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JEE Main 6 September 2020 Shift 1 Question Paper with Answers

6 September 2020 · September session · 66 questions

66 of the 75 questions from the JEE Main 6 September 2020 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

9 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
20
Chemistry
24
Mathematics
22

Physics — JEE Main 6 September 2020 Shift 1

Q1·PhysicsSingle correct
A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5 mm is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively:
  1. (A)Negative, 2 μm
  2. (B)Positive, 10 μm
  3. (C)Positive, 0.1 mm
  4. (D)Positive, 0.1 μm

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
A sound source S is moving along a straight track with speed v, and is emitting sound of frequency ν0\nu_0ν0​ (see figure). An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by: (t0t_0t0​ represents the instant when the distance between the source and observer is minimum)
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q3·PhysicsSingle correct
In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m. The separation between P and Q is 5 m and the phase of P is ahead of that of Q by 90∘90^{\circ}90∘. A, B and C are three distinct points of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:
  1. (A)0 : 1 : 4
  2. (B)2 : 1 : 0
  3. (C)0: 1 : 2
  4. (D)4 : 1 : 0

Correct answer: (B)

Step-by-step solution →
Q4·PhysicsSingle correct
Charge Q1Q_1Q1​ and Q2Q_2Q2​ are at point A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then Q1Q2\dfrac{Q_1}{Q_2}Q2​Q1​​ is proportional to:
  1. (A)x13x23\dfrac{x_1^{3}}{x_2^{3}}x23​x13​​
  2. (B)x2x1\dfrac{x_2}{x_1}x1​x2​​
  3. (C)x1x2\dfrac{x_1}{x_2}x2​x1​​
  4. (D)x22x12\dfrac{x_2^{2}}{x_1^{2}}x12​x22​​

Correct answer: (C)

Step-by-step solution →
Q5·PhysicsSingle correct
Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its top, R and height, H, then its moment of inertia about its axis is:
  1. (A)MR22\dfrac{MR^{2}}{2}2MR2​
  2. (B)M(R2+H2)4\dfrac{M\left(R^{2}+H^{2}\right)}{4}4M(R2+H2)​
  3. (C)MH23\dfrac{MH^{2}}{3}3MH2​
  4. (D)MR23\dfrac{MR^{2}}{3}3MR2​

Correct answer: (A)

Step-by-step solution →
Q6·PhysicsSingle correct
Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is rotating with angular frequency ω\omegaω, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is:
  1. (A)ml2ωml^{2}\omegaml2ω
  2. (B)5ml2ω5ml^{2}\omega5ml2ω
  3. (C)3ml2ω3ml^{2}\omega3ml2ω
  4. (D)2ml2ω2ml^{2}\omega2ml2ω

Correct answer: (C)

Step-by-step solution →
Q7·PhysicsSingle correct
For the given input voltage waveform Vin(t)V_{in}(t)Vin​(t), the output voltage waveform V0(t)V_0(t)V0​(t), across the capacitor is correctly depicted by:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
An insect is at the bottom of a hemispherical ditch or radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is: (g=10 ms−2)\left(g=10\,ms^{-2}\right)(g=10ms−2)
  1. (A)0.20 m
  2. (B)0.45 m
  3. (C)0.60 m
  4. (D)0.80 m

Correct answer: (A)

Step-by-step solution →
Q9·PhysicsSingle correct
A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:
  1. (A)1 : 6
  2. (B)1 : 3
  3. (C)1 : 2
  4. (D)3 : 4

Correct answer: (A)

Step-by-step solution →
Q10·PhysicsSingle correct
An electron, a doubly ionized helium ion (He++)\left(He^{++}\right)(He++) and a proton are having the same kinetic energy. The relation between their respective de – Broglie wavelength λe,λHe++\lambda_e, \lambda_{He^{++}}λe​,λHe++​ and λp\lambda_pλp​ is:
  1. (A)λe>λHe++>λP\lambda_e > \lambda_{He^{++}} > \lambda_Pλe​>λHe++​>λP​
  2. (B)λe<λHe++=λP\lambda_e < \lambda_{He^{++}} = \lambda_Pλe​<λHe++​=λP​
  3. (C)λe>λP>λHe++\lambda_e > \lambda_P > \lambda_{He^{++}}λe​>λP​>λHe++​
  4. (D)λe<λP<λHe++\lambda_e < \lambda_P < \lambda_{He^{++}}λe​<λP​<λHe++​

