# JEE Main-2019 Online CBT Mode Dt.10-01.2019 Morning Question Paper With Answer Key

**JEE Main-2019 Online CBT Mode Dt.10-01.2019 Morning**

**PHYSICS**

1. To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is μ, the torque, applied by the machine on the mop is

(1)

(2)

(3)

(4)

2. Two electric dipoles, A, B with respective dipole moments are placed on the x-axis with a separation R, as shown in the figure

The distance from A at which both of them produce the same potential is

(1)

(2)

(3)

(4)

3. To get output ‘1’ at R, for the given logic gate circuit the input values must be

(1) X = 1, Y = 1

(2) X = 0, Y = 0

(3) X = 1, Y = 0

(4) X = 0, Y = 1

4. A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is

(1) 12 mV

(2) 2 mV

(3) 6 mV

(4) 1 mV

5. A plano convex lens of refractive index μ_{1 }and focal length f_{1}is kept in contact with another plano concave lens of refractive index μ_{2} and focal length f_{2}. If the radius of curvature of their spherical faces is R each and f_{1}= 2f_{2}, then μ_{1}and μ_{2} are related as

(1) 2 μ_{1} – μ_{2} = 1

(2) 3μ_{2} – 2μ_{1 }= 1

(3) 2μ_{1} – μ_{1} = 1

(4) μ_{1} + μ_{2} = 3

6. Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to

(1) 400

(2) 360

(3) 150

(4) 200

7. Water flows into a large tank with flat bottom at the rate of 10^{–4} m^{3}s^{–1}. Water is also leaking out of a hole of area 1 cm^{2} at its bottom. If the height of the water in the tank remains steady, then this height is

(1) 5.1 cm

(2) 1.7 cm

(3) 2.9 cm

(4) 4 cm

8. A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower in LOS (Line of Sight) mode? (Given : radius of earth = 6.4 × 10^{6} m)

(1) 65 km

(2) 80 km

(3) 40 km

(4) 48 km

9. A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in fig. Work done by normal reaction on block in time t is

(1)

(2)

(3) 0

(4)

10. A magnet of total magnetic moment is placed ina time varying magnetic field, where B = 1 Tesla and ω = 0.125 rad/s. The work done for reversing the direction of the magnetic moment at t = 1 second, is

(1) 0.028 J

(2) 0.007 J

(3) 0.014 J

(4) 0.01 J

11. A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f_{1}. If the speed of the train is reduced to 17 m/s, the frequency registered is f_{2}. If speed of sound is 340 m/s, then the ratio f_{1}/f_{2} is

(1) 21/20

(2) 20/19

(3) 18/17

(4) 19/18

12. In the given circuit the cells have zero internal resistance. The currents (in amperes) passing through resistance R_{1 }and R_{2} respectively, are

(1) 1, 2

(2) 0, 1

(3) 0.5, 0

(4) 2, 2

13. In a Young’s double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle 1/40 rad by using light of wavelength λ_{1 }. When the light of wavelength λ_{2} is used a bright fringe is seen at the same angle in the same set up. Given that λ_{1} and λ_{2} are in visible range (380 nm to 740 nm), their values are

(1) 380 nm, 500 nm

(2) 625 nm, 500 nm

(3) 380 nm, 525 nm

(4) 400 nm, 500 nm

14. Three Carnot engines operate in series between a heat source at a temperature T_{1} and a heat sink at temperature T_{4} (see figure). There are two other reservoirs at temperature T_{2} and T_{3}, as shown, with T_{1} > T_{2} > T_{3} > T_{4} . The three engines are equally efficient if

(1)

(2)

(3)

(4)

15. In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be

(1)

(2)

(3)

(4)

16. A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is

(1) 20 mA

(2) 0.4 mA

(3) 100 mA

(4) 63 mA

17. If the magnetic field of a plane electromagnetic wave is given by (The speed of light = 3 × 10^{8} m/s) then the maximum electric field associated with it is

