·PhysicsSingle correct
If VAV_AVA​ and VBV_BVB​ are the input voltages (either 5V or 0V) and VoV_oVo​ is the output voltage then the two gates represented in the following circuit (A) and (B) are:-
  1. (A)AND and OR Gate
  2. (B)OR and NOT Gate
  3. (C)NAND and NOR Gate
  4. (D)AND and NOT Gate

Correct answer: (B)

Step-by-step solution →
Q8·PhysicsSingle correct
Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-
  1. (A)(mpme)3/2\left(\frac{m_p}{m_e}\right)^{3/2}(me​mp​​)3/2
  2. (B)memp\sqrt{\frac{m_e}{m_p}}mp​me​​​
  3. (C)mpme\sqrt{\frac{m_p}{m_e}}me​mp​​​
  4. (D)mpme\frac{m_p}{m_e}me​mp​​

Correct answer: (C)

Step-by-step solution →
Q9·PhysicsSingle correct
A bob of mass 'm' suspended by a thread of length lll undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density 14\frac{1}{4}41​ times that of the bob and the length of the thread is increased by 1/3rd1/3^{rd}1/3rd of the original length, then the time period of the simple harmonic oscillations will be :-
  1. (A)T
  2. (B)32\frac{3}{2}23​ T
  3. (C)34\frac{3}{4}43​ T
  4. (D)43\frac{4}{3}34​ T

Correct answer: (D)

Step-by-step solution →
Q10·PhysicsSingle correct
Statement :1 If three forces F⃗1,F⃗2\vec{F}_1, \vec{F}_2F1​,F2​ and F⃗3\vec{F}_3F3​ are represented by three sides of a triangle and F⃗1+F⃗2=−F⃗3\vec{F}_1 + \vec{F}_2 = -\vec{F}_3F1​+F2​=−F3​, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement : II A triangle made up of three forces F⃗1,F⃗2\vec{F}_1, \vec{F}_2F1​,F2​ and F⃗3\vec{F}_3F3​ as its sides taken in the same order, satisfy the condition for translatory equilibrium. 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 false
  4. (D)Both Statement-I and Statement-II are true.

Correct answer: (D)

Step-by-step solution →
Q11·PhysicsSingle correct
If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :
  1. (A)[FT−1V−1][FT^{-1} V^{-1}][FT−1V−1]
  2. (B)[FTV−1][FTV^{-1}][FTV−1]
  3. (C)[FT2V][FT^{2} V][FT2V]
  4. (D)[FVT−1][FVT^{-1}][FVT−1]

Correct answer: (B)

Step-by-step solution →
Q12·PhysicsSingle correct
The magnetic field vector of an electromagnetic wave is given by B=Boi^+j^2cos⁡(kz−ωt)B = B_o \frac{\hat{i} + \hat{j}}{\sqrt{2}} \cos(kz - \omega t)B=Bo​2​i^+j^​​cos(kz−ωt); where i^,j^\hat{i}, \hat{j}i^,j^​ represents unit vector along x and y-axis respectively. At t=0t = 0t=0 s, two electric charges q1q_1q1​ of 4π4\pi4π coulomb and q2q_2q2​ of 2π2\pi2π coulomb located at (0,0,πk)\left(0, 0, \frac{\pi}{k}\right)(0,0,kπ​) and (0,0,3πk)\left(0, 0, \frac{3\pi}{k}\right)(0,0,k3π​), respectively, have the same velocity of 0.5 c i^0.5\, c\, \hat{i}0.5ci^, (where c is the velocity of light). The ratio of the force acting on charge q1q_1q1​ to q2q_2q2​ is :-
  1. (A)22:12\sqrt{2} : 122​:1
  2. (B)1:21 : \sqrt{2}1:2​
  3. (C)2:12 : 12:1
  4. (D)2:1\sqrt{2} : 12​:1

Correct answer: (C)

Step-by-step solution →
Q13·PhysicsSingle correct
The equivalent resistance of the given circuit between the terminals A and B is :
  1. (A)0Ω0\Omega0Ω
  2. (B)3Ω3\Omega3Ω
  3. (C)92Ω\frac{9}{2}\Omega29​Ω
  4. (D)1Ω1\Omega1Ω

Correct answer: (D)

Step-by-step solution →
Q14·PhysicsSingle correct
Choose the incorrect statement : (a) The electric lines of force entering into a Gaussian surface provide negative flux. (b) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same. (c) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero. (d) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux. Choose the most appropriate answer from the options given below
  1. (A)(c) and (d) only
  2. (B)(b) and (d) only
  3. (C)(d) only
  4. (D)(a) and (c) only

Correct answer: (C)

Step-by-step solution →
Q15·PhysicsSingle correct
A mixture of hydrogen and oxygen has volume 500 cm3^33, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-
  1. (A)3 : 8
  2. (B)3 : 16
  3. (C)16 : 3
  4. (D)8 : 3

Correct answer: (C)

Step-by-step solution →
Q16·PhysicsSingle correct
A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1:2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is :-
  1. (A)13\frac{1}{3}31​
  2. (B)23\frac{2}{3}32​
  3. (C)18\frac{1}{8}81​
  4. (D)14\frac{1}{4}41​

Correct answer: (C)

Step-by-step solution →
Q17·PhysicsSingle correct
A coil is placed in a magnetic field B⃗\vec{B}B as shown below : A current is induced in the coil because B⃗\vec{B}B is :
  1. (A)Outward and decreasing with time
  2. (B)Parallel to the plane of coil and decreasing with time
  3. (C)Outward and increasing with time
  4. (D)Parallel to the plane of coil and increasing with time

