## JEE Main September 6 2020 Shift 2 Question Paper with Answer Key

Physics

1. For a plane electromagnetic wave, the magnetic field at a point x and time t is  The instantaneous electric field E corresponding to B is:

(speed of light c = 3 × 108 ms1)

(1)

(2)

(3)

(4)

2. Particle A of mass m1 moving with velocity  collides with another particle B of mass m2 which is at rest initially. Let be the velocities of particles A and B after collision  respectively. If m1 = 2m2 and after collision  the angle between  is:

(1)  105°

(2)  15°

(3)  −45°

(4)  60°

3. When a car is at rest, its driver sees raindrops falling on it vertically. When driving the car with speed v, he sees that raindrops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1 + β) v, this angle changes to 45°. The value β is close to:

(1)  0.50

(2)  0.73

(3)  0.37

(4)  0.41

4. A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field  The magnetic moment of this moving particle:

(1)

(2)

(3)

(4)

5. A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5 P is:

(1)  R/3

(2)  3R/2

(3)  R/2

(4)  2R

6. A circuit to verify Ohm’s law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit:

(1)  Ammeter is always connected in series and voltmeter in parallel.

(2)  Both, ammeter and voltmeter must be connected in series.

(3)  Both ammeter and voltmeter must be connected in parallel.

(4)  The ammeter is always used in parallel and voltmeter in series.

7. A square loop of side 2a and carrying current I is kept in the xz plane with its centre at the origin. A long wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about z-axis will be:

(1)

(2)

(3)

(4)

8. In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as:

(1)  √T

(2)  1/T

(3)  T

(4)  1/√T

9. When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by y (t) = y0sin2ωt, where ‘y’ is measured from the lower end of unstretched spring. Then ω is:

(1)

(2)

(3)

(4)

10. The linear mass density of a thin rod AB of length L varies from A to B as  where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:

(1)

(2)

(3)

(4)

11. A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms–1 at a point where the pressure is P pascal. At another point where pressure is P/2 Pascal its speed is V ms–1. If the density of the fluid is kg m–3 and the flow is streamlined, then V is equal to:

(1)

(2)

(3)

(4)

12. Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity K1, K2 and K3, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100°C and the other at 0°C (see figure). If the joints of the rod are at 70°C and 20°C in steady-state and there is no loss of energy from the surface of the rod, the correct relationship between K1, K2 and K3 are:

(1)  K1 : K2 = 5 : 2, K1 : K3 = 3 : 5

(2)  K1 < K2 < K3

(3)  K1 : K3 = 2 : 3, K2 : K3 = 2 : 5

(4)  K1 > K2 > K3

13. Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to (Given: nitrogen molecule weight: 4.64 × 10–26 kg, Boltzman constant: 1.38 × 10–23 J/K, Planck constant: 6.63 × 10–34s)

(1)  0.44 Å

(2)  0.34 Å

(3)  0.20 Å

(4)  0.24 Å

14. Consider the force F on a charge ‘q’ due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if ‘q’ is placed at distance r from the centre of the shell?

(1)

(2)

(3)

(4)

15. Two identical electric point dipoles have dipole moments  are held on the x-axis at distance ‘a’ from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is ‘m’, their speed when they are infinitely far apart is:

(1)

(2)

(3)

(4)

16. Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of the smaller planet, the minimum firing speed needed is:

(1)

(2)

(3)

(4)

17. In the figure shown, the current in the 10 V battery is close to:

(1)  0.21 A from positive to the negative terminal

(2)  0.36 A from negative to the positive terminal

(3)  0.42 A from positive to the negative terminal

(4)  0.71 A from positive to the negative terminal

18. A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm, 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as:

(1)  (5.54 ± 0.07) mm

(2)  (5.5375 ± 0.0740) mm

(3)  (5.5375 ± 0.0739) mm

(4)  (5.538 ± 0.074) mm

19. Given the masses of various atomic particles mp = 1.0072 u, mn = 1.0087 u, me = 0.000548 u, mv[bar] = 0, md = 2.0141 u, where p ≡ proton, n ≡ neutron, e ≡ electron, v [bar] ≡ antineutrino and d ≡ deuteron. Which of the following processes is allowed by momentum and energy conservation?

(1)  n + n deuterium atom (electron bound to the nucleus)

(2)  e+ + e → γ

(3)  p → n + e+ + v [bar]

(4)  n + p → d + γ

20. A particle moving in the xy plane experiences a velocity-dependent force, where vx and vy are the x and y components of its velocity v. If a is the acceleration of the particle, then which of the following statements is true for the particle?

(1)  The kinetic energy of the particle is constant in time.

(2)  quantity v × a is constant in time

(3)  quantity v . a is constant in time

(4)  F arises due to a magnetic field

21. A Young’s double-slit experiment is performed using monochromatic light of wavelength λ. The intensity of light at a point on the screen, where the path difference is λ, is K units. The intensity of light at a point where the path difference is λ / 6 is given by nK/12, where n is an integer. The value of n is __________.

22. The centre of mass of the solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then the value of x is __________.

23. The output characteristics of a transistor is shown in the figure. When VCE is 10V and IC = 4.0 mA, then the value of βac is __________.

24. An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to __________.

25. In a series LR circuit, power of 400W is dissipated from a source of 250 V, 50 Hz. The power factor of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as (n/3π) μF, then the value of n is __________.

Chemistry

1. Match the following :

(1)  (i)-(d),(ii)-(c),(iii)-(e),(iv)-(a)

(2)  (i)-(b),(ii)-(a),(iii)-(c),(iv)-(d)

(3)  (i)-(b),(ii)-(d),(iii)-(e),(iv)-(a)

(4)  (i)-(d),(ii)-(c),(iii)-(b)-(iv)-(e)

2. The IUPAC name of the following compound is:

(1)  2-nitro-4-hydroxymethyl-5-amino benzaldehyde

(2)  3-amino-4-hydroxymethyl-5-nitro benzaldehyde

(3)  4-amino-2-formyl-5-hydroxymehtyl nitrobenzene

(4)  5-amino-4-hydroxymethyl-2-nitro benzaldehyde

3. For the given cell;

Cu(s)|Cu2+(C1M)||Cu2+(C2M)|Cu(s)

Change in Gibbs energy (ΔG) is negative, if :

(1)  C2 = √2 C1

(2)  C2 = C1/√2

(3)  C1 = 2C2

(4)  C2 = C1

4. Reaction of an inorganic sulphite X with dilute H2SO4 generates compound Y. Reaction of Y with NaOH gives X. Further, the reaction of X with Y and water affords compound Z. Y and Z, respectively, are :

(1)  SO2 and NaHSO3

(2)  S and Na2SO3

(3)  SO2 and Na2SO3

(4)  SO3 and NaHSO3

5. The value of KC is 64 at 800 K for the reaction N2(g) + 3H2(g) ⇌ 2NH3(g)

The value of KC for the following reaction is:

(1)  1/4

(2)  8

(3)  1/8

(4)  1/64

6. The correct match between Item – I (Starting material) and Item – II (reagent) for the preparation of benzaldehyde is :

7. For a d4 metal ion in an octahedral field, the correct electronic configuration is :

(1)  e2g t22g when ∆0 < P

(2)  t42g e0g when ∆0 < P

(3)  t32g e1g when ∆0 > P

(4)  e1g t32g when ∆0 < P

8. The correct match between Item – I and Item – II is :

Item-I                                Item-II

(a) Natural rubber              (I) 1, 3-butadiene + styrene

(b) Neoprene                     (II) 1, 3-butadiene + acrylonitrile

(c) Buna-N                        (III) Chloroprene

(d) Buna-S                        (IV) Isoprene

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

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

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

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

9. Which one of the following statement is not true?

(1)  Lactose contains α-glycosidic linkage between C1 of galactose and C4 of glucose.

(2)  Lactose is a reducing sugar and it gives Fehling’s test.

(3)  On acid hydrolysis, lactose gives one molecule of D(+)-glucose and one molecule of D(+)-galactose.

(4)  Lactose(C11H22O11) is a disaccharide and it contains 8 hydroxyl groups.

10. The element that can be refined by distillation is :

(1)  tin

(2)  gallium

(3)  zinc

(4)  nickel

11. Match the following compounds (Column-I) with their uses (Column-II) :

Column-I                           Column-II

(I) Ca(OH)2                       (A) Casts of statues

(II) NaCl                           (B) White wash

(III)          (C) Antacid

(IV) CaCO­3                      (D) Washing soda preparation

(1)  (I)-(B),(II)-(C),(III)-(D),(IV)-(A)

(2)  (I)-(C),(II)-(D),(III)-(B),(IV)-(A)

(3)  (I)-(B),(II)-(D),(III)-(A),(IV)-(C)

(4)  (I)-(D),(II)-(A),(III)-(C),(IV)-(B)

12. Mischmetal is an alloy consisting mainly of :

(1)  lanthanoid and actinoid metals

(2)  lanthanoid metals

(3)  actinoid metals

(4)  actinoid and transition metals

13. For a reaction, 4M(s) + n O2(g) → 2 M2 On (s) the free energy change is plotted as a function of temperature. The temperature below which the oxide is stable could be inferred from the plot as the point at which :

(1)  the free energy change shows a change from negative to positive value.

(2)  the slope changes from positive to zero

(3)  the slope changes from positive to negative.

(4)  the slope changes from negative to positive.

14. The increasing order of the boiling points of the major products A,B and C of the following reaction will be :

(1)  A < B < C

(2)  C < A < B

(3)  A < C < B

(4)  B < C < A

15. The average molar mass of chlorine is 35.5g mol1. The ratio of 35Cl to 37Cl in naturally occurring chlorine is close to :

(1)  1 : 1

(2)  3 : 1

(3)  2 : 1

(4)  4 : 1

16. Which of the following compound can be prepared in good yield by Gabriel phthalimide synthesis?

17. The reaction of NO with N2O4 at 250 K gives:

(1)  N2O

(2)  NO2

(3)  N2O5

(4)  N2O3

18. A set of solution is prepared using 180 g of water as a solvent and 10g of different nonvolatile solutes A, B and C. The relative lowering of vapour pressure in the presence of these solutes are in the order [Given, molar mass of A = 100 g mol1 ; B = 200g mol1 ; C = 10,000g mol1]

(1)  A > C > B

(2)  B > C > A

(3)  C > B > A

(4)  A > B > C

19. Dihydrogen of high purity (> 99.95%) is obtained through :

(1)  the electrolysis of acidified water using Pt electrodes.

(2)  the reaction of Zn with dilute HCl

(3)  the electrolysis of brine solution

(4)  the electrolysis of warm Ba(OH)2

20. A crystal is made up of metal iron ‘M1‘ and ‘M2‘ and oxide ions. Oxide ions form a ccp lattice structure. The cation ‘M1‘ occupies 50% of octahedral voids and the cation ‘M2‘ occupies 12.5% of tetrahedral voids of oxide lattice. The oxidation number of ‘M1‘ and ‘M2‘ are, respectively:

(1)  +2, +4

(2)  +3, +1

(3)  +4, +2

(4)  +1, +3

21. For Freundlich adsorption isotherm, a plot of log (x/m) (y-axis) and log p (x-axis) gives a straight line. The intercept and slope for the line is 0.4771 and 2, respectively. The mass of gas, adsorbed per gram of adsorbent if the initial pressure is 0.04 atm, is…………….×104 (log 3=0.4771)

22. The atomic number of Unnilunium is …………….

23. A solution of phenol in chloroform when treated with aqueous NaOH gives compound P as a major product. The mass percentage of carbon in P is ……………. (to the nearest integer)

(Atomic mass : C = 12; H = 1; O = 16)

24. The rate of a reaction decreased by 3.555 times when the temperature was changed from 40°C to 30oC. The activation energy (in KJ mol1) of the reaction is……… [Take; R = 8.314 J mol1 K1 In 3.555 = 1.268]

25. If the solubility product of AB2 is 3.20 × 1011 M3, then the solubility of AB2 in pure water is ……….× 104 mol L1 [Assuming that neither kind of ion reacts with water].

Answer: (2 × 104 mol/lit)

Mathematics

1. If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies:

(1)  e4 + 2e2 – 1 = 0

(2)  e2 + 2e – 1 = 0

(3)  e4 + e2 – 1 = 0

(4)  e2 + e – 1 =0

2. The set of all real values of λ for which the function f(x) = (1− cos2 x) (λ + sin x),  has exactly one maxima and exactly one minima, is:

(1)  (−3/2, 3/2)

(2)  (−1/2, 1/2)

(3)  (−3/2, 3/2)

(4)  (−1/2, 1/2)

3. The probabilities of three events A, B and C are given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5. If P (A ∪ B) = 0.8, P (A ∩ C) = 0.3, P (A ∩ B ∩ C) = 0.2, P (B ∩ C) = β and P(A ∪ B ∪C) = α , where 0.85 ≤ α ≤ 0.95 , then β lies in the interval:

(1)  [0.36,0.40]

(2)  [0.25,0.35]

(3)  [0.35,0.36]

(4)  [0.20,0.25]

4. The common difference of the A.P. b1, b2,….. bm is 2 more than the common difference of A.P. a1, a2, …an. If a40 = −159, a100 = −399 and b100 = a70, then b1 is equal to:

(1)  −17

(2)  81

(3)  127

(4)  −81

5. The integral  equals:

(1)  e(4e – 1)

(2)  e(4e + 1)

(3)  4e2 – 1

(4)  e(2e – 1)

6. If the tangent to the curve, y = f(x) = xlogex, (x > 0) at a point (c, f(c)) is parallel to the line-segment joining the points (1,0) and (e, e), then c is equal to:

(1)

(2)

(3)

(4)

7. If  is the solution of the differential equation,   then the function p(x) is equal to:

(1)  cosec x

(2)  cot x

(3)  tan x

(4)  sec x

8. If α and β are the roots of the equation 2x(2x + 1) = 1, then β is equal to:

(1)  2α(α – 1)

(2)  −2α(α + 1)

(3)  2α2

(4)  2α(α + 1)

9. For all twice differentiable functions f: R→ R, with f(0) = f(1) = f´(0) = 0,

(1)  f”(x) = 0, at every point x∈(0,1)

(2)  f”(x) ≠ 0, at every point x∈(0,1)

(3)  f”(x) = 0, for some x∈(0,1)

(4)  f”(0) = 0

10. The area (in sq. units) of the region enclosed by the curves y = x2−1 and y = 1−x2 is equal to:

(1)  4/3

(2)  7/2

(3)  16/3

(4)  8/3

11. For a suitably chosen real constant a, let a function, f:R−{−a}→R be defined by  Further suppose that for any real number x ≠ −a and f(x) ≠ −a, (fof) (x) = x. Then f(−1/2) is equal to:

(1)  −3

(2)  3

(3)  1/3

(4)  −1/3

12. Let  If B = A + A4, then det (B):

(1)  is one

(2)  lies in (1, 2)

(3)  lies in (2, 3)

(4)  is zero

13. The centre of the circle passing through the point (0,1) and touching the parabola y = x2 at the point (2, 4) is :

(1)  (3/10, 16/5)

(2)  (6/5, 53/10)

(3)  (−16/5, 53/10)

(4)  (−53/10, 16/5)

14. A plane P meets the coordinate axes at A, B and C respectively. The centroid of a triangle ABC is given to be (1, 1, 2). Then the equation of the line through this centroid and perpendicular to the plane P is:

(1)

(2)

(3)

(4)

15. Let f : R→ R be a function defined by f(x) = max {x, x2}. Let S denote the set of all points in R, where f is not differentiable. Then

(1)  {0, 1}

(2)  an empty set

(3)  {1}

(4)  {0}

16. The angle of elevation of the summit of a mountain from a point on the ground is 450. After climbing up one km towards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is:

(1)

(2)

(3)

(4)

17. If the constant term in the binomial expansion of  is 405, then |k| equals:

(1)  1

(2)  9

(3)  2

(4)  3

18. Let z = x + iy be a non-zero complex number such that z2 = i|z|2, where i = √−1 , then z lies on the

(1)  line, y = x

(2)  real axis

(3)  imaginary axis

(4)  line, y = −x

19. Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (−1, −4) in this line is:

(1)  (11/5, 28/5)

(2)  (8/5, 29/5)

(3)  (29/5, 11/5)

(4)  (29/5, 8/5)

20. Consider the statement : “For an integer n, if n3 − 1 is even, then n is odd.” The contrapositive statement of this statement is:

(1)  For an integer n, if n is even, then n3−1 is even

(2)  For an integer n, if n is odd, then n3−1 is even

(3)  For an integer n, if n3−1 is not even, then n is not odd.

