# JEE MAIN-2019 Online CBT Mode Dt. 11.01.2019 Morning Question Paper With Answer Key

**JEE MAIN-2019 Online CBT Mode Dt. 11.01.2019 Morning**

**PHYSICS**

1. An amplitude modulated signal is given by V(t) = 10 [1 + 0.3cos (2.2 × 10^{4}t)] sin(5.5 × 10^{5}t). Here t is in seconds. The sideband frequencies (in kHz) are, [Given π =22/7]

(1) 1785 and 1715

(2) 178.5 and 171.5

(3) 89.25 and 85.75

(4) 892.5 and 857.5

2. In the circuit shown,

the switch S_{1} is closed at time t = 0 and the switch S_{2} is kept open. At some later time(t_{0}), the switch S_{1} is opened and S_{2} is closed. The behaviour of the

current I as a function of time ‘t ’ is given by

(1)

(2)

(3)

(4)

3. The force of interaction between two atoms is given by where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is

(1) M^{0}L^{2}T^{−}^{4}

(2) M^{2}LT^{−}^{4}

(3) MLT^{−}^{2}

(4) M^{2}L^{2}T^{−}^{2}

4. The given graph shows variation (with distance r from centre) of

(1) Potential of a uniformly charged spherical shell

(2) Electric field of a uniformly charged sphere

(3) Electric field of uniformly charged spherical shell

(4) Potential of a uniformly charged sphere

5. A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60° around the centre of the circle?

(1) 10 m/s

(2) Zero

(3) 10√3 m/s

(4) 10√2 m/s

6. A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980 Å. The radius of the atom in the excited state, in terms of Bohr radius a_{0}, will be

(hc = 12500 eV-Å)

(1) 4a_{0}

(2) 9a_{0}

(3) 25a_{0}

(4) 16a_{0}

7. Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be

(1) 60 W

(2) 30 W

(3) 120 W

(4) 240 W

8. Three charges Q, +q and +q are placed at the vertices of a right-angle isosceles triangles as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is

(1)

(2) +q

(3) −2q

(4)

9. In a Wheatstone bridge (see fig.), Resistances P and Q are approximately equal. When R = 400 Ω, the bridge is balanced. On interchanging P and Q, the value of R, for balance, is 405 Ω. The value of X is close to

(1) 404.5 ohm

(2) 401.5 ohm

(3) 402.5 ohm

(4) 403.5 ohm

10. There are two long co-axial solenoids of same length l. The inner and outer coils have radii r_{1} and r_{2} and number of turns per unit length n_{1} and n_{2}, respectively. The ratio of mutual inductance to the self inductance of the inner-coil is

(1)

(2)

(3)

(4)

11. The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if D_{m} is the angle of minimum deviation?

(1)

(2)

(3)

(4)

12. A particle undergoing simple harmonic motion has time dependent displacement given by The ratio of kinetic to potential energy of this particle at t = 210 s will be

(1) 1

(2) 3

(3) 2

(4) 1/9

13. In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 × 10^{–19} C, Mass of the electron = 9.1 × 10^{–31} kg]

(1) 7.5 × 10^{−}^{3} m

(2) 7.5 m

(3) 7.5 × 10^{−}^{2} m

(4) 7.5 × 10^{−}^{4} m

14. An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D, E and F are the midpoints of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I_{0}. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then

(1)

(2)

(3)

(4)

15. A body is projected at t = 0 with a velocity 10 ms^{–1} at an angle of 60° with the horizontal. The radius of curvature of its trajectory at t = 1 s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms^{–2}, the value of R is

(1) 5.1 m

(2) 2.5 m

(3) 2.8 m

(4) 10.3 m

16. Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450t – 9x) where distance and time are measured in SI units. The tension in the string is

(1) 10 N

(2) 7.5 N

(3) 5 N

(4) 12.5 N

17. A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is

(1) 4RT

(2) 12RT

(3) 15RT

(4) 20 RT

18. In the figure shown below, the charge on the left plate of the 10 μF capacitor is –30 μ The charge on the right plate of the 6 μF capacitor is

