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JEE Main 12 January 2019 Shift 2 Question Paper with Answers

12 January 2019 · January session · 85 questions

85 of the 90 questions from the JEE Main 12 January 2019 Shift 2 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

5 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
27
Chemistry
30
Mathematics
28

Physics — JEE Main 12 January 2019 Shift 2

Q1·PhysicsSingle correct
The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I(x)'. Which one of the graphs represents the variation of I(x) with x correctly?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q2·PhysicsSingle correct
A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is:
  1. (A)3.0 mm
  2. (B)4.0 mm
  3. (C)5.0 mm
  4. (D)zero

Correct answer: (A)

Step-by-step solution →
Q3·PhysicsSingle correct
An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is 6×10−86\times10^{-8}6×10−8s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to :
  1. (A)2×10−72\times10^{-7}2×10−7s
  2. (B)4×10−84\times10^{-8}4×10−8s
  3. (C)0.5×10−80.5\times10^{-8}0.5×10−8s
  4. (D)3×10−63\times10^{-6}3×10−6s

Correct answer: (B)

Step-by-step solution →
Q4·PhysicsSingle correct
In the figure, given that VBB_{BB}BB​ supply can vary from 0 to 5.0 V, VCC_{CC}CC​ = 5 V, βdc\beta_{dc}βdc​ = 200, RB_BB​ = 100, kΩ\OmegaΩ, RC_CC​ = 1 kΩ\OmegaΩ an VBE_{BE}BE​ = 1.0 V, The minimum base current and the input voltage at which the transistor will go to saturation, will be respectively :
  1. (A)25 μA and 3.5 V
  2. (B)20 μA and 3.5 V
  3. (C)25 μA and 2.8 V
  4. (D)20 μA and 2.8 V

Correct answer: (A)

Step-by-step solution →
Q5·PhysicsSingle correct
In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μF. All values in the circuit are in μF.
  1. (A)711\frac{7}{11}117​ μF
  2. (B)65\frac{6}{5}56​ μF
  3. (C)4 μF
  4. (D)710\frac{7}{10}107​ μF

Correct answer: (A)

Step-by-step solution →
Q6·PhysicsSingle correct
An alpha-particle of mass m suffers 1-deminsional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is :
  1. (A)2 m
  2. (B)3.5 m
  3. (C)1.5 m
  4. (D)4 m

Correct answer: (D)

Step-by-step solution →
Q7·PhysicsSingle correct
A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms−1^{-1}−1, at right angles to the horizontal component of the earth's magnetic field, of 0.3×10−40.3\times10^{-4}0.3×10−4 Wb/m2^{2}2. The value of the induced emf in wire is :
  1. (A)1.5×10−31.5\times10^{-3}1.5×10−3 V
  2. (B)1.1×10−31.1\times10^{-3}1.1×10−3 V
  3. (C)2.5×10−32.5\times10^{-3}2.5×10−3 V
  4. (D)0.3×10−30.3\times10^{-3}0.3×10−3 V

Correct answer: (B)

Step-by-step solution →
Q8·PhysicsSingle correct
To double the covering range of a TV transition tower, its height should be multiplied by :
  1. (A)12\frac{1}{\sqrt{2}}2​1​
  2. (B)2
  3. (C)4
  4. (D)2\sqrt{2}2​

Correct answer: (C)

Step-by-step solution →
Q9·PhysicsSingle correct
A plano-convex lens (focal length f2_22​, refractive index μ2\mu_2μ2​, radius of curvature R) fits exactly into a plano-concave lens (focal length f1_11​, refractive index μ1\mu_1μ1​, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :
  1. (A)f1_11​ − f2_22​
  2. (B)Rμ2−μ1\frac{R}{\mu_2-\mu_1}μ2​−μ1​R​
  3. (C)2f1f2f1+f2\frac{2f_1f_2}{f_1+f_2}f1​+f2​2f1​f2​​
  4. (D)f1_11​ + f2_22​

Correct answer: (B)

Step-by-step solution →
Q10·PhysicsSingle correct
A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder .The length of the cylinder above the piston is l1_11​, and that below the piston is l2_22​, such that l1_11​ > l2_22​. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by: (R is universal gas constant and g is the acceleration due to gravity)
  1. (A)RTng[l1−3l2l1l2]\frac{RT}{ng}\left[\frac{l_1-3l_2}{l_1l_2}\right]ngRT​[l1​l2​l1​−3l2​​]
  2. (B)RTg[2l1+l2l1l2]\frac{RT}{g}\left[\frac{2l_1+l_2}{l_1l_2}\right]gRT​[l1​l2​2l1​+l2​​]
  3. (C)nRTng[1l2+1l1]\frac{nRT}{ng}\left[\frac{1}{l_2}+\frac{1}{l_1}\right]ngnRT​[l2​1​+l1​1​]
  4. (D)nRTg[l1−l2l1l2]\frac{nRT}{g}\left[\frac{l_1-l_2}{l_1l_2}\right]gnRT​[l1​l2​l1​−l2​​]

Correct answer: (D)