Correct answer: (C)

Step-by-step solution →
Q11·PhysicsSingle correct
A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms−2\text{ms}^{-2}ms−2) is of the order of:
  1. (A)10−310^{-3}10−3
  2. (B)10−410^{-4}10−4
  3. (C)10−210^{-2}10−2
  4. (D)10−110^{-1}10−1

Correct answer: (A)

Step-by-step solution →
Q12·PhysicsSingle correct
You are given that Mass of 27Li=7.0160u^7_2\text{Li} = 7.0160\text{u}27​Li=7.0160u Mass of 24He=4.0026u^4_2\text{He} = 4.0026\text{u}24​He=4.0026u and 11H=1.0079u^1_1\text{H} = 1.0079\text{u}11​H=1.0079u. When 20 g of 37Li^7_3\text{Li}37​Li is converted into 24He^4_2\text{He}24​He by proton capture, the energy liberated, (in kWh), is [Mass of nucleon =1Gevc2=\dfrac{1\text{Gev}}{c^2}=c21Gev​]
  1. (A)4.5×1054.5\times10^54.5×105
  2. (B)8×1068\times10^68×106
  3. (C)6.82×1056.82\times10^56.82×105
  4. (D)1.33×1061.33\times10^61.33×106

Correct answer: (D)

Step-by-step solution →
Q13·PhysicsSingle correct
A point like object is placed at a distance of 1 m in front of convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2m behind the lens. The position and nature of the final image formed by the system is:
  1. (A)2.6 m from the mirror, real
  2. (B)1 m from the mirror, virtual
  3. (C)1 m from the mirror, real
  4. (D)2.6 m from the mirror, virtual

Correct answer: (A)

Step-by-step solution →
Q14·PhysicsSingle correct
Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of γ(=CPCv)\gamma\left(=\dfrac{C_P}{C_v}\right)γ(=Cv​CP​​) are given, respectively, by:
  1. (A)U=52RTU=\dfrac{5}{2}RTU=25​RT and γ=65\gamma=\dfrac{6}{5}γ=56​
  2. (B)U=5RTU=5RTU=5RT and γ=75\gamma=\dfrac{7}{5}γ=57​
  3. (C)U=52RTU=\dfrac{5}{2}RTU=25​RT and γ=75\gamma=\dfrac{7}{5}γ=57​
  4. (D)U=5RTU=5RTU=5RT and γ=65\gamma=\dfrac{6}{5}γ=56​

Correct answer: (C)

Step-by-step solution →
Q15·PhysicsSingle correct
An object of mass m is suspended at the end of a massless wire of length L and area of cross – selection, A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:
  1. (A)f=12πmLYAf=\dfrac{1}{2\pi}\sqrt{\dfrac{mL}{YA}}f=2π1​YAmL​​
  2. (B)f=12πYAmLf=\dfrac{1}{2\pi}\sqrt{\dfrac{YA}{mL}}f=2π1​mLYA​​
  3. (C)f=12πmAYLf=\dfrac{1}{2\pi}\sqrt{\dfrac{mA}{YL}}f=2π1​YLmA​​
  4. (D)f=12πYLmAf=\dfrac{1}{2\pi}\sqrt{\dfrac{YL}{mA}}f=2π1​mAYL​​

Correct answer: (B)

Step-by-step solution →
Q16·PhysicsSingle correct
An electron is moving along + x direction with a velocity of 6×106ms−16\times10^6\text{ms}^{-1}6×106ms−1. It enters a region of uniform electric field of 300 V/cm pointing along + y direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the x direction will be:
  1. (A)3×10−43\times10^{-4}3×10−4T, along + z direction
  2. (B)5×10−35\times10^{-3}5×10−3T, along – z direction
  3. (C)5×10−35\times10^{-3}5×10−3T, along + z direction
  4. (D)3×10−43\times10^{-4}3×10−4T, along – z direction

Correct answer: (C)

Step-by-step solution →
Q17·PhysicsNumerical
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is (x100)%\left(\dfrac{x}{100}\right)\%(100x​)%. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is __________.

Correct answer: 1050.00

Step-by-step solution →
Q18·PhysicsNumerical
Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is __________.