(1) +18 μC

(2) −12 μC

(3) +12 μC

(4) −18 μC

19. An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be

(1) 0.92 × 10^{–3} m/s away from the lens

(2) 2.26 × 10^{–3} m/s away from the lens

(3) 1.16 × 10^{–3} m/s towards the lens

(4) 3.22 × 10^{–3} m/s towards the lens

20. A slab is subjected to two forces of same magnitude F as shown in the figure. Force is in XY-plane while force F_{1} acts along z-axis at the point moment of these forces about point O will be

(1)

(2)

(3)

(4)

21. An electromagnetic wave of intensity 50 Wm^{–2} enters in a medium of refractive index ‘n’ without any loss. The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by

(1)

(2)

(3)

(4)

22. A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be

(1)

(2)

(3)

(4)

23. The resistance of the metre bridge AB in given figure is 4 Ω. With a cell of emf ε = 0.5 V and rheostat resistance Rh = 2 Ω the null point is obtained at some point J. When the cell is replaced by another one of emf ε = ε_{2} the same null point J is found for Rh = 6 Ω.The emf ε_{2} is

(1) 0.6 V

(2) 0.5 V

(3) 0.3 V

(4) 0.4 V

24. A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 10^{6} N/m. The body sticks to the platform and the spring’s maximum compression is found to be x. Given that g = 10 ms^{–2}, the value of x will be close to

(1) 80 cm

(2) 8 cm

(3) 4 cm

(4) 40 cm

25. In a Young’s double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is 1/8th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to

(1) 0.74

(2) 0.94

(3) 0.80

(4) 0.85

26. A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is

(1)

(2)

(3)

(4)

27. In the given circuit the current through Zener Diode is close to

(1) 6.7 mA

(2) 0.0 mA

(3) 4.0 mA

(4) 6.0 mA

28. A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TV^{x} = constant, then x is

(1) 2/5

(2) 2/3

(3) 5/3

(4) 3/5

29. Ice at –20°C is added to 50 g of water at 40°C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still unmelted. The amount off ice added to the water was close to (Specific heat of water = 4.2 J/g/°C Specific heat of Ice = 2.1 J/g/°C Heat of fusion of water at 0°C = 334 J/g)

(1) 100 g

(2) 40 g

(3) 50 g

(4) 60 g

30. If the deBroglie wavelength of an electron is equal to 10^{–3} times the wavelength of a photon of frequency 6 × 10^{14} Hz, then the speed of electron is equal to :

(Speed of light = 3 × 10^{8} m/s

Planck’s constant = 6.63 × 10^{–34} J-s

Mass of electron = 9.1 × 10^{–31} kg)

(1) 1.7 × 10^{6} m/s

(2) 1.45 × 10^{6} m/s

(3) 1.8 × 10^{6} m/s

(4) 1.1 × 10^{6} m/s

**CHEMISTRY**

1. Match the ores (column A) with the metals (column B):

(**Column A) (Column B)**

**Ores Metals**

(I) Siderite (a) Zinc

(II) Kaolinite (b) Copper

(III) Malachite (c) Iron

(IV) Calamine (d) Aluminium

(1) (I) – (a); (II) – (b); (III) – (c); (IV) – (d)

(2) (I) – (c); (II) – (d); (III) – (a); (IV) – (b)

(3) (I) – (c); (II) – (d); (III) – (b); (IV) – (a)

(4) (I) – (b); (II) – (c); (III) – (d); (IV) – (a)

2. The concentration of dissolved oxygen (DO) in cold water can go upto:

(1) 14 ppm

(2) 16 ppm

(3) 10 ppm

(4) 8 ppm

3. The freezing point of a diluted milk sample is found to be –0.2°C, while it should have been –0.5°C for pure milk. How much water has been added to pure milk to make the diluted sample?

