# JEE MAIN 2019 Online CBT Mode Dt. 09-01-2019 Evening Question Paper With Answer Key

**JEE MAIN 2019 Online CBT Mode Evening Final Dt. 09-01-2019**

**Physics**

1. A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to

(1) 500 Hz

(2) 753 Hz

(3) 333 Hz

(4) 666 Hz

2. One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop (B_{L}) to that at the centre of the coil (B_{C}) i.e. B_{L}/B_{C }will be

(1) 1/N

(2) N^{2}

(3) N

(4) 1/N^{2}

3. Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of V_{0} changes by : (assume that the Ge diode has large breakdown voltage)

(1) 0.2 V

(2) 0.4 V

(3) 0.6 V

(4) 0.8 V

4. In a Young’s double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength λ = 500 nm is incident on the slits. The total number of bright fringes that are observed in the angular range – 30° ≤ θ ≤ 30° is

(1) 640

(2) 320

(3) 321

(4) 641

5. A series AC circuit containing an inductor (20 mH), a capacitor (120 μF) and a resistor (60 Ω) is driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is

(1) 5.65 × 10^{2} J

(2) 5.17 × 10^{2} J

(3) 2.26 × 10^{3} J

(4) 3.39 × 10^{3} J

6. Two point charges q_{1} (√10 μC) and q_{2}(−25 μC) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 on y-axis is,

(1)

(2)

(3)

(4)

7. A mass of 10 kg is suspended vertically by a ropefrom the roof. When a horizontal force is applied on the roof at some point, the rope deviated at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 ms^{–2})

(1) 100 N

(2) 200 N

(3) 70 N

(4) 140 N

8. Two Carnot engines A and B are operated in series. The first one, A, receives heat at T_{1} (=600 K) and rejects to a reservoir at temperature T_{2} . The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at T_{3} (= 400 K). Calculate the temperature T_{2} if the work outputs of the two engines are equal

(1) 300 K

(2) 400 K

(3) 600 K

(4) 500 K

9. A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about:

[Take R = 83 J/K mole]

(1) 3 kJ

(2) 14 kJ

(3) 10 kJ

(4) 0.9 kJ

10. At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio R_{B}/R_{A} of their activities after time t itself decays with time t as e^{−}^{3t}. If the half-life of A is ln2, the half-life of B is

(1) 4 ln2

(2) ln2/2

(3) ln2/4

(4) 2 ln2

11. A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential energy (PE) equals kinetic energy (KE), the position of the particle will be

(1) A/√2

(2) A

(3) A/2√2

(4) A/2

12. A carbon resistance has a following colour code. What is the value of the resistance?

(1) 6.4 MΩ ± 5%

(2) 5.3 MΩ ± 5%

(3) 64 kΩ ± 10%

(4) 530 kΩ ± 5%

13. In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accomodated for transmitting TV signals of band width 6 MHz are (take velocity of light c = 3 × 10^{8} m/s, h = 6.6 × 10^{−}^{34} J-s)

(1) 3.75 × 10^{6}

(2) 3.86 × 10^{6}

(3) 6.25 × 10^{5}

(4) 4.87 × 10^{5}

14. The energy associated with electric field is (U_{E} ) and with magnetic field is U_{B} ) for an electro magneticwave in free space, Then

(1) U_{E} < U_{B}

(2) U_{E} = U_{B}/2

(3) U_{E} = U_{B}

(4) U_{E} > U_{B}

15. The energy required to take a satellite to a height ‘h’ above Earth surface (radius of Earth = 6.4 × 10^{3} km) is E 1and kinetic energy required for the satellite to be in a circular orbit at this height is E_{2} . The value of h for which E_{1} and E_{2} are equal, is

(1) 3.2 × 10^{3} km

(2) 1.6 × 10^{3} km

(3) 1.28 × 10^{4} km

(4) 6.4 × 10^{3} km

16. A force acts on a 2 kg object so that its position is given as a function of time as x = 3t^{2} + 5. What is the work done by this force in first 5 seconds?