(1) 6 × 10^{4} N/C

(2) 3 × 10^{4} N/C

(3) 4.5 × 10^{4} N/C

(4) 4 × 10^{4} N/C

18. A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is

(1) F/2mR

(2) 2F/3mR

(3) F/3mR

(4) 3F/2mR

19. A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is

(1) 2mv^{2}

(2) mv^{2}

(3)

(4)

20. A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be

(1)

(2)

(3)

(4)

21. An insulating, thin rod of length l has a linear charge density on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is

(1) πnρl^{3}

(2) nρl^{3}

(3)

(4)

22. In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10^{–12} m, the minimum electron energy required is close to

(1) 100 keV

(2) 1 keV

(3) 500 keV

(4) 25 keV

23. A heat source at T = 10^{3} K is connected to another heat reservoir at T = 10^{2} K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 WK^{–1}m^{–1}, the energy flux through it in the steady state is

(1) 200 Wm^{−}^{2}

(2) 65 Wm^{−}^{2}

(3) 120 Wm^{−}^{2}

(4) 90 Wm^{−}^{2}

24. The density of a material is SI units is 128 kg m^{–3}. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is

(1) 640

(2) 410

(3) 40

(4) 16

25. Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is

(1) 1 : 4

(2) 1 : 8

(3) 1 : 2

(4) 1 : 16

26. A parallel plate capacitor is of area 6 cm2 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K_{1}= 10, K_{2}= 12 and K_{3} = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be

(1) 36

(2) 14

(3) 12

(4) 4

27. A uniform metallic wire has a resistance of 18 Ω and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is

(1) 4 Ω

(2) 12 Ω

(3) 8 Ω

(4) 2 Ω

28. A potentiometer wire AB having length L and resistance 12r is joined to a cell D of emf ε and internal resistance r. A cell C having emf ε/2 and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in fig. shows no deflection is

(1)

(2)

(3)

(4)

29. A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to

(1) 33.3 cm

(2) 10.0 cm

(3) 16.6 cm

(4) 20.0 cm

30. A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upwards, with a velocity 100 ms^{–1}, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is (g = 10 ms^{–2})

(1) 30 m

(2) 40 m

(3) 20 m

(4) 10 m

CHEMISTRY

1. The major product of the following reaction is

(1)

(2)

(3)

(4)

2. The chemical nature of hydrogen peroxide is

(1) Oxidising and reducing agent in both acidic and basic medium

(2) Oxidising and reducing agent in acidic medium, but not in basic medium

(3) Reducing agent in basic medium, but not in acidic medium

(4) Oxidising agent in acidic medium, but not in basic medium

3. Consider the following reduction processes:

Zn^{2+} + 2e^{–} → Zn(s); Eº = –0.76 V

Ca^{2+} + 2e^{–} → Ca(s); Eº = –2.87 V

Mg^{2+} + 2e^{–} → Mg(s); Eº = –2.36 V

Ni^{2+} + 2e^{–}→ Ni(s); Eº = –0.25 V

The reducing power of the metals increases in the order :

(1) Ca < Mg < Zn < Ni

(2) Ni < Zn < Mg < Ca

(3) Ca < Zn < Mg < Ni

(4) Zn < Mg < Ni < Ca

4. Consider the given plots for a reaction obeying Arrhenius equation (0°C < T < 300°C) : (k and E_{a} are rate constant and activation energy, respectively)

Choose the correct option:

(1) I is wrong but II is right

(2) Both I and II are correct

(3) Both I and II are wrong

(4) I is right but II is wrong

5. The electronegativity of aluminium is similar to

(1) Beryllium

(2) Carbon

(3) Lithium

(4) Boron

6. The values of for the following reactions at 300 K are, respectively (At 300 K, RT = 24.62 dm^{3} atm mol^{–1})

N_{2}(g) + O_{2}(g) ⇌ 2NO(g)

N_{2}O_{4}(g) ⇌ 2NO_{2}(g)

N_{2}(g) + 3H_{2}(g) ⇌ 2NH_{3}(g)