Correct answer: (A)

Step-by-step solution →
Q18·PhysicsSingle correct
For a body executing S.H.M. : (a) Potential energy is always equal to its K.E. (b) Average potential and kinetic energy over any given time interval are always equal. (c) Sum of the kinetic and potential energy at any point of time is constant. (d) Average K.E. in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below :
  1. (A)(c) and (d)
  2. (B)only (c)
  3. (C)(b) and (c)
  4. (D)only (b)

Correct answer: (A)

Step-by-step solution →
Q19·PhysicsSingle correct
Statement-I : To get a steady dc output from the pulsating voltage received from a full wave rectifier we can connect a capacitor across the output parallel to the load RLR_LRL​. Statement-II : To get a steady dc output from the pulsating voltage received from a full wave rectifier we can connect an inductor in series with RLR_LRL​. In the light of the above statements, choose the most appropriate answer from the options given below :
  1. (A)Statement I is true but Statement II is false
  2. (B)Statement I is false but Statement II is true
  3. (C)Both Statement I and Statement II are false
  4. (D)Both Statement I and Statement II are true

Correct answer: (D)

Step-by-step solution →
Q20·PhysicsSingle correct
If RER_ERE​ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 'r' below and a height 'r' above the earth surface is : (Given : r<REr < R_Er<RE​)
  1. (A)1−rRE−r2RE2−r3RE31 - \frac{r}{R_E} - \frac{r^2}{R_E^2} - \frac{r^3}{R_E^3}1−RE​r​−RE2​r2​−RE3​r3​
  2. (B)1+rRE+r2RE2+r3RE31 + \frac{r}{R_E} + \frac{r^2}{R_E^2} + \frac{r^3}{R_E^3}1+RE​r​+RE2​r2​+RE3​r3​
  3. (C)1+rRE−r2RE2+r3RE31 + \frac{r}{R_E} - \frac{r^2}{R_E^2} + \frac{r^3}{R_E^3}1+RE​r​−RE2​r2​+RE3​r3​
  4. (D)1+rRE−r2RE2−r3RE31 + \frac{r}{R_E} - \frac{r^2}{R_E^2} - \frac{r^3}{R_E^3}1+RE​r​−RE2​r2​−RE3​r3​

Correct answer: (D)

Step-by-step solution →
Q21·PhysicsNumerical
A bandwidth of 6 MHz is available for A.M. transmission. If the maximum audio signal frequency used for modulating the carrier wave is not to exceed 6 kHz. The number of stations that can be broadcasted within this band simultaneously without interfering with each other will be______.

Correct answer: 500

Step-by-step solution →
Q22·PhysicsNumerical
A parallel plate capacitor of capacitance 200 μ\muμF is connected to a battery of 200 V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be______J.

Correct answer: 4

Step-by-step solution →
Q23·PhysicsNumerical
A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 103^{3}3 cm3^{3}3. If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of 0.75 A in the solenoid, the fractional change in the magnetic moment of the core would be approximately (x499)\left(\frac{x}{499}\right)(499x​). Find the value of x.

Correct answer: 250

Step-by-step solution →
Q24·PhysicsNumerical
A particle is moving with constant acceleration 'a'. Following graph shows v2^{2}2 versus x(displacement) plot. The acceleration of the particle is___m/s2^{2}2.

Correct answer: 1

Step-by-step solution →
Q25·PhysicsNumerical
In a Young's double slit experiment, the slits are separated by 0.3 mm and the screen is 1.5 m away from the plane of slits. Distance between fourth bright fringes on both sides of central bright is 2.4 cm. The frequency of light used is______×\times× 1014^{14}14 Hz.

Correct answer: 5

Step-by-step solution →
Q26·PhysicsNumerical
The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisions of vernier scale. One main scale division is 1 mm. The main scale reading is 10 mm and 8th^{th}th division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of 0.04 cm, then the radius of the bob is______×\times× 10−2^{-2}−2 cm.

Correct answer: 52

Step-by-step solution →
Q27·PhysicsNumerical
A sample of gas with γ\gammaγ = 1.5 is taken through an adiabatic process in which the volume is compressed from 1200 cm3^{3}3 to 300 cm3^{3}3. If the initial pressure is 200 kPa. The absolute value of the workdone by the gas in the process =______J.

Correct answer: 480

Step-by-step solution →
Q28·PhysicsNumerical
At very high frequencies, the effective impendance of the given circuit will be_______Ω\OmegaΩ.

Correct answer: 2

Step-by-step solution →
Q29·PhysicsNumerical
Cross-section view of a prism is the equilateral triangle ABC in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from P (midpoint of BC) to A is______×\times× 10−10^{-10}−10 s. (Given, speed of light in vacuum = 3 ×\times× 108^{8}8 m/s and cos⁡30∘=32\cos 30^\circ = \frac{\sqrt{3}}{2}cos30∘=23​​ )

Correct answer: 5

Step-by-step solution →
Q30·PhysicsNumerical
A resistor dissipates 192 J of energy in 1 s when a current of 4A is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in 5 s in______J.