Correct answer: 120.00

Step-by-step solution →
Q19·PhysicsNumerical
Initially a gas of diatomic molecules is contained in a cylinder of volume V1V_1V1​ at a pressure P1P_1P1​ and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a volume 2V12V_12V1​ is given by P2P_2P2​. The ratio P2P1\dfrac{P_2}{P_1}P1​P2​​ is __________.

Correct answer: 05.00

Step-by-step solution →
Q20·PhysicsNumerical
A part of complete circuit is shown in the figure. At some instant, the value of current I is 1 A and it is decreasing at a rate of 102As−110^2\text{As}^{-1}102As−1. The value of the potential difference VP−VQV_P-V_QVP​−VQ​, (in volts) at that instant, is __________.

Correct answer: 33.00

Step-by-step solution →

Chemistry — JEE Main 6 September 2020 Shift 1

Q21·ChemistrySingle correct
The correct statement with respect to dinitrogen is:
  1. (A)N2N_2N2​ is paramagnetic in nature
  2. (B)It can combine with dioxygen at 25∘25^\circ25∘ C.
  3. (C)Liquid dinitrogen is not used in cryosurgery
  4. (D)It can be used as an inert diluent for reactive chemicals

Correct answer: (D)

Step-by-step solution →
Q22·ChemistrySingle correct
The major product obtained from the following reaction is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q23·ChemistrySingle correct
A solution of two components containing n1n_1n1​ moles of the 1st1^{st}1st component and n2n^2n2 moles of the 2nd2^{nd}2nd component is prepared. M1M_1M1​ and M2M_2M2​ are the molecular weights of component 1 and 2 respectively. If d is the density of the solution in gmL−1gmL^{-1}gmL−1, C2C_2C2​ is the molarity and x2x_2x2​ is the mole fraction of the 2nd2^{nd}2nd component, then C2C_2C2​ can be expressed as:
  1. (A)C2=1000x2M1+x2(M2−M1)C_2 = \dfrac{1000x_2}{M_1+x_2(M_2-M_1)}C2​=M1​+x2​(M2​−M1​)1000x2​​
  2. (B)C2=dx2M2+x2(M2−M1)C_2 = \dfrac{dx_2}{M_2+x_2(M_2-M_1)}C2​=M2​+x2​(M2​−M1​)dx2​​
  3. (C)C2=1000dx2M1+x2(M2−M1)C_2 = \dfrac{1000dx_2}{M_1+x_2(M_2-M_1)}C2​=M1​+x2​(M2​−M1​)1000dx2​​
  4. (D)C2=dx1M2+x2(M2−M1)C_2 = \dfrac{dx_1}{M_2+x_2(M_2-M_1)}C2​=M2​+x2​(M2​−M1​)dx1​​

Correct answer: (C)

Step-by-step solution →
Q24·ChemistrySingle correct
The INCORRECT statement is:
  1. (A)bronze is an alloy of copper and tin
  2. (B)cast iron is used to manufacture wrought iron
  3. (C)german silver is an alloy of zinc, copper and nickel
  4. (D)brass is an alloy of copper and nickel.

Correct answer: (D)

Step-by-step solution →
Q25·ChemistrySingle correct
Consider the Assertion and Reason given below. Assertion (A): Ethene polymerized in the presence of Ziegler Natta Catalyst at high temperature and pressure is used to make buckets and dustbins. Reason (R): High density polymers are closely packed and are chemically inert. Choose the correct answer from the following:
  1. (A)(A) is correct but (R) is wrong
  2. (B)Both (A) and (R) are correct but (R) is not the correct explanation of (A)
  3. (C)Both (A) and (R) are correct and (R) is the correct explanation of (A)
  4. (D)(A) and (R) both are wrong.

Correct answer: (C)

Step-by-step solution →
Q26·ChemistrySingle correct
Arrange the following solutions in the decreasing order of pOH (1) 0.01 M HCl (2) 0.01 M NaOH (3) 0.01 M CH3COONaCH_3COONaCH3​COONa (4) 0.01 M NaCl
  1. (A)(1) > (3) > (4) > (2)
  2. (B)(1) > (4) > (3) > (2)
  3. (C)(2) > (3) > (4) > (1)
  4. (D)(2) > (4) > (3) > (1)

Correct answer: (B)