(1) 24.62 dm^{3} atm mol^{–1}, 606.0 dm^{6} atm^{2} mol^{–2}, 1.65 × 10^{–3} dm^{–6} atm^{–2 }mol^{2}

(2) 1, 24.62 dm^{3} atm mol^{–1}, 1.65 × 10^{–3} dm^{–6} atm^{–2} mol^{2}

(3) 1, 24.62 dm^{3} atm mol^{–1}, 606.0 dm^{6} atm^{2} mol^{–2}

(4) 1, 4.1 × 10^{–2} dm^{–3} atm^{–1} mol, 606 dm^{6} atm^{2} mol^{–2}

7. Liquids A and B form an ideal solution in the entire composition range. At 350 K, the vapor pressures of pure A and pure B are 7 × 10^{3} Pa and 12 × 10^{3} Pa, respectively. The composition of the vapor in equilibrium with a solution containing 40 mole percent of A at this temperature is

(1) x_{A} = 0.76; x_{B} = 0.24

(2) x_{A} = 0.37; x_{B} = 0.63

(3) x_{A} = 0.28; x_{B} = 0.72

(4) x_{A} = 0.4; x_{B} = 0.6

8. If dichloromethane (DCM) and water (H_{2}O) are used for differential extraction, which one of the following statements is correct?

(1) DCM and H_{2}O will make turbid/colloidal mixture

(2) DCM and H_{2}O will be miscible clearly

(3) DCM and H_{2}O would stay as upper and lower layer respectively in the separating funnel (S.F.)

(4) DCM and H_{2}O would stay as lower and upper layer respectively in the S.F.

9. The type of hybridisation and number of lone pair(s) of electrons of Xe in XeOF_{4}, respectively, are

(1) sp^{3}d and 2

(2) sp^{3}d^{2} and 2

(3) sp^{3}d^{2} and 1

(4) sp^{3}d and 1

10. Wilkinson catalyst is (Et = C_{2}H_{5})

(1) [(Ph_{3}P)_{3}lrCl]

(2) [(Ph_{3}P)_{3}RhCl]

(3) [(Et_{3}P)_{3}lrCl]

(4) [(Et_{3}P)_{3}RhCl]

11. The metal used for making X-ray tube window is

(1) Ca

(2) Na

(3) Mg

(4) Be

12. The major product ‘X’ formed in the following reaction is

(1)

(2)

(3)

(4)

13. Hall-Heroult’s process is given by

(1)

(2) Cr_{2}O_{3} + 2Al → Al_{2}O_{3} + 2Cr

(3) 2Al_{2}O_{3} + 3C → 4Al + 3CO_{2}

(4) Cu^{2+}(aq) + H_{2}(g) → Cu(s) + 2H^{+}(aq)

14. The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are

(1) 2 and 1

(2) 3 and 2

(3) 2 and 0

(4) 3 and 1

15. The increasing order of the pK_{a }values of the following compounds is

(1) D < A < C < B

(2) B < C < D < A

(3) B < C < A < D

(4) C < B < A < D

16. The total number of isomers for a square planar complex [M(F)(Cl)(SCN)(NO_{2})] is

(1) 8

(2) 12

(3) 4

(4) 16

17. Which of the following is not an example of heterogeneous catalytic reaction?

(1) Combustion of coal

(2) Ostwald’s process

(3) Hydrogenation of vegetable oils

(4) Haber’s process

18. A process had ΔH = 200 Jmol^{–1} and ∆S = 40 JK^{–1} mol^{–1}. Out of the values given below, choose the minimum temperature above which the process will be spontaneous

(1) 4 K

(2) 12 K

(3) 5 K

(4) 20 K

19. The major product of the following reaction is

20. Which dicarboxylic acid in presence of a dehydrating agent is least reactive to give an anhydride?

(1)

(2)

(3)

(4)

21. Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface?