Step-by-step solution →
Q11·PhysicsSingle correct
Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA_AA​/TB_BB​, is :
  1. (A)12\frac{1}{2}21​
  2. (B)1
  3. (C)2
  4. (D)12\sqrt{\frac{1}{2}}21​​

Correct answer: (B)

Step-by-step solution →
Q12·PhysicsSingle correct
A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :
  1. (A)2.0
  2. (B)0.1
  3. (C)0.4
  4. (D)1.2

Correct answer: (A)

Step-by-step solution →
Q13·PhysicsSingle correct
A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is : [Take g = 10 m/s2^{2}2]
  1. (A)32\frac{\sqrt{3}}{2}23​​
  2. (B)34\frac{\sqrt{3}}{4}43​​
  3. (C)12\frac{1}{2}21​
  4. (D)23\frac{2}{3}32​

Correct answer: (A)

Step-by-step solution →
Q14·PhysicsSingle correct
In a Frank-hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to :
  1. (A)1700 nm
  2. (B)2020 nm
  3. (C)220 nm
  4. (D)250 nm

Correct answer: (D)

Step-by-step solution →
Q15·PhysicsSingle correct
A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be : [Take g = 10 m/s2^{2}2]
  1. (A)2 kg-m2^{2}2/s
  2. (B)8 kg-m2^{2}2/s
  3. (C)6 kg-m2^{2}2/s
  4. (D)3 kg-m2^{2}2/s

Correct answer: (C)

Step-by-step solution →
Q16·PhysicsSingle correct
A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4×10−44 \times 10^{-4}4×10−4 A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of :
  1. (A)250 ohm
  2. (B)200 ohm
  3. (C)6200 ohm
  4. (D)6250 ohm

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
In the given circuit diagram, the currents, I1_{1}1​ = −0.3 A, I4_{4}4​ = 0.8 A and I5_{5}5​ = 0.4 A, are flowing as shown. The currents I2_{2}2​, I3_{3}3​ and I6_{6}6​, respectively are :
  1. (A)1.1 A, −0.4 A, 0.4 A
  2. (B)1.1 A, 0.4 A, 0.4 A
  3. (C)0.4 A, 1.1 A, 0.4 A
  4. (D)−0.4 A, 0.4 A, 1.1 A

Correct answer: (B)

Step-by-step solution →
Q18·PhysicsSingle correct
A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to :
  1. (A)322 ms−1^{-1}−1
  2. (B)341 ms−1^{-1}−1
  3. (C)335 ms−1^{-1}−1
  4. (D)328 ms−1^{-1}−1

Correct answer: (D)

Step-by-step solution →
Q19·PhysicsSingle correct
A paramagnetic material has 102810^{28}1028 atoms/m3^{3}3. Its magnetic susceptibility at temperature 350 K is 2.8×10−42.8 \times 10^{-4}2.8×10−4. Its susceptibility at 300 K is :
  1. (A)3.267×10−43.267 \times 10^{-4}3.267×10−4
  2. (B)3.672×10−43.672 \times 10^{-4}3.672×10−4
  3. (C)3.726×10−43.726 \times 10^{-4}3.726×10−4
  4. (D)2.672×10−42.672 \times 10^{-4}2.672×10−4

Correct answer: (A)

Step-by-step solution →
Q20·PhysicsSingle correct
In a radioactive decay chain, the initial nucleus is 90232Th_{90}^{232}\text{Th}90232​Th. At the end there are 6 α-particles and 4 β-particles with are emitted. If the end nucleus is ZAX_{Z}^{A}XZA​X, A and Z are given by :
  1. (A)A = 208; Z = 80
  2. (B)A = 202; Z = 80
  3. (C)A = 208; Z = 82
  4. (D)A = 200; Z = 81

Correct answer: (C)

Step-by-step solution →
Q21·PhysicsSingle correct
Formation of real image using a biconvex lens is shown below : If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?
  1. (A)Image disappears
  2. (B)Magnified image
  3. (C)Erect real image
  4. (D)No change

Correct answer: (A)

Step-by-step solution →
Q22·PhysicsSingle correct
When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photo current is −V0_{0}0​/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is −V0_{0}0​. The threshold frequency for photoelectric emission is :
  1. (A)5v3\frac{5v}{3}35v​
  2. (B)43v\frac{4}{3}v34​v
  3. (C)2 v
  4. (D)3v2\frac{3v}{2}23v​

Correct answer: (D)

Step-by-step solution →
Q23·PhysicsSingle correct
A simple harmonic motion is represented by : y=5(sin⁡3πt+3cos⁡3πt)y = 5(\sin 3\pi t + \sqrt{3} \cos 3\pi t)y=5(sin3πt+3​cos3πt) cm The amplitude and time period of the motion are :
  1. (A)10 cm, 23\frac{2}{3}32​ s
  2. (B)10 cm, 32\frac{3}{2}23​ s
  3. (C)5 cm, 32\frac{3}{2}23​ s
  4. (D)5 cm, 23\frac{2}{3}32​ s

Correct answer: (A)