(4)  For an integer n, if n is even, then n3−1 is odd

21. The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is:

22. If  be two non-zero vectors such that  is perpendicular to  then the value of λ is________

23. Consider the data on x taking the values 0, 2, 4, 8, …..,2n with frequencies nC0, nC1, nC2nCn, respectively. If the mean of this data is 728/2n, then n is equal to:________

24. Suppose that function f : R→R satisfies f(x+y) = f(x) f(y) for all x, y ∈ R and f(1) = 3. If  then n is equal to ………..

25. The sum of distinct values of λ for which the system of equations

(λ − 1)x + (3λ + 1)y + 2λz = 0

(λ − 1) x + (4λ − 2)y + (λ + 3)z = 0

2x + (3λ + 1)y + 3(λ − 1)z = 0 has non-zero solutions, is:

## JEE Main September 6 2020 Shift 1 Question Paper with Answer Key

Physics

1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is rotating with angular frequency ω, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is:

(1)  4ml2ω

(2)  2ml2ω

(3)  3ml2ω

(4)  ml2ω

2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least count of the screw gauge, are respectively:

(1)  Positive, 0.1 mm

(2)  Positive, 0.1μ m

(3)  Positive, 10 μm

(4)  Negative, 2 μm

3. An electron, a doubly ionized helium ion (He++) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths λe, λHe++ and λp is:

(1)  λe > λp > λHe++

(2)  λe > λHe++ > λp

(3)  λe < λp < λHe++

(4)  λe < λHe++ = λp

4. For the given input voltage waveform Vin(t), the output voltage waveform Vo(t), across the capacitor is correctly depicted by:

5. Shown in the figure is a hollow ice cream cone (it is open at the top). If its mass is M, the radius of its top, R and height, H, then its moment of inertia about its axis is:

(1)  MR2/2

(2)  MR2/3

(3)

(4)  MH2/3

6. A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:

(1)  1 : 2

(2)  1 : 3

(3)  1 : 6

(4)  3 : 4

7. You are given that mass of

Mass of

and Mass off

When 20 g of  is converted into  by proton capture, the energy liberated, (in kWh), is: [Mass of nucleon = 1 GeV/c2]

(1)  6.82 × 105

(2)  4.5 × 105

(3)  8 × 106

(4)  1.33 × 106

8. If the potential energy between two molecules is given by  then at equilibrium, the separation between molecules, and the potential energy are:

(1)

(2)

(3)

(4)

9. A clock has a continuously moving second’s hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms–2) is of the order of

(1)  10−3

(2)  10−1

(3)  10−2

(4)  10−4

10. Identify the correct output signal Y in the given combination of gates (as shown) for the given inputs A and B.

11. An electron is moving along +x direction with a velocity of 6 × 106 ms–1. It enters a region of the uniform electric field of 300 V/cm pointing along +y direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the x-direction will be

(1)  3 × 10–4 T, along –z direction

(2)  5 × 10–3 T, along –z direction

(3)  5 × 10–3 T, along +z direction

(4)  3 × 10–4 T, along +z direction

12. In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m. The separation between P and Q is 5 m and the phase of P is ahead of that of Q by 90°. A, B and C are three distinct points of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:

(1)  4 : 1 : 0

(2)  2 : 1 : 0

(3)  0 : 1 : 2

(4)  0 : 1 : 4

13. A point-like object is placed at a distance of 1 m in front of a convex lens of the focal length of 0.5 m. A plane mirror is placed at a distance of 2 m behind the lens. The position and nature of the final image formed by the system are:

(1)  1 m from the mirror, virtual

(2)  2.6 m from the mirror, virtual

(3)  1 m from the mirror, real

(4)  2.6 m from the mirror, real

14. An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is: (g = 10 ms–2)

(1)  0.45 m

(2)  0.60 m

(3)  0.20 m

(4)  0.80 m

15. Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of  are given, respectively by:

(1)

(2)

(3)

(4)

16. An object of mass m is suspended at the end of a massless wire of length L and area of cross-section A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:

(1)

(2)

(3)

(4)

17. An AC circuit has R = 100Ω, C = 2μF and L = 80 mH, connected in series. The quality factor of the circuit is:

(1)  20

(2)  2

(3)  0.5

(4)  400

18. Charges Q1 and Q2 are at points A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then Q1/Q2 is proportional to:

(1)

(2)

(3)

(4)

19. A sound source S is moving along a straight track with speed v, and is emitting, the sound of frequency vO (see figure). An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by (t0 represents the instant when the distance between the source and observer is minimum)

20. A particle of charge q and mass m is moving with velocity –vi (v ≠ 0) towards a large screen placed in the Y-Z plane at a distance d. If there is a magnetic field B = B0k, the minimum value of v for which the particle will not hit the screen is:

(1)  qdB0/m

(2)  qdB0/3m

(3)  2qdB0/m

(4)  qdB0/2m

21. Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is ________.

22. Suppose that intensity of a laser is The rms electric field, in units of V/m associated with this source is close to the nearest integer is __________. (∈0 = 8.86 × 10–12 C2Nm–2; c = 3 × 108 ms–1)

23. The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is  If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is_______.

24. Initially a gas of diatomic molecules are contained in a cylinder of volume V1 at a pressure P1 and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in the number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a volume 2V1 is given by P2. The ratio P2/P1 is ________.

25. A part of a complete circuit is shown in the figure. At some instant, the value of current I is 1A and it is decreasing at a rate of 102 As–1. The value of the potential difference VP – VQ, (in volts) at that instant, is _________.

Chemistry

1. The INCORRECT statement is:

(1)  Cast iron is used to manufacture wrought iron.

(2)  Brass is an alloy of copper and nickel.

(3)  German silver is an alloy of zinc, copper and nickel.

(4)  Bronze is an alloy of copper and tin

2. The species that has a spin-only magnetic moment of 5.9 BM, is: (Td= tetrahedral)

(1)  [Ni(CN)4]2 (square planar)

(2)  Ni(CO)4(Td)

(3)  [MnBr4]2(Td)

(4)  [NiCl4]2(Td)

3. For the reaction

(1)  Kc = Kp(RT)1/2

(2)  Kc = Kp(RT)1/2

(3)  Kc = Kp(RT)3/2

(4)  Kc = Kp (RT)

4. Consider the following reactions:

A is:

5. Arrange the following solutions in the decreasing order of pOH:

(A) 0.01 M HCl

(B) 0.01 M NaOH

(C) 0.01 M CH3COONa

(D) 0.01 M NaCl

(1)  (A) > (C) > (D) > (B)

(2)  (B) > (D) > (C) > (A)

(3)  (B) > (C) > (D) > (A)

(4)  (A) > (D) > (C) > (B)

6. The variation of equilibrium constant with temperature is given below :

Temperature Equilibrium Constant

T1= 25°C K1= 10

T2= 100°C K2= 100

The value of ∆H°, ∆G° at T1 and ∆G° at T2 (in Kj mol1) respectively, are close to

[use R = 8.314JK1 mol1]

(1)  28.4, −7.14 and −5.71

(2)  0.64, −7.14 and −5.71

(3)  28.4, −5.71 and −14.29

(4)  0.64, −5.71 and −14.29

7. Consider the following reactions

A→ P1; B→ P2; C→ P3; D →P4,

The order of the above reactions are a, b, c and d, respectively. The following graph is obtained when log[rate] vs. log[conc.] are plotted.

Among the following the correct sequence for the order of the reactions is:

(1)  c > a > b > d

(2)  d > a > b > c

(3)  d > b > a > c

(4)  a > b > c > d

8. The major product obtained from the following reactions is:

9. Which of the following compounds shows geometrical isomerism?

(1)  2-methylpent-1-ene

(2)  4-methylpent-2-ene

(3)  2-methylpent-2-ene

(4)  4-methylpent-1-ene

10. The lanthanoid that does NOT shows +4 oxidation state is:

(1)  Dy

(2)  Ce

(3)  Tb

(4)  Eu

11. The major products of the following reactions are:

12. The major product of the following reaction is:

13. The increasing order of pKb values of the following compounds is:

(1)  I < II < III < IV

(2)  II < IV < III < I

(3)  I < II < IV < III

(4)  II < I < III < IV

14. kraft temperature is the temperature :

(1)  Above which the aqueous solution of detergents starts boiling

(2)  Below which the formation of micelles takes place.

(3)  Above which the formation of micelles takes place.

(4)  Below which the aqueous solution of detergents starts freezing.

15. The set that contains atomic numbers of only transition elements, is?

(1)  9, 17, 34, 38

(2)  21, 25, 42, 72

(3)  37, 42, 50, 64

(4)  21, 32, 53, 64

16. Consider the Assertion and Reason given below.

Assertion (A): Ethene polymerized in the presence of Ziegler Natta Catalyst at high temperature and pressure is used to make buckets and dustbins.

Reason (R): High density polymers are closely packed and are chemically inert. Choose the correct answer from the following:

(1)  (A) and (R) both are wrong.

(2)  Both (A) and (R) are correct and (R) is the correct explanation of (A)

(3)  (A) is correct but (R) is wrong

(4)  Both (A) and (R) are correct but (R) is not the correct explanation of (A)

17. A solution of two components containing n1 moles of the 1st component and n2 moles of the 2nd component is prepared. M1 and M2 are the molecular weights of component 1 and 2 respectively. If d is the density of the solution in g mL1, C2 is the molarity and x2 is the mole fraction of the 2nd component, then C2 can be expressed as:

(1)

(2)

(3)

(4)

18. The correct statement with respect to dinitrogen is?

(1)  Liquid dinitrogen is not used in cryosurgery.

(2)  N2 is paramagnetic in nature

(3)  It can combine with dioxygen at 25°C

(4)  It can be used as an inert diluent for reactive chemicals.

19. Among the sulphates of alkaline earth metals, the solubility of BeSO4 and MgSO4 in water, respectively, are:

(1)  Poor and High

(2)  High and high

(3)  Poor and poor

(4)  High and poor

20. The presence of soluble fluoride ion upto 1ppm concentration in drinking water, is:

(1)  Harmful to skin

(2)  Harmful to bones

(3)  Safe for teeth

(4)  Harmful for teeth

21. A spherical balloon of radius 3cm containing helium gas has a pressure of 48 × 103 At the same temperature, the pressure, of a spherical balloon of radius 12 cm containing the same amount of gas will be…………………….× 106 bar.

22. The elevation of boiling point of 0.10m aqueous CrCl3 xNH3 solution is two times that of 0.05 m aqueous CaCl2 The value of x is……………..

[Assume 100% ionisation of the complex and CaCl2, coordination number of Cr as 6, and that all NH3 molecules are present inside the coordination sphere]

23. Potassium chlorate is prepared by the electrolysis of KCl in basic solution

If only 60% of the current is utilized in the reaction, the time (rounded to the nearesthour) required to produce 10g of KClO3 using a current of 2A is ………….

(Given: F = 96,500 C mol1; molar mass of KClO3=122 g mol1)

24. In an estimation of bromine by Carius method, 1.6 g of an organic compound gave 1.88 g of AgBr. The mass percentage of bromine in the compound is……. .(Atomic mass, Ag=108, Br=80 g mol–1)

25. The number of Cl = O bonds in perchloric acid is, “……………”

Mathematics

1. The region represented by {z = x + iy ∈ C : z − Re(z) ≤ 1} is also given by the inequality: {z = x + iy ∈ C : z − Re(z) ≤ 1}

(1)

(2)

(3)  y2 ≥ 2 (x + 1)

(4)  y2 ≥ x + 1

2. The negation of the Boolean expression p (~p ∧ q) is equivalent to:

(1)  p∧~q

(2)  ~p~q

(3)  ~pq

(4)  ~p∧~q

3. The general solution of the differential equation  is:

(1)

(2)

(3)

(4)

4. Let L1 be a tangent to the parabola y2 = 4(x+1) and L2 be a tangent to the parabola y2 = 8(x+2) such that L1 and L2 intersect at right angles. Then L1 and L2 meet on the straight line:

(1)  x + 2y =0

(2)  x + 2 = 0

(3)  2x + 1 = 0

(4)  x + 3 = 0

5. The area (in sq. units) of the region A = {(x, y): |x| + |y| ≤ 1, 2y2|x|}

(1)  1/6

(2)  5/6

(3)  1/3

(4)  7/6

6. The shortest distance between the lines  and x + y + z + 1 = 0, 2x – y + z + 3 = 0 is:

(1)  1

(2)  1/√2

(3)  1/√3

(4)  1/2

7. Let a, b, c, d and p be any non zero distinct real numbers such that (a2 + b2 + c2) p2 − 2(ab + bc + cd) p + (b2 + c2 + d2) = 0. Then:

(1)  a, c, p are in G.P.

(2)  a, b, c, d are in G.P.

(3)  a, b, c, d are in A.P.

(4)  a, c, p are in A.P.

8. Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

(1)  2! 3! 4!

(2)  (3!)3(4!)

(3)  3!(4!)3

(4)  (3!)2(4!)

9. The values of λ and μ for which the system of linear equations

x + y + z = 2

x + 2y + 3z = 5

x + 3y + λz = μ

has infinitely many solutions are, respectively:

(1)  6 and 8

(2)  5 and 8

(3)  5 and 7

(4)  4 and 9

10. Let m and M be respectively the minimum and maximum values of

Then the ordered pair (m, M) is equal to:

(1)  (−3, −1)

(2)  (−4, −1)

(3)  (1, 3)

(4)  (−3, 3)

11. A ray of light coming from the point (2, 2√3) is incident at an angle 30° on the line x = 1 at the point A. The ray gets reflected on the line x = 1 and meets x-axis at the point B. Then, the line AB passes through the point:

(1)  (4, −√3)

(2)  (3, −1/√3)

(3)  (3, −√3)

(4)  (4, −√3/2)

12. Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:

(1)  10/99

(2)  5/33

(3)  15/101

(4)  5/101

13. If f(x + y) = f(x) f(y) and  where N is the set of all natural number, then the value of   is:

(1)  2/3

(2)  1/9

(3)  1/3

(4)  4/9

14. If {p} denotes the fractional part of the number p, then  is equal to:

(1)  5/8

(2)  1/8

(3)  7/8

(4)  3/8

15. Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse  from any of its foci?

(1)  (−1, √3)

(2)  (−2, √3)

(3)  (−1, √2)

(4)  (1, 2)

16.

(1)  is equal to 1

(2)  is equal to 1/2

(3)  does not exist

(4)  is equal to −1/2

17. If  (n, a > 1) then the standard deviation of n observations x1, x2, x3…xn is:

(1)

(2)

(3)  a – 1

(4)

18. If α and β be two roots of the equation x2 − 64x + 256 = 0. Then the value of  is :

(1)  1

(2)  3

(3)  2

(4)  4

19. The position of a moving car at time t is given by f(t) = at2 + bt + c, t > 0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t1, t2] is attained at the point :

(1)  (t1 + t2)/2

(2)  2a(t1 + t2) + b

(3)  (t2 – t1)/2

(4)  a(t2 – t1) + b

20. If  and  such that I2 = αI1 then α equals to:

(1)  5050/5049

(2)  5050/5051

(3)  5051/5050

(4)  5049/5050

21. If  are unit vectors, then the greatest value of  is ______.

22. Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters) of a point M on AB from the point A such that MD2 + MC2 is minimum is:

23. Let f : R → R be defined as

The value of λ for which f´´(0) exists, is _______.