(1)

(2)

(3)

(4)

22. Which hydrogen in compound (E) is easily replaceable during bromination reaction in presence of light?

(1) γ-hydrogen

(2) α-hydrogen

(3) δ-hydrogen

(4) β-hydrogen

23. Water filled in two glasses A and B have BOD values of 10 and 20, respectively. The correct statement regarding them, is

(1) Both A and B are suitable for drinking

(2) A is suitable for drinking, whereas B is not

(3) B is more polluted than A

(4) A is more polluted than B

24. The major product formed in the reaction given below will be

(1)

(2)

(3)

(4)

25. The correct structure of product ‘P’ in the following reaction is

(1)

(2)

(3)

(4)

26. The effect of lanthanoid contraction in the lanthanoid series of elements by and large means

(1) Increase in atomic radii and decrease in ionic radii

(2) Decrease in atomic radii and increase in ionic radii

(3) Decrease in both atomic and ionic radii

(4) Increase in both atomic and ionic radii

27. A mixture of 100 m mol of Ca(OH)_{2} and 2 g of sodium sulphate was dissolved in water and the volume was made up to 100 mL. The mass of calcium sulphate formed and the concentration of OH^{–} in resulting solution, respectively, are (Molar mass of Ca(OH)_{2}, Na_{2} SO_{4}and CaSO_{4} are 74, 143 and 136 g mol^{–1}, respectively; K_{sp} of Ca(OH)_{2} is 5.5 × 10^{–6})

(1) 1.9 g, 0.14 mol L^{−}^{1}

(2) 13.6 g, 0.28 mol L^{−}^{1}

(3) 13.6 g, 0.14 mol L^{−}^{1}

(4) 1.9 g, 0.28 mol L^{−}^{1}

28. Two pi and half sigma bonds are present in

(1) O_{2}^{+}

(2) O_{2}

(3) N_{2}^{+}

(4) N_{2}

29. Which primitive unit cell has unequal edge lengths (a ≠ b ≠ c) and all axial angles different from 90°?

(1) Hexagonal

(2) Monoclinic

(3) Triclinic

(4) Tetragonal

30. The decreasing order of ease of alkaline hydrolysis for the following esters is

(1) III > II > IV > I

(2) IV > II > III > I

(3) II > III > I > IV

(4) III > II > I > IV

**MATHEMATICS**

1. Let d ∈ R, and θ ∈[0, 2π]. If the minimum value of det(A) is 8, then a value f d is

(1) −5

(2) 2(√2 + 1)

(3) −7

(4) 2(√2 + 2)

2. If a circle C passing through the point (4, 0) touches the circle x^{2} + y^{2} + 4x – 6y = 12 externally at the point (1, –1), then the radius of C is

(1) 5

(2) 2√5

(3) √57

(4) 4

3. If then k equals

(1) 400

(2) 100

(3) 200

(4) 50

4. The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is

(1) 1465

(2) 1356

(3) 1365

(4) 1256

5. If and equals

(1)

(2)

(3) 1/3

(4) −4/3

6. Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m. A vertical lamp-post at the mid point D of AC subtends an angle 30° at B. The height (in m) of the lamp-post is

(1) 2√21

(2) 7√3

(3)

(4)

7. Let If I is minimum then the ordered pair (a, b) is

(1) (−√2, 0)

(2) (0, √2)

(3) (√2, −√2)

(4) (−√2, √2)

8. An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, …, 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is

(1) 13/36

(2) 15/72

(3) 19/36

(4) 19/72

9. Consider the quadratic equation (c – 5)x2 – 2cx + (c – 4) = 0, c ≠ Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is

(1) 11

(2) 18

(3) 12

(4) 10

10. If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin is

(1) (4, 3)

(2) (3, 4)

(3) (4, 4)

(4) (2, 2)

11. If the third term in the binomial expansion of equals 2560, then a possible value of x is

(1) 2√2

(2) 1/4

(3) 4√2

(4) 1/8

12. Let z_{1} and z_{2} be any two non-zero complex numbers such that 3|z_{1}| = 4|z_{2}|. If then

(1) lm(z) = 0

(2)