Step-by-step solution →
Q27·ChemistrySingle correct
Among the sulphates of alkaline earth metals, the solubilities of BeSO4BeSO_4BeSO4​ and MgSO4MgSO_4MgSO4​ in water, respectively, are:
  1. (A)poor and poor
  2. (B)high and poor
  3. (C)high and high
  4. (D)poor and high

Correct answer: (C)

Step-by-step solution →
Q28·ChemistrySingle correct
The major products of the following reaction are: CH3−CH(CH3)−CH(OSO2CH3)−CH3CH_3-CH(CH_3)-CH(OSO_2CH_3)-CH_3CH3​−CH(CH3​)−CH(OSO2​CH3​)−CH3​ →(i) KOtBu/Δ(ii) O3/H2O2\xrightarrow{(i)\ KO^tBu/\Delta\quad (ii)\ O_3/H_2O_2}(i) KOtBu/Δ(ii) O3​/H2​O2​​
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q29·ChemistrySingle correct
The major product of the following reaction is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q30·ChemistrySingle correct
The present of soluble fluoride ion upto 1 ppm concentration in drinking water, is:
  1. (A)harmful for teeth
  2. (B)harmful to skin
  3. (C)harmful to bones
  4. (D)safe for teeth

Correct answer: (D)

Step-by-step solution →
Q31·ChemistrySingle correct
The increasing order of pKbpK_bpKb​ values of the following compounds is:
  1. (A)II < IV < III < I
  2. (B)I < II < IV < III
  3. (C)II < I < III < IV
  4. (D)I < II < III < IV

Correct answer: (B)

Step-by-step solution →
Q32·ChemistrySingle correct
Which of the following compounds shows geometrical isomerism?
  1. (A)2 – methylpent 2 – ene
  2. (B)4 – methylpent 2 – ene
  3. (C)4 – methylpent – 1 – ene
  4. (D)2 – methylpent –1 – ene

Correct answer: (B)

Step-by-step solution →
Q33·ChemistrySingle correct
The set that contains atomic numbers of only transition elements, is
  1. (A)37, 42, 50, 64
  2. (B)21, 25, 42, 72
  3. (C)9, 17, 34, 38
  4. (D)21, 32, 53, 64

Correct answer: (B)

Step-by-step solution →
Q34·ChemistrySingle correct
The variation of equilibrium constant with temperature is given below: The value of ΔHo\Delta H^oΔHo, ΔGo\Delta G^oΔGo at T1T_1T1​ and ΔGo\Delta G^oΔGo at T2T_2T2​ (in kJ mol−1^{-1}−1) respectively, are close to [Use R=8.314JK−1mol−1R = 8.314 J K^{-1} mol^{-1}R=8.314JK−1mol−1]
TemperatureEquilibrium Constant
T1=25oCT_1 = 25^oCT1​=25oCK1=10K_1 = 10K1​=10
T2=100oCT_2 = 100^oCT2​=100oCK2=100K_2 = 100K2​=100
  1. (A)28.7, − 7.14 and − 5.71
  2. (B)0.64 − 7.14 and − 5.71
  3. (C)28.4, − 5.71 and − 14.29
  4. (D)0.64, − 5.71 and −14.29

Correct answer: (C)

Step-by-step solution →
Q35·ChemistrySingle correct
Kraft temperature is the temperature:
  1. (A)below which the aqueous solution of detergents starts freezing
  2. (B)below which the formation of micelles takes place
  3. (C)above which the aqueous solution of detergents starts boiling
  4. (D)above which the formation of micelles takes place.

Correct answer: (D)

Step-by-step solution →
Q36·ChemistrySingle correct
For the reaction Fe2N(s)+32H2(g)=2Fe(s)+NH3(g)Fe_2N(s) + \dfrac{3}{2}H_2(g) = 2Fe(s) + NH_3(g)Fe2​N(s)+23​H2​(g)=2Fe(s)+NH3​(g)
  1. (A)Kc=Kp(RT)K_c = K_p(RT)Kc​=Kp​(RT)
  2. (B)Kc=KP(RT)−1/2K_c = K_P(RT)^{-1/2}Kc​=KP​(RT)−1/2
  3. (C)Kc=KP(RT)1/2K_c = K_P(RT)^{1/2}Kc​=KP​(RT)1/2
  4. (D)Kc=KP(RT)3/2K_c = K_P(RT)^{3/2}Kc​=KP​(RT)3/2

Correct answer: (C)