Correct answer: 3840

Step-by-step solution →

Chemistry — JEE Main 31 August 2021 Shift 2

Q31·Chemistry·IsomerismSingle correct
Arrange the following conformational isomers of n-butane in order of their increasing potential energy :
  1. (A)II < III < IV < I
  2. (B)I < IV < III < II
  3. (C)II < IV < III < I
  4. (D)I < III < IV < II

Correct answer: (D)

Step-by-step solution →
Q32·ChemistrySingle correct
The Eu2+\mathrm{Eu^{2+}}Eu2+ ion is a strong reducing agent in spite of its ground state electronic configuration (outermost) : [Atomic number of Eu = 63]
  1. (A)4f76s24f^{7}6s^{2}4f76s2
  2. (B)4f64f^{6}4f6
  3. (C)4f74f^{7}4f7
  4. (D)4f66s24f^{6}6s^{2}4f66s2

Correct answer: (C)

Step-by-step solution →
Q33·ChemistrySingle correct
The structures of A and B formed in the following reaction are : [Ph = −C6H5-\mathrm{C_6H_5}−C6​H5​]
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (A)

Step-by-step solution →
Q34·Chemistry·Redox Reactions and ElectrochemistrySingle correct
Match List-I with List-II List-I (Parameter) (a) Cell constant (b) Molar conductivity (c) Conductivity (d) Degree of dissociation of electrolyte List-II (Unit) (i) S cm2 mol−1\mathrm{S\ cm^2\ mol^{-1}}S cm2 mol−1 (ii) Dimensionless (iii) m−1\mathrm{m^{-1}}m−1 (iv) Ω−1 m−1\mathrm{\Omega^{-1}\ m^{-1}}Ω−1 m−1 Choose the most appropriate answer from the options given below :
  1. (A)(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)
  2. (B)(a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)
  3. (C)(a)-(i), (b)-(iv), (c)-(iii), (d)-(ii)
  4. (D)(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)

Correct answer: (A)

Step-by-step solution →
Q35·ChemistrySingle correct
The major products A and B formed in the following reaction sequence are :
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q36·ChemistrySingle correct
Which of the following is NOT an example of fibrous protein ?
  1. (A)Keratin
  2. (B)Albumin
  3. (C)Collagen
  4. (D)Myosin

Correct answer: (B)

Step-by-step solution →
Q37·ChemistrySingle correct
The deposition of X and Y on ground surfaces is referred as wet and dry depositions, respectively. X and Y are :
  1. (A)X = Ammonium salts, Y = CO2\mathrm{CO_2}CO2​
  2. (B)X = SO2\mathrm{SO_2}SO2​, Y = Ammonium salts
  3. (C)X = Ammonium salts, Y = SO2\mathrm{SO_2}SO2​
  4. (D)X = CO2\mathrm{CO_2}CO2​, Y = SO2\mathrm{SO_2}SO2​

Correct answer: (C)

Step-by-step solution →
Q38·ChemistrySingle correct
For the reaction given below : The compound which is not formed as a product in the reaction is a :
  1. (A)compound with both alcohol and acid functional groups
  2. (B)monocarboxylic acid
  3. (C)dicarboxylic acid
  4. (D)diol

Correct answer: (C)

Step-by-step solution →
Q39·ChemistrySingle correct
Spin only magnetic moment in BM of [Fe(CO)4(C2O4)]+\mathrm{[Fe(CO)_4(C_2O_4)]^+}[Fe(CO)4​(C2​O4​)]+ is :
  1. (A)5.92
  2. (B)0
  3. (C)1
  4. (D)1.73

Correct answer: (D)

Step-by-step solution →
Q40·ChemistrySingle correct
The incorrect expression among the following is:
  1. (A)ΔGSystemΔSTotal=−T\dfrac{\Delta \mathrm{G_{System}}}{\Delta \mathrm{S_{Total}}} = -\mathrm{T}ΔSTotal​ΔGSystem​​=−T (at constant P)
  2. (B)ln⁡K=ΔHo−TΔSoRT\ln \mathrm{K} = \dfrac{\Delta \mathrm{H^{o}} - \mathrm{T}\Delta \mathrm{S^{o}}}{\mathrm{RT}}lnK=RTΔHo−TΔSo​
  3. (C)K=e−ΔGo/RT\mathrm{K} = e^{-\Delta \mathrm{G^{o}}/\mathrm{RT}}K=e−ΔGo/RT
  4. (D)For isothermal process wreversible=− nRTln⁡VfVi\mathrm{w_{reversible}} = -\ \mathrm{nRT} \ln \dfrac{\mathrm{V}_f}{\mathrm{V}_i}wreversible​=− nRTlnVi​Vf​​

Correct answer: (B)

Step-by-step solution →
Q41·ChemistrySingle correct
Which one of the following statements is incorrect ?
  1. (A)Atomic hydrogen is produced when H2\mathrm{H_2}H2​ molecules at a high temperature are irradiated with UV radiation.
  2. (B)At around 2000 K, the dissociation of dihydrogen into its atoms is nearly 8.1%.
  3. (C)Bond dissociation enthalpy of H2\mathrm{H_2}H2​ is highest among diatomic gaseous molecules which contain a single bond .
  4. (D)Dihydrogen is produced on reacting zinc with HCl as well as NaOH(aq)\mathrm{NaOH_{(aq)}}NaOH(aq)​.

