JEE MAIN-2019 Online CBT Mode Exam Dt. 12-01-2019 Morning
PHYSICS
1. A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60° with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is
(1) 2v/√3
(2) 
(3) v/2
(4) v
2. In the figure shown, a circuit contains two identical resistors with resistance R = 5 Ω and an inductance with L = 2 mH. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is closed?
(1) 7.5 A
(2) 3 A
(3) 6 A
(4) 5.5 A
3. The galvanometer deflection, when key K1 is closed but K2 is open, equal θ0 (see figure). On closing K2 also and adjusting R 2 to 5 Ω, the deflection in galvanometer becomes θ0/5. The resistance of the galvanometer is, then given by [Neglect the internal resistance of battery]
(1) 22 Ω
(2) 25 Ω
(3) 5 Ω
(4) 12 Ω
4. The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 μm diameter of a wire is
(1) 200
(2) 50
(3) 100
(4) 500
5. A travelling harmonic wave is represented by the equation y(x, t) = 10–3 sin (50t + 2x), where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave?
(1) The wave is propagating along the negative x-axis with speed 25 ms–1.
(2) The wave is propagating along the positive x-axis with speed 100 ms–1.
(3) The wave is propagating along the negative x-axis with speed 100 ms–1.
(4) The wave is propagating along the positive x-axis with speed 25 ms–1.
6. A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass ‘m’ at x = 0, if the mass per unit length of the rod is A + Bx2, is given by
7. There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is
8. A proton and an α-particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp : rα of the circular paths described by them will be
(1) 1 : 3
(2) 1 : 2
(3) 1 : √3
(4) 1 : √2
9. For the given cyclic process CAB as shown for a gas, the work done is
(1) 30 J
(2) 10 J
(3) 5 J
(4) 1 J
10. In a meter bridge, the wire of length 1 m has a nonuniform cross-section such that, the variation dR/dl of its resistance R with length l is 
. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?
(1) 0.2 m
(2) 0.35 m
(3) 0.25 m
(4) 0.3 m
11. The output of the given logic circuit is
(1) 
(2) 
(3) 
(4) 
12. As shown in the figure, two infinitely long, identical wires are bent by 90° and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4 cm, and the magnitude of the magnetic field at O is 10–4 T, and the two wires carry equal currents (see figure), the magnitude of the currents in each wire and the direction of the magnetic field at O will be (μ0 = 4π × 10–7 NA–2)
(1) 40 A, perpendicular into the page
(2) 20 A, perpendicular into the page
(3) 40 A, perpendicular out of the page
(4) 20 A, perpendicular out of the page
13. An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance 5 Ω. The value of R, to give an potential difference of 5 mV across 10 cm of potentiometer wire, is
(1) 480 Ω
(2) 490 Ω
(3) 495 Ω
(4) 395 Ω
14. A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and that of the outer cylinder is K2 . Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is
(1) 
(2) 
(3) K1 + K2
(4) 
15. A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction, and (ii) in the opposite directions is
(1) 25/11
(2) 5/2
(3) 11/5
(4) 3/2
16. Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P1 and P2 respectively, then