Step-by-step solution →
Q37·ChemistrySingle correct
The species that has a spin – only magnetic moment of 5.9 BM, is: (TdT_dTd​ = tetrahedral)
  1. (A)[Ni(CN)4]2−[Ni(CN)_4]^{2-}[Ni(CN)4​]2− (square planar)
  2. (B)[NiCl4]2−(Td)[NiCl_4]^{2-}(T_d)[NiCl4​]2−(Td​)
  3. (C)Ni(CO)4(Td)Ni(CO)_4(T_d)Ni(CO)4​(Td​)
  4. (D)[MnBr4]2−(Td)[MnBr_4]^{2-}(T_d)[MnBr4​]2−(Td​)

Correct answer: (D)

Step-by-step solution →
Q38·ChemistrySingle correct
The lanthanoid that does NOT show +4 oxidation state is:
  1. (A)Dy
  2. (B)Ce
  3. (C)Eu
  4. (D)Tb

Correct answer: (C)

Step-by-step solution →
Q39·ChemistrySingle correct
Consider the following reactions A→P1;B→P2;C→P3;D→P4A \rightarrow P1; B \rightarrow P2; C \rightarrow P3; D \rightarrow P4A→P1;B→P2;C→P3;D→P4, The order of the above reactions are a, b, c and d, respectively. The following graph is obtained when log[rate] vs. log[conc.] are plotted: Among the following, the correct sequence for the order of the reactions is:
  1. (A)d > a > b > c
  2. (B)a > b > c > d
  3. (C)c > a > b > d
  4. (D)d > b > a > c

Correct answer: (D)

Step-by-step solution →
Q40·ChemistryNumerical
In an estimation of bromine by Carius method, 1.6 g of an organic compound gave 1.88 g of AgBr. The mass percentage of bromine in the compound is ______________ (Atomic mass, Ag = 108, Br = 80 g mol−1^{-1}−1)

Correct answer: 50

Step-by-step solution →
Q41·ChemistryNumerical
Potassium chlorate is prepared by the electrolysis of KCl in basic solution 6HO−+Cl−→ClO3−+3H2O+6e−6HO^- + Cl^- \rightarrow ClO_3^- + 3H_2O + 6e^-6HO−+Cl−→ClO3−​+3H2​O+6e− If only 60% of the current is utilized in the reaction, the time (rounded to the nearest hour) required to produce 10 g of KClO3KClO_3KClO3​ using a current of 2A is ________________. (Given : F = 96,500 C mol−1^{-1}−1; molar mass of KClO3KClO_3KClO3​ = 122 g mol−1^{-1}−1)

Correct answer: 11

Step-by-step solution →
Q42·ChemistryNumerical
The number of Cl = O bonds in perchloric acid is," ______________".

Correct answer: 3

Step-by-step solution →
Q43·ChemistryNumerical
The elevation of boiling point of 0.10 m aqueous CrCl3xNH3CrCl_3xNH_3CrCl3​xNH3​ solution is two times that of 0.05 m aqueous CaCl2CaCl_2CaCl2​ solution. The value of x is ______________ [Assume 100% ionisation of the complex and CaCl2CaCl_2CaCl2​, coordination number of Cr as 6, and that all NH3NH_3NH3​ molecules are present inside the coordination sphere]

Correct answer: 5

Step-by-step solution →
Q44·ChemistryNumerical
A spherical balloon of radius 3 cm containing helium gas has a pressure of 48×10−348\times10^{-3}48×10−3 bar. At the same temperature, the pressure, of a spherical balloon of radius 12 cm containing the same amount of gas will be ______________×10−6\times10^{-6}×10−6 bar.

Correct answer: 750

Step-by-step solution →

Mathematics — JEE Main 6 September 2020 Shift 1

Q45·MathematicsSingle correct
The area (in sq. units) of the region A={(x,y):∣x∣+∣y∣≤1, 2y2≥∣x∣}A = \{(x,y) : |x| + |y| \le 1,\ 2y^2 \ge |x|\}A={(x,y):∣x∣+∣y∣≤1, 2y2≥∣x∣} is:
  1. (A)13\dfrac{1}{3}31​
  2. (B)76\dfrac{7}{6}67​
  3. (C)16\dfrac{1}{6}61​
  4. (D)56\dfrac{5}{6}65​

Correct answer: (D)