Correct answer: (B)

Step-by-step solution →
Q42·ChemistrySingle correct
Which among the following is not a polyester ?
  1. (A)Novolac
  2. (B)PHBV
  3. (C)Dacron
  4. (D)Glyptal

Correct answer: (A)

Step-by-step solution →
Q43·ChemistrySingle correct
Which one of the following correctly represents the order of stability of oxides, X2O\mathrm{X_2O}X2​O; (X = halogen) ?
  1. (A)Br > Cl > I
  2. (B)Br > I > Cl
  3. (C)Cl > I > Br
  4. (D)I > Cl > Br

Correct answer: (D)

Step-by-step solution →
Q44·ChemistrySingle correct
Match List-I with List-II : List-I (Metal Ion) (a) Mn2+\mathrm{Mn^{2+}}Mn2+ (b) As3+\mathrm{As^{3+}}As3+ (c) Cu2+\mathrm{Cu^{2+}}Cu2+ (d) Al3+\mathrm{Al^{3+}}Al3+ List-II (Group in Qualitative analysis) (i) Group - III (ii) Group - IIA (iii) Group - IV (iv) Group - IIB Choose the most appropriate answer from the options given below :
  1. (A)(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
  2. (B)(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)
  3. (C)(a)-(i), (b)-(iv), (c)-(ii), (d)-(iii)
  4. (D)(a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)

Correct answer: (B)

Step-by-step solution →
Q45·ChemistrySingle correct
The major product of the following reaction is :
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (D)

Step-by-step solution →
Q46·ChemistrySingle correct
For the following :
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q47·ChemistrySingle correct
Identify correct A, B and C in the reaction sequence given below :
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (A)

Step-by-step solution →
Q48·ChemistrySingle correct
The number of S=O\mathrm{S=O}S=O bonds present in sulphurous acid, peroxodisulphuric acid and pyrosulphuric acid, respectively are :
  1. (A)2, 3 and 4
  2. (B)1, 4 and 3
  3. (C)2, 4 and 3
  4. (D)1, 4 and 4

Correct answer: (D)

Step-by-step solution →
Q49·ChemistryNumerical
CH4\mathrm{CH_4}CH4​ is adsorbed on 1 g charcoal at 0°C following the Freundlich adsorption isotherm. 10.0 mL of CH4\mathrm{CH_4}CH4​ is adsorbed at 100 mm of Hg, whereas 15.0 mL is adsorbed at 200 mm of Hg. The volume of CH4\mathrm{CH_4}CH4​ adsorbed at 300 mm of Hg is 10x^{x}x mL. The value of x is ________ ×\times× 10−2^{-2}−2. (Nearest integer) [Use log⁡102=0.3010\log_{10}2 = 0.3010log10​2=0.3010, log⁡103=0.4771\log_{10}3 = 0.4771log10​3=0.4771]

Correct answer: 128

Step-by-step solution →
Q50·ChemistryNumerical
1.22 g of an organic acid is separately dissolved in 100 g of benzene (Kb\mathrm{K_b}Kb​ = 2.6 K kg mol−1^{-1}−1) and 100 g of acetone (Kb\mathrm{K_b}Kb​ = 1.7 K kg mol−1^{-1}−1). The acid is known to dimerize in benzene but remain as a monomer in acetone. The boiling point of the solution in acetone increases by 0.17°C. The increase in boiling point of solution in benzene in °C is x ×\times× 10−2^{-2}−2. The value of x is ________.(Nearest integer) [Atomic mass : C = 12.0, H = 1.0, O= 16.0]

Correct answer: 13

Step-by-step solution →
Q51·ChemistryNumerical
The value of magnetic quantum number of the outermost electron of Zn+\mathrm{Zn^+}Zn+ ion is __________.

Correct answer: 0

Step-by-step solution →
Q52·ChemistryNumerical
The empirical formula for a compound with a cubic close packed arrangement of anions and with cations occupying all the octahedral sites in AxB\mathrm{A_xB}Ax​B. The value of x is __________ (Integer answer)

Correct answer: 1

Step-by-step solution →
Q53·ChemistryNumerical
In the electrolytic refining of blister copper, the total number of main impurities, from the following, removed as anode mud is ________ Pb, Sb, Se, Te, Ru, Ag, Au and Pt

Correct answer: 6

Step-by-step solution →
Q54·ChemistryNumerical
The pH of a solution obtained by mixing 50 mL of 1 M HCl and 30 mL of 1 M NaOH is x ×\times× 10−4^{-4}−4. The value of x is __________. (Nearest integer) [log⁡2.5=0.3979\log 2.5 = 0.3979log2.5=0.3979]

Correct answer: 6021

Step-by-step solution →
Q55·ChemistryNumerical
For the reaction A →\rightarrow→ B, the rate constant k(in s−1^{-1}−1) is given by log⁡10k=20.35−(2.47×103)T\log_{10} \mathrm{k} = 20.35 - \frac{(2.47 \times 10^{3})}{\mathrm{T}}log10​k=20.35−T(2.47×103)​ The energy of activation in kJ mol−1^{-1}−1 is ________. (Nearest integer) [Given : R = 8.314 J K−1^{-1}−1 mol−1^{-1}−1]

Correct answer: 47

Step-by-step solution →
Q56·ChemistryNumerical
Sodium oxide reacts with water to produce sodium hydroxide. 20.0 g of sodium oxide is dissolved in 500 mL of water. Neglecting the change in volume, the concentration of the resulting NaOH solution is ___________ ×\times× 10−1^{-1}−1 M. (Nearest integer) [Atomic mass : Na = 23.0, O = 16.0, H = 1.0]

Correct answer: 13

Step-by-step solution →
Q57·ChemistryNumerical
According to molecular orbital theory, the number of unpaired electron(s) in O22−\mathrm{O_2^{2-}}O22−​ is :