(1) P1 = 9 W, P2 = 16 W
(2) P1 = 4 W, P2 = 16 W
(3) P1 = 16 W, P2 = 9 W
(4) P1 = 16 W, P2 = 4 W
17. A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?
(1) 0.5
(2) 0.4
(3) 0.6
(4) 0.3
18. Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre ‘O’ and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is
(1) 
(2) 
(3) 
(4) 
19. A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ0. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1 . Then M is given by
(1) 
(2) 
(3) 
(4) 
20. Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is
(1) 14 cm
(2) 12 cm
(3) 16 cm
(4) 18 cm
21. A particle A of mass ‘m’ and charge ‘q’ is accelerated by a potential difference of 50 V. Another particle B of mass ‘4 m’ and charge ‘q’ is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths λA/λB is close to
(1) 0.07
(2) 14.14
(3) 4.47
(4) 10.00
22. The position vector of the centre of mass 
of an asymmetric unifom bar of negligible area of cross-section as shown in figure is
23. An ideal gas occupies a volume of 2 m3 at a pressure of 3 × 106 Pa. The energy of the gas is
(1) 108 J
(2) 9 × 106 J
(3) 6 × 104 J
(4) 3 × 102 J
24. A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be
(1) Such that it escapes to infinity
(2) In a circular orbit of a different radius
(3) In an elliptical orbit
(4) In the same circular orbit of radius R
25. A point source of light, S is placed at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below. The distance over which the man can see the image of the light source in the mirror is
(1) d/2
(2) 3d
(3) 2d
(4) d
26. A particle of mass m moves in a circular orbit in a central potential field 
If Bohr’s quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as
(1) rn ∝ n, En ∝ n
(2) rn ∝ √n, En ∝ n
(3) rn ∝ √n, En ∝ 1/n
(4) rn ∝ n2, En ∝ 1/n
27. A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propogating in the glass medium will be
(1) 6 V/m
(2) 10 V/m
(3) 24 V/m
(4) 30 V/m
28. What is the position and nature of image formed by lens combination shown in figure? (f 1, f 2 are focal lengths)
(1) 20/3 cm from point B at right; real
(2) 70 cm from point B at right; real
(3) 40 cm from point B at right; real
(4) 70 cm from point B at left; virtual
29. In the figure shown, after the switch ‘S’ is turned from position ‘A’ to position ‘B’, the energy dissipated in the circuit in terms of capacitance ‘C’ and total charge ‘Q’ is
30. Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure
(1) 
(2) 
(3) 
(4) 
CHEMISTRY
1. Water samples with BOD values of 4 ppm and 18 ppm, respectively, are
(1) Clean and Highly polluted
(2) Clean and Clean
(3) Highly polluted and Clean
(4) Highly polluted and Highly polluted
2. Given
Gas H2 CH4 CO2 SO2
Critical 33 190 304 630
Temperature/K
On the basis of data given above, predict which of the following gases shows least adsorption on a definite amount of charcoal?
(1) SO2
(2) CO2
(3) CH4
(4) H2
3. The metal d-orbitals that are directly facing the ligands in K3[Co(CN)6] are
(1) dxy, dxz and dyz
(2) 
(3) 
(4) 
4. A metal on combustion in excess air forms X. X upon hydrolysis with water yields H2O2 and O2 along with another product. The metal is
(1) Rb
(2) Li
(3) Mg
(4) Na
5. The correct order for acid strength of compounds
CH ≡ CH, CH3 – C ≡ CH and CH2 = CH2 is as follows :
(1) CH3 – C ≡ CH > CH ≡ CH > CH2 = CH2
(2) CH3 – C ≡ CH > CH2 = CH2 > HC ≡ CH
(3) CH ≡ CH > CH2 = CH2 > CH3 – C ≡ CH
(4) HC ≡ CH > CH3 – C ≡ CH > CH2 = CH2
6. The hardness of a water sample (in terms of equivalents of CaCO3) containing 10–3 M CaSO4 is (molar mass of CaSO4 = 136 g mol–1)
(1) 10 ppm
(2) 100 ppm
(3) 90 ppm
(4) 50 ppm
7. In the following reaction
Adehyde Alcohol
HCHO BuOH
CH3CHO MeOH
The best combination is
(1) HCHO and MeOH
(2) HCHO and tBuOH
(3) CH3CHO and tBuOH
(4) CH3CHO and MeOH
8. Poly-β-hydroxybutyrate-co- β -hydroxyvalerate (PHBV) is a copolymer of ___.
(1) 3-hydroxybutanoic acid and 4-hydroxypentanoic acid
(2) 3-hydroxybutanoic acid and 2-hydroxypentanoic acid
(3) 2-hydroxybutanoic acid and 3-hydroxypentanoic acid
(4) 3-hydroxybutanoic acid and 3-hydroxypentanoic acid
9. The molecule that has minimum/no role in the formation of photochemical smog, is
(1) NO
(2) CH2 = O
(3) O3
(4) N2
10. The increasing order of reactivity of the following compounds towards reaction with alkyl halides directly is
(1) (A) < (B) < (C) < (D)
(2) (B) < (A) < (C) < (D)
(3) (B) < (A) < (D) < (C)
(4) (A) < (C) < (D) < (B)
11. 
cannot be prepared by
(1) PhCOCH2CH3 + CH3MgX
(2) CH3CH2COCH3 + PhMgX
(3) HCHO + PhCH(CH3)CH2MgX
(4) PhCOCH3 + CH3CH2MgX
12. Two solids dissociate as follows
The total pressure when both the solids dissociate simultaneously is
(1) x2 + y2 atm
(2) (x + y) atm
(3) 
(4) 
13. The standard electrode potential E⊝ and its temperature coefficient (dE⊝/dT) for a cell are 2 V and −5 × 10−4 VK−1 at 300 K respectively. The cell reaction is
Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(S)
The standard reaction enthalpy (∆rH⊝) at 300 K in kJ mol−1 is,
[Use R = 8 JK−1 mol−1 and F = 96,000 C mol−1]
(1) 206.4
(2) −384.0
(3) −412.8
(4) 192.0
14. Decomposition of X exhibits a rate constant of 0.05 μg/year. How many years are required for the decomposition of 5 μg of X into 2.5 μg?