Step-by-step solution →
Q46·MathematicsSingle correct
Let L1L_1L1​ be a tangent to the parabola y2=4(x+1)y^2 = 4(x+1)y2=4(x+1) and L2L_2L2​ be a tangent to the parabola y2=8(x+2)y^2 = 8(x+2)y2=8(x+2) such that L1L_1L1​ and L2L_2L2​ intersect at right angles. Then L1L_1L1​ and L2L_2L2​ meet on the straight line:
  1. (A)x+3=0x+3=0x+3=0
  2. (B)2x+1=02x+1=02x+1=0
  3. (C)x+2=0x+2=0x+2=0
  4. (D)x+2y=0x+2y=0x+2y=0

Correct answer: (A)

Step-by-step solution →
Q47·MathematicsSingle correct
If f(x+y)=f(x)f(y)f(x+y) = f(x)f(y)f(x+y)=f(x)f(y) and ∑x=1∞f(x)=2, x,y∈N\displaystyle\sum_{x=1}^{\infty} f(x) = 2,\ x, y \in Nx=1∑∞​f(x)=2, x,y∈N where N is the set of all natural numbers, then the value of f(4)f(2)\dfrac{f(4)}{f(2)}f(2)f(4)​ is:
  1. (A)23\dfrac{2}{3}32​
  2. (B)19\dfrac{1}{9}91​
  3. (C)13\dfrac{1}{3}31​
  4. (D)49\dfrac{4}{9}94​

Correct answer: (D)

Step-by-step solution →
Q48·MathematicsSingle correct
If I1=∫01(1−x50)100 dxI_1 = \displaystyle\int_0^1 (1-x^{50})^{100}\,dxI1​=∫01​(1−x50)100dx and I2=∫01(1−x50)101 dxI_2 = \displaystyle\int_0^1 (1-x^{50})^{101}\,dxI2​=∫01​(1−x50)101dx such that I2=αI1I_2 = \alpha I_1I2​=αI1​ then α\alphaα equals to:
  1. (A)50495050\dfrac{5049}{5050}50505049​
  2. (B)50505049\dfrac{5050}{5049}50495050​
  3. (C)50505051\dfrac{5050}{5051}50515050​
  4. (D)50515050\dfrac{5051}{5050}50505051​

Correct answer: (C)

Step-by-step solution →
Q49·MathematicsSingle correct
Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:
  1. (A)15101\dfrac{15}{101}10115​
  2. (B)5101\dfrac{5}{101}1015​
  3. (C)533\dfrac{5}{33}335​
  4. (D)1099\dfrac{10}{99}9910​

Correct answer: (C)

Step-by-step solution →
Q50·MathematicsSingle correct
A ray of light coming from the point (2,23)(2, 2\sqrt{3})(2,23​) is incident at an angle 30∘30^\circ30∘ on the line x=1x=1x=1 at the point A. The ray gets reflected on the line x=1x=1x=1 and meets xxx-axis at the point B. Then, the line AB passes through the point:
  1. (A)(3,−13)\left(3, -\dfrac{1}{\sqrt{3}}\right)(3,−3​1​)
  2. (B)(4,−32)\left(4, -\dfrac{\sqrt{3}}{2}\right)(4,−23​​)
  3. (C)(3,−3)\left(3, -\sqrt{3}\right)(3,−3​)
  4. (D)(4,−3)\left(4, -\sqrt{3}\right)(4,−3​)

Correct answer: (C)

Step-by-step solution →
Q51·MathematicsSingle correct
Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, x24+y22=1\dfrac{x^2}{4} + \dfrac{y^2}{2} = 14x2​+2y2​=1 from any of its foci?
  1. (A)(−2,3)(-2, \sqrt{3})(−2,3​)
  2. (B)(−1,2)(-1, \sqrt{2})(−1,2​)
  3. (C)(−1,3)(-1, \sqrt{3})(−1,3​)
  4. (D)(1,2)(1, 2)(1,2)

Correct answer: (C)

Step-by-step solution →
Q52·MathematicsSingle correct
The region represented by {z=x+iy∈C:∣z∣−Re(z)≤1}\{z = x+iy \in C : |z| - \mathrm{Re}(z) \le 1\}{z=x+iy∈C:∣z∣−Re(z)≤1} is also given by the inequality:
  1. (A)y2≥2(x+1)y^2 \ge 2(x+1)y2≥2(x+1)
  2. (B)y2≤2(x+12)y^2 \le 2\left(x+\dfrac{1}{2}\right)y2≤2(x+21​)
  3. (C)y2≤x+12y^2 \le x + \dfrac{1}{2}y2≤x+21​
  4. (D)y2≥x+1y^2 \ge x+1y2≥x+1