(1) 3 cups of water and 2 cups of pure milk

(2) 1 cup of water and 2 cups of pure milk

(3) 2 cups of water to 3 cups of pure milk

(4) 1 cup of water to 3 cups of pure milk

4. The correct match between item (I) and item (II) is:

Item – I Item – II

(A) Norethindrone (P) Anti-biotic

(B) Ofloxacin (Q) Anti-fertility

(C) Equanil (R) Hypertension

(S) Analgesics

(1) (A) → (R) ; (B) → (P) ; (C) → (R)

(2) (A) → (R) ; (B) → (P) ; (C) → (S)

(3) (A) → (Q) ; (B) → (P) ; (C) → (R)

(d) (A) → (Q) ; (B) → (R) ; (C) → (S)

5. The major product of the following reaction is

6. The major product of the following reaction is:

(2)

(3)

(4)

7. The chloride that CANNOT get hydrolysed is:

(1) PbCl_{4}

(2) CCl_{4}

(3) SnCl_{4}

(4) SiCl_{4}

8. If a reaction follows the Arrhenius equation, the plot Ink vs gives straight line with a gradient (–y) unit. The energy required to activate the reactant is:

(1) yR unit

(2) y/R unit

(3) −y unit

(4) y unit

9. The major product of the following reaction is

(1)

(2)

(3)

(4)

10. The major product of the following reaction is:

11. A solid having density of 9 × 10^{3} kg m^{–3} forms face centred cubic crystals of edge length 200√2 pm. What is the molar mass of the solid?

[Avogadro constant ≅ 6 × 10^{23} mol^{–1}, π ≅ 3 ]

(1) 0.0305 kg mol^{−}^{1}

(2) 0.4320 kg mol^{−}^{1}

(3) 0.0432 kg mol^{−}^{1}

(4) 0.0216 kg mol^{−}^{1}

12. The correct match between items I and II is

**Item-I (Mixture) Item-II**

**(Separation method)**

(A) H2O : Sugar (P) Sublimation

(B) H2O : Aniline (Q) Recrystallization

(C) H2O : Toluene (R) Steam distillation

(S) Differential extraction

(1) (A) → (R), (B) → (P), (C) → (S)

(2) (A) → (S), (B) → (R), (C) → (P)

(3) (A) → (Q), (B) → (R), (C) → (P)

(4) (A) → (Q), (B) → (R), (C) → (S)

13. The correct order of the atomic radii of C, Cs, Al, and S is

(1) S < C < Al < Cs

(2) C < S < Cs < Al

(3) S < C < Cs < Al

(4) C < S < Al < Cs

14. For the cell Zn(s)|Zn^{2+}(aq)||M^{x+}(aq)| M(s), different half cells and their standard electrode potentials are given below

If which cathode will give a maximum value of

E°_{cell} per electron transferred?

(1) Fe^{2+}/Fe

(2) Ag^{+}/Ag

(3) Fe^{3+}/Fe^{2+}

(4) Au^{3+}/Au

15. Consider the reaction

N_{2}(g) + 3H_{2}(g) ⇌ 2NH_{3} (g)

The equilibrium constant of the above reaction is K_{P}. If pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by (Assume that at equilibrium)

(1)

(2)

(3)

(4)

16. For the chemical reaction X ⇌ Y, the standard reaction Gibbs energy depends on temperature T (in K) as

The major component of the reaction mixture at T is

(1) Y if T = 280 K

(2) X if T = 315 K

(3) X if T = 300 K

(4) X if T = 350 K

17. An organic compound is estimated through Dumas method and was found to evolve 6 moles of CO_{2}, 4 moles of H_{2}O and 1 mole of nitrogen gas. The formula of the compound is

(1) C_{6}H_{8}N

(2) C_{12}H_{8}N

(3) C_{6}H_{8}N

(4) C_{12}H_{8}N_{2}

18. Match the metals (column I) with the coordination compound(s)/enzyme(s) (column II)

**(Column I) (Column II)**

** Metals Coordination**

** compound(s)/**

** enzyme(s)**

(A) Co (i) Wilkinson catalyst

(B) Zn (ii) Chlorophyll

(C) Rh (iii) Vitamin B12

(D) Mg (iv) Carbonic anhydrase

(1) (A) – (iv), (B) – (iii), (C) – (i), (D) – (ii)

(2) (A) – (i), (B) – (ii), (C) – (iii), (D) – (iv)

(3) (A) – (ii), (B) – (i), (C) – (iv), (D) – (iii)

(4) (A) – (iii), (B) – (iv), (C) – (i), (D) – (ii)

19. Two blocks of the same metal having same mass and at temperature T_{1} and T_{2}, respectively, are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, ∆S, for this process is

(1)

(2)

(3)

(4)

20. The correct statements among (a) to (d) regarding H_{2} as a fuel are

(a) It produces less pollutants than petrol.