Step-by-step solution →
Q24·PhysicsSingle correct
Two particles A, B are moving on two concentric circles of radii R1_{1}1​ and R2_{2}2​ with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure : The relative velocity v⃗A−v⃗B\vec{v}_{A} - \vec{v}_{B}vA​−vB​ at t=π2ωt = \frac{\pi}{2\omega}t=2ωπ​ is given by :
  1. (A)ω(R1+R2)i^\omega(R_{1} + R_{2})\hat{i}ω(R1​+R2​)i^
  2. (B)−ω(R1+R2)i^-\omega(R_{1} + R_{2})\hat{i}−ω(R1​+R2​)i^
  3. (C)ω(R2−R1)i^\omega(R_{2} - R_{1})\hat{i}ω(R2​−R1​)i^
  4. (D)ω(R1−R2)i^\omega(R_{1} - R_{2})\hat{i}ω(R1​−R2​)i^

Correct answer: (C)

Step-by-step solution →
Q25·PhysicsSingle correct
The mean intensity of radiation on the surface of the Sun is about 10810^{8}108 W/m2^{2}2. The rms value of the corresponding magnetic field is closet to :
  1. (A)1 T
  2. (B)10210^{2}102 T
  3. (C)10−210^{-2}10−2 T
  4. (D)10−410^{-4}10−4 T

Correct answer: (D)

Step-by-step solution →
Q26·PhysicsSingle correct
A parallel plate capacitor with plates of area 1 m2^{2}2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is:
  1. (A)7.85×10−107.85 \times 10^{-10}7.85×10−10 C
  2. (B)6.85×10−106.85 \times 10^{-10}6.85×10−10 C
  3. (C)8.85×10−108.85 \times 10^{-10}8.85×10−10 C
  4. (D)9.85×10−109.85 \times 10^{-10}9.85×10−10 C

Correct answer: (C)

Step-by-step solution →
Q27·PhysicsSingle correct
The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure : What is the value of current at t = 4 s?
  1. (A)zero
  2. (B)3 μA
  3. (C)2 μA
  4. (D)1.5 μA

Correct answer: (A)

Step-by-step solution →

Chemistry — JEE Main 12 January 2019 Shift 2

Q28·ChemistrySingle correct
8 g of NaOH is dissolved in 18 g of H2_{2}2​O. Mole fraction of NaOH in solution and molality (in mol kg−1^{-1}−1) of the solution respectively are :
  1. (A)0.2, 22.20
  2. (B)0.2, 11.11
  3. (C)0.167, 11.11
  4. (D)0.167, 22.20

Correct answer: (C)

Step-by-step solution →
Q29·ChemistrySingle correct
The magnetic moment of an octahedral homoleptic Mn(II) complex is 5.9 BM. The suitable ligand for this complex is :
  1. (A)ethylenediamine
  2. (B)CN−^{-}−
  3. (C)NCS−^{-}−
  4. (D)CO

Correct answer: (C)

Step-by-step solution →
Q30·ChemistrySingle correct
The element that does NOT show catenation is :
  1. (A)Ge
  2. (B)Si
  3. (C)Sn
  4. (D)Pb

Correct answer: (D)

Step-by-step solution →
Q31·ChemistrySingle correct
Among the following, the false statement is :
  1. (A)It is possible to cause artificial rain by throwing electrified sand carrying charge opposite to the one on clouds from an aeroplane.
  2. (B)Tyndall effect can be used to distinguish between a colloidal solution and a true solution.
  3. (C)Lyophilic sol can be coagulated by adding an electrolyte.
  4. (D)Latex is a colloidal solution of rubber particles which are positively charged.

Correct answer: (D)

Step-by-step solution →
Q32·ChemistrySingle correct
The correct structure of histidine in a strongly acidic solution (pH = 2) is :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q33·ChemistrySingle correct
The major product of the following reaction is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q34·ChemistrySingle correct
∧m∘\wedge^{\circ}_{m}∧m∘​ for NaCl, HCl and NaA are 126.4, 425.9 and 100.5 S cm2^{2}2mol−1^{-1}−1, respectively. If the conductivity of 0.001 M HA is 5×10−55\times10^{-5}5×10−5 S cm−1^{-1}−1, degree of dissociation of HA is :
  1. (A)0.50
  2. (B)0.25
  3. (C)0.125
  4. (D)0.75

Correct answer: (C)

Step-by-step solution →
Q35·ChemistrySingle correct
Molecules of benzoic acid (C6_{6}6​H5_{5}5​COOH) dimerise in benzene. 'w' g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is : (Given that Kf_{f}f​ = 5 K kg mol−1^{-1}−1, Molar mass of benzoic acid = 122 g mol−1^{-1}−1)
  1. (A)2.4 g
  2. (B)1.0 g
  3. (C)1.5 g
  4. (D)1.8 g

Correct answer: (A)

Step-by-step solution →
Q36·ChemistrySingle correct
Chlorine on reaction with hot and concentrated sodium hydroxide gives :
  1. (A)Cl−^{-}− and ClO3−_{3}^{-}3−​
  2. (B)Cl−^{-}− and ClO−^{-}−
  3. (C)ClO3−_{3}^{-}3−​ and ClO2−_{2}^{-}2−​
  4. (D)Cl−^{-}− and ClO2−_{2}^{-}2−​