Correct answer: 0

Step-by-step solution →
Q58·ChemistryNumerical
The transformation occurring in Duma's method is given below : C2H7N+(2x+y2)CuO→xCO2+y2H2O+z2N2+(2x+y2)Cu\mathrm{C_2H_7N} + \left(2\mathrm{x} + \frac{y}{2}\right)\mathrm{CuO} \rightarrow \mathrm{xCO_2} + \frac{y}{2}\mathrm{H_2O} + \frac{z}{2}\mathrm{N_2} + \left(2\mathrm{x} + \frac{y}{2}\right)\mathrm{Cu}C2​H7​N+(2x+2y​)CuO→xCO2​+2y​H2​O+2z​N2​+(2x+2y​)Cu The value of yyy is ________. (Integer answer)

Correct answer: 7

Step-by-step solution →

Mathematics — JEE Main 31 August 2021 Shift 2

Q59·MathematicsSingle correct
If α+β+γ=2π\alpha + \beta + \gamma = 2\piα+β+γ=2π, then the system of equations x+(cos⁡γ)y+(cos⁡β)z=0x + (\cos \gamma)y + (\cos \beta)z = 0x+(cosγ)y+(cosβ)z=0 (cos⁡γ)x+y+(cos⁡α)z=0(\cos \gamma)x + y + (\cos \alpha)z = 0(cosγ)x+y+(cosα)z=0 (cos⁡β)x+(cos⁡α)y+z=0(\cos \beta)x + (\cos \alpha)y + z = 0(cosβ)x+(cosα)y+z=0 has :
  1. (A)no solution
  2. (B)infinitely many solution
  3. (C)exactly two solutions
  4. (D)a unique solution

Correct answer: (B)

Step-by-step solution →
Q60·MathematicsSingle correct
Let a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c}a,b,c be three vectors mutually perpendicular to each other and have same magnitude. If a vector r⃗\vec{r}r satisfies. a⃗×{(r⃗−b⃗)×a⃗}+b⃗×{(r⃗−c⃗)×b⃗}+c⃗×{(r⃗−a⃗)×c⃗}=0⃗\vec{a} \times \{(\vec{r} - \vec{b}) \times \vec{a}\} + \vec{b} \times \{(\vec{r} - \vec{c}) \times \vec{b}\} + \vec{c} \times \{(\vec{r} - \vec{a}) \times \vec{c}\} = \vec{0}a×{(r−b)×a}+b×{(r−c)×b}+c×{(r−a)×c}=0, then r⃗\vec{r}r is equal to :
  1. (A)13(a⃗+b⃗+c⃗)\frac{1}{3}(\vec{a} + \vec{b} + \vec{c})31​(a+b+c)
  2. (B)13(2a⃗+b⃗−c⃗)\frac{1}{3}(2\vec{a} + \vec{b} - \vec{c})31​(2a+b−c)
  3. (C)12(a⃗+b⃗+c⃗)\frac{1}{2}(\vec{a} + \vec{b} + \vec{c})21​(a+b+c)
  4. (D)12(a⃗+b⃗+2c⃗)\frac{1}{2}(\vec{a} + \vec{b} + 2\vec{c})21​(a+b+2c)

Correct answer: (C)

Step-by-step solution →
Q61·MathematicsSingle correct
The domain of the function f(x)=sin⁡−1(3x2+x−1(x−1)2)+cos⁡−1(x−1x+1)f(x) = \sin^{-1}\left(\frac{3x^2 + x - 1}{(x - 1)^2}\right) + \cos^{-1}\left(\frac{x - 1}{x + 1}\right)f(x)=sin−1((x−1)23x2+x−1​)+cos−1(x+1x−1​) is :
  1. (A)[0,14]\left[0, \frac{1}{4}\right][0,41​]
  2. (B)[−2,0]∪[14,12][-2, 0] \cup \left[\frac{1}{4}, \frac{1}{2}\right][−2,0]∪[41​,21​]
  3. (C)[14,12]∪{0}\left[\frac{1}{4}, \frac{1}{2}\right] \cup \{0\}[41​,21​]∪{0}
  4. (D)[0,12]\left[0, \frac{1}{2}\right][0,21​]

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
Let S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}S={1,2,3,4,5,6}. Then the probability that a randomly chosen onto function ggg from S to S satisfies g(3)=2g(1)g(3) = 2g(1)g(3)=2g(1) is :
  1. (A)110\frac{1}{10}101​
  2. (B)115\frac{1}{15}151​
  3. (C)15\frac{1}{5}51​
  4. (D)130\frac{1}{30}301​

Correct answer: (A)

Step-by-step solution →
Q63·MathematicsSingle correct
Let f:N→Nf : \mathbf{N} \to \mathbf{N}f:N→N be a function such that f(m+n)=f(m)+f(n)f(m + n) = f(m) + f(n)f(m+n)=f(m)+f(n) for every m,n∈Nm, n \in \mathbf{N}m,n∈N. If f(6)=18f(6) = 18f(6)=18, then f(2)⋅f(3)f(2) \cdot f(3)f(2)⋅f(3) is equal to :
  1. (A)6
  2. (B)54
  3. (C)18
  4. (D)36

Correct answer: (B)