(1) 950 J

(2) 900 J

(3) 850 J

(4) 875 J

17. The magnetic field associated with a light wave is given, at the origin, by B = B_{0} [sin(3.14 × 10^{7})ct +sin(6.28 × 10^{7})ct]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons?

(c = 3 × 10^{8} ms^{−}^{1}, h = 6.6 × 10^{−}^{34} J-s)

(1) 8.52 eV

(2) 7.72 eV

(3) 12.5 eV

(4) 6.82 eV

18. In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed ‘v’ more than that of car B. Both the cars start from rest and travel with constant acceleration a_{1} and a_{2} Then ‘v’ is equal to:

(1)

(2)

(3)

(4)

19. A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K_{1}, K_{2}, K_{3}, K_{4} arranged as shown in the figure. The effective dielectric constant K will be:

(1)

(2)

(3)

(4)

20. The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line.

The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is:

(1) 5.725 mm

(2) 5.740 mm

(3) 5.755 mm

(4) 5.950 mm

21. A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of 30° from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s^{–1}) will be (g = 10 ms^{–2})

(1)

(2)

(3)

(4)

22. A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary winding of the transformer is 5 A and its efficiency is 90%, the output current would be:

(1) 25 A

(2) 50 A

(3) 45 A

(4) 35 A

23. In the given circuit the internal resistance of the 18 V cells is negligible. If R_{1} = 400 Ω, R_{3} = 100 Ω and R_{4} = 500 Ω and the reading of an ideal voltmeter across R_{4} is 5 V, then the value of R_{2} will be:

(1) 230 Ω

(2) 450 Ω

(3) 550 Ω

(4) 300 Ω

24. Expression for time in terms of G(universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

(1)

(2)

(3)

(4)

25. A rod of mass ‘M’ and length ‘2L’ is suspended at its middle by a wire. It exhibits torsional oscillations; if two masses each of ‘m’ are attached at distance ‘L/2’ from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to:

(1) 0.77

(2) 0.17

(3) 0.37

(4) 0.57

26. Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M_{1}) and parallel to the second mirror (M_{2}) is finally reflected from the second mirror (M2) parallel to the first mirror (M_{1}). The angle between the two mirrors will be:

(1) 75°

(2) 45°

(3) 90°

(4) 60°

27. Charge is distributed within a sphere of radius R with volume charge density where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :

(1)

(2)

(3)

(4)

28. A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = 1.6 × 10^{–19} C)

(1) 9.1 × 10^{−}^{31} kg

(2) 1.6 × 10^{−}^{27} kg

(3) 1.6 × 10^{−}^{19} kg

(4) 2.0 × 10^{−}^{24} kg

29. The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m^{3} water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:

(1) 9.6 m

(2) 2.9 m

(3) 4.8 m

(4) 6.0 m

30. The position co-ordinates of a particle moving in a 3-D coordinate system is given by

x = a cos ωt

y = a sin ωt

and z = aωt

The speed of the particle is:

(1) 2aωt

(2) √2 aω

(3) √3 aω

(4) aω

**CHEMISTRY**

1. The products formed in the reaction of cumene with O_{2} followed by treatment with dil. HCl are :

(1)

(2)

(3)

(4)

2. The correct match between Item I and Item II is :

**Item I Item II**

(A) Benzaldehyde (P) Mobile phase

(B) Alumina (Q) Adsorbent

(C) Acetonitrile (R) Adsorbate

(1) (A) → (Q), (B) → (R), (C) → (P)

(2) (A) → (Q), (B) → (P), (C) → (R)

(3) (A) → (P), (B) → (R), (C) → (Q)

(4) (A) → (R), (B) → (Q), (C) → (P)

3. The tests performed on compound X and their inferences are :

**Test Inference**

(a) 2,4-DNP test Coloured precipitate

(b) Iodoform test Yellow precipitate

(c) Azo-dye test No dye formation

Compound ‘X’ is :

(1)

(2)

(3)

(4)

4. The major product obtained in the following reaction is

(1)

(2)

(3)

(4)