Correct answer: (A)

Step-by-step solution →
Q37·ChemistrySingle correct
The major product of the following reaction is :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q38·ChemistrySingle correct
The combination of plots which do not represent isothermal expansion of an ideal gas is:
  1. (A)(b) and (d)
  2. (B)(a) and (c)
  3. (C)(b) and (c)
  4. (D)(a) and (d)

Correct answer: (A)

Step-by-step solution →
Q39·ChemistrySingle correct
The major product in the following conversion is :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q40·ChemistrySingle correct
The major product of the following reaction is :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q41·ChemistrySingle correct
The correct order of atomic radii is :
  1. (A)Nd > Ce > Eu > Ho
  2. (B)Ho > Nd > Eu > Ce
  3. (C)Ce > Eu > Ho > Nd
  4. (D)Eu > Ce > Nd > Ho

Correct answer: (D)

Step-by-step solution →
Q42·ChemistrySingle correct
The element that shows greater ability to form pπ\piπ-pπ\piπ multiple bonds, is:
  1. (A)Sn
  2. (B)C
  3. (C)Ge
  4. (D)Si

Correct answer: (B)

Step-by-step solution →
Q43·ChemistrySingle correct
The two monomers for the synthesis of Nylon 6, 6 are :
  1. (A)HOOC(CH2)4COOH, H2N(CH2)6NH2
  2. (B)HOOC(CH2)6COOH, H2N(CH2)6NH2
  3. (C)HOOC(CH2)4COOH, H2N(CH2)4NH2
  4. (D)HOOC(CH2)6COOH, H2N(CH2)4NH2

Correct answer: (A)

Step-by-step solution →
Q44·ChemistrySingle correct
The aldehydes which will not form Grignard product with one equivalent Grignard reagents are:
  1. (A)(b), (d)
  2. (B)(b), (c)
  3. (C)(b), (c), (d)
  4. (D)(c), (d)

Correct answer: (A)

Step-by-step solution →
Q45·ChemistrySingle correct
Given : (i) C(graphite)+O2(g)→CO2(g)C(graphite) + O_2(g) \rightarrow CO_2(g)C(graphite)+O2​(g)→CO2​(g); ΔrH°=x\Delta rH° = xΔrH°=x kJ mol−1^{-1}−1 (ii) C(graphite)+12O2(g)→CO(g)C(graphite) + \frac{1}{2}O_2(g) \rightarrow CO(g)C(graphite)+21​O2​(g)→CO(g); ΔrH°=y\Delta rH° = yΔrH°=y kJ mol−1^{-1}−1 (iii) CO(g)+12O2(g)→CO2(g)CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g)CO(g)+21​O2​(g)→CO2​(g); ΔrH°=z\Delta rH° = zΔrH°=z kJ mol−1^{-1}−1 Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?
  1. (A)x=y+zx = y + zx=y+z
  2. (B)z=x+yz = x + yz=x+y
  3. (C)y=2z−xy = 2z - xy=2z−x
  4. (D)x=y−zx = y - zx=y−z

Correct answer: (A)

Step-by-step solution →
Q46·ChemistrySingle correct
The volume strength of 1M H2O2H_2O_2H2​O2​ is : (Molar mass of H2O2H_2O_2H2​O2​ = 34 g mol−1^{-1}−1)
  1. (A)5.6
  2. (B)16.8
  3. (C)11.35
  4. (D)22.4

Correct answer: (C)

Step-by-step solution →
Q47·ChemistrySingle correct
The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are : I. They activate many enzymes II. They participate in the oxidation of glucose to produce ATP III. Along with sodium ions, they are responsible for the transmission of nerve signals
  1. (A)I and II only
  2. (B)I and III only
  3. (C)I, II and III
  4. (D)III only

Correct answer: (C)

Step-by-step solution →
Q48·ChemistrySingle correct
The compound that is NOT a common component of photochemical smog is :
  1. (A)O3
  2. (B)H3C-C(=O)-OONO2
  3. (C)CH2=CHCHO
  4. (D)CF2Cl2

Correct answer: (D)

Step-by-step solution →
Q49·ChemistrySingle correct
For a certain reaction consider the plot of ℓnk versus 1/T given in the figure. If the rate constant of this reaction at 400 K is 10−510^{-5}10−5 s−1^{-1}−1, then the rate constant at 500 K is:
  1. (A)10−610^{-6}10−6 s−1^{-1}−1
  2. (B)2×10−42\times10^{-4}2×10−4 s−1^{-1}−1
  3. (C)10−410^{-4}10−4 s−1^{-1}−1
  4. (D)4×10−44\times10^{-4}4×10−4 s−1^{-1}−1

Correct answer: (C)

Step-by-step solution →
Q50·ChemistrySingle correct
An open vessel at 27°C is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is :
  1. (A)500°C
  2. (B)500 K
  3. (C)750°C
  4. (D)750 K

Correct answer: (B)