(1) 40
(2) 20
(3) 50
(4) 25
15. In the Hall-Heroult process, aluminium is formed at the cathode. The cathode is made out of
(1) Carbon
(2) Copper
(3) Platinum
(4) Pure aluminium
16. What is the work function of the metal if the light of wavelength 4000 Å generates photoelectrons of velocity 6 × 105 ms–1 from it?
(Mass of electron = 9 × 10–31 kg
Velocity of light = 3 × 108 ms–1
Planck’s constant = 6.626 × 10–34 Js
Charge of electron = 1.6 × 10–19 JeV–1)
(1) 4.0 eV
(2) 2.1 eV
(3) 3.1 eV
(4) 0.9 eV
17. Among the following four aromatic compounds, which one will have the lowest melting point?
(1) 
(2) 
(3) 
(4) 
18. In the following reactions, products A and B are
19. The pair of metal ions that can give a spin only magnetic moment of 3.9 BM for the complex [M(H2O)6]Cl2, is
(1) V2+ and Co2+
(2) Co2+ and Fe2+
(3) V2+ and Fe2+
(4) Cr2+ and Mn2+
20. In a chemical reaction, 
the initial concentration of B was 1.5 times of the concentration of A, but the equilibrium concentrations of A and B were found to be equal. The equilibrium constant (K) for the aforesaid chemical reaction is
(1) 1
(2) 16
(3) 4
(4) 1/4
21. The major product of the following reaction
(1) 
(2) 
(3) 
(4) 
22. For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?
(1) 
(2) 
(3) 
(4) 
23. The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressure of the gases for equal number of moles are
(1) PA = 2PB
(2) PA = 3PB
(3) 3PA = 2PB
(4) 2PA = 3PB
24. Among the following compounds most basic amino acid is
(1) Serine
(2) Lysine
(3) Histidine
(4) Asparagine
25. Mn2(CO)10 is an organometallic compound due to the presence of
(1) Mn – C bond
(2) Mn – Mn bond
(3) Mn – O bond
(4) C – O bond
26. The major product of the following reaction is
(1) 
(2) 
(3) 
(4) 
27. Iodine reacts with concentrated HNO3 to yield Y along with other products. The oxidation state of iodine in Y, is
(1) 7
(2) 1
(3) 5
(4) 3
28. The element with Z = 120 (not yet discovered) will be an/a
(1) Inner-transition metal
(2) Transition metal
(3) Alkaline earth metal
(4) Alkali metal
29. Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A, then molecular weight of Y is
(1) 2A
(2) 3A
(3) A
(4) 4A
30. 50 mL of 0.5 M oxalic acid is needed to neutralize 25 mL of sodium hydroxide solution. The amount of NaOH in 50 mL of the given sodium hydroxide solution is
(1) 10 g
(2) 40 g
(3) 20 g
(4) 80 g
MATHEMATICS
1. The maximum value of 
for any real value of θ is
(1) √34
(2) √19
(3) √79/2
(4) √31
2. A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of 
is
(1) 1 : 4(16)1/3
(2) 1 : 2(6)1/3
(3) 2(36)1/3 : 1
(4) 4(36)1/3 : 1
3. Let f and g be continuous functions on [0, a] such that f(x) = f(a – x) and g(x) + g(a – x) = 4, then 
is equal to
(1) 
(2) 
(3) 
(4) 
4. An ordered pair (α, β) for which the system of linear equations
(1 + α) x + β y + z = 2
αx + (1 + β)y + z = 3
αx + βy + 2z = 2
has a unique solution, is
(1) (1, –3)
(2) (2, 4)
(3) (–3, 1)
(4) (–4, 2)
5. The perpendicular distance from the origin to the plane containing the two lines, 
and 
is
(1) 11√6
(2) 6√11
(3) 11
(4) 11/√6
6. Consider three boxes, each containing 10 balls labelled 1, 2, …,10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n1< n2< n3is
(1) 240
(2) 120
(3) 164
(4) 82
7. In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to
(1) 150/65