24. The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of 30° to the horizontal plane, the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is:

25. Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m∙n is

## JEE Main September 5 2020 Shift 2 Question Paper with Answer Key

Physics

1. A ring is hung on a nail. It can oscillate, without slipping or sliding

(i) in its plane with a time period T1 and,

(ii) back and forth in a direction perpendicular to its plane, with a period T2.

The ratio T1/T2 will be:

(1)  3/√2

(2)  √2/3

(3)  2/√3

(4)  2/3

2. The correct match between the entries in column I and column II are:

 I II Radiation Wavelength (a) Microwave (i) 100 m (b) Gamma rays (ii) 10–15 m (c) A.M. radio waves (iii) 10–10 m (d) X-rays (iv) 10–3 m

(1)  (a) – (ii), (b)-(i), (c)-(iv), (d)-(iii)

(2)  (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)

(3)  (a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)

(4)  (a)-(i),(b)-(iii), (c)-(iv), (d)-(ii)

3. In an experiment to verify Stokes law, a small spherical ball of radius r and density falls under gravity through a distance h in the air before entering a tank of water. If the terminal velocity of the ball inside water is the same as its velocity just before entering the water surface, then the value of h is proportional to (ignore viscosity of air)

(1)  r4

(2)  r

(3)  r3

(4)  r2

4. Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively: (Take V= 0 at infinity)

(1)  V = 0; E = 0

(2)

(3)

(4)

5. A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate  where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is:

(1)  −bv3(t)

(2)

(3)

(4)

6. Two different wires having lengths L1 and L2, and respective temperature coefficient of linear expansion α1 and α2, are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

(1)

(2)

(3)

(4)

7. In the circuit, given in the figure currents in different branches and the value of one resistor are shown. Then potential at point B with respect to the point A is:

(1)  +2 V

(2)  −2 V

(3)  +1 V

(4)  −1 V

8. The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is:

(1)  37/3 m

(2)  49/4 m

(3)  12 m

(4)  11 m

9. An infinitely long straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown in the figure. The connector has length l and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self-inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is:

(1)

(2)

(3)

(4)

10. Two Zener diodes (A and B) having breakdown voltages of 6 V and 4 V respectively, are connected as shown in the circuit below. The output voltage VO variation with input voltage linearly increasing with time is given by (Vinput = 0 V at t = 0) (figures are qualitative)

11. In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is:

(1)  32

(2)  1/32

(3)  326

(4)  128

12. A galvanometer is used in the laboratory for detecting the null point in electrical experiments. If on passing a current of 6 mA it produces a deflection of 2°, its figure of merit is close to:

(1)  6 × 10–3 A/div.

(2)  3 × 10–3 A/div.

(3)  666° A/div.

(4)  333° A/div.

13. In the circuit shown, charge on the 5μF capacitor is:

(1)  5.45 μc

(2)  18.00 μc

(3)  10.90 μc

(4)  16.36 μc

14. A parallel plate capacitor has a plate of length ‘l’, width ‘w’ and separation of plates is ‘d’. It is connected to a battery of emf V. A dielectric slab of the same thickness ‘d’ and of dielectric constant k = 4 is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?

(1)  2I/3

(2)  I/2

(3)  I/4

(4)  I/3

15. A radioactive nucleus decays by two different processes. The half-life for the first process is 10 s and that for the second is 100 s. The effective half-life of the nucleus is close to:

(1)  55 sec.

(2)  6 sec.

(3)  12 sec.

(4)  9 sec.

16. A driver in a car, approaching a vertical wall, notices that the frequency of his car horn has changed from 440 Hz to 480 Hz when it gets reflected from the wall. If the speed of sound in air is 345 m/s, then the speed of the car is:

(1)  24 km/hr

(2)  36 km/hr

(3)  54 km/hr

(4)  18 km/hr

17. An iron rod of volume 10–3m3 and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be:

(1)  0.5 × 102 Am2

(2)  50 × 102 Am2

(3)  5 × 102 Am2

(4)  500 × 102 Am2

18. Two coherent sources of sound, S1 and S2, produce sound waves of the same wavelength, λ = 1 m, in phase. S1 and S2 are placed 1.5 m apart (see fig). A listener, located at L, directly in front of S2 finds that the intensity is at a minimum when he is 2 m away from S2. The listener moves away from S1, keeping his distance from S2 The adjacent maximum of intensity is observed when the listener is at a distance d from S1. Then, d is :

(1)  12 m

(2)  2 m

(3)  3 m

(4)  5 m

19. The quantities  are defined where C – capacitance, R – Resistance, L – length, E – Electric field, B – magnetic field and ε0, μ0 – free space permittivity and permeability respectively. Then:

(1)  Only y and z have the same dimension

(2)  x, y and z have the same dimension

(3)  Only x and y have the same dimension

(4)  Only x and z have the same dimension

20. The acceleration due to gravity on the earth’s surface at the poles is g and angular velocity of the earth about the axis passing through the pole is ω. An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is : (h < < R, where R is the radius of the earth)

(1)  R2ω2/g

(2)  R2ω2/8g

(3)  R2ω2/4g

(4)  R2ω2/2g

21. Nitrogen gas is at 300° C temperature. The temperature (in K) at which the rms speed of a H2 molecule would be equal to the rms speed of a nitrogen molecule, is _________. (Molar mass of N2 gas 28 g).

22. The surface of a metal is illuminated alternately with photons of energies E1 = 4 eV and E2 = 2.5 eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is _________.

23. A prism of angle A = 1° has a refractive index μ = 1.5. A good estimate for the minimum angle of deviation (in degrees) is close to N/10. Value of N is

24. A body of mass 2 kg is driven by an engine delivering a constant power of 1 J/s. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) _____________.

25. A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of mass 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rod immediately after the collision will be __________.

Chemistry

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

(1)  CH3CH(Br)CH2CH(CH3)2

(2)  CH3CH2CH2C(Br)(CH3)2

(3)  CH3CH2CH(Br)CH(CH3)2

(4)  Br(CH2)3CH(CH3)2

2. Hydrogen peroxide, in the pure state, is:

(1)  Linear and blue in color

(2)  Linear and almost colorless

(3)  Non-planar and almost colorless

(4)  Planar and blue in color

3. Boron and silicon of very high purity can be obtained through:

(1)  Liquation

(2)  Electrolytic refining

(3)  Zone refining

(4)  Vapour phase refining

4. The following molecule acts as an:

(1)  Anti-histamine

(2)  Antiseptic

(3)  Anti-depressant

(4)  Anti-bacterial

5. Among the following compounds, geometrical isomerism is exhibited by:

Answer: (1 and 2)

6. Adsorption of a gas follows Freundlich adsorption isotherm. If x is the mass of the gas adsorbed on mass m of the adsorbent, the correct plot of x/m versus p is:

7. The compound that has the largest H–M–H bond angle (M=N, O, S, C) is:

(1)  CH4

(2)  H2S

(3)  NH3

(4)  H2O

8. The correct statement about probability density (except at infinite distance from nucleus) is :

(1)  It can be zero for 3p orbital

(2)  It can be zero for 1s orbital

(3)  It can never be zero for 2s orbital

(4)  It can negative for 2p orbital

9. The rate constant (k) of a reaction is measured at different temperatures (T), and the data are plotted in the given figure. The activation energy of the reaction in kJ mol–1 is: (R is gas constant)

(1)  R

(2)  2/R

(3)  1/R

(4)  2R

10. The variation of molar conductivity with concentration of an electrolyte (X) in aqueous solution is shown in the given figure.

The electrolyte X is:

(1)  HCl

(2)  CH + COOH

(3)  NaCl

(4)  KNO3

11. The final major product of the following reaction is:

12. The major product of the following reaction is :

13. Lattice enthalpy and enthalpy of solution of NaCl are 788 kJ mol–1, and 4 kJ mol–1, respectively. The hydration enthalpy of NaCl is:

(1)  −780kJ mol1

(2)  784 kJ mol1

(3)  −784kJ mol1

(4)  780 kJ mol1

14. Reaction of ammonia with excess Cl2 gives:

(1)  NH4Cl and N2

(2)  NH4Cl and HCl

(3)  NCl3 and HCl

(4)  NCl3 and NH4Cl

15. Which one of the following polymers is not obtained by condensation polymerisation?

(1)  Bakelite

(2)  Nylon 6

(3)  Buna-N

(4)  Nylon 6, 6

16. Consider the comples ions, trans-[Co(en)2Cl2]+ (A) and cis-[Co(en)2Cl2]+ (B). The correct statement regarding them is:

(1)  Both (A) and (B) can be optically active.

(2)  (A) can be optically active, but (B) cannot be optically active.

(3)  Both (A) and (B) cannot be optically active.

(4)  (A) cannot be optically active, but (B) can be optically active.

17. An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of two nearest octahedral voids in the crystal lattice is:

(1)  a

(2)  a/2

(3)  √2a

(4)  a/√2

18. The correct order of the ionic radii of O2–, N3–, F, Mg2+, Na+ and Al3+ is:

(1)  N3– < O2– < F < Na+ < Mg2+ < Al3+

(2)  N3– < F < O2– < Mg2+ < Na+ < Al3+

(3)  Al3+ < Na+ < Mg2+ < O2– < F < N3–

(4)  Al3+ < Mg2+ < Na+ < F < O2– < N3–

19. The increasing order of boiling points of the following compounds is:

(1)  I < III < IV < II

(2)  IV < I < II < III

(3)  I < IV < III < II

(4)  III < I < II < IV

20. The one that is NOT suitable for the removal of permanent hardness of water is:

(1)  Ion-exchange method

(2)  Calgon’s method

(3)  Treatment with sodium carbonate

(4)  Clark’s method

21. For a reaction X + Y ⇌ 2Z, 1.0 mol of X, 1.5 mol of Y and 0.5 mol of Z were taken in a 1 L vessel and allowed to react. At equilibrium, the concentration of Z was 1.0 mol L–1. The equilibrium constant of reaction is ________ x/15. The value of x is _________.

22. The volume, in mL, of 0.02 M K2Cr2O7 solution required to react with 0.288 g of ferrous oxalate in acidic medium is ________. (Molar mass of Fe= 56 g mol–1)

23. Considering that ∆0 > P, the magnetic moment (in BM) of [Ru(H2O)6]2+ would be ________.

24. For a demerization reaction, 2A(g) → A2(g) at 298 K, ∆U = −20 kJ mol1, ∆S = −30 kJ mol1, then the ∆G will be__________ J

25. The number of chiral carbons present in sucrose is ______.

Mathematics

1. If x = 1 is a critical point of the function f(x) = (3x2 + ax – 2 – a)ex, then:

(1)  x = 1 is a local minima and x = −2/3 is a local maxima of f.

(2)  x = 1 is a local maxima and x = −2/3 is a local minima of f.

(3)  x = 1 and x = −2/3 are local minima of f.

(4)  x = 1 and x = −2/3 are local maxima of f.

2.

(1)  is equal to √e

(2)  is equal to 1

(3)  is equal to 0

(4)  does not exist

3. The statement (p → (q → p)) → (p → (p ˅ q)) is:

(1)  equivalent to (p˅q)˄ (~ p)

(2)  equivalent to (p˄q)˅(~ p)

(4)  a tautology

4. If  and  then:

(1)

(2)

(3)

(4)

5. If the sum of the first 20 terms of the series  is 460, then x is equal to:

(1)  71/2

(2)  72

(3)  e2

(4)  746/21

6. There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:

(1)  2250

(2)  2255

(3)  1500

(4)  3000

7. If the mean and the standard deviation of the data 3,5,7,a,b are 5 and 2 respectively, then a and b are the roots of the equation:

(1)  x2 – 20x + 18 = 0

(2)  x2 – 10x + 19 = 0

(3)  2x2 – 20x + 19 = 0

(4)  x2 – 10x + 18 = 0

8. The derivative of  with respect to  is:

(1)  2√3/3

(2)  2√3/5

(3)  √3/12

(4)  √3/10

9. If  where C is a constant of integration, then  can be:

(1)

(2)

(3)

(4)

10. If the length of the chord of the circle, x2 + y2 = r2 (r > 0) along the line, y-2x = 3 is r, then r2 is equal to:

(1)  12

(2)  24/5

(3)  9/5

(4)  12/5

11. If α and β are the roots of the equation, 7x2 – 3x – 2 = 0, then the value of  is equal to:

(1)  27/32

(2)  1/24

(3)  27/16

(4)  3/8

12. If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is:

(1)

(2)

(3)

(4)

13. If the line y = mx + c is a common tangent to the hyperbola  and the circle x2 + y2 = 36, then which one of the following is true?

(1)  4c2 = 369

(2)  c2 = 369

(3)  8m + 5 = 0

(4)  5m = 4

14. The area (in sq. units) of the region A = {(x,y): (x – 1) [x] ≤ y ≤ 2√x, 0 ≤ x ≤ 2} where [t] denotes the greatest integer function, is:

(1)

(2)

(3)

(4)

15. If a + x = b + y = c + z + 1, where a, b, c, x, y, z are non-zero distinct real numbers, then  is equal to:

(1)  y(a – b)

(2)  0

(3)  y(b – a)

(4)  y(a – c)

16. If for some α ∈ R, the lines  and  coplanar, then the line L2 passes through the point:

(1)  (2, −10, −2)

(2)  (10, −2, −2)

(3)  (10, 2, 2)

(4)  (−2, 10, 2)

17. The value of  is:

(1)  215i

(2)  −215

(3)  −215i

(4)  65

18. Let y = y(x) be the solution of the differential equation  If y(π/3) = 0, then y(π/4) is equal to:

(1)  2 + √2

(2)  √2 – 2

(3)

(4)  2 – √2

19. If the system of linear equations

x + y + 3z = 0

x + 3y + k2z = 0

3x + y + 3z = 0

has a non-zero solution (x, y, z) for some k ∈ R, then  is equal to:

(1)  −9

(2)  9

(3)  −3

(4)  3

20. Which of the following points lies on the tangent to the curve  at the point (1, 0) ?

(1)  (2, 6)

(2)  (2, 2)

(3)  (−2, 6)

(4)  (−2, 4)

21. Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the number of elements in the set C = {f : A → B 2 ∈ f(A)and f is not one-one} is_______

22. The coefficient of x4 in the expansion of (1 + x + x2 + x3)6 in powers of x, is_______

23. Let the vectors,  such that  If the projection of  is equal to the projection of  is perpendicular to     is______

24. If the lines x+y = a and x-y = b touch the curve y = x2 − 3x + 2 at the points where the curve intersects the x-axis, then a/b is equal to______

25. In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is_____

## JEE Main September 5 2020 Shift 1 Question Paper with Answer Key

Physics

1. Three different processes that can occur in an ideal monatomic gas are shown in the P vs V diagram. The paths are labelled as A → B, A → C and A → D. The change in internal energies during these processes are taken as EAB, EAC and EAD and the work done as WAB, WAC and WAD. The correct relation between these parameters are:

(1)  EAB = EAC = EAD, WAB > 0, WAC = 0, WAD < 0

(2)  EAB > EAC > EAD, WAB < WAC < WAD

(3)  EAB < EAC < EAD, WAB > 0, WAC > WAD

(4)  EAB = EAC = EAD, WAB > 0, WAC = 0, WAD > 0

2. With increasing biasing voltage of a photodiode, the photocurrent magnitude :

(1)  increases initially and saturates finally

(2)  remains constant

(3)  increases linearly

(4)  increases initially and after attaining certain value, it decreases

3. A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at the origin. A long wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b, 0), (b > > a). The magnitude of the torque on the loop about the z-axis is given by:

(1)

(2)

(3)

(4)

4. Assume that the displacement (s) of air is proportional to the pressure difference (Δp) created by a sound wave. Displacement(s) further depends on the speed of sound (v), the density of air (⍴) and the frequency (f). If Δp ~ 10Pa, v ~ 300 m/s, ⍴ ~ 1 kg / m3 and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1)

(1)  1 mm

(2)  10 mm

(3)  1/10 mm

(4)  3/100 mm

5. Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:

(1)  zero

(2)

(3)

(4)

6. A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to [g is the acceleration due to gravity]:

(1)

(2)

(3)

(4)

7. A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030 cal/(g – °C) (1 cal = 4.2 × 107 ergs) close to:

(1)  38.4°C

(2)  87.5°C

(3)  83.3°C

(4)  119.2°C

8. A wheel is rotating freely with an angular speed on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of the moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

(1)  3/4

(2)  0

(3)  5/6

(4)  1/4

9. A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a distance d(point B) from A (see figure) sees it at an angle 45° with respect to the vertical. When the balloon climbs up a further height h2, it is seen at an angle 60° with respect to the vertical if the girl moves further by a distance 2.464 d (point C). Then the height h2 is (given tan 30° = 0.5774):

(1)  0.464 d

(2)  d

(3)  0.732 d

(4)  1.464 d

10. An electrical power line, having a total resistance of 2Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately:

(1)  72%

(2)  91%

(3)  85%

(4)  96%

11. Activities of three radioactive substances A, B and C are represented by the curves A, B and C, in the figure. Then their half-lives T1/2 (A) : T1/2 (B) : T1/2 (C) are in the ratio:

(1)  3 : 2 : 1

(2)  2 : 1 : 1

(3)  4 : 3 : 1

(4)  2 : 1 : 3

12. The value of the acceleration due to gravity is g1 at a height h = R/ 2 (R = radius of the earth) from the surface of the earth. It is again equal to g1 at a depth d below the surface of the earth. The ratio (d / R) equals :

(1)  4/9

(2)  1/3

(3)  5/9

(4)  7/9

13. A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is 27 / 8 w.r.t water, the value of r is:

(1)  4/9 R

(2)  8/9 R

(3)  1/3 R

(4)  2/3 R

14. In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from the bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm. If the velocity of sound in air is 330 m/s, the tuning fork frequency is:

(1)  2200 Hz

(2)  550 Hz

(3)  3300 Hz

(4)  1100 Hz

15. A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point-like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height y (see figure), then : (assume the remaining portion to be spherical).