(b) A cylinder of compressed dihydrogen weighs ~ 30 times more than a petrol tank producing the same amount of energy.

(c) Dihydrogen is stored in tanks of metal alloys like NaNi_{5}.

(d) On combustion, values of energy released per gram of liquid dihydrogen and LPG are 50 and 142 kJ, respectively.

(1) (b) and (d) only

(2) (a) and (c) only

(3) (b), (c) and (d) only

(4) (a), (b) and (c) only

21. The element that usually does NOT show variable oxidation states is

(1) Cu

(2) Ti

(3) V

(4) Sc

22. Among the following compounds, which one is found in RNA?

23. The polymer obtained from the following reactions is

24. NaH is an example of

(1) Metallic hydride

(2) Electron –rich hydride

(3) Molecular hydride

(4) Saline hydride

25. The amphoteric hydroxide is

(1) Mg(OH)_{2}

(2) Be(OH)_{2}

(3) Sr(OH)_{2}

(4) Ca(OH)_{2}

26. Which compound(s) out of following is/are not aromatic?

(1) (B), (C) and (D)

(2) (A) and (C)

(3) (C) and (D)

(4) (B)

27. Peroxyacetyl nitrate (PAN), an eye irritant is produced by

(1) Classical smog

(2) Acid rain

(3) Organic waste

(4) Photochemical smog

28. A 10 mg effervescent tablet containing sodium bicarbonate and oxalic acid releases 0.25 ml of CO_{2} at T = 298.15 K and p = 1 bar. If molar volume of CO_{2} is 25.0 L under such condition, what is the percentage of sodium bicarbonate in each tablet?

[Molar mass of NaHCO_{3} = 84 g mol^{–1}]

(1) 33.6

(2) 8.4

(3) 0.84

(4) 16.8

29. Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this purpose?

[RH= 1 × 10^{5} cm, h = 6.6 × 10^{–34} Js, c = 3 × 10^{8} ms^{–1}]

(1) Balmer, ∞ → 2

(2) Lyman, ∞ → 1

(3) Paschen, 5 → 3

(4) Paschen, ∞ → 3

30. An example of solid sol is.

(1) Butter

(2) Hair cream

(3) Paint

(4) Gem stones

**MATHEMATICS**

1. Let and g(x) = | f(x)|+f(|x|). Then, in the interval (–2, 2), g is

(1) not differentiable at two points

(2) not differentiable at one point

(3) not continuous

(4) differentiable at all points

2. The plane containing the line and also containing its projection on the plane 2x + 3y – z = 5, contains which one of the following points?

(1) (0, –2, 2)

(2) (2, 2, 0)

(3) (–2, 2, 2)

(4) (2, 0, –2)

3. Let f : R → R be defined by Then the range of f is

(1) R – [−1/2, 1/2]

(2) [−1/2, 1/2]

(3) [–1, 1) – {0}

(4) R – [–1, 1]

4. The outcome of each of 30 items was observed; 10 items gave an outcome each, 10 items gave outcome 1/2 each and the remaining 10 items gave outcome . If the variance of this outcome data is 4/3 then |d| equals.

(1) √2

(2) √5/2

(3) 2/3

(4) 2

5. Let and be coplanar vectors. Then the none-zero vector is:

(1)

(2)

(3)

(4)

6. The area (in sq. units) of the region bounded by the curve x^{2} = 4y and the straight line x = 4y – 2 is

(1) 7/8

(2) 5/4

(3) 9/8

(4) 3/4

7. Let a_{1}, a_{2}, …, a_{10} be a G.P. If equals

(1) 5^{3}

(2) 5^{4}

(3) 2(5^{2})

(4) 4(5^{2})