Step-by-step solution →
Q64·MathematicsSingle correct
The distance of the point (−1,2,−2)(-1, 2, -2)(−1,2,−2) from the line of intersection of the planes 2x+3y+2z=02x + 3y + 2z = 02x+3y+2z=0 and x−2y+z=0x - 2y + z = 0x−2y+z=0 is :
  1. (A)12\frac{1}{\sqrt{2}}2​1​
  2. (B)52\frac{5}{2}25​
  3. (C)422\frac{\sqrt{42}}{2}242​​
  4. (D)342\frac{\sqrt{34}}{2}234​​

Correct answer: (D)

Step-by-step solution →
Q65·MathematicsSingle correct
Negation of the statement (p∨r)⇒(q∨r)(p \vee r) \Rightarrow (q \vee r)(p∨r)⇒(q∨r) is :
  1. (A)p∧∼q∧∼rp \wedge \sim q \wedge \sim rp∧∼q∧∼r
  2. (B)∼p∧q∧∼r\sim p \wedge q \wedge \sim r∼p∧q∧∼r
  3. (C)∼p∧q∧r\sim p \wedge q \wedge r∼p∧q∧r
  4. (D)p∧q∧rp \wedge q \wedge rp∧q∧r

Correct answer: (A)

Step-by-step solution →
Q66·MathematicsSingle correct
If α=lim⁡x→π/4tan⁡3x−tan⁡xcos⁡(x+π4)\alpha = \lim_{x \to \pi/4} \frac{\tan^3 x - \tan x}{\cos\left(x + \frac{\pi}{4}\right)}α=limx→π/4​cos(x+4π​)tan3x−tanx​ and β=lim⁡x→0(cos⁡x)cot⁡x\beta = \lim_{x \to 0} (\cos x)^{\cot x}β=limx→0​(cosx)cotx are the roots of the equation, ax2+bx−4=0ax^2 + bx - 4 = 0ax2+bx−4=0, then the ordered pair (a,b)(a, b)(a,b) is :
  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)(1,3)(1, 3)(1,3)

Correct answer: (D)

Step-by-step solution →
Q67·MathematicsSingle correct
The locus of mid-points of the line segments joining (−3,−5)(-3, -5)(−3,−5) and the points on the ellipse x24+y29=1\frac{x^2}{4} + \frac{y^2}{9} = 14x2​+9y2​=1 is :
  1. (A)9x2+4y2+18x+8y+145=09x^2 + 4y^2 + 18x + 8y + 145 = 09x2+4y2+18x+8y+145=0
  2. (B)36x2+16y2+90x+56y+145=036x^2 + 16y^2 + 90x + 56y + 145 = 036x2+16y2+90x+56y+145=0
  3. (C)36x2+16y2+108x+80y+145=036x^2 + 16y^2 + 108x + 80y + 145 = 036x2+16y2+108x+80y+145=0
  4. (D)36x2+16y2+72x+32y+145=036x^2 + 16y^2 + 72x + 32y + 145 = 036x2+16y2+72x+32y+145=0

Correct answer: (C)

Step-by-step solution →
Q68·MathematicsSingle correct
If dydx=2xy+2y⋅2x2x+2x+ylog⁡e2\frac{dy}{dx} = \frac{2^x y + 2^y \cdot 2^x}{2^x + 2^{x+y} \log_e 2}dxdy​=2x+2x+yloge​22xy+2y⋅2x​, y(0)=0y(0) = 0y(0)=0, then for y=1y = 1y=1, the value of xxx lies in the interval:
  1. (A)(1,2)(1, 2)(1,2)
  2. (B)(12,1]\left(\frac{1}{2}, 1\right](21​,1]
  3. (C)(2,3)(2, 3)(2,3)
  4. (D)(0,12]\left(0, \frac{1}{2}\right](0,21​]

Correct answer: (A)

Step-by-step solution →
Q69·MathematicsSingle correct
An angle of intersection of the curves, x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1a2x2​+b2y2​=1 and x2+y2=abx^2 + y^2 = abx2+y2=ab, a>ba > ba>b, is :
  1. (A)tan⁡−1(a+bab)\tan^{-1}\left(\frac{a + b}{\sqrt{ab}}\right)tan−1(ab​a+b​)
  2. (B)tan⁡−1(a−b2ab)\tan^{-1}\left(\frac{a - b}{2\sqrt{ab}}\right)tan−1(2ab​a−b​)
  3. (C)tan⁡−1(a−bab)\tan^{-1}\left(\frac{a - b}{\sqrt{ab}}\right)tan−1(ab​a−b​)
  4. (D)tan⁡−1(2ab)\tan^{-1}\left(2\sqrt{ab}\right)tan−1(2ab​)

Correct answer: (C)

Step-by-step solution →
Q70·MathematicsSingle correct
If ydydx=x[y2x2+ϕ(y2x2)ϕ′(y2x2)]y \frac{dy}{dx} = x\left[\frac{y^2}{x^2} + \frac{\phi\left(\frac{y^2}{x^2}\right)}{\phi'\left(\frac{y^2}{x^2}\right)}\right]ydxdy​=x​x2y2​+ϕ′(x2y2​)ϕ(x2y2​)​​, x>0x > 0x>0, ϕ>0\phi > 0ϕ>0, and y(1)=−1y(1) = -1y(1)=−1, then ϕ(y24)\phi\left(\frac{y^2}{4}\right)ϕ(4y2​) is equal to :
  1. (A)4 ϕ(2)4\,\phi(2)4ϕ(2)
  2. (B)4 ϕ(1)4\,\phi(1)4ϕ(1)
  3. (C)2 ϕ(1)2\,\phi(1)2ϕ(1)
  4. (D)ϕ(1)\phi(1)ϕ(1)