(3)

(4) Re(z) = 0

13. The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is

(1) 4 : 9

(2) 6 : 7

(3) 10 : 3

(4) 5 : 8

14. Let

Let S be the set of points in the interval (–4, 4) at which f is not differentiable. Then S

(1) Equals {–2, –1, 0, 1, 2}

(2) Equals {–2, 2}

(3) Is an empty set

(4) Equals {–2, –1, 1, 2}

15. Consider the statement : “P(n) : n^{2} – n + 41” is prime.” Then which one of the following is true?

(1) P(5) is false but P(3) is true

(2) P(3) is false but P(5) is true

(3) Both P(3) and P(5) are false

(4) Both P(3) and P(5) are true

16. A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R(3, –2) are fixed points, then the locus of the centroid of ∆PQR is a line

(1) Parallel to y-axis

(2) With slope 3/2

(3) With slope 2/3

(4) Parallel to x-axis

17. If the parabolas y^{2} = 4b(x – c) and y^{2} = 8ax have a common normal, then which one of the following is a valid choice for the ordered triad (a, b, c)?

(1) (1/2, 2, 0)

(2) (1/2, 2, 3)

(3) (1, 1, 0)

(4) (1, 1, 3)

18. The sum of all values of θ ∈(0, π/2) satisfying sin^{2 }2θ + cos^{4} 2θ = 3/4 is

(1) 5π/4

(2) π/2

(3) 3π/8

(4) π

19. The equation of a tangent to the hyperbola 4x^{2} – 5y^{2} = 20 parallel to the line x – y = 2 is

(1) x – y + 7 = 0

(2) x – y + 1 = 0

(3) x – y – 3 = 0

(4) x – y + 9 = 0

20. Let f : R → R be a function such that f(x) = x^{3} + x^{2}f ʹ(1) + xfʹʹ (2) + f ʹ ʹ ʹ (3), ∈ x R. Then f(2) equals

(1) 8

(2) −4

(3) −2

(4) 30

21. If the system of equations

x + y + z = 5

x + 2y + 3z = 9

x + 3y + αz = β

has infinitely many solutions, then β – α equals

(1) 18

(2) 21

(3) 8

(4) 5

22. The shortest distance between the point (3/2, 0) and the curve y = √x, (x > 0), is

(1) 3/2

(2) 5/4

(3) √3/2

(4) √5/2

23. In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

(1) 1

(2) 38

(3) 102

(4) 42

24. Let n ≥ 2 be a natural number and 0 < θ < π/2. Then is equal to (where C is a constant of integration)

(1)

(2)

(3)

(4)

25. The plane passing through the point (4, –1, 2) and parallel to the lines and also passes through the point :

(1) (–1, –1, –1)

(2) (–1, –1, 1)

(3) (1, 1, 1)

(4) (1, 1, –1)

26. If 5, 5r, 5r^{2} are the lengths of the sides of a triangle, then r cannot be equal to :

(1) 3/4

(2) 7/4

(3) 3/4

(4) 5/4

27. For each t∈ R, let [t] be the greatest integer less than or equal to t. Then,

(1) Equals 0

(2) Equals 1

(3) Equals −1

(4) Does not exist

28. Let and be three vectors such that is perpendicular to Then a possible value of (λ_{1}, λ_{2}, λ_{3}) is :

(1) (1, 3, 1)

(2) (1, 5, 1)

(3) (1/2, 4, −2)

(4) (−1/2, 4, 0)

29. If the area enclosed between the curves y = kx^{2} and x = ky^{2}, (k > 0), is 1 square unit. Then k is :

(1) √3

(2) 1/√3

(3) √3/2

(4) 2/√3

30. Let A be a point on the line and B(3, 2, 6) be a point in the space. Then the value of μ for which the vector is parallel to the plane x – 4y + 3z = 1 is :

(1) 1/4

(2) 1/2

(3) 1/8

(4) −1/4