(1)

(2)

(3)

(4)

16. A galvanometer of resistance G is converted into a voltmeter of range 0 – 1V by connecting a resistance R1 in series with it. The additional resistance that should be connected in series with R1 to increase the range of the voltmeter to 0 – 2V will be:

(1)  G

(2)  R1

(3)  R1 – G

(4)  R1 + G

17. Number of molecules in a volume of 4 cm3 of a perfect monatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4 × 10–14 erg, g = 980 cm/s2, density of mercury = 13.6 g/cm3)

(1)  4.0 × 1018

(2)  4.0 × 106

(3)  5.8 × 1016

(4)  5.8 × 1018

18. An electron is constrained to move along the y-axis with a speed of 0.1 c (c is the speed of light) in the presence of electromagnetic wave, whose electric field is E = 30j sin (1.5 × 107 t – 5 × 10–2x) V/m. The maximum magnetic force experienced by the electron will be : (given c = 3 × 108 ms–1 and electron charge = 1.6 × 10–19C)

(1)  2.4 × 10–18 N

(2)  4.8 × 10–19 N

(3)  3.2 × 10–18 N

(4)  1.6 × 10–19 N

19. For a concave lens of focal length f, the relationship between object and image distances u and v, respectively, from its pole can best be represented by (u = is the reference line) :

20. A physical quantity z depends on four observables a, b, c and d, as  The percentages of error in the measurement of a, b, c and d are 2% , 1.5%, 4% and 2.5% respectively. The percentage of error in z is :

(1)  16.5%

(2)  12.25%

(3)  13.5%

(4)  14.5%

21. A particle of mass 200 Me V/c2 collides with a hydrogen atom at rest. Soon after the collision, the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is N/4. The value of N is : (Given the mass of the hydrogen atom to be 1 GeV/c2)_____.

22. Two concentric circular coils, C1 and C2, are placed in the XY plane. C1 has 500 turns, and a radius of 1 cm. C2 has 200 turns and a radius of 20 cm. C2 carries a time-dependent current I (t) = (5t2 – 2t + 3) A where t is in s. The emf induced in C1 (in mV), at the instant t = 1s is 4/x. The value of x is_____.

23. A beam of electrons of energy E scatters from a target having atomic spacing of 1Å. The first maximum intensity occurs at θ = 60° Then E (in eV) is ______. (Planck constant h = 6.64 × 10–34 Js, 1 eV = 1.6 × 10–19 J, electron mass m = 9.1 × 10–31 kg)

24. A compound microscope consists of an objective lens of focal length 1 cm and an eyepiece of focal length 5 cm with a separation of 10 cm. The distance between an object and the objective lens, at which the strain on the eye is minimum is n/40 cm. The value of n is _____.

25. A force  acts at a point Then the magnitude of torque about the point  will be √x N–m. The value of x is ______.

Chemistry

1. The potential energy curve for the H2 molecule as a function of internuclear distance is:

2.The most appropriate reagent for conversion of C2H5CN into CH3CH2CH2NH2 is:

(1)  NaBH4

(2)  Na(CN)BH3

(3)  CaH2

(4)  LIAlH4

3. Which of the following is not an essential amino acid?

(1)  Valine

(2)  Tyrosine

(3)  Lysine

(4)  Leucine

4. Which of the following derivatives of alcohols is unstable in an aqueous base?

5. The structure of PCl5 in the solid state is:

(1)  Square planar [PCl4]+ and octahedral [PCl6]

(2)  Tetrahedral [PCl4]+ and octahedral [PCl6]

(3)  Trigonal bipyramidal

(4)  Square pyramidal

6. A diatomic molecule X2 has a body-centred cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is 6.17 g cm–3. The number of molecules present in 200 g of X2 is:(Avogadro constant (NA) = 6 × 1023 mol–1)

(1)  8 NA

(2)  2 NA

(3)  40 NA

(4)  4 NA

7. The equation that represents the water-gas shift reaction is:

8. The increasing order of the acidity of the α-hydrogen of the following compounds

(1)  (D) < (C) < (A) < (B)

(2)  (A) < (C) < (D) < (B)

(3)  (C) < (A) < (B) < (D)

(4)  (B) < (C) < (A) < (D)

9. Indentify the correct molecular picture showing what happens at the critical micellar concentration (CMC) of an aqueous solution of a surfactant

(1)  (B)

(2)  (A)

(3)  (C)

(4)  (D)

10. If a person is suffering from the deficiency of nor-adrenaline, what kind of drug can be suggested?

(1)  Antihistamine

(2)  Antidepressant

(3)  Anti-inflammatory

(4)  Analgesic

11. The values of the crystal field stabilization energies for a high spin d6 metal ion in octahedral and tetrahedral fields, respectively, are:

(1)  –2.4 Δ0 and –0.6 Δt

(2)  –1.6 Δ0 and –0.4 Δt

(3)  –0.4 Δ0 and –0.27 Δt

(4)  –0.4 Δ0 and –0.6 Δt

12. A flask contains a mixture of compounds A and B. Both compounds decompose by first order kinetics. The half-lives for A and B are 300 s and 180 s, respectively. If the concentrations of A and B are equal initially, the time required for the concentration of A to be four times that of B (in s) is: (Use ln 2 = 0.693)

(1)  180

(2)  300

(3)  120

(4)  900

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

(1)  (D) < (A) < (B) < (C)

(2)  (A) < (B) < (C) < (D)

(3)  (B) < (A) < (D) < (C)

(4)  (B) < (A) < (C) < (D)

14. The condition that indicates a polluted environment is:

(1)  pH of rain water to be 5.6

(2)  BOD value of 5 ppm

(3)  0.03% of CO2 in the atmosphere

(4)  eutrophication

15. In the sixth period, the orbitals that are filled are:

(1)  6s, 5d, 5f, 6p

(2)  6s, 4f, 5d, 6p

(3)  6s, 6p, 6d, 6f

(4)  6s, 5f, 6d, 6p

16. The difference between the radii of 3rd and 4th orbits of Li2+ is ΔR1. The difference between the radii of 3rd and 4th orbits of He+ is ΔR2. Ratio ΔR1: ΔR2 is:

(1)  8 : 3

(2)  3 : 8

(3)  3 : 2

(4)  2 : 3

17. In the following reaction sequence the major products A and B are:

18. The correct electronic configuration and spin-only magnetic moment (BM) of Gd3+ (Z = 64), respectively, are:

(1)  [Xe] 5f7 and 7.9

(2)  [Xe] 4f7 and 7.9

(3)  [Xe] 5f7 and 8.9

(4)  [Xe] 4f7 and 8.9

19. An Ellingham diagram provides information about:

(1)  The pressure dependence of the standard electrode potentials of reduction reactions involved in the extraction of metals.

(2)  The conditions of pH and potential under which a species is thermodynamically stable.

(3)  The kinetics of the reduction process.

(4)  The temperature dependence of the standard Gibbs energies of formation of some metal oxides.

20. Consider the following reaction:

N2O4(g) ⇌ 2NO2(g); ∆H° = +58 kJ

For each of the following cases (a, b), the direction in which the equilibrium shifts is:

(a) Temperature is decreased.

(b) Pressure is increased by adding N2 at constant T.

(1)  (a) towards reactant, (b) towards product

(2)  (a) towards reactant, (b) no change

(3)  (a) towards product, (b) towards reactant

(4)  (a) towards product, (b) no change

21. The minimum number of moles of O2 required for complete combustion of 1 mole of propane and 2 moles of butane is _____.

22. The number of chiral carbon(s) present in piptide, Iie-Arg-Pro, is ______ .

23. A soft drink was bottled with a partial pressure of CO2 of 3 bar over the liquid at room temperature. The partial pressure of CO2 over the solution approaches a value of 30 bar when 44 g of CO2 is dissolved in 1 kg of water at room temperature. The approximate pH of the soft drink is ______ × 10–1

(First dissociation constant of H2CO3= 4.0 × 10–7; log 2 = 0.3; density of the soft drink= 1 g mL–1)

24. An oxidation-reduction reaction in which 3 electrons are transferred has a ΔGº of 17.37 kJmol–1 at 250C. The value of E0cell (in V) is ______ × 10–2. (1 F = 96,500 C mol–1)

25. The total number of coordination sites in ethylenediaminetetraacetate (EDTA4–) is _____.

Mathematics

1. If the volume of a parallelopiped, whose coterminuous edges are given by the vectors  and  is 158 cu. units then:

(1)

(2)

(3)  n = 9

(4)  n = 7

2. A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:

(1)  63

(2)  54

(3)  38

(4)  36

3. The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2,4,10,12,14, then the absolute difference of the remaining two observations is:

(1)  1

(2)  4

(3)  3

(4)  2

4. If 210 + 29 × 31 + 28 × 32 +…..+ 2 × 39 + 310 = S−211, then S is equal to:

(1)  311

(2)

(3)  2 ∙ 311

(4)  311 − 212

5. If 32 sin1,14 and 342sin2α are the first three terms of an A.P. for some α , then the sixth term of this A.P. is:

(1)  65

(2)  81

(3)  78

(4)  66

6. If the common tangent to the parabolas, y2 = 4x and x2 = 4y also touches the circle, x2 + y2 = c2, then c is equal to:

(1)  1/2

(2)  1/4

(3)  1/√2

(4)  1/2√2

7. If the minimum and the maximum values of the function  defined by  are m and M respectively, then the ordered pair (m, M) is equal to:

(1)  (0, 4)

(2)  (−4, 0)

(3)  (−4, 4)

(4)  (0, 2√2)

8. Let λ ∈ the system of linear equations

2x1 − 4x2 + λx3 = 1

x1 − 6x2 + x3 = 2

λx1 − 10x2 + 4x3 = 3

is inconsistent for:

(1)  exactly two values of λ

(2)  exactly one negative value of λ.

(3)  every value of λ.

(4)  exactly one positive value of λ.

9. If the point P on the curve, 4x2 + 5y2 = 20 is farthest from the point Q(0, −4), then PQ2 is equal to:

(1)  48

(2)  29

(3)  21

(4)  36

10. The product of the roots of the equation 9x2 – 18 |x| + 5 = 0 is :

(1)  25/81

(2)  5/9

(3)  5/27

(4)  25/9

11. If y = y(x) is the solution of the differential equation  satisfying y(0) = 1, then the value of y(loge 13) is:

(1)  1

(2)  0

(3)  2

(4)  −1

12. If S is the sum of the first 10 terms of the series  then tan(S) is equal to:

(1)  5/11

(2)  5/6

(3)  −6/5

(4)  10/11

13. The value of  is:

(1)  π/2

(2)  π/4

(3)  π

(4)  3π/2

14. If (a, b, c) is the image of the point (1,2,−3) in the line,  then a + b + c is

(1)  2

(2)  3

(3)  −1

(4)  1

15. If the function  is twice differentiable, then the ordered pair (k1, k2) is equal to:

(1)  (1, 1)

(2)  (1, 0)

(3)  (1/2, −1)

(4)  (1/2, 1)

16. If the four complex numbers  and z – 2Re(z) represent the vertices of a square of side 4 units in the Argand plane, then |z| is equal to:

(1)  2

(2)  4

(3)  4√2

(4)  2√2

17. If  where c is a constant of integration, then g(0) is equal to:

(1) 2

(2)  e

(3)  1

(4)  e2

18. The negation of the Boolean expression x y is equivalent to:

(1)  (x˄y) ˄(∼x˅∼y)

(2)  (x˄y) ˅ (∼x˄∼y)

(3)  (x˄∼y) ˅ (∼x˄∼y)

(4)  (∼x˄y) ˅ (∼x˄∼y)

19. If α is positive root of the equation, p(x) = x2 – x – 2 = 0, then  is equal to :

(1)  1/2

(2)  3/√2

(3)  3/2

(4)  1/√2

20. If the co-ordinates of two points A and B are (√7, 0) and (−√7, 0) respectively and P is any point on the conic, 9x2 + 16y2 = 144, then PA+PB is equal to :

(1)  6

(2)  16

(3)  9

(4)  8

21. The natural number m, for which the coefficient of x in the binomial expansion of is  1540 is………….

22. Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is……………

23. Let  for −10 < x < 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to………….

24. The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is

25. If the line, 2x − y + 3 = 0 is at a distance 1/√5 and 2/√5 from the lines 4x − 2y + α = 0 and 6x − 3y + β = 0, respectively, then the sum of all possible values of α and β is………………

## JEE Main September 4 2020 Shift 2 Question Paper with Answer Key

Physics

1. A circular coil has moment of inertia 0.8 kg m2 around any diameter and is carrying current to produce a magnetic moment of 20 Am2. The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60° will be:

(1)  10 π rad s–1

(2)  20 rad s–1

(3)  20 π rad s–1

(4)  10 rad s–1

2. A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

(1)  5690 J

(2)  5250 J

(3)  2780 J

(4)  3280 J

3. Match the thermodynamic processes taking place in a system with the correct conditions. In the table: ∆Q is the heat supplied, ∆W is the work done and ∆U is change in internal energy of the system.

Process – Condition

(I) Adiabatic – (1) ∆W = 0

(II) Isothermal – (2) ∆ Q = 0

(III) Isochoric – (3) ∆U ≠0, ∆W ≠ 0, ∆Q ≠ 0

(IV) Isobaric – (4) ∆U = 0

(1)  (I) – (1), (II) – (1), (III) – (2), (IV) – (3)

(2)  (I) – (1), (II) – (2), (III) – (4), (IV) – (4)

(3)  (I) – (2), (II) – (4), (III) – (1), (IV) – (3)

(4)  (I) – (2), (II) – (1), (III) – (4), (IV) – (3)

4. The driver of a bus approaching a big wall notices that the frequency of his bus’s horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is 330 ms–1.