Correct answer: (B)

Step-by-step solution →
Q71·MathematicsSingle correct
The sum of the roots of the equation x+1−2log⁡2(3+2x)+2log⁡4(10−2−x)=0x + 1 - 2\log_2(3 + 2^x) + 2\log_4(10 - 2^{-x}) = 0x+1−2log2​(3+2x)+2log4​(10−2−x)=0, is :
  1. (A)log⁡214\log_2 14log2​14
  2. (B)log⁡211\log_2 11log2​11
  3. (C)log⁡212\log_2 12log2​12
  4. (D)log⁡213\log_2 13log2​13

Correct answer: (B)

Step-by-step solution →
Q72·MathematicsSingle correct
If zzz is a complex number such that z−iz−1\frac{z - i}{z - 1}z−1z−i​ is purely imaginary, then the minimum value of ∣z−(3+3i)∣|z - (3 + 3i)|∣z−(3+3i)∣ is :
  1. (A)22−12\sqrt{2} - 122​−1
  2. (B)323\sqrt{2}32​
  3. (C)626\sqrt{2}62​
  4. (D)222\sqrt{2}22​

Correct answer: (D)

Step-by-step solution →
Q73·MathematicsSingle correct
Let a1,a2,a3,…a_1, a_2, a_3, \ldotsa1​,a2​,a3​,… be an A.P. If a1+a2+…+a10a1+a2+…+ap=100p2\frac{a_1 + a_2 + \ldots + a_{10}}{a_1 + a_2 + \ldots + a_p} = \frac{100}{p^2}a1​+a2​+…+ap​a1​+a2​+…+a10​​=p2100​, p≠10p \neq 10p=10, then a11a10\frac{a_{11}}{a_{10}}a10​a11​​ is equal to :
  1. (A)1921\frac{19}{21}2119​
  2. (B)100121\frac{100}{121}121100​
  3. (C)2119\frac{21}{19}1921​
  4. (D)121100\frac{121}{100}100121​

Correct answer: (C)

Step-by-step solution →
Q74·MathematicsSingle correct
Let A be the set of all points (α,β)(\alpha, \beta)(α,β) such that the area of triangle formed by the points (5,6)(5, 6)(5,6), (3,2)(3, 2)(3,2) and (α,β)(\alpha, \beta)(α,β) is 12 square units. Then the least possible length of a line segment joining the origin to a point in A, is :
  1. (A)45\frac{4}{\sqrt{5}}5​4​
  2. (B)165\frac{16}{\sqrt{5}}5​16​
  3. (C)85\frac{8}{\sqrt{5}}5​8​
  4. (D)125\frac{12}{\sqrt{5}}5​12​

Correct answer: (C)

Step-by-step solution →
Q75·MathematicsSingle correct
The number of solutions of the equation 32tan⁡2x+32sec⁡2x=8132^{\tan^2 x} + 32^{\sec^2 x} = 8132tan2x+32sec2x=81, 0≤x≤π40 \leq x \leq \frac{\pi}{4}0≤x≤4π​ is :
  1. (A)3
  2. (B)1
  3. (C)0
  4. (D)2

Correct answer: (B)

Step-by-step solution →
Q76·MathematicsSingle correct
Let fff be any continuous function on [0,2][0, 2][0,2] and twice differentiable on (0,2)(0, 2)(0,2). If f(0)=0f(0) = 0f(0)=0, f(1)=1f(1) = 1f(1)=1 and f(2)=2f(2) = 2f(2)=2, then
  1. (A)f′′(x)=0f''(x) = 0f′′(x)=0 for all x∈(0,2)x \in (0, 2)x∈(0,2)
  2. (B)f′′(x)=0f''(x) = 0f′′(x)=0 for some x∈(0,2)x \in (0, 2)x∈(0,2)
  3. (C)f′(x)=0f'(x) = 0f′(x)=0 for some x∈[0,2]x \in [0, 2]x∈[0,2]
  4. (D)f′′(x)>0f''(x) > 0f′′(x)>0 for all x∈(0,2)x \in (0, 2)x∈(0,2)

Correct answer: (B)

Step-by-step solution →
Q77·MathematicsSingle correct
If [x][x][x] is the greatest integer ≤x\leq x≤x, then π2∫02(sin⁡πx2)(x−[x])[x] dx\pi^2 \int_{0}^{2} \left(\sin \frac{\pi x}{2}\right)(x - [x])^{[x]} \, dxπ2∫02​(sin2πx​)(x−[x])[x]dx is equal to :
  1. (A)2(π−1)2(\pi - 1)2(π−1)
  2. (B)4(π−1)4(\pi - 1)4(π−1)
  3. (C)4(π+1)4(\pi + 1)4(π+1)
  4. (D)2(π+1)2(\pi + 1)2(π+1)

Correct answer: (B)

Step-by-step solution →
Q78·MathematicsSingle correct
The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :
  1. (A)925\frac{92}{5}592​
  2. (B)1345\frac{134}{5}5134​
  3. (C)53625\frac{536}{25}25536​
  4. (D)1125\frac{112}{5}5112​

Correct answer: (C)

Step-by-step solution →
Q79·MathematicsNumerical
If the coefficient of a7b8a^{7}b^{8}a7b8 in the expansion of (a+2b+4ab)10(a + 2b + 4ab)^{10}(a+2b+4ab)10 is K.216K.2^{16}K.216, then K is equal to ______.