Step-by-step solution →
Q51·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 →
Q52·ChemistrySingle correct
The increasing order of the reactivity of the following with LiAlH4 is :
  1. (A)(b) < (a) < (c) < (d)
  2. (B)(b) < (a) < (d) < (c)
  3. (C)(a) < (b) < (d) < (c)
  4. (D)(a) < (b) < (c) < (d)

Correct answer: (C)

Step-by-step solution →
Q53·ChemistrySingle correct
The pair that does NOT require calcination is :
  1. (A)ZnO and MgO
  2. (B)ZnO and Fe2O3·xH2O
  3. (C)ZnCO3 and CaO
  4. (D)Fe2O3 and CaCO3·MgCO3

Correct answer: (A)

Step-by-step solution →
Q54·ChemistrySingle correct
The major product of the following reaction is :
  1. (A)CH3CH=C=CH2CH_3CH=C=CH_2CH3​CH=C=CH2​
  2. (B)CH3CH2CH(NH2)CH2NH2CH_3CH_2CH(NH_2)CH_2NH_2CH3​CH2​CH(NH2​)CH2​NH2​
  3. (C)CH3CH=CHCH2NH2CH_3CH=CHCH_2NH_2CH3​CH=CHCH2​NH2​
  4. (D)CH3CH2C≡CHCH_3CH_2C\equiv CHCH3​CH2​C≡CH

Correct answer: (D)

Step-by-step solution →
Q55·ChemistrySingle correct
If Ksp of Ag2CO3 is 8×10−128\times10^{-12}8×10−12, the molar solubility of Ag2CO3 in 0.1 M AgNO3 is :
  1. (A)8×10−128\times10^{-12}8×10−12 M
  2. (B)8×10−118\times10^{-11}8×10−11 M
  3. (C)8×10−108\times10^{-10}8×10−10 M
  4. (D)8×10−138\times10^{-13}8×10−13 M

Correct answer: (C)

Step-by-step solution →
Q56·ChemistrySingle correct
The upper stratosphere consisting of the ozone layer protects us from the sun's radiation that falls in the wavelength region of :
  1. (A)200 - 315 nm
  2. (B)400 - 550 nm
  3. (C)0.8 - 1.5 nm
  4. (D)600 - 750 nm

Correct answer: (A)

Step-by-step solution →
Q57·ChemistrySingle correct
If the de Brogile wavelength of the electron in nth^{th}th Bohr orbit in a hydrogenic atom is equal to 1.5πa01.5\pi a_01.5πa0​ (a0a_0a0​ is Bohr radius), then the value of n/z is :
  1. (A)0.40
  2. (B)1.50
  3. (C)1.0
  4. (D)0.75

Correct answer: (D)

Step-by-step solution →

Mathematics — JEE Main 12 January 2019 Shift 2

Q58·MathematicsSingle correct
lim⁡x→1−π−2sin⁡−1x1−x\lim_{x\to 1^{-}} \dfrac{\sqrt{\pi} - \sqrt{2\sin^{-1} x}}{\sqrt{1-x}}limx→1−​1−x​π​−2sin−1x​​ is equal to :
  1. (A)12π\dfrac{1}{\sqrt{2\pi}}2π​1​
  2. (B)2π\sqrt{\dfrac{2}{\pi}}π2​​
  3. (C)π2\sqrt{\dfrac{\pi}{2}}2π​​
  4. (D)π\sqrt{\pi}π​

Correct answer: (B)

Step-by-step solution →
Q59·MathematicsSingle correct
Let f be a differentiable function such that f(1) = 2 and f'(x) = f(x) for all x∈R. If h(x) = f(f(x)), then h'(1) is equal to :
  1. (A)2e22e^{2}2e2
  2. (B)4e4e4e
  3. (C)2e2e2e
  4. (D)4e24e^{2}4e2

Correct answer: (B)

Step-by-step solution →
Q60·MathematicsSingle correct
The integral ∫1e{(xe)2x−(ex)x}log⁡ex dx\displaystyle\int_{1}^{e} \left\{ \left(\dfrac{x}{e}\right)^{2x} - \left(\dfrac{e}{x}\right)^{x} \right\} \log_{e} x \, dx∫1e​{(ex​)2x−(xe​)x}loge​xdx is equal to :
  1. (A)12−e−1e2\dfrac{1}{2} - e - \dfrac{1}{e^{2}}21​−e−e21​
  2. (B)−12+1e−12e2-\dfrac{1}{2} + \dfrac{1}{e} - \dfrac{1}{2e^{2}}−21​+e1​−2e21​
  3. (C)32−1e−12e2\dfrac{3}{2} - \dfrac{1}{e} - \dfrac{1}{2e^{2}}23​−e1​−2e21​
  4. (D)32−e−12e2\dfrac{3}{2} - e - \dfrac{1}{2e^{2}}23​−e−2e21​

Correct answer: (D)