(1)  81 kmh–1

(2)  91 kmh–1

(3)  71 kmh–1

(4)  61 kmh–1

5. A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv2 where v is its speed. The maximum height attained by the ball is:

(1)

(2)

(3)

(4)

6. Consider two uniform discs of the same thickness and different radii R1= R and R2 =αR made of the same material. If the ratio of their moments of inertia I1 and I2, respectively, about their axes is I1: I2 = 1 : 16 then the value of α is

(1)  √2

(2)  2

(3)  2√2

(4)  4

7. A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t =0, then the time at which the energy stored in the inductor reaches (1/n) times of its maximum value, is:

(1)

(2)

(3)

(4)

8. The electric field of a plane electromagnetic wave is given by  Its magnetic field will be given  by:

(1)

(2)

(3)

(4)

9. A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, B = 8 × 1010 Pa)

(1)  0.6

(2)  20

(3)  1.67

(4)  5

10. A paramagnetic sample shows a net magnetisation of 6 A/m when it is placed in an external magnetic field of 0.4 T at a temperature of 4 K. When the sample is placed in an external magnetic field of 0.3 T at a temperature of 24 K, then the magnetisation will be:

(1)  4 A/m

(2)  1 A/m

(3)  0.75 A/m

(4)  2.25 A/m

11. A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:

(1)  2

(2)  √2

(3)  1

(4)  1/√2

12. A particle of charge q and mass m is subjected to an electric field E = E0 (1 – ax2) in the x-direction, where a and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

(1)

(2)  a

(3)

(4)

13. A capacitor C is fully charged with voltage V0. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance C/2. The energy loss in the process after the charge is distributed between the two capacitors is:

(1)

(2)

(3)

(4)

14. Find the Binding energy per nucleon for  Mass of proton mp = 1.00783 U, mass of neutron mn = 1.00867 U and mass of tin nucleus mSn = 119.902199 U. (take 1U = 931 MeV)

(1)  8.0 MeV

(2)  9.0 MeV

(3)  7.5 MeV

(4)  8.5 MeV

15. The value of current i1 flowing from A to C in the circuit diagram is:

(1)  4 A

(2)  5 A

(3)  2 A

(4)  1 A

16. Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other, x2. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:

(1)  gdS(x2 + x1)2

(2)

(3)

(4)

17. A quantity x is given by (IFv2/WL4) in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of:

(1)  coefficient of viscosity

(2)  energy density

(3)  force constant

(4)  planck’s constant

18. For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O’ (corner point) is:

(1)  1/2

(2)  2/3

(3)  1/4

(4)  1/8

19. Identify the operation performed by the circuit given below:

(1)  NOT

(2)  OR

(3)  AND

(4)  NAND

20. In a photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased:

(1)  Straight line shifts to right

(2)  Straight line shifts to left

(3)  Slope of the straight line get more steep

(4)  Graph does not change

21. The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be________.

22. Four resistances 40 Ω, 60 Ω, 90 Ω and 110 Ω make the arms of a quadrilateral ABCD. Across AC is a battery of emf 40 V and internal resistance negligible. The potential difference across BD in V is _______.

23. The change in the magnitude of the volume of an ideal gas when a small additional pressure ∆P is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity ∆T at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm. respectively. If │∆T│= C│∆ P│ then value of C in (K/atm.) is _________.

24. Orange light of wavelength 6000 × 10–10 m illuminates a single slit of width 0.6 × 10–4 The maximum possible number of diffraction minima produced on both sides of the central maximum is ___________.

25. The distance between an object and a screen is 100 cm. A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is 40 cm. If the power of the lens is close to (N/100)D where N is an integer, the value of N is _________.

Chemistry

1. The reaction in which the hybridisation of the underlined atom is affected is:

2. The process that is NOT endothermic in nature is :

(1)  H(g) + e → H(g)

(2)  Na(g) → Na(g) → e

(3)  Ar(g) + e → Ar(g)

(4)  O(g) + e → O(g)2−

3. If the equilibrium constant for  the equilibrium constant for A ⇌ P is:

4. A sample of red ink (a colloidal suspension) is prepared by mixing eosin dye, egg white, HCHO and water. The component which ensures the stability of the ink sample is :

(1)  HCHO

(2)  Water

(3)  Eosin dye

(4)  Egg white

5. The one that can exhibit the highest paramagnetic behaviour among the following is: gly = glycinato; bpy = 2, 2’-bipyridine

(1)  [Ti (NH3)6]3+

(2)  [Co (OX)2 (OH)2]

(3)  [Pd (gly)2]

(4)  [Fe (en) (bpy) (NH3)2]2+

6. Which of the following compounds will form the precipitate with aq. AgNO3 solution most readily?

7. Five moles of an ideal gas at 1 bar and 298 K is expanded into the vacuum to double the volume. The work done is:

(1)  zero

(2)  CV[T2 – T1]

(3)  −RT(V2 – V1)

(4)  −RT ln(V2/V1)

8. 250 mL of a waste solution obtained from the workshop of a goldsmith contains 0.1 M AgNO3 and 0.1 M AuCl. The solution was electrolyzed at 2 V by passing a current of 1 A for 15 minutes. The metal/metals electrodeposited will be:

(1)  Silver and gold in proportion to their atomic weights

(2)  Silver and gold in equal mass proportion

(3)  only silver

(4)  only gold

9. The mechanism of action of “Terfenadine” (Seldane) is:

(1)  Helps in the secretion of histamine

(2)  Activates the histamine receptor

(3)  Inhibits the secretion of histamine

(4)  Inhibits the action of histamine receptor

10. The shortest wavelength of the H atom in the Lyman series is λ1. The longest wavelength in the Balmer series of He+ is:

(1)  9λ1/5

(2)  27λ1/5

(3)  36λ1/5

(4)  5λ1/9

11. The major product [B] in the following reactions is:

12. The major product [C] of the following reaction sequence will be:

13. The Crystal Field Stabilization Energy (CFSE) of [CoF3(H2O)3] (Δ0 < P) is:

(1)  – 0.8Δ0

(2)  – 0.8Δ0 + 2P

(3)  – 0.4Δ0 + P

(4)  – 0.4Δ0

14. Among the following compounds, which one has the shortest C – Cl bond?

15. The major product [R] in the following sequence of reactions is:

16. The molecule in which hybrid AOs involve only one d-orbital of the central atom is:

(1)  [CrF6]3

(2)  XeF4

(3)  BrF5

(4)  [Ni(CN)4]2

17. In the following reaction sequence, [C] is:

18. The processes of calcination and roasting in metallurgical industries, respectively, can lead to:

(1)  Photochemical smog and ozone layer depletion

(2)  Photochemical smog and global warming

(3)  Global warming and photochemical smog

(4)  Global warming and acid rain

19. The incorrect statement(s) among (a) – (c) is (are):

(a) W(VI) is more stable than Cr(VI).

(b) in the presence of HCl, permanganate titrations provide satisfactory results.

(c) some lanthanoid oxides can be used as phosphors.

(1)  (a) only

(2)  (b) and (c) only

(3)  (a) and (b) only

(4)  (b) only

20. An alkaline earth metal ‘M’ readily forms water-soluble sulphate and water-insoluble hydroxide. Its oxide MO is very stable to heat and does not have a rock-salt structure. M is :

(1)  Ca

(2)  Be

(3)  Mg

(4)  S

21. The osmotic pressure of a solution of NaCl is 0.10 atm and that of a glucose solution is 0.20 atm. The osmotic pressure of a solution formed by mixing 1 L of the sodium chloride solution with 2 L of the glucose solution is x × 103 x is _______. (nearest integer)

22. The number of molecules with energy greater than the threshold energy for a reaction increases fivefold by a rise of temperature from 27°C to 42 °C. Its energy of activation in J/mol is ________. (Take ln 5 = 1.6094 ; R = 8.314 J mol1K1)

23. A 100 mL solution was made by adding 1.43 g of Na2CO3 . xH2 The normality of the solution is 0.1 N. The value of x is ________. (The atomic mass of Na is 23 g/mol).

24. Consider the following equations:

2 Fe2+ + H2O2 → x A + y B (in basic medium)

2 MnO4 + 6 H+ + 5 H2O2 → x ‘C + y ‘D + z’E (in acidic medium).

The sum of the stoichiometric coefficients x, y, x’,y’ and z’ for products A, B, C, D and E, respectively, is _________.

25. The number of chiral centres present in threonine is ________.

Mathematics

1. Suppose the vectors x1, x2 and x3 are the solutions of the system of linear equations, Ax = b when the vector b on the right side is equal to b1, b2 and b3 If  then the determinant of A is equal to

(1)  2

(2)  1/2

(3)  3/2

(4)  4

2. If a and b are real numbers such that (2+α)4 = a + bα, where  then a + b is equal to:

(1)  33

(2)  57

(3)  9

(4)  24

3. The distance of the point (1, −2, 3) from the plane x – y + z = 5 measured parallel to the line  is:

(1)  1/7

(2)  7

(3)  7/5

(4)  1

4. Let f: (0, ∞) → (0, ∞) be a differentiable function such that f(1) = e and  If f(x) = 1, then x is equal to:

(1)  e

(2)  2e

(3)  1/e

(4)  1/2e

5. Contra positive of the statement :

‘If a function f is differentiable at a, then it is also continuous at a’, is:

(1)  If a function f is not continuous at a, then it is not differentiable at a.

(2)  If a function f is continuous at a, then it is differentiable at a.

(3)  If a function f is continuous at a, then it is not differentiable at a.

(4)  If a function f is not continuous at a, then it is differentiable at a.

6. The minimum value of 2sinx + 2cosx is:

(1)  21 – 2

(2)  21 – 1/2

(3)  2– 1 + 2

(4)  2–1 + 1/2

7. If the perpendicular bisector of the line segment joining the points P(1 ,4) and Q(k, 3) has y-intercept equal to −4, then a value of k is:

(1)  −2

(2)  √15

(3)  √14

(4)  −4

8. The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the parabola, y = x2 − 1 below the x-axis, is:

(1)  2/3√3

(2)  4/3

(3)  1/3√3

(4)  4/3√3

9. The integral  (2 sec2x ∙ sin2 3x + 3 tan x ∙ sin 6x) dx is equal to:

(1)  9/2

(2)  −1/18

(3)  −1/9

(4)  7/18

10. If the system of equations

x + y + z = 2

2x + 4y – z = 6

3x + 2y + λz = μ

has infinitely many solutions, then

(1)  λ −2μ = -5

(2)  2λ + μ = 14

(3)  λ + 2μ = 14

(4)  2λ – μ = 5

11. In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six The game stops as soon as either of the players wins. The probability of A winning the game is :

(1)  5/31

(2)  31/61

(3)  30/61

(4)  5/6

12. If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1 + x)n+5 are in the ratio 5:10:14, then the largest coefficient in this expansion is :

(1)  792

(2)  252

(3)  462

(4)  330

13. The function  is:

(1)  both continuous and differentiable on R−{−1}

(2)  continuous on R−{−1} and differentiable on R−{−1,1}

(3)  continuous on R−{1} and differentiable on R−{−1, 1}

(4)  both continuous and differentiable on R−{1}

14. The solution of the differential equation  is: (where c is a constant of integration)

(1)  x – loge(y + 3x) = C

(2)

(3)  x – 2loge(y + 3x) = C

(4)

15. Let λ ≠ 0 be in R. If α and β are the roots of the equation, x2 – x + 2λ = 0 and α and γ are the roots of the equation, 3x2 − 10x + 27λ = 0, then βγ/λ is equal to:

(1)  27

(2)  9

(3)  18

(4)  36

16. The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C in the lake from the point P is 60°, then PC (in m) is equal to :

(1)  200√3

(2)  400√3

(3)  400

(4)  100

17. Let  where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi ’s and exactly 6 of sets Yi’s, then n is equal to :

(1)  15

(2)  30

(3)  50

(4)  45

18. Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 1/2. If P(1, β ), β > 0 is a point on this ellipse, then the equation of the normal to it at P is :

(1)  8x – 2y = 5

(2)  4x – 2y = 1

(3)  7x – 4y = 1

(4)  4x – 3y = 2

19. Let a1, a2, …, an be a given A.P. whose common difference is an integer and Sn = a1 + a2 + …. + an. If a1 = 1, an = 300 and 15 ≤ n ≤ 50, then the ordered pair (Sn4, an4) is equal to:

(1)  (2480, 248)

(2)  (2480, 249)

(3)  (2490, 249)

(4)  (2490, 248)

20. The circle passing through the intersection of the circles, x2 + y2 − 6x = 0 and x2 + y2 − 4y = 0, having its centre on the line, 2x − 3y + 12 = 0, also passes through the point:

(1)  (−1, 3)

(2)  (1, −3)

(3)  (−3, 6)

(4)  (−3, 1)

21. Let {x} and [x] denote the fractional part of x and the greatest integer ≤ x respectively of a real number x. If and 10(n2 – n), (n ∈ N, n > 1) are three consecutive terms of a G.P., then n is equal to______

22. A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is______

23. If  then the value of  is equal to ______

24. Let PQ be a diameter of the circle x2 + y2 = 9. If α and β are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of αβ is____

25. If the variance of the following frequency distribution :

Class                      :           10-20   20-0     30-40

Frequency             :           2             x           2

is 50, then x is equal to _______

## JEE Main September 4 2020 Shift 1 Question Paper with Answer Key

Physics

1. Starting from the origin at time t = 0, with initial velocity  a particle moves in the x-y plane with a constant acceleration of  At time t, its coordinates are (20 m, y0 m). The values of t and y0 are, respectively:

(1)  5s and 25 m

(2)  2s and 18 m

(3)  2s and 24 m

(4)  4s and 52 m

2. A small bar magnet placed with its axis at 30° with an external field of 0.06 T experiences a torque of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilibrium position is:

(1)  7.2 × 102 J

(2)  6.4 × 102 J

(3)  9.2 × 103 J

(4)  11.7 × 103 J

3.Choose the correct option relating wave lengths of different parts of electromagnetic wave spectrum:

(1)  λradio waves > λmicro waves > λvisible > λx-rays

(2)  λvisible > λx-rays > λradio waves > λmicro waves

(3)  λvisible < λmicro waves < λradio waves < λx-rays

(4)  λx-rays < λmicro waves < λradio waves < λvisible

4. On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is given by  in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity, is:

(1)  A(x2 + a2)3/2

(2)

(3)  A(x2 + a2)1/2

(4)

5. A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil?

6. A battery of 3.0V is connected to a resistor dissipating 0.5 W of power. If the terminal voltage of the battery is 2.5V, the power dissipated within the internal resistance is:

(1)  0.072 W

(2)  0.10 W

(3)  0.125 W

(4)  0.50 W

7. Two charged thin infinite plane sheets of uniform surface charge density σ + and σ –, where| σ+| > |σ|, intersects at right angle. Which of the following best represents the electric field lines for this system?

8. An air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s–2. The density of water is 1 gm cm–3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm/s2).

(1)  1.52 gm

(2)  4.51 gm

(3)  3.15 gm

(4)  4.15 gm

9. A wire A, bent in the shape of an arc of a circle, carrying a current of 2A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm, are placed as shown in the figure. The ratio of the magnetic field due to the wires A and B at the common centre O is:

(1)  2 : 5

(2)  6 : 5

(3)  6 : 4

(4)  4 : 6

10. Particle A of mass mA=m/2 moving along the x-axis with velocity v0 collides elastically with another particle B at rest having mass mB = m/3. If both particles move along the x-axis after the collision, the change ∆λ in de-Broglie wavelength of particle A, in terms of its de-Broglie wavelength (λ0) before collision is:

(1)

(2)  ∆λ = 2λ0

(3)  ∆λ = 4λ0

(4)

11. Blocks of masses m, 2m, 4m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of ‘p’ is close to:

(1)  94

(2)  87

(3)  37

(4)  77

12. Given figure shows few data points in a photo-electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surface is: (Planck’s constant h = 6.62 × 10–34s)

(1)  2.10 eV

(2)  2.27 eV

(3)  2.59 eV

(4)  1.93 eV

13. The specific heat of water = 4200 J kg–1K–1 and the latent heat of ice = 3.4 × 105 J kg1.100 grams of ice at 0°C is placed in 200 g of water at 25°C. The amount of ice that will melt as the temperature of water reaches 0°C is close to (in grams):

(1)  63.8

(2)  64.6

(3)  61.7

(4)  69.3

14. A beam of plane polarised light of large cross-sectional area and uniform intensity of 3.3 Wm–2 falls normally on a polariser (cross sectional area 3 × 10–4 m2) which rotates about its axis with an angular speed of 31.4 rad/s. The energy of light passing through the polariser per revolution is close to:

(1)  1.0 × 104 J

(2)  1.0 × 105 J

(3)  5.0 × 104 J

(4)  1.5 × 104 J

15. For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5m, while the distance between one crest and one trough is 1.5m. The possible wavelengths (in m) of the waves are:

(1)  1, 3, 5,…..