Correct answer: (B)

Step-by-step solution →
Q53·MathematicsSingle correct
The position of a moving car at time t is given by f(t)=at2+bt+c, t>0f(t) = at^2+bt+c,\ t>0f(t)=at2+bt+c, t>0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t1,t2][t_1, t_2][t1​,t2​] is attained at the point:
  1. (A)(t2−t1)2\dfrac{(t_2-t_1)}{2}2(t2​−t1​)​
  2. (B)a(t2−t1)+ba(t_2-t_1)+ba(t2​−t1​)+b
  3. (C)(t1+t2)2\dfrac{(t_1+t_2)}{2}2(t1​+t2​)​
  4. (D)2a(t1+t2)+b2a(t_1+t_2)+b2a(t1​+t2​)+b

Correct answer: (C)

Step-by-step solution →
Q54·MathematicsSingle correct
If ∑i=1n(xi−a)=n\displaystyle\sum_{i=1}^{n}(x_i-a) = ni=1∑n​(xi​−a)=n and ∑i=1n(xi−a)2=na, (n,a>1)\displaystyle\sum_{i=1}^{n}(x_i-a)^2 = na,\ (n,a>1)i=1∑n​(xi​−a)2=na, (n,a>1) then the standard deviation of n observations x1,x2,…,xnx_1, x_2, \ldots, x_nx1​,x2​,…,xn​ is:
  1. (A)a−1a-1a−1
  2. (B)na−1n\sqrt{a-1}na−1​
  3. (C)n(a−1)\sqrt{n(a-1)}n(a−1)​
  4. (D)a−1\sqrt{a-1}a−1​

Correct answer: (D)

Step-by-step solution →
Q55·MathematicsSingle correct
If {p} denotes the fractional part of the number p, then {32008}\left\{\dfrac{3^{200}}{8}\right\}{83200​}, is equal to
  1. (A)58\dfrac{5}{8}85​
  2. (B)78\dfrac{7}{8}87​
  3. (C)38\dfrac{3}{8}83​
  4. (D)18\dfrac{1}{8}81​

Correct answer: (D)

Step-by-step solution →
Q56·MathematicsSingle correct
The shortest distance between the lines x−10=y+1−1=z1\dfrac{x-1}{0}=\dfrac{y+1}{-1}=\dfrac{z}{1}0x−1​=−1y+1​=1z​ and x+y+z+1=0,2x−y+z+3=0x+y+z+1=0, 2x-y+z+3=0x+y+z+1=0,2x−y+z+3=0 is:
  1. (A)111
  2. (B)13\dfrac{1}{\sqrt{3}}3​1​
  3. (C)12\dfrac{1}{\sqrt{2}}2​1​
  4. (D)12\dfrac{1}{2}21​

Correct answer: (B)

Step-by-step solution →
Q57·MathematicsSingle correct
The negation of the Boolean expression p ∨ (~p ∧ q) is equivalent to:
  1. (A)p ∧ ~q
  2. (B)~p ∧ ~q
  3. (C)~p ∨ ~q
  4. (D)~p ∨ q

Correct answer: (B)

Step-by-step solution →
Q58·MathematicsSingle correct
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
  1. (A)2!3!4!2!3!4!2!3!4!
  2. (B)(3!)3.(4!)(3!)^{3}.(4!)(3!)3.(4!)
  3. (C)(3!)2.(4!)(3!)^{2}.(4!)(3!)2.(4!)
  4. (D)3!(4!)33!(4!)^{3}3!(4!)3

Correct answer: (B)

Step-by-step solution →
Q59·MathematicsSingle correct
Let m and M be respectively the minimum and maximum values of ∣cos⁡2x1+sin⁡2xsin⁡2x1+cos⁡2xsin⁡2xsin⁡2xcos⁡2xsin⁡2x1+sin⁡2x∣\begin{vmatrix}\cos^{2}x & 1+\sin^{2}x & \sin 2x\\ 1+\cos^{2}x & \sin^{2}x & \sin 2x\\ \cos^{2}x & \sin^{2}x & 1+\sin 2x\end{vmatrix}​cos2x1+cos2xcos2x​1+sin2xsin2xsin2x​sin2xsin2x1+sin2x​​. Then the ordered pair (m, M) is equal to:
  1. (A)(−3,3)(-3,3)(−3,3)
  2. (B)(−3,−1)(-3,-1)(−3,−1)
  3. (C)(−4,−1)(-4,-1)(−4,−1)
  4. (D)(1,3)(1,3)(1,3)