(2) 225/65
(3) 175/65
(4) 200/65
8. If a variable line, 3x + 4y – λ = 0 is such that the two circles x2 + y2 – 2x – 2y + 1 = 0 and x2 + y2 – 18x – 2y + 78 = 0 are on its opposite sides, then the setof all values of λ is the interval
(1) (2, 17)
(2) (12, 21)
(3) (13, 23)
(4) (23, 31)
9. Let 
and Q = [qij] two 3 × 3 matrices such that Q – P5 = l3 . Then 
is equal to
(1) 10
(2) 135
(3) 9
(4) 15
10. The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is
(1) 36
(2) 32
(3) 24
(4) 28
11. A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(–1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is
(1) cos−1 (19/35)
(2) cos−1 (9/35)
(3) cos−1 (17/31)
(4) cos−1 (7/31)
12. If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is
(1) 31
(2) 30
(3) 50
(4) 51
13. Let y = y(x) be the solution of the differential equation, 
If 2y(2) =loge 4 – 1, then y(e) is equal to
(1) e2/4
(2) −e/2
(3) −e2/2
(4) e/4
14. 
is
(1) 8√2
(2) 4
(3) 4√2
(4) 8
15. The area (in sq. units) of the region bounded by the parabola, y = x2 + 2 and the lines, y = x + 1, x = 0 and x = 3, is
(1) 15/2
(2) 21/2
(3) 15/4
(4) 17/4
16. Let P(4, –4) and Q(9, 6) be two points on the parabola, y2 = 4x and let X be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of ∆PXQ is maximum. Then this maximum area (in sq. units) is
(1) 75/2
(2) 125/4
(3) 625/4
(4) 125/2
17. Let C1and C2 be the centres of the circles x2 + y2 – 2x – 2y – 2 = 0 and x2 + y2 – 6x – 6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2is
(1) 4
(2) 9
(3) 6
(4) 8
18. The sum of the distinct real values of μ, for which the vectors, 
are co-planar, is
(1) 2
(2) 1
(3) −1
(4) 0
19. If λ be the ratio of the roots of the quadratic equation in x, 3m2x2 + m(m – 4)x + 2 = 0, then the least value of m for which 
is
(1) 4 – 2√3
(2) 4 – 3√2
(3) 2 – √3
(4) −2 + √2
20. Considering only the principal values of inverse functions, the set
(1) Is a singleton
(2) Contains two elements
(3) Contains more than two elements
(4) Is an empty set
21. If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals
(1) −35/3
(2) −5
(3) 5
(4) 35/3
22. If 
is a purely imaginary number and |z| = 2, then a value of α is
(1) √2
(2) 2
(3) 1/2
(4) 1
23. The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 – x2 such that the rectangle lies inside the parabola, is
(1) 32
(2) 36
(3) 20√2
(4) 18√3
24. If the vertices of a hyperbola be at (–2, 0) and (2, 0) and one of its foci be at (–3, 0), then which one of the following points does not lie on this hyperbola?
(1) (4, √15)
(2) (6, 5√2)
(3) (2√6, 5)
(4) (−6, 2√10)
25. For x > 1, if (2x)2y = 4e2x – 2y, then is equal to
(1) loge 2x
(2) x loge 2x
(3) 
(4) 
26. Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is
(1) 2100 – 1
(2) 250 + 1
(3) 250(250 – 1)
(4) 250 – 1
27. Let S be the set of all points in (–π, π) at which the function, f(x) = min {sinx, cosx} is not differentiable. Then S is a subset of which of the following?
(1) 
(2) 
(3) 
(4) 
28. The integral ∫ cos(log e x) dx is equal to (where C is a constant of integration)
(1) 
(2) 
(3) 
(4) 
29. Let 
. If 
then A is equal to
(1) 303
(2) 156
(3) 301
(4) 283
30. The Boolean expression ((p ⋀ q) ⋁ (p ⋁ ~ q)) ( ~ p ⋀ ~ q) is equivalent to
(1) p ⋀ q
(2) (~ p) ⋀ (~ q)
(3) p ⋀ (~ q)
(4) p ⋁ (~ q)
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