(2)  1, 2, 3,……

(3)  1/2, 1/4, 1/6…..

(4)  1/1, 1/3, 1/5…..

16. Match the CP/CV ratio for ideal gases with different type of molecules:

17. Two points charges 4q and –q are fixed on the x-axis at x = −(d/2) and x = (d/2), respectively. If a third point charge ‘q’ is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will:

(1)  decrease by q2/4π∈0d

(2)  decrease by 4q2/3π∈0d

(3)  increase by 3q2/4π∈0d

(4)  increase by 2q2/3π∈0d

18. A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height h/2. The velocity versus height of the ball during its motion may be represented graphically by: (graphs are drawn schematically and are not to scale)

19. Dimensional formula for thermal conductivity is (here K denotes the temperature):

(1)  MLT3K1

(2)  MLT2K2

(3)  MLT2K

(4)  MLT3K

20. Take the breakdown voltage of the zener diode used in the given circuit as 6V. For the input voltage shown in figure below, the time variation of the output voltage is : (Graphs drawn are schematic and not to scale)

21. In the line spectra of hydrogen atoms, difference between the largest and the shortest wavelengths of the Lyman series is 304Å. The corresponding difference for the Paschen series in Å is : ___________.

22. A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.

23. ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I0. If part ADE is removed, the moment of inertia of the remaining part about the same axis is NI0 /16 where N is an integer. Value of N is _____________.

24. In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The focal length of its objective lens is 1 cm. If the magnification is 100 and the tube length of the microscope is 20 cm, then the focal length of the eyepiece lens (in cm) is __________.

25. A circular disc of mass M and radius R is rotating about its axis with angular speed ω1. If another stationary disc having radius R/2 and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω2. The energy lost in the process is p% of the initial energy. Value of p is __________.

Chemistry

1. The IUPAC name of the following compound is:

(1)  3-Bromo-5-methyl cyclopentane carboxylic acid

(2)  4-Bromo-2-methyl cyclopentane carboxylic acid

(3)  5-Bromo-3-methyl cyclopentanoic acid

(4)  3-Bromo-5-methyl cyclopentanoic acid

2. On heating, lead(II) nitrate gives a brown gas (A). The gas (A) on cooling changes to a colourless solid/liquid (B). (B) on heating with NO changes to a blue solid (C). The oxidation number of nitrogen in solid (C) is:

(1)  +3

(2)  +4

(3)  +2

(4)  +5

3. The ionic radii of O2–, F, Na+ and Mg2+ are in the order:

(1)  F > O2– > Na+ > Mg2+

(2)  Mg2+ > Na+ > F > O2

(3)  O2– > F > Na+ > Mg2+

(4)  O2– > F > Mg2+ > Na+

4. When neopentyl alcohol is heated with an acid, it is slowly converted into an 85:15 mixture of alkenes A and B, respectively. What are these alkenes?

5. The region in the electromagnetic spectrum where the Balmer series lines appear is:

(1)  Microwave

(2)  Infrared

(3)  Ultraviolet

(4)  Visible

6. Identify the incorrect statement from the options below for the above cell:

(1)  If Eext = 1.1 V, no flow of e or current occurs

(2)  If Eext > 1.1 V, Zn dissolves at Zn electrode and Cu deposits at Cu electrode

(3)  If Eext > 1.1 V, e flow from Cu to Zn

(4)  If Eext < 1.1 V, Zn dissolves at the anode and Cu deposits at the cathode

7. What are the functional groups present in the structure of maltose?

(1)  One acetal and one hemiacetal

(2)  One acetal and one ketal

(3)  One ketal and one hemiketal

(4)  Two acetals

8. Match the following:

(i) Foam                (a) smoke

(ii) Gel                   (b) cell fluid

(iii) Aerosol          (c) jellies

(iv) Emulsion       (d) rubber

(e) froth

(f) milk

(1)  (i)-(e), (ii)-(c), (iii)-(a), (iv)-(f)

(2)  (i)-(b), (ii)-(c), (iii)-(e), (iv)-(d)

(3)  (i)-(d), (ii)-(b), (iii)-(a), (iv)-(e)

(4)  (i)-(d), (ii)-(b), (iii)-(e), (iv)-(f)

9. An organic compound (A) (molecular formula C6H12O2) was hydrolysed with dilute H2SO4 to give a carboxylic acid (B) and alcohol (C). ‘C’ gives white turbidity immediately when treated with anhydrous ZnCl2 and conc. HCl. The organic compound (A) is:

10. Among the statements (a)-(d), the correct ones are:

(a) Limestone is decomposed to CaO during the extraction of iron from its oxides.

(b) In the extraction of silver, silver is extracted as an anionic complex.

(c) Nickel is purified by Mond’s process.

(d) Zr and Ti are purified by Van Arkel method.

(1)  (c) and (d) only

(2)  (b), (c) and (d) only

(3)  (a), (b), (c) and (d)

(4)  (a), (c) and (d) only

11. For one mole of an ideal gas, which of these statements must be true?

(a) U and H each depends only on temperature

(b) Compressibility factor z is not equal to 1

(c) CP,m – CV,m = R

(d) dU = CV dT for any process

(1)  (a), (c) and (d)

(2)  (a) and (c)

(3)  (c) and (d)

(4)  (b), (c) and (d)

12. [P] on treatment with Br2/FeBr3 in CCl4 produced a single isomer C8H7O2Br while heating [P] with soda lime gave toluene. The compound [P] is:

13. For the equilibrium A ⇌ B the variation of the rate of the forward (a) and reverse (b) reaction with time is given by :

14. The pair in which both the species have the same magnetic moment (spin only) is:

(1)  [Co(OH)4]2– and [Fe(NH3)6]2+

(2)  [Mn(H2O)6]2+ and [Cr(H2O)]2+

(3)  [Cr(H2O)6]2+ and [CoCl4]2–

(4)  [Cr(H2O)6]2+ and [Fe(H2O)6]2+

15. The number of isomers possible for [Pt(en)(NO2)2] is:

(1)  2

(2)  3

(3)  4

(4)  1

16. The decreasing order of reactivity of the following organic molecules towards the AgNO3 solution is:

(1)  (B) > (A) > (C) > (D)

(2)  (A) > (B) > (C) > (D)

(3)  (A) > (B) > (D) > (C)

(4)  (C) > (D) > (A) > (B)

17. The intermolecular potential energy for the molecules A, B, C and D given below suggests that:

(1)  A–A has the largest bond enthalpy.

(2)  D is more electronegative than other atoms.

(3)  A–D has the shortest bond length.

(4)  A–B has the stiffest bond.

18. Which of the following will react with CHCl3 + alc. KOH?

(1)  Thymine and proline

(2)  Adenine and thymine

(3)  Adenine and lysine

(4)  Adenine and proline

19. The elements with atomic numbers 101 and 104 belong to, respectively:

(1)  Actinoids and Group 6

(2)  Group 11 and Group 4

(3)  Group 6 and Actinoids

(4)  Actinoids and Group 4

20. On combustion of Li, Na and K in excess of air, the major oxides formed, respectively, are :

(1)  Li2O2, Na2O2 and K2O2

(2)  Li2O, Na2O2 and KO2

(3)  Li2O, Na2O and K2O2

(4)  Li2O, Na2O2 and K2O

21. The number of chiral centres present in [B] is ________.

22. At 300 K, the vapour pressure of a solution containing 1 mole of n-hexane and 3 moles of n-heptane is 550 mm of Hg. At the same temperature, if one more mole of n-heptane is added to this solution, the vapour pressure of the solution increases by 10 mm of Hg. What is the vapour pressure in mm of Hg of n-heptane in its pure state _______?

23. The mass of ammonia in grams produced when 2.8 kg of dinitrogen quantitatively reacts with 1 kg of dihydrogen is _________.

24. If 75% of a first order reaction was completed in 90 minutes, 60% of the same reaction would be completed in approximately (in minutes) ________. (take : log 2 = 0.30; log 2.5 = 0.40)

25. A 20.0 mL solution containing 0.2 g impure H2O2 reacts completely with 0.316 g of KMnO4 in acid solution. The purity of H2O2 (in %) is _______ (mol. wt. of H2O2 = 34’ mole wt. of KMnO4 = 158)

Mathematics

1. Let y = y(x) be the solution of the differential equation, xy’− y = x2(x cos x + sin x), x > 0. If y(π) = π, then  is equal to

(1)

(2)

(3)

(4)

2. The value of  is equal to:

(1)  51C730C7

(2)  51C7 + 30C7

(3)  50C730C7

(4)  50C630C6

3. Let [t] denote the greatest integer ≤ t. Then the equation in x, [x]2 + 2[x + 2] − 7 = 0 has:

(1)  exactly four integral solutions.

(2)  infinitely many solutions.

(3)  no integral solution.

(4)  exactly two solutions.

4. Let P(3, 3) be a point on the hyperbola,  If the normal to it at P intersects the x-axis at (9, 0) and e is its eccentricity, then the ordered pair (a2, e2) is equal to:

(1)  (9, 3)

(2)  (9/2, 2)

(3)  (9/2, 3)

(4)  (3/2, 2)

5. Let  be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function,   then a2 + b2 is equal to

(1)  135

(2)  116

(3)  126

(4)  145

6. Let  Then f(3) – f(1) is equal to:

(1)

(2)

(3)

(4)

7. If 1 + (1 − 22 × 1) + (1 − 42 × 3) + (1 − 62 × 5) + …… + (1 − 202 × 19) = α – 220 β, then an ordered pair (α, β) is equal to:

(1)  (10, 97)

(2)  (11, 103)

(3)  (11, 97)

(4)  (10, 103)

8. The integral  is equal to

(where C is a constant of integration):

(1)

(2)

(3)

(4)

9. Let f(x) = |x – 2| and g(x) = f(f(x)), x ∈ [0, 4]. Then  is equal to:

(1)  1/2

(2)  0

(3)  1

(4)  3/2

10. Let x0 be the point of local maxima of  where   and  Then the value of  at x = x0 is :

(1)  2

(2)  −4

(3)  −30

(4)  14

11. A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If ∠BAC = 90° and ar(ΔABC) = 5√5 s units, then the abscissa of the vertex C is:

(1)  1 + √5

(2)  1 + 2√5

(3)  2√5 − 1

(4)  2 + √5

12. Let f be a twice differentiable function on (1,6). If f(2) = 8, f´(2) = 5, f´(x) ≥ 1 and f´´(x) ≥ 4, for all x ∈ (1, 6), then:

(1)  f(5) + f´(5) ≥ 28

(2)  f´(5) + f´´(5) ≤ 20

(3)  f(5) ≤ 10

(4)  f(5) + f´(5) ≤ 26

13. Let α and β be the roots of x2 − 3x + p = 0 and γ and δ be the roots of x2 − 6x + q = 0. If α, β, γ, δ form a geometric progression. Then ratio (2q + p): (2q − p) is:

(1)  33: 31

(2)  9: 7

(3)  3 : 1

(4)  5 :3

14. Let  z = x + iy and k > 0. If the curve represented by Re(u) + Im(u) =1 intersects the y-axis at the points P and Q where PQ =5, then the value of k is:

(1)  4

(2)  1/2

(3)  2

(4)  3/2

15. If and  where i = √−1 then which one of the following is not true?

(1)  a2 – d2 = 0

(2)  a2 – c2 = 1

(3)  0 ≤ a2 + b2 ≤ 1

(4)  a2 – b2 = 1/2

16. The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is:

(1)  3

(2)  9

(3)  7

(4)  5

17. A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% of the people read both the newspapers, then a possible value of x can be:

(1)  37

(2)  29

(3)  65

(4)  55

18. Given the following two statements

(S1): (q˅p)→(p ↔ ~q) is a tautology.

(S2): ~q ˄ (~p ↔ q) is a fallacy. Then:

(1) only (S1) is correct.

(2)  both (S1) and (S2) are correct.

(3)  only (S2) is correct

(4)  both (S1) and (S2) are not correct.

19. Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is:

(1)  5

(2)  20/3

(3)  10/3

(4)  6

20. If (a + √2b cos x)( a − √2b cos y) = a2 − b2, where a > b > 0, then  is:

(1)

(2)

(3)

(4)

21. Suppose a differentiable function f(x) satisfies the identity f(x + y) = f(x) + f(y) + xy2 + x2y,for all real x and y. If  then f´(3) is equal to…………

22. If the equation of a plane P, passing through the intersection of the planes, x + 4y – z + 7 = 0 and 3x + y + 5z = 8 is ax + by + 6z = 15 for some a, b ∈ R, then the distance of the point (3, 2, −1) from the plane P is ….. units.

23. If the system of equations

x – 2y + 3z = 9

2x + y + z = b

x – 7y + az = 24, has infinitely many solutions, then a – b is equal to…………..

24. Let  Then a7/a13 is equal to………..

25. The probability of a man hitting a target is 1/10. The least number of shots required, so that the probability of his hitting the target at least once is greater than 1/4 is……….

## JEE Main September 3 2020 Shift 2 Question Paper with Answer Key

Physics

1. A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of f is:

(1)  1/√2

(2)  1/2

(3)  1

(4)  √2

2. The mass density of a planet of radius R varies with the distance r from its centre as  Then the gravitational field is maximum at:

(1)

(2)

(3)  r = R

(4)

3. Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of photons of the visible light of the given wavelengths is:

(1)  1/500

(2)  1/250

(3)  500

(4)  250

4. If a semiconductor photodiode can detect a photon with a maximum wavelength of 400nm, then its band gap energy is : Planck’s constant h = 6.63 × 10–34s. Speed of light c = 3 × 108 m/s

(1)  1.5 eV

(2)  2.0 eV

(3)  3.1 eV

(4)  1.1 eV

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5. Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:

(1)  ML0T3

(2)  MLT2

(3)  M2L0T1

(4)  ML2T2

6. A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) – time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale:

7. Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?

(1)  Multimeter shows NO deflection in both cases i.e. before and after reversing the probes if the chosen component is metal wire.

(2)  Multimeter shows a deflection, accompanied by a splash of light out of connected component in one direction and NO deflection on reversing the probes if the chosen component is LED.

(3)  Multimeter shows an equal deflection in both cases i.e. before and after reversing the probes if the chosen component is resistor.

(4)  Multimeter shows NO deflection in both cases i.e. before and after reversing the probes if the chosen component is capacitor.

8. A uniform rod of length ‘l’ is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω the rod makes an angle θ with it (see figure). To find θ equate the rate of change of angular momentum (direction going into the paper)  about the centre of mass (CM) to the torque provided by the horizontal and vertical forces FH and FV about the CM. The value of θ is then such that:

(1)  cos θ = 2g/3l ω2

(2)  cos θ = 3g/2l ω2

(3)  cos θ = g/2l ω2

(4)  cos θ = g/I ω2

9. Two resistors 400 Ω and 800 Ω are connected in series across a 6 V battery. The potential difference measured by a voltmeter of 10 k Ω across 400 Ω resistors is close to:

(1)  2.05 V

(2)  2 V

(3)  1.95 V

(4)  1.8 V

10. A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m/s2 . Assume there is no rotational motion and loss of energy after the collision is negligible.]