Correct answer: (B)

Step-by-step solution →
Q60·MathematicsSingle correct
Let a, b, c, d and p be any non zero distinct real numbers such that (a2+b2+c2)p2−2(ab+bc+cd)p+(b2+c2+d2)=0(a^{2}+b^{2}+c^{2})p^{2}-2(ab+bc+cd)p+(b^{2}+c^{2}+d^{2})=0(a2+b2+c2)p2−2(ab+bc+cd)p+(b2+c2+d2)=0. Then:
  1. (A)a, c, p are in A.P.
  2. (B)a, c, p are in G.P.
  3. (C)a, b, c, d are in G.P.
  4. (D)a, b, c, d are in A.P.

Correct answer: (C)

Step-by-step solution →
Q61·MathematicsSingle correct
The value of λ\lambdaλ and μ\muμ for which the system of linear equations x+y+z=2x+y+z=2x+y+z=2, x+2y+3z=5x+2y+3z=5x+2y+3z=5, x+3y+λz=μx+3y+\lambda z=\mux+3y+λz=μ has infinitely many solutions are, respectively:
  1. (A)6 and 8
  2. (B)5 and 7
  3. (C)5 and 8
  4. (D)4 and 9

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsNumerical
Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is ____.

Correct answer: 28

Step-by-step solution →
Q63·MathematicsNumerical
Let f:R→Rf:R\to Rf:R→R be defined as f(x)={x5sin⁡(1x)+5x2,x<00,x=0x5cos⁡(1x)+λx2,x>0f(x)=\begin{cases}x^{5}\sin\left(\dfrac{1}{x}\right)+5x^{2}, & x<0\\ 0, & x=0\\ x^{5}\cos\left(\dfrac{1}{x}\right)+\lambda x^{2}, & x>0\end{cases}f(x)=⎩⎨⎧​x5sin(x1​)+5x2,0,x5cos(x1​)+λx2,​x<0x=0x>0​. The value of λ\lambdaλ for which f′′(0)f''(0)f′′(0) exists, is ____.

Correct answer: 05

Step-by-step solution →
Q64·MathematicsNumerical
If a⃗\vec{a}a and b⃗\vec{b}b are unit vectors, then the greatest value of 3∣a⃗+b⃗∣+∣a⃗−b⃗∣\sqrt{3}\left|\vec{a}+\vec{b}\right|+\left|\vec{a}-\vec{b}\right|3​​a+b​+​a−b​ is ____.

Correct answer: 04

Step-by-step solution →
Q65·MathematicsNumerical
Let AD and BC be two vertical poles at A and b respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters) of a point M on AB from the point A such that MD2+MC2MD^{2}+MC^{2}MD2+MC2 is minimum is ____.

Correct answer: 05

Step-by-step solution →
Q66·MathematicsNumerical
The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45∘45^{\circ}45∘. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of 30∘30^{\circ}30∘ to the horizontal plane, the angle of elevation of the top of the hill becomes 75∘75^{\circ}75∘. Then the height of the hill (in metres) is ____.

Correct answer: 80

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.

  • 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
  • Probability 176/186
  • Permutations and Combinations 162/186
  • Magnetic Field of Current 147/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Chemical Bonding and Molecular Structure 151/186
  • Application of Derivatives 139/186
  • d- and f-Block Elements 126/186
  • 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
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Dual Nature of Matter and Radiation 155/186
  • Amines 133/186
  • Work, Energy and Power 132/186
  • 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
  • Nuclei 116/186
  • Straight Lines 114/186
  • Waves 109/186
  • Parabola 101/186
  • Statistics 118/186
  • Ellipse 103/186
  • Differentiability 91/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Environmental Chemistry 83/186
  • Experimental Skills 68/186
  • Polymers 64/186
  • States of Matter: Gases and Liquids 52/186
  • Isomerism 51/186
  • Reaction Mechanism 29/186
  • Mathematical Reasoning 26/186
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