8. If the system of linear equations

2x + 2y + 3z = a

3x – y + 5z = b

x – 3y + 2z = c

where a, b, c are non-zero real numbers, has more than one solution, then

(1) b – c + a = 0

(2) b + c – a = 0

(3) a + b + c = 0

(4) b – c – a = 0

9. The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is

(1) √5/4

(2) √5/2

(3) 4√5

(4) 2√5

10 Let [x] denote the greatest integer less than or equal to x. Then

(1) equals 0

(2) equals π + 1

(3) equals π

(4) does not exist

11. Let If AA^{T} = I_{3}, then |p| is:

(1) 1/√3

(2) 1/√6

(3) 1/√5

(4) 1/√2

12. Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is:

(1) 1

(2) √2

(3) 2√2

(4) 2

13. The value of r for which ^{20}C_{r} ^{20}C_{0} + ^{20}C_{r – 1} ^{20}C_{1} + ^{20}C_{r – 2 }^{20}C_{2}+ … + ^{20}C_{0} ^{20}C_{r} is maximum, is :

(1) 10

(2) 20

(3) 15

(4) 11

14. If x log_{e} (log_{e} x) – x^{2} + y^{2} = 4 (y > 0), then dy/dx at x = e is equal to :

(1)

(2)

(3)

(4)

15. If for a suitable chosen integer m and a function A(x), where C is a constant of integration, then (A(x))^{m} equals:

(1) −1/3x^{3}

(2) 1/27x^{6}

(3) 1/9x^{4}

(4) −1/27x^{9}

16. Two integers are selected at random from the set {1, 2, …, 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:

(1) 3/5

(2) 7/10

(3) 1/2

(4) 2/5

17. Equation of a common tangent to the parabola y^{2} = 4x and the hyperbola xy = 2 is:

(1) 4x + 2y + 1 = 0

(2) x + 2y + 4 = 0

(3) x – 2y + 4 = 0

(4) x + y + 1 = 0

18. If tangents are drawn to the ellipse x^{2} + 2y^{2} = 2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve:

(1)

(2)

(3)

(4)

19. A square is inscribed in the circle x^{2} + y^{2} – 6x + 8y – 103 = 0 with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is:

(1) 6

(2) √41

(3) 13

(4) √137

20. In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x^{2} – c^{2} = y, where c is the length of the third side of the triangle, then the circum radius of the triangle is:

(1) c/√3

(2)

(3) c/3

(4) y/√3

21. Let where x and y are real numbers, the y – x equals

(1) −85

(2) −91

(3) 85

(4) 91

22. If q is false and p ⋀ q ↔ r is true, then which one of the following statements is a tautology?

(1) p ⋁ r

(2) (p ⋀ r) → (p ⋁ r)

(3) (p ⋁ r) → (p ⋀ r)

(4) p ⋀ r

23. If y(x) is the solution of the differential equation then

(1) y(x) is decreasing in (1/2, 1)

(2)

(3) y(log_{e} 2) = log_{e} 4

(4) y(x) is decreasing in (0, 1)

24. The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) and making an angle π/4 with the plane y – z + 5 = 0 are

(1) 2√3, 1, −1

(2) 2, √2, −√2

(3) 2, −1, 1

(4) √2, 1, −1

25. The maximum value of the function f(x) = 3x^{3} – 18x^{2} + 27x – 40 on the set S = {x ∈ R: x^{2} + 30 ≤ 11x} is

(1) 122

(2) −122

(3) 222

(4) −222

26. Let for k = 1, 2, 3, …. Then for all x ∈ R, the value of f_{4}(x) – f_{6}(x) is equal to

(1) −1/12

(2) 1/12

(3) 5/12

(4) 1/4

27. The sum of the real values of x for which the middle term in the binomial expansion of equals 5670 is

(1) 4

(2) 8

(3) 0

(4) 6

28. The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is 27/19. Then the common ratio of this series is

(1) 1/3

(2) 2/9

(3) 2/3

(4) 4/9

29. The value of the integral (where [x] denotes the greatest integer less than or equal to x) is

(1) sin 4

(2) 4 – sin 4

(3) 0

(4) 4

30. If one real root of the quadratic equation 81x^{2} + kx + 256 = 0 is cube of the other root, then a value of k is

(1) −300

(2) 144

(3) −81

(4) 100