(1)  23 J

(2)  21 J

(3)  20 J

(4)  19 J

11. A metallic sphere cools from 50°C to 40°C in 300 s. If atmospheric temperature around is 20°C, then the sphere’s temperature after the next 5 minutes will be close to :

(1)  35°C

(2)  31°C

(3)  33°C

(4)  28°C

12. To raise the temperature of a certain mass of gas by 50°C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100°C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

(1)  6

(2)  7

(3)  5

(4)  3

13. The radius R of a nucleus of mass number A can be estimated by the formula R = (1.3 × 10–15)A 1/3 m. It follows that the mass density of a nucleus is of the order of: (M = Mneut =1.67 × 10–27 kg)

(1)  1017 kg m3

(2)  1010 kg m3

(3)  1024 kg m3

(4)  103 kg m3

14. A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field B. Then the field inside the paramagnetic substance is:

(1)  much large than and parallel to

(2)  zero

(3)

(4)  much large than but opposite to

15. Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is:

(1)

(2)

(3)

(4)

16. The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is  The magnetic field  at the moment t = 0 is:

(1)

(2)

(3)

(4)

17. A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate dB/dt = 0.032 Ts–1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 × 10–8 Ωm)

(1)  0.53 A

(2)  0.61 A

(3)  0.34 A

(4)  0.43 A

18. Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:

(1)  2:1

(2)  1:2

(3)  5:7

(4)  10:7

19. Two light waves having the same wavelength λ in vacuum are in phase initially. Then the first wave travels a path L1 through a medium of refractive index n1 while the second wave travels a path of length L2 through a medium of refractive index n2. After this the phase difference between the two waves is:

(1)

(2)

(3)

(4)

20. A calorimeter of water equivalent 20 g contains 180 g of water at 25°C. ‘m’ grams of steam at 100°C is mixed in it till the temperature of the mixture is 31°C. The value of ‘m’ is close to (Latent heat of water = 540 cal g–1, specific heat of water = 1 cal g–1 °C–1)

(1)  2

(2)  2.6

(3)  4

(4)  3.2

21. If minimum possible work is done by a refrigerator in converting 100 grams of water at 0°C to ice, how much heat (in calories) is released to the surroundings at temperature 27°C (Latent heat of ice = 80 Cal/gram) to the nearest integer?

22. An massless equilateral triangle EFG of side ‘a’ (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the each line EX perpendicular to EG in the plane of EFG is  where N is an integer. The value of N is _____.

23. A galvanometer coil has 500 turns and each turn has an average area of 3 × 10–4 m2. If a torque of 1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5 A is flowing through it, the strength of the field (in T) is ______.

24. A block starts moving up an inclined plane of inclination 30° with an initial velocity of v0. It comes back to its initial position with velocity v0/2. . The value of the coefficient of kinetic friction between the block and the inclined plane is close to 1/1000. The nearest integer to I is____.

25. When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 cms–1, the speed (in cms–1) with which image moves at that instant is ____.

Chemistry

1. The five successive ionization enthalpies of an element are 800, 2427, 3658, 25024 and 32824 kJ mol–1. The number of valence electrons in the element is:

(1)  2

(2)  4

(3)  3

(4)  5

2. The incorrect statement is:

(1)  Manganate and permanganate ions are tetrahedral

(2)  In manganate and permanganate ions, the -bonding takes place by the overlap of p orbitals of oxygen and d-orbitals of manganese

(3)  Manganate and permanganate ions are paramagnetic

(4)  Manganate ion is green in colour and permanganate ion is purple in colour

3. Match the following drugs with their therapeutic actions:

(i) Ranitidine (a) Antidepressant

(ii) Nardil (Phenelzine) (b) Antibiotic

(iii)Chloramphenicol (c) Antihistamine

(iv) Dimetane (Brompheniramine) (d) Antacid

(e) Analgesic

(1)  (i)-(d); (ii)-(a); (iii)-(b); (iv)-(c)

(2)  (i)-(d); (ii)-(c); (iii)-(a); (iv)-(e)

(3)  (i)-(a); (ii)-(c); (iii)-(b); (iv)-(e)

(4)  (i)-(e); (ii)-(a); (iii)-(c); (iv)-(d)

4. An ionic micelle is formed on the addition of

(1)  liquid diethyl ether to aqueous NaCl solution

(2)  sodium stearate to pure toluene

(3)  excess water to liquid

(4)  excess water to liquid

5. Among the statements (I–IV), the correct ones are:

(I) Be has a smaller atomic radius compared to Mg.

(II) Be has higher ionization enthalpy than Al.

(III) Charge/radius ratio of Be is greater than that of Al.

(IV) Both Be and Al form mainly covalent compounds.

(1)  (I), (II) and (IV)

(2)  (I), (II) and (III)

(3)  (II), (III) and (IV)

(4)  (I), (III) and (IV)

6. Complex A has a composition of H12O6Cl3 If the complex on treatment with conc. H2SO4 loses 13.5% of its original mass, the correct molecular formula of A is: [Given: the atomic mass of Cr = 52 amu and Cl = 35 amu]

(1)  [Cr(H2O)5Cl]Cl2 .H2O

(2)  [Cr(H2O)4Cl2]Cl.2H2O

(3)  [Cr(H2O)3Cl3].3H2O

(4)  [Cr(H2O)6]Cl3

7. The decreasing order of reactivity of the following compounds towards nucleophilic substitution (SN2) is:

(1)  (III) > (II) > (IV) > (I)

(2)  (IV) > (II) > (III) > (I)

(3)  (II) > (III) > (IV) > (I)

(4)  (II) > (III) > (I) > (IV)

8. The increasing order of the reactivity of the following compounds in nucleophilic addition reaction is: Propanal, Benzaldehyde, Propanone, Butanone

(1)  Benzaldehyde < Propanal < Propanone < Butanone

(2)  Propanal < Propanone < Butanone < Benzaldehyde

(3)  Butanone < Propanone < Benzaldehyde < Propanal

(4)  Benzaldehyde < Butanone < Propanone < Propanal

9. The major product in the following reaction is:

10. The incorrect statement(s) among (a) – (d) regarding acid rain is (are):

(a) It can corrode water pipes.

(b) It can damage structures made up of stone.

(c) It cannot cause respiratory ailments in animals

(d) It is not harmful for trees

(1)  (a), (b) and (d)

(2)  (a), (c) and (d)

(3)  (c) and (d)

(4)  (c) only

11. 100 mL of 0.1 M HCl is taken in a beaker and to it, 100 mL of 0.1 M NaOH is added in steps of 2 mL and the pH is continuously measured. Which of the following graphs correctly depicts the change in pH?

12. Consider the hypothetical situation where the azimuthal quantum number, l, takes values 0, 1, 2, …… n + 1, where n is the principal quantum number. Then, the element with atomic number:

(1)  13 has a half-filled valence subshell

(2)  9 is the first alkali metal

(3)  8 is the first noble gas

(4)  6 has a 2p-valence subshell

13. The d-electron configuration of [Ru(en)3]Cl2 and [Fe(H2O)6]Cl2, respectively are:

(1)  t42g e2g and t62g eog

(2)  t62g eog and t62g eog

(3)  t42g e2g and t42g e2g

(4)  t62g e0g and t42g e2g

14. Consider the following molecules and statements related to them:

(a) (B) is more likely to be crystalline than (A)

(b) (B) has a higher boiling point than (A)

(c) (B) dissolves more readily than (A) in water

Identify the correct option from below:

(1)  (a) and (c) is true

(2)  only (a) is true

(3)  (b) and (c) are true

(4)  (a) and (b) are true

15. The strengths of 5.6 volume hydrogen peroxide (of density 1 g/mL) in terms of mass percentage and molarity (M), respectively, are: (Take the molar mass of hydrogen peroxide as 34 g/mol)

(1)  0.85 and 0.5

(2)  0.85 and 0.25

(3)  1.7 and 0.25

(4)  1.7 and 0.5

16. The compound A in the following reactions is:

17. A mixture of one mole each of H2, He and O2 each are enclosed in a cylinder of volume V at temperature T. If the partial pressure of H2 is 2 atm, the total pressure of the gases in the cylinder is:

(1)  6 atm

(2)  14 atm

(3)  38 atm

(4)  22 atm

18. Three isomers A, B and C (mol. formula C8H11N) give the following results:

19. For the reaction 2A + 3B + (3 / 2) C → 3P, which statement is correct?

(1)

(2)

(3)

(4)

20. Consider the following reaction:

The product ‘P’ gives positive ceric ammonium nitrate test. This is because of the presence of which of these –OH group(s)?

(1)  (b) only

(2)  (b) and (d)

(3)  (c) and (d)

(4)  (d) only

21. The volume (in mL) of 0.1 N NaOH required to neutralise 10 mL of 0.1 N phosphinic acid is ___________.

22. An acidic solution of dichromate is electrolyzed for 8 minutes using 2A current. As per the following equation

The amount of Cr3+ obtained was 0.104 g. The efficiency of the process (in %) is (Take: F = 96000 C, At. mass of chromium = 52) _______.

23. If 250 cm3 of an aqueous solution containing 0.73 g of a protein A is isotonic with one litre of another aqueous solution containing 1.65 g of a protein B, at 298 K, the ratio of the molecular masses of A and B is ______ × 10–2 (to the nearest integer).

24. 6.023 × 1022 molecules are present in 10 g of a substance ‘x’. The molarity of a solution containing 5 g of substance ‘x’ in 2 L solution is _____ × 10–3.

25. The number of

groups present in a tripeptide Asp–Glu–Lys is ____.

Mathematics

1. If x3dy+xy dx = x2dy+2y dx; y(2) = e and x>1, then y(4) is equal to:

(1)

(2)

(3)

(4)

2. Let A be a 3×3 matrix such that  and B = adj(adj A). If |A| = λ and |(B1)T|=μ, then the ordered pair, (|λ|, μ) is equal to:

(1)  (9, 1/81)

(2)  (9, 1/9)

(3)  (3, 1/81)

(4)  (3, 81)

3. Let a, b, c ε R be such that a2 + b2 + c2 = 1, if  where θ = π/9, then the angle between the vectors  and  is

(1)  π/2

(2)  2π/3

(3)  π/9

(4)  0

4. Suppose f(x) is a polynomial of degree four, having critical points at (−1, 0, 1). If T = {x ε R f(x) = f(0)}, then the sum of squares of all the elements of T is:

(1)  6

(2)  2

(3)  8

(4)  4

5. If the value of the integral  then k is equal to:

(1)  2√3 + π

(2)  3√2 + π

(3)  3√2 − π

(4)  2√3 − π

6. If the term independent of x in the expansion of  is k, then 18 k is equal to:

(1)  5

(2)  9

(3)  7

(4)  11

7. If a triangle ABC has vertices A(−1, 7), B(−7, 1) and C(5, −5), then its orthocentre has coordinates;

(1)  (−3, 3)

(2)  (−3/5, 3/5)

(3)  (3/5, −3/5)

(4)  (3, −3)

8. Let e1 and e2 be the eccentricities of the ellipse,  (b < 5) and the hyperbola,  respectively satisfying e1e2 = 1. If α and β are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair (α, β) is equal to:

(1)  (8, 12)

(2)  (24/5, 10)

(3)  (20/3, 12)

(4)  (8, 10)

9. If z1, z2 are complex numbers such that Re(z1) = |z1 − 1|, Re(z2) = |z2 − 1| and arg (z1 − z2) = π/6, then Im(z1 + z2) is equal to:

(1)  2√3

(2)  2/√3

(3)  1/√3

(4)  √3/2

10. The set of all real values of λ for which the quadratic equations, (λ2 + 1) x2 − 4λx + 2 = 0 always have exactly one root in the interval (0,1) is:

(1)  (−3, −1)

(2)  (2, 4)

(3)  (1, 3)

(4)  (0, 2)

11. Let the latus rectum of the parabola y2 = 4x be the common chord to the circles C1 and C2 each of them having radius 2√5. Then, the distance between the centres of the circles C1 and C2 is:

(1)  8

(2)  8√5

(3)  4√5

(4)  12

12. The plane which bisects the line joining the points (4, −2, 3) and (2, 4, −1) at right angles also passes through the point:

(1)  (0, −1, 1)

(2)  (4, 0, 1)

(3)  (4, 0, −1)

(4)  (0, 1, −1)

13. is equal to:

(1)  (2/9)4/3

(2)  (2/3)4/3

(3)  (2/3) (2/9)1/3

(4)  (2/9) (2/3)1/3

14. Let xi (1 ≤ i ≤ 10)be ten observations of a random variable X. If  and  where 0 ≠ p ε R , then the standard deviation of these observations is :

(1)  7/10

(2)  9/10

(3)

(4)  4/5

15. The probability that a randomly chosen 5 digit number is made from exactly two digits

(1)  134/104

(2)  121/104

(3)  135/104

(4)  150/104

16. If where C is a constant of integration, then the ordered pair (A(x), B(x)) can be:

(1)  (x + 1, −√x)

(2)  (x – 1, −√x)

(3)  (x + 1, √x)

(4)  (x – 1, √x)

17. If the sum of the series  nth term is 488 and then nth term is negative, then:

(1)  n = 60

(2)  n = 41

(3)  nth term is −4

(4)  nth term is

18. Let p, q, r be three statements such that the truth value of (p ˄ q) → (∼q ˅ r) is F. Then the truth values of p, q, r are respectively:

(1)  F, T, F

(2)  T, F, T

(3)  T, T, F

(4)  T, T, T

19. If the surface area of a cube is increasing at a rate of 3.6 cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec), when the length of a side of the cube is 10cm, is :

(1)  9

(2)  10

(3)  18

(4)  20

20. Let R1 and R2 be two relations defined as follows:

R1 = {(a,b) ∈ R2 : a2 + b2 ∈ Q} and

R2 = {(a,b) ∈ R2 : a2 + b2 ∉Q}, where Q is the set of all rational numbers. Then :

(1)  R1 is transitive but R2 is not transitive

(2)  R1 and R2 are both transitive

(3)  R2 is transitive but R1 is not transitive

(4)  Neither R1 nor R2 is transitive

21. If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4th A.M. is equal to 2nd G.M., then m is equal to

22. Let a plane P contain two lines  and  If Q(α, β, γ) is the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then 3(α + β + γ) equals_____

23. Let S be the set of all integer solutions, (x, y, z), of the system of equations

x – 2y + 5z = 0

−2x + 4y + z = 0

−7x + 14y + 9z = 0

such that 15 ≤ x2 + y2 + z2 ≤ 150. Then, the number of elements in the set S is equal to ______

24. The total number of 3 digit numbers, whose sum of digits is 10, is:

25. If the tangent to the curve, y = ex at a point (c, ec) and the normal to the parabola, y2 = 4x at the point (1,2) intersect at the same point on the x-axis, then the value of c is:

## JEE Main September 3 2020 Shift 1 Question Paper with Answer Key

Physics

1. A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. If the rod has mass M = 2 kg, and length l = 1m, the value θ of is approximately: (take g = 10 m/s2)

(1)  49°

(2)  63°

(3)  69°

(4)  55°

2. A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave train of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wave train (in cm) when it reaches the top of the rope?