5. Consider the following reversible chemical reactions

The relation between K_{1} and K_{2} is

(1) K_{2} = K_{1}^{3}

(2) K_{1}K_{2} = 1/3

(3) K_{2} = K_{1}^{−}^{3}

(4) K_{1}K_{2} = 3

6. Which of the following conditions in drinking water causes methemoglobinemia?

(1) > 50 ppm of nitrate

(2) > 50 ppm of lead

(3) > 50 ppm of chloride

(4) > 100 ppm of sulphate

7. The metal that forms nitride by reacting directly with N_{2} of air, is

(1) Li

(2) Rb

(3) Cs

(4) K

8. The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is (Specific heat of water liquid and water vapour are 4.2 K^{−}^{1} kg^{−}^{1} and 2.0 kJK^{−}^{1 }kg^{−}^{1}; heat of liquid fusion and vapourisation of water are 334 kJ kg^{−}^{1 }and 2491 kJ kg^{−}^{1}, respectively). (log 273 = 2.436, log 373 = 2.572, log 383 = 2.583)

(1) 8.49 kJ kg^{−}^{1} K^{−}^{1}

(2) 7.90 kJ kg^{−}^{1} K^{−}^{1}

(3) 9.26 kJ kg^{−}^{1} K^{−}^{1}

(4) 2.64 kJ kg^{−}^{1} K^{−}^{1}

9. The transition element that has lowest enthalpy of atomisation, is

(1) V

(2) Cu

(3) Fe

(4) Zn

10. If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for the reaction

Zn(s) + Cu^{2+} (aq) ⇌ Zn^{2+} (aq) + Cu (s) at 300 K is approximately

(R = 8 JK^{−}^{1} mol^{−}^{1}, F = 96000 Cmol^{−}^{1}

(1) e^{320}

(2) e^{160}

(3) e^{−}^{160}

(4) e^{−}^{80}

11. For coagulation of arsenious sulphide sol, which one of the following salt solution will be most effective?

(1) Na_{3}PO_{4}

(2) AlCl_{3}

(3) NaCl

(4) BaCl_{2}

12. In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?

(1) N_{2} → N_{2}^{+}

(2) O_{2} → O_{2}^{+}

(3) O_{2} → O_{2}^{2}^{−}

(4) NO → NO^{+}

13. When the first electron gain enthalpy (∆_{eg }H) of oxygen is –141 kJ/mol, its second electron gain enthalpy is

(1) Almost the same as that of the first

(2) A more negative value than the first

(3) Negative, but less negative than the first

(4) A positive value

14. The pH of rain water, is approximately

(1) 7.0

(2) 7.5

(3) 5.6

(4) 6.5

15. A solution containing 62 g ethylene glycol in 250 g water is cooled to –10°C. If K_{f} for water is 1.86 K kg mol^{–1}, the amount of water (in g) separated as ice is

(1) 64

(2) 32

(3) 16

(4) 48

16. The major product of the following reaction

(1)

(2)

(3)

(4)

17. The temporary hardness of water is due to

(1) CaCl_{2}

(2) NaCl

(3) Na_{2}SO_{4}

(4) Ca(HCO_{3})_{2}

18. At 100°C, copper (Cu) has FCC unit cell structure with cell edge length of x Å. What is the approximate density of Cu (in g cm^{–3}) at this temperature?

[Atomic Mass of Cu = 63.55 u]

(1) 422/x^{3}

(2) 205/x^{3}

(3) 105/x^{3}

(4) 211/x^{3}

19. The correct statement regarding the given Ellingham diagram is

(1) At 800°C, Cu can be used for the extraction of Zn from ZnO

(2) At 500ºC, coke can be used for the extraction of Zn from ZnO

(3) At 1400°C, Al can be used for the extraction of Zn from ZnO

(4) Coke cannot be used for the extraction of Cu from Cu_{2}O

20. Homoleptic octahedral complexes of a metal ion ‘M^{3+}’ with three monodentate ligands L_{1}, L_{2} and L_{3} absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is:

(1) L_{1} < L_{2} < L_{3}

(2) L_{3} < L_{2} < L_{1}

(3) L_{3} < L_{1} < L_{2}

(4) L_{2} < L_{1} < L_{3}

21. The complex that has highest crystal field splitting energy (∆), is

(1) [Co(NH_{3})_{5}Cl]Cl_{2}

(2) K_{2}[CoCl_{4}]

(3) K_{3}[Co(CN)_{6}]

(4) [Co(NH_{3})_{5}(H_{2}O)]Cl_{3}

22. The major product formed in the following reaction is:

(1)

(2)

(3)

(4)

23. Good reducing nature of H_{3}PO_{2} is attributed to the presence of:

(1) Two P – OH bonds

(2) One P – H bond

(3) One P – OH bond

(4) Two P – H bonds

24. For the reaction, 2A + B → products, when the concentration of A and B both were doubled, the rate of the reaction increased from 0.3 mol L^{–1}s^{–1} to 2.4 mol L^{–1}s^{–1}. When the concentration of A alone is doubled, the rate increased from 0.3 mol L^{–1}s^{–1} to 0.6 mol L^{–1}s^{–1}. Which one of the following statements is correct

(1) Order of the reaction with respect to A is 2

(2) Order of the reaction with respect to B is 1

(3) Order of the reaction with respect to B is 2

(4) Total order of the reaction is 4

25. The increasing basicity order of the following compounds is:

(1) (D) < (C) < (B) < (A)

(2) (A) < (B) < (C) < (D)

(3) (A) < (B) < (D) < (C)

(4) (D) < (C) < (A) < (B)

26. The major product of the following reaction is:

(1)

(2)

(3)

(4)

27. For the following reaction, the mass of water produced from 445 g of C_{57}H_{110}O_{6} is:

2C_{57}H_{110}O_{6}(s) + 163O_{2}(g) → 114CO_{2}(g) + 110H_{2}O(l)

(1) 890 g

(2) 490 g

(3) 445 g

(4) 495 g

28. Which of the following compounds is not aromatic?

(1)

(2)

(3)

(4)

29. Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?

(a) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum

(b) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number.

(c) According to wave mechanics, the ground state angular momentum is equal to h/2π

(d) The plot of Ψ Vs r for various azimuthul quantum numbers, shows peak shifting towards higher r value.

(1) (a), (d)

(2) (b). (c)

(3) (a), (c)

(4) (a), (b)

30. The correct sequence of amino acids present in the tripeptide given below is :

The given tripeptide contains.

(1) Leu – Ser – Thr

(2) Thr – Ser – Val

(3) Val – Ser – Thr

(4) Thr – Ser – Leu

**MATHEMATICS**

1. If and f(0) = 0, then the value of f(1) is

(1) 1/2

(2) 1/4

(3) −1/2

(4) −1/4

2. Let f : [0, 1] → R be such that f(xy) = f(x).f(y), for all x, y ∈ [0, 1], and f(0) ≠ If y = y(x) satisfies the differential equation, with y(0) = 1, then

(1) 4

(2) 3

(3) 2

(4) 5

3. If the lines x = ay + b, z = cy + d and x =aʹz + bʹ, y = cʹz + dʹ are perpendicular, then

(1) abʹ + bcʹ + 1 = 0

(2) ccʹ + a + aʹ = 0

(3) aaʹ + c + cʹ = 0

(4) bbʹ + ccʹ + 1 = 0

4. If then the number of values of x for which sinx – sin2x + sin3x = 0, is

(1) 2

(2) 3

(3) 1

(4) 4

5. If the system of linear equations

x – 4y + 7z = g

3y – 5z = h

– 2x + 5y – 9z = k

is consistent, then

(1) g + h + k = 0

(2) g + 2h + k = 0

(3) g + h + 2k = 0

(4) 2g + h + k = 0

6. The logical statement

[~(~p ⋁ q) ⋁ (p ⋀ r)] ⋀ (~q ⋀ r) is equivalent to

(1) (p ⋀ r) ⋀ ~ q

(2) (p ⋀ ~q) ⋁ r

(3) (~ p ⋀ ~q) ⋀ r

(4) ~ p ⋁ r

7. Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:

(1) 9

(2) 32

(3) 36

(4) 18

8. Let f be a differentiable function from R to R such that |f(x) – f(y)| ≤ 2|x – y|^{3/2}, for all x, y ∈ If f(0) = 1 then equal to

(1) 1

(2) 0

(3) 1/2

(4) 2

9. If x = sin^{–1}(sin10) and y = cos^{–1}(cos10), then y – x is equal to

(1) 7π

(2) 10

(3) 0

(4) π

10. If both the roots of the quadratic equation x2 – mx + 4 = 0 are real and distinct and they lie in the interval [1, 5] then m lies in the interval:

(1) (−5, −4)

(2) (3, 4)

(3) (4, 5)

(4) (5, 6)

11. Let z_{0} be a root of the quadratic equation, x^{2} + x + 1 = 0. If z = 3 + 6iz_{0}^{81} – 3iz_{0}^{93}, then arg z is equal to

(1) 0

(2) π/3

(3) π/4

(4) π/6

12. If then A is

(1) Invertible only if t = π

(2) Invertible for all t ∈ R

(3) Invertible only if t = π/2

(4) Not invertible for any t ∈ R.

13. Let A = {x ∈ R : x is not a positive integer}. Define a function f : A → R as

(1) Injective but not surjective

(2) Neither injective nor surjective

(3) Surjective but not injective

(4) Not injective

14. The coefficient of t^{4} in the expansion of is

(1) 15

(2) 14

(3) 12

(4) 10

15. For each x ∈ R, let [x] be the greatest integer less than or equal to x. Then is equal to

(1) −sin1

(2) 1

(3) sin1

(4) 0

16. Let A(4, –4) and B(9, 6) be points on the parabola, y^{2} = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of ∆ACB is maximum. Then, the area (in sq. units) of ∆ACB, is

(1) 32

(2)

(3)

(4)

17. If then the value of k is

(1) 4

(2) 2

(3) 1

(4) 1/2

18. The sum of the following series up to terms, is

(1) 7830

(2) 7820

(3) 7520

(4) 7510

19. If x = 3 tant and y = 3 sect, then the value of at t = π/4, is

(1) 1/6√2

(2) 1/3√2

(3) 3/2√2

(4) 1/6

20. Let and be three vectors such that the projection vector of perpendicular to is equal to :

(1) √22

(2) √32

(3) 4

(4) 6

21. The number of all possible positive integral values of α for which the roots of the quadratic equation, 6×2 – 11x + α = 0 are rational numbers is

(1) 4

(2) 5

(3) 2

(4) 3

22. Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then a/c is equal to

(1) 1/2

(2) 4

(3) 7/13

(4) 2

23. If the circles x^{2} + y^{2} – 16x – 20y + 164 = r^{2} and (x – 4)^{2} + (y – 7)^{2} = 36 intersect at two distinct points, then

(1) 1 < r < 11

(2) r > 11

(3) r = 11

(4) 0 < r < 1

24. A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is

(1) 3/2

(2) √3

(3) 2/√3

(4) 2

25. The equation of the plane containing the straight line and perpendicular to the plane containing the straight lines is

(1) x – 2y + z = 0

(2) x + 2y – 2z = 0

(3) 5x + 2y – 4z = 0

(4) 3x + 2y – 3z =0

26. A data consists of n observations x_{1}, x_{2}, …, x_{n}. If then the standard deviation of this data is

(1) √7

(2) 5

(3) √5

(4) 2

27. The area of the region A = {(x, y) : 0 ≤ y ≤ x|x| + 1 and –1 ≤ x ≤ 1} in sq. units, is

(1) 2

(2) 4/3

(3) 2/3

(4) 1/3

28. An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is

(1) 26/49

(2) 21/49

(3) 32/49

(4) 27/49

29. Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1, 1), then the equation of its third side is

(1) 26x – 122y – 1675 = 0

(2) 122y – 26x – 1675 = 0

(3) 122y + 26x + 1675 = 0

(4) 26x + 61y + 1675 = 0

30. The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digits allowed) is equal to

(1) 374

(2) 375

(3) 250

(4) 372