Step-by-step solution →
Q61·MathematicsSingle correct
Let a⃗\vec{a}a, b⃗\vec{b}b, and c⃗\vec{c}c be three unit vectors, out of which vectors b⃗\vec{b}b and c⃗\vec{c}c are non-parallel. If α and β are the angles which vector a⃗\vec{a}a makes with vectors b⃗\vec{b}b and c⃗\vec{c}c respectively and a⃗×(b⃗×c⃗)=12b⃗\vec{a} \times (\vec{b} \times \vec{c}) = \dfrac{1}{2}\vec{b}a×(b×c)=21​b, then |α − β| is equal to :
  1. (A)30°30°30°
  2. (B)90°90°90°
  3. (C)60°60°60°
  4. (D)45°45°45°

Correct answer: (A)

Step-by-step solution →
Q62·MathematicsSingle correct
The integral ∫3x13+2x11(2x4+3x2+1)4 dx\displaystyle\int \dfrac{3x^{13} + 2x^{11}}{\left(2x^{4} + 3x^{2} + 1\right)^{4}} \, dx∫(2x4+3x2+1)43x13+2x11​dx is equal to (where C is a constant of integration)
  1. (A)x46(2x4+3x2+1)3+C\dfrac{x^{4}}{6\left(2x^{4}+3x^{2}+1\right)^{3}} + C6(2x4+3x2+1)3x4​+C
  2. (B)x126(2x4+3x2+1)3+C\dfrac{x^{12}}{6\left(2x^{4}+3x^{2}+1\right)^{3}} + C6(2x4+3x2+1)3x12​+C
  3. (C)x4(2x4+3x2+1)3+C\dfrac{x^{4}}{\left(2x^{4}+3x^{2}+1\right)^{3}} + C(2x4+3x2+1)3x4​+C
  4. (D)x12(2x4+3x2+1)3+C\dfrac{x^{12}}{\left(2x^{4}+3x^{2}+1\right)^{3}} + C(2x4+3x2+1)3x12​+C

Correct answer: (B)

Step-by-step solution →
Q63·MathematicsSingle correct
If a curve passes through the point (1, −2) and has slope of the tangent at any point (x, y) on it as x2−2yx\dfrac{x^{2} - 2y}{x}xx2−2y​, then the curve also passes through the point :
  1. (A)(3,0)(3, 0)(3,0)
  2. (B)(3,0)(\sqrt{3}, 0)(3​,0)
  3. (C)(−1,2)(-1, 2)(−1,2)
  4. (D)(−2,1)(-\sqrt{2}, 1)(−2​,1)

Correct answer: (B)

Step-by-step solution →
Q64·MathematicsSingle correct
If an angle between the line, x+12=y−21=z−3−2\dfrac{x+1}{2} = \dfrac{y-2}{1} = \dfrac{z-3}{-2}2x+1​=1y−2​=−2z−3​ and the plane, x − 2y − kz = 3 is cos⁡−1(223)\cos^{-1}\left(\dfrac{2\sqrt{2}}{3}\right)cos−1(322​​), then a value of k is :
  1. (A)53\sqrt{\dfrac{5}{3}}35​​
  2. (B)35\sqrt{\dfrac{3}{5}}53​​
  3. (C)−35-\dfrac{3}{5}−53​
  4. (D)−53-\dfrac{5}{3}−35​

Correct answer: (A)

Step-by-step solution →
Q65·MathematicsSingle correct
lim⁡x→∞(nn2+12+nn2+22+nn2+32+…+15n)\lim_{x\to\infty} \left( \dfrac{n}{n^{2}+1^{2}} + \dfrac{n}{n^{2}+2^{2}} + \dfrac{n}{n^{2}+3^{2}} + \ldots + \dfrac{1}{5n} \right)limx→∞​(n2+12n​+n2+22n​+n2+32n​+…+5n1​) is equal to
  1. (A)π4\dfrac{\pi}{4}4π​
  2. (B)tan⁡−1(3)\tan^{-1}(3)tan−1(3)
  3. (C)π2\dfrac{\pi}{2}2π​
  4. (D)tan⁡−1(2)\tan^{-1}(2)tan−1(2)

Correct answer: (D)

Step-by-step solution →
Q66·MathematicsSingle correct
In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :
  1. (A)4009\dfrac{400}{9}9400​ loss
  2. (B)000
  3. (C)4003\dfrac{400}{3}3400​ gain
  4. (D)4003\dfrac{400}{3}3400​ loss

Correct answer: (B)

Step-by-step solution →
Q67·MathematicsSingle correct
If a straight line passing through the point P(−3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :
  1. (A)3x−4y+25=03x - 4y + 25 = 03x−4y+25=0
  2. (B)4x−3y+24=04x - 3y + 24 = 04x−3y+24=0
  3. (C)x−y+7=0x - y + 7 = 0x−y+7=0
  4. (D)4x+3y=04x + 3y = 04x+3y=0

Correct answer: (B)

Step-by-step solution →
Q68·MathematicsSingle correct
There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is :
  1. (A)121212
  2. (B)111111
  3. (C)999
  4. (D)777

Correct answer: (A)