Correct answer: 315

Step-by-step solution →
Q80·MathematicsNumerical
Suppose the line x−2α=y−2−5=z+22\frac{x - 2}{\alpha} = \frac{y - 2}{-5} = \frac{z + 2}{2}αx−2​=−5y−2​=2z+2​ lies on the plane x+3y−2z+β=0x + 3y - 2z + \beta = 0x+3y−2z+β=0. Then (α+β)(\alpha + \beta)(α+β) is equal to ______.

Correct answer: 7

Step-by-step solution →
Q81·MathematicsNumerical
The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is ______.

Correct answer: 5143

Step-by-step solution →
Q82·MathematicsNumerical
If ∫sin⁡xsin⁡3x+cos⁡3xdx=αlog⁡e∣1+tan⁡x∣+βlog⁡e∣1−tan⁡x+tan⁡2x∣+γtan⁡−1(2tan⁡x−13)+C\int \frac{\sin x}{\sin^{3} x + \cos^{3} x} dx = \alpha \log_{e} \left| 1 + \tan x \right| + \beta \log_{e} \left| 1 - \tan x + \tan^{2} x \right| + \gamma \tan^{-1} \left( \frac{2 \tan x - 1}{\sqrt{3}} \right) + C∫sin3x+cos3xsinx​dx=αloge​∣1+tanx∣+βloge​​1−tanx+tan2x​+γtan−1(3​2tanx−1​)+C, when C is constant of integration, then the value of 18(α+β+γ2)18(\alpha + \beta + \gamma^{2})18(α+β+γ2) is ______.

Correct answer: 3

Step-by-step solution →
Q83·MathematicsNumerical
A tangent line L is drawn at the point (2, -4) on the parabola y2=8xy^{2} = 8xy2=8x. If the line L is also tangent to the circle x2+y2=ax^{2} + y^{2} = ax2+y2=a, then 'a' is equal to ______.

Correct answer: 2

Step-by-step solution →
Q84·MathematicsNumerical
If S=75+952+1353+1954+....S = \frac{7}{5} + \frac{9}{5^{2}} + \frac{13}{5^{3}} + \frac{19}{5^{4}} + ....S=57​+529​+5313​+5419​+...., then 160 S is equal to ______.

Correct answer: 305

Step-by-step solution →
Q85·MathematicsNumerical
The number of elements in the set {A=(ab0d):a,b,d∈{−1,0,1} and (I−A)3=I−A3}\left\{ A = \begin{pmatrix} a & b \\ 0 & d \end{pmatrix} : a, b, d \in \{-1, 0, 1\} \text{ and } (I - A)^{3} = I - A^{3} \right\}{A=(a0​bd​):a,b,d∈{−1,0,1} and (I−A)3=I−A3}, where I is 2×22 \times 22×2 identity matrix, is :

Correct answer: 8

Step-by-step solution →
Q86·MathematicsNumerical
If the line y=mxy = mxy=mx bisects the area enclosed by the lines x=0x = 0x=0, y=0y = 0y=0, x=32x = \frac{3}{2}x=23​ and the curve y=1+4x−x2y = 1 + 4x - x^{2}y=1+4x−x2, then 12 m is equal to ______.

Correct answer: 26

Step-by-step solution →
Q87·MathematicsNumerical
Let B be the centre of the circle x2+y2−2x+4y+1=0x^{2} + y^{2} - 2x + 4y + 1 = 0x2+y2−2x+4y+1=0. Let the tangents at two points P and Q on the circle intersect at the point A(3, 1). Then 8.(area ΔAPQarea ΔBPQ)8.\left( \frac{\text{area } \Delta APQ}{\text{area } \Delta BPQ} \right)8.(area ΔBPQarea ΔAPQ​) is equal to ______.

Correct answer: 18

Step-by-step solution →
Q88·MathematicsNumerical
Let f(x) be a cubic polynomial with f(1) = -10, f(-1) = 6, and has a local minima at x = 1, and f'(x) has a local minima at x = -1. Then f(3) is equal to ______.

Correct answer: 22

Step-by-step solution →

Chapters tested in this paper

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

  • Properties of Solids and Liquids 172/186
  • Three Dimensional Geometry 176/186
  • Matrices and Determinants 180/186
  • Coordination Compounds 176/186
  • Sets, Relations and Functions 165/186
  • Current Electricity 160/186
  • Sequence and Series 164/186
  • p-Block Elements 164/186
  • Definite Integration 168/186
  • Rotational Motion 172/186
  • Redox Reactions and Electrochemistry 177/186
  • Geometrical Optics 172/186
  • 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
  • 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
  • Electromagnetic Induction 120/186
  • Wave Optics 130/186
  • Area Under Curves 139/186
  • Kinetic Theory of Gases 135/186
  • Purification and Characterisation of Organic Compounds 116/186
  • Oscillations 117/186
  • Alternating Currents 108/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Parabola 101/186
  • Statistics 118/186
  • Ellipse 103/186
  • Isolation of Metals 106/186
  • Differentiability 91/186
  • Surface Chemistry 98/186
  • Inverse Trigonometric Functions 93/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Experimental Skills 68/186
  • Indefinite Integration 66/186
  • Polymers 64/186
  • Solid State 63/186
  • Principles of Qualitative Analysis 58/186
  • Isomerism 51/186
  • Magnetism and Matter 50/186
← 31 Aug Shift 1 2021All papers1 Sep Shift 2 2021 →

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