Step-by-step solution →
Q69·MathematicsSingle correct
The tangent to the curve y=x2−5x+5y = x^{2} - 5x + 5y=x2−5x+5, parallel to the line 2y=4x+12y = 4x + 12y=4x+1, also passes through the point :
  1. (A)(72,14)\left(\dfrac{7}{2}, \dfrac{1}{4}\right)(27​,41​)
  2. (B)(18,−7)\left(\dfrac{1}{8}, -7\right)(81​,−7)
  3. (C)(−18,7)\left(-\dfrac{1}{8}, 7\right)(−81​,7)
  4. (D)(14,72)\left(\dfrac{1}{4}, \dfrac{7}{2}\right)(41​,27​)

Correct answer: (B)

Step-by-step solution →
Q70·MathematicsSingle correct
Let S be the set of all real values of λ such that a plane passing through the points (−λ2,1,1)(-\lambda^{2}, 1, 1)(−λ2,1,1), (1,−λ2,1)(1, -\lambda^{2}, 1)(1,−λ2,1) and (1,1,−λ2)(1, 1, -\lambda^{2})(1,1,−λ2) also passes through the point (−1, −1, 1). Then S is equal to:
  1. (A){3}\{\sqrt{3}\}{3​}
  2. (B){3,−3}\{\sqrt{3}, -\sqrt{3}\}{3​,−3​}
  3. (C){1,−1}\{1, -1\}{1,−1}
  4. (D){3,−3}\{3, -3\}{3,−3}

Correct answer: (B)

Step-by-step solution →
Q71·MathematicsSingle correct
Let z1z_{1}z1​ and z2z_{2}z2​ be two complex numbers satisfying ∣z1∣=9|z_{1}| = 9∣z1​∣=9 and ∣z2−3−4i∣=4|z_{2} - 3 - 4i| = 4∣z2​−3−4i∣=4. Then the minimum value of ∣z1−z2∣|z_{1} - z_{2}|∣z1​−z2​∣ is :
  1. (A)000
  2. (B)2\sqrt{2}2​
  3. (C)111
  4. (D)222

Correct answer: (A)

Step-by-step solution →
Q72·MathematicsSingle correct
The total number or irrational terms in the binomial expansion of (71/5−31/10)60\left(7^{1/5} - 3^{1/10}\right)^{60}(71/5−31/10)60 is :
  1. (A)55
  2. (B)49
  3. (C)48
  4. (D)54

Correct answer: (D)

Step-by-step solution →
Q73·MathematicsSingle correct
The equation of a tangent to the parabola, x2=8yx^{2} = 8yx2=8y, which makes an angle θ\thetaθ with the positive direction of x-axis, is :
  1. (A)y=xtan⁡θ+2cot⁡θy = x\tan\theta + 2\cot\thetay=xtanθ+2cotθ
  2. (B)y=xtan⁡θ−2cot⁡θy = x\tan\theta - 2\cot\thetay=xtanθ−2cotθ
  3. (C)x=ycot⁡θ+2tan⁡θx = y\cot\theta + 2\tan\thetax=ycotθ+2tanθ
  4. (D)x=ycot⁡θ−2tan⁡θx = y\cot\theta - 2\tan\thetax=ycotθ−2tanθ

Correct answer: (C)

Step-by-step solution →
Q74·MathematicsSingle correct
In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :
  1. (A)16\frac{1}{6}61​
  2. (B)13\frac{1}{3}31​
  3. (C)23\frac{2}{3}32​
  4. (D)56\frac{5}{6}65​

Correct answer: (A)

Step-by-step solution →
Q75·MathematicsSingle correct
The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is :
  1. (A)7
  2. (B)5
  3. (C)1
  4. (D)3

Correct answer: (A)

Step-by-step solution →
Q76·MathematicsSingle correct
If A=[1sin⁡θ1−sin⁡θ1sin⁡θ−1−sin⁡θ1]A = \begin{bmatrix} 1 & \sin\theta & 1 \\ -\sin\theta & 1 & \sin\theta \\ -1 & -\sin\theta & 1 \end{bmatrix}A=​1−sinθ−1​sinθ1−sinθ​1sinθ1​​; then for all θ∈(3π4,5π4)\theta \in \left(\frac{3\pi}{4}, \frac{5\pi}{4}\right)θ∈(43π​,45π​), det (A) lies in the interval :
  1. (A)(1,52]\left(1, \frac{5}{2}\right](1,25​]
  2. (B)[52,4)\left[\frac{5}{2}, 4\right)[25​,4)
  3. (C)(0,32]\left(0, \frac{3}{2}\right](0,23​]
  4. (D)(32,3]\left(\frac{3}{2}, 3\right](23​,3]

Correct answer: (D)

Step-by-step solution →
Q77·MathematicsSingle correct
If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from O on AB is :
  1. (A)(x2+y2)2=4R2x2y2(x^{2} + y^{2})^{2} = 4R^{2}x^{2}y^{2}(x2+y2)2=4R2x2y2
  2. (B)(x2+y2)3=4R2x2y2(x^{2} + y^{2})^{3} = 4R^{2}x^{2}y^{2}(x2+y2)3=4R2x2y2
  3. (C)(x2+y2)2=4Rx2y2(x^{2} + y^{2})^{2} = 4Rx^{2}y^{2}(x2+y2)2=4Rx2y2
  4. (D)(x2+y2)(x+y)=R2xy(x^{2} + y^{2})(x + y) = R^{2}xy(x2+y2)(x+y)=R2xy

Correct answer: (B)

Step-by-step solution →
Q78·MathematicsSingle correct
If the function f given by f(x)=x3−3(a−2)x2+3ax+7f(x) = x^{3} - 3(a-2)x^{2} + 3ax + 7f(x)=x3−3(a−2)x2+3ax+7, for some a∈Ra \in Ra∈R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, f(x)−14(x−1)2=0\frac{f(x) - 14}{(x-1)^{2}} = 0(x−1)2f(x)−14​=0 (x≠1)(x \neq 1)(x=1) is :
  1. (A)−7
  2. (B)5
  3. (C)7
  4. (D)6

Correct answer: (C)

Step-by-step solution →
Q79·MathematicsSingle correct
Let Z be the set of integers. If A={x∈Z:2(x+2)(x2−5x+6)=1}A = \{x \in Z : 2^{(x+2)(x^{2}-5x+6)} = 1\}A={x∈Z:2(x+2)(x2−5x+6)=1} and B={x∈Z:−3<2x−1<9}B = \{x \in Z : -3 < 2x - 1 < 9\}B={x∈Z:−3<2x−1<9}, then the number of subsets of the set A ×\times× B, is :
  1. (A)2152^{15}215
  2. (B)2182^{18}218
  3. (C)2122^{12}212
  4. (D)2102^{10}210

Correct answer: (A)

Step-by-step solution →
Q80·MathematicsSingle correct
If nC4,nC5^{n}C_{4}, {}^{n}C_{5}nC4​,nC5​ and nC6^{n}C_{6}nC6​ are in A.P., then n can be :
  1. (A)9
  2. (B)14
  3. (C)11
  4. (D)12

Correct answer: (B)

Step-by-step solution →
Q81·MathematicsSingle correct
Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor axis. If △S′BS\triangle S'BS△S′BS is a right angled triangle with right angle at B and area (△S′BS)=8(\triangle S'BS) = 8(△S′BS)=8 sq. units, then the length of a latus rectum of the ellipse is :
  1. (A)4
  2. (B)222\sqrt{2}22​
  3. (C)424\sqrt{2}42​
  4. (D)2

Correct answer: (A)

Step-by-step solution →
Q82·MathematicsSingle correct
If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30°30°30° and the angle of depression of reflection of the cloud in the lake from P be 60°60°60°, then the height of the cloud (in meters) from the surface of the lake is :
  1. (A)60
  2. (B)50
  3. (C)45
  4. (D)42

Correct answer: (B)

Step-by-step solution →
Q83·MathematicsSingle correct
The expression ∼(∼p→q)\sim(\sim p \rightarrow q)∼(∼p→q) is logically equivalent to :
  1. (A)∼p∧∼q\sim p \wedge \sim q∼p∧∼q
  2. (B)p∧∼qp \wedge \sim qp∧∼q
  3. (C)∼p∧q\sim p \wedge q∼p∧q
  4. (D)p∧qp \wedge qp∧q

Correct answer: (A)

Step-by-step solution →
Q84·MathematicsSingle correct
If the sum of the first 15 terms of the series (34)3+(112)3+(214)3+33+(334)3+.....\left(\frac{3}{4}\right)^{3} + \left(1\frac{1}{2}\right)^{3} + \left(2\frac{1}{4}\right)^{3} + 3^{3} + \left(3\frac{3}{4}\right)^{3} + .....(43​)3+(121​)3+(241​)3+33+(343​)3+..... is equal to 225 k, then k is equal to :
  1. (A)108
  2. (B)27
  3. (C)54
  4. (D)9

Correct answer: (B)

Step-by-step solution →
Q85·MathematicsSingle correct
The number of integral values of m for which the quadratic expression, (1+2m)x2−2(1+3m)x+4(1+m)(1 + 2m)x^{2} - 2(1 + 3m)x + 4(1 + m)(1+2m)x2−2(1+3m)x+4(1+m), x∈Rx \in Rx∈R, is always positive, is :
  1. (A)3
  2. (B)8
  3. (C)7
  4. (D)6

Correct answer: (C)

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
  • Binomial Theorem and Its Simple Applications 158/186
  • Electromagnetic Waves 144/186
  • Application of Derivatives 139/186
  • Limits and Continuity 149/186
  • d- and f-Block Elements 126/186
  • 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
  • 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
  • Electromagnetic Induction 120/186
  • Kinetic Theory of Gases 135/186
  • Alcohols and Ethers 106/186
  • Oscillations 117/186
  • Nuclei 116/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Waves 109/186
  • 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
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Indefinite Integration 66/186
  • Polymers 64/186
  • Carboxylic Acids and Derivatives 54/186
  • States of Matter: Gases and Liquids 52/186
  • Magnetism and Matter 50/186
  • Mathematical Reasoning 26/186
  • Communication Systems 11/186
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