(1)  12

(2)  3

(3)  9

(4)  6

3. When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is:

(1)  300 Ω

(2)  200 Ω

(3)  50 Ω

(4)  100 Ω

4. Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as:

(1)  2.125 cm

(2)  2.124 cm

(3)  2.123 cm

(4)  2.121 cm

5. Model a torch battery of length l to be made up of a thin cylindrical bar of radius ‘a’ and a concentric thin cylindrical shell of radius ‘b’ filled in between with an electrolyte of resistivity ρ (see figure). If the battery is connected to a resistance of value R, the maximum joule heating in R will take place for:

(1)

(2)

(3)

(4)

6. Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is:

(1)

(2)  3RT

(3)

(4)

7. An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency ω, the average power loss in the loop due to Joule heating is:

(1)

(2)

(3)

(4)  Zero

8. A balloon filled with helium (32° C and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as:

(1)  reversible isothermal

(2)  irreversible isothermal

9. When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:

(1)  1.02 eV

(2)  0.61 eV

(3)  0.52 eV

(4)  0.81 eV

10. Two isolated conducting spheres S1 and S2 of radius (2/3) R and (1/3) R have 12 μC and –3μC charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on S1 and S2 are respectively:

(1)  6 μC and 3 μC

(2)  4.5 μC on both

(3)  + 4.5 μC and –4.5 μC

(4)  3 μC and 6 μC

11. In a radioactive material, fraction of active material remaining after time t is 9/16. The fraction that was remaining after t/2 is:

(1)  3/4

(2)  7/8

(3)  4/5

(4)  3/5

12. Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder is  If such a cylinder is to be made for a given mass of a material, the ratio L /R for it to have minimum possible I is:

(1)  2/3

(2)  3/2

(3)  √2/3

(4)  √3/2

13. A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius Re. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become √3/2 times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is:

(1)  2Re

(2)  3Re

(3)  4Re

(4)  2.5 Re

14. Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is:

(1)  4 : 1

(2)  2 : 1

(3)  0.8 : 1

(4)  8 : 1

15. In a Young’s double slit experiment, light of 500 nm is used to produce an interference pattern. When the distance between the slits is 0.05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to:

(1)  0.17°

(2)  0.07°

(3)  0.57°

(4)  1.7°

16. A 750 Hz, 20 V (rms) source is connected to a resistance of 100 Ω, an inductance of 0.1803 H and a capacitance of 10 μ F all in series. The time in which the resistance (heat capacity 2 J/°C) will get heated by 10°C. (assume no loss of heat to the surroundings) is close to:

(1)  245 s

(2)  365 s

(3)  418 s

(4)  348 s

17. Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of μ0I/π is:

(1)  250√3

(2)  50√3

(3)  500√3

(4)  5√3

18. The magnetic field of a plane electromagnetic wave is  where c = 3 × 108 ms1 is the speed of light.

The corresponding electric field is:

(1)

(2)

(3)

(4)

19. A charged particle carrying charge 1 μC is moving with velocity  If an external magnetic field of  exists in the region where the particle is moving then the force on the particle is  The vector  is:

(1)

(2)

(3)

(4)

20. In the circuit shown in the figure, the total charge is 750 μC and the voltage across capacitor C2 is 20 V. Then the charge on capacitor C2 is:

(1)  650 μC

(2)  450 μC

(3)  590 μC

(4)  160 μC

21. A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre _____?

22. An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at height of 15 cm from the bottom (see figure). The hole is at a height of 45 cm. When the jar is filled with a liquid up to a height of 30 cm the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is N/100, where N is an integer, the value of N is _____.

23. A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of F(in N) is (g = 10 ms–2)_____.

24. When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0°, the surface tension of the liquid, in milli Newton m–1 is [ρ(liquid) =900 kgm–3 , g = 10 ms–2] (Give answer in closes integer)____.

25. A bakelite beaker has volume capacity of 500 cc at 30°C. When it is partially filled with Vm volume (at 30°C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If γ(beaker) = 6 × 10–6 °C–1 and γ(mercury)= 1.5 × 10–4 °C–1, where γ is the coefficient of volume expansion, then Vm (in cc) is close to ____.

Chemistry

1. It is true that:

(a)  A second order reaction is always a multistep reaction

(b)  A first order reaction is always a single step reaction

(c)  A zero order reaction is a multistep reaction

(d) A zero order reaction is a single step reaction

2. An acidic buffer is obtained on mixing:

(a)  100 mL of 0.1 M HCl and 200 mL of 0.1 M CH3COONa

(b)  100 mL of 0.1 M HCl and 200 mL of 0.1 M NaCl

(c)  100 mL of 0.1 M CH3 COOH and 100 mL of 0.1 M NaOH

(d) 100 mL of 0.1 M CH3COOH and 200 mL of 0.1 M NaOH

3. The Kjeldahl method of Nitrogen estimation fails for which of the following reaction products?

(a)  (a), (c) and (d)

(b)  (b) and (c)

(c)  (c) and (d)

(d) (a) and (d)

4. If the boiling point of H2O is 373 K, the boiling point of H2S will be :

(a)  greater than 300 K but less than 373 K

(b)  equal to 373 K

(c)  more than 373 K

(d) less than 300 K

5. The complex that can show optical activity is :

(a)  cis– [CrCl2 (ox)2]3− (ox – oxalate)

(b)  trans – [Fe (NH3)2 (CN)4]

(c)  trans – [Cr (Cl2) (ox)2]3−

(d) cis– [Fe (NH3)2 (CN)4]−

6. Which one of the following compounds possesses the most acidic hydrogen?

7. Aqua regia is used for dissolving noble metals (Au, Pt, etc.). The gas evolved in this process is :

(a)  N2O3

(b)  N2

(c)  N2O5

(d) NO

8. The antifertility drug “Novestrol” can react with:

(a)  Br2 / water; ZnCl2 / HCl; FeCl3

(b)  Br2 / water; ZnCl2 / HCl; NaOCl

(c)  Alcoholic HCN; NaOCl; ZnCl2 / HCl

(d) ZnCl2 / HCl; FeCl3; Alcoholic HCN

9. Which of the following compounds produces an optically inactive compound on hydrogenation?

10. Of the species, NO, NO+, NO2+ and NO, the one with minimum bond strength is:

(a)  NO

(b)  NO+

(c)  NO2+

(d) NO

11. Glycerol is separated in soap industries by:

(a)  Fractional distillation

(b)  Distillation under reduced pressure

(c)  Differential extraction

(d) Steam distillation

12. Thermal power plants can lead to:

(a)  Ozone layer depletion

(b)  Blue baby syndrome

(c)  Eutrophication

(d) Acid rain

13. Henry’s constant (in kbar) for four gases ɑ, β, 𝛾, δ and δ in water at 298 K is given below:

 α β γ δ KH 50 2 2 × 10−5 0.5

(density of water = 103 kg m3 at 298 K)

This stable implies that :

(a)  solubility of γ at 308 K is lower than at 298 K

(b)  The pressure of a 55.5 molal solution of δ is 250 bar

(c)  α has the highest solubility in water at a given pressure

(d) The pressure of a 55.5 molal solution of γ is 1 bar

14. The electronic spectrum of [Ti(H2O)6]3+ shows a single broad peak with a maximum at 20,300 cm-1. The crystal field stabilization energy (CFSE) of the complex ion, in kJ mol−1, is:

(1 kJ mol−1 = 83.7 cm−1)

(a)  83.7

(b)  242.5

(c)  145.5

(d) 97

15. The atomic number of the element unnilennium is:

(a)  109

(b)  102

(c)  119

(d) 108

16. An organic compound [A], molecular formula C10H20O2 was hydrolyzed with dilute sulphuric acid to give a carboxylic acid [B] and an alcohol [C]. Oxidation of [C] with CrO3−H2SO4 produced [B]. Which of the following structures are not possible for [A]?

17. The mechanism of SN1 reaction is given as:

A student writes general characteristics based on the given mechanism as:

(1) The reaction is favoured by weak nucleophiles.

(2) RΘ would be easily formed if the substituents are bulky.

(3) The reaction is accompanied by racemization.

(4) The reaction is favoured by non-polar solvents. Which observations are correct?

(a)  (1) and (2)

(b)  (1), (2) and (3)

(c)  (1) and (3)

(d) (2) and (4)

18. Tyndall effect is observed when:

(a)  The diameter of dispersed particles is much smaller than the wavelength of light used.

(b)  The diameter of dispersed particles is much larger than the wavelength of light used.

(c)  The refractive index of the dispersed phase is greater than that of the dispersion medium.

(d) The diameter of dispersed particles is similar to the wavelength of light used.

19. Let CNaCl and CBaSO4 be the conductances (in S) measured for saturated aqueous solutions of NaCl and BaSO4, respectively, at a temperature T. Which of the following is false?

(a)  CNaCl (T2) > CBaSo4 (T1) for T2 > T1

(b)  CBaSo4 (T2) > CNaCl (T1) for T2 > T1

(c)  Ionic mobilities of ions from both salts increase with T.

(d) CNaCl >> CBaSo4 at a given T

20. In a molecule of pyrophosphoric acid, the number of P−OH, P = O and P − O − P bonds / moiety(ies) respectively are:

(a)  3, 3 and 3

(b)  4, 2 and 1

(c)  2, 4 and 1

(d) 4, 2 and 0

21. The mole fraction of glucose (C6H12O6) in an aqueous binary solution is 0.1. The mass percentage of water in it, to the nearest integer, is _______.

22. The volume strength of 8.9 M H2O2 solution calculated at 273 K and 1 atm is ______. (R = 0.0821 L atm K1 mol1) (rounded off to the nearest integer)

23. An element with molar mass 2.7 10−2 kg mol−1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 103 kg m−3, the radius of the element is approximately ______ 10−12 m (to the nearest integer).

24. The total number of monohalogenated organic products in the following (including stereoisomers) reaction is ______.

25. The photoelectric current from Na (Work function, w0 = 2.3 eV) is stopped by the output voltage of the cell Pt(s) H2 (g, 1 Bar) HCl (aq. pH =1) AgCl s Ag(s). The pH of aq. HCl required to stop the photoelectric current form K(w0 = 2.25 eV), all other conditions remaining the same, is _______ 102 (to the nearest integer). Given,

Mathematics

1. The value of (2.1P02P1+4.3P2….. up to 51th term) +(1!-2!+3!-…… up to 51th term) is equal to:

(1)  1 – 51(51)!

(2)  1 + (52)!

(3)  1

(4)  1 5 (51)!

2. Let P be a point on the parabola, y2 = 12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is 4/3 , then:

(1)  PN = 4

(2)  MQ = 1/3

(3)  PN = 3

(4)  MQ = 1/4

3. If = AX3 + BX2 + Cx + D, then B + C is equal to:

(1)  1

(2)  −1

(3)  −3

(4)  9

4. The foot of the perpendicular drawn from the point (4,2,3) to the line joining the points (1,2,3) and (1,1,0) lies on the plane:

(1)  x – y – 2z = 1

(2)  x – 2y + z = 1

(3)  2x + y – z = 1

(4)  x + 2y – z = 1

5. If y2 + loge(cos2x) = y, x∈(−π/2, π/2), then

(1)  |y´(0)|+|y´´(0)| = 1

(2)  |y´´(0)| = 0

(3)  |y´(0)|+|y´´(0)| = 3

(4)  |y´´(0)| = 2

6. is equal to:

(1)  5π/4

(2)  3π/2

(3)  7π/4

(4)  π/2

7. A hyperbola having the transverse axis of length √2 has the same foci as that of the ellipse 3x2 + 4y2 = 12, then this hyperbola does not pass through which of the following points ?

(1)

(2)

(3)

(4)

8. For the frequency distribution

Variant (X): x1 x2 x3…x15

Frequency (f): f1 f2 f3…f15

where 0 < x1 < x2 < x3 <… x15 ≤ 10 and  the standard deviation cannot be:

(1)  1

(2)  4

(3)  6

(4)  2

9. A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is:

(1)  1/3

(2)  1/4

(3)  1/8

(4)  1/9

10. If the number of integral terms in the expansion of (31/2 +51/8)n is exactly 33, then the least value of n is:

(1)  128

(2)  248

(3)  256

(4)  264

11.

(1)  π2

(2)  π2/2

(3)  √2π2

(4)  2π2

12. Consider the two sets:

A = {m ∈ R : both the roots of x2 − (m + 1) x + m + 4 = 0 are real} and B = [−3, 5).

Which of the following is not true ?

(1)  A-B = (−∞,−3) ∪ (5, ∞)

(2)  A ∩ B = {−3}

(3)  B-A = (−3, 5)

(4)  A U B = R

13. The proposition p − > ∼ (p ˄ q) is equivalent to:

(1)  (∼p) ˅(∼ q)

(2)  (∼ p) ˄q

(3)  q

(4)  (∼ p) ˅q

14. The function, f(x) = (3x − 7)x2/3, x ∈ R is increasing for all x lying in:

(1)

(2)

(3)

(4)

15. If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is:

(1)  1/6

(2)  1/5

(3)  1/4

(4)  1/7

16. The solution curve of the differential equation,  which passes through the point (0, 1), is:

(1)

(2)

(3)

(4)

17. The area (in sq. units) of the region  is

(1)  23/16

(2)  79/16

(3)  23/6

(4)  79/24

18. If α and β are the roots of the equation x2 + px + 2 = 0 and 1/α and 1/β are the roots of the equation 2x2 + 2qx + 1 = 0, then is  equal to:

(1)

(2)

(3)

(4)

19. The lines  and

(1)  do not intersect for any values of l and m

(2)  intersect when l = 1 and m = 2

(3)  intersect when l = 2 and m = 1/2

(4)  intersect for all values of l and m

20. Let [t] denote the greatest integer ≤t. If for some λ ∈ R −{0, 1},  then L is equal to:

(1)  0

(2)  2

(3)  1/2

(4)  1

21. If  then the value of k is …….

22. The diameter of the circle, whose centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2, is ……

23. The value of  is equal to………..

24. Let  and A4[aij]. If a11 = 109, then a22 is equal to…………….

25. If  (m, n ∈ N) then the greatest common divisor of the least values of m and n is……………..

## JEE Main September 2 2020 Shift 2 Question Paper with Answer Key

Physics

1. If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is:

(1)  [P1/2 AT–1]

(2)  [PA1/2 T–1]

(3)  [PA1/2 T–1]

(4)  [P2 AT–2]

2. Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg –m2 and 10 rad s–1 respectively while those for the second one are 0.2 kg–m2 and 5 rad s–1 At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The Kinetic energy of the combined system is:

(1)  2/3 J

(2)  10/3 J

(3)  5/3 J

(4)  20/3 J

3. A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 × 10–4. The mass of the particle is close to:

(1)  4.8 × 10–27 kg

(2)  9.1 × 10–31 kg

(3)  9.7 × 10–28 kg

(4)  1.2 × 10–28 kg

4. A potentiometer wire PQ of 1 m length is connected to a standard cell E1. Another cell E2 of emf 1.02 V is connected with a resistance ‘r’ and switch S (as shown in figure). With switch S open, the null position is obtained at a distance of 49 cm from Q. The potential gradient in the potentiometer wire is:

(1)  0.03 V/cm

(2)  0.02 V/cm

(3)  0.04 V/cm

(4)  0.01 V/cm

5. In the following digital circuit, what will be the output at ‘Z’, when the input (A,B) are (1,0), (0,0), (1,1), (0,1):

(1)  0, 1, 0, 0

(2)  1, 1, 0, 1

(3)  0, 0, 1, 0

(4)  1, 0, 1, 1

6. A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is:

(1)

(2)

(3)

(4)

7. A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale).

8. In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by  What is the unit vector along direction of propagation of the wave.

(1)

(2)

(3)

(4)

9. An inductance coil has a reactance of 100 Ω. When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45°. The self-inductance of the coil is:

(1)  6.7 × 10–7 H

(2)  5.5 × 10–5 H

(3)  1.1 × 10–1 H

(4)  1.1 × 10–2 H

10. This displacement time graph of a particle executing S.H.M. is given in figure : (sketch is schematic and not to scale)

Which of the following statements is/are true for this motion?

(A) The force is zero at t = 3T/4

(B) The acceleration is maximum at t=T

(C) The speed is maximum at t = T/4

(D) The P.E. is equal to K.E. of the oscillation at t = T/2

(1)  (B), (C) and (D)

(2)  (A), (B) and (D)

(3)  (A) and (D)

(4)  (A), (B) and (C)

11. In a Young’s double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength 700 nm is used. If the wavelength of light is changed to 400 nm, the number of fringes observed in the same segment of the screen would be:

(1)  28

(2)  24

(3)  30

(4)  18

12. A heat engine is involved with exchange of heat of 1915 J, –40J, + 125J and –QJ, during one cycle achieving an efficiency of 50.0%. The value of Q is:

(1)  980 J

(2)  640 J

(3)  40 J

(4)  400 J

13. In a hydrogen atom the electron makes a transition from (n + 1)th level to the nth level. If n>>1, the frequency of radiation emitted is proportional to:

(1)  1/n2

(2)  1/n

(3)  1/n3

(4)  1/n4

14. When the temperature of a metal wire is increased from 0°C to 10°C, its length increases by 0.02%. The percentage change in its mass density will be closest to:

(1)  0.06

(2)  0.008

(3)  2.3

(4)  0.8

15. A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

(1)

(2)

(3)

(4)

16. A 10 μF capacitor is fully charged to a potential difference of 50V. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20 V. The capacitance of the second capacitor is:

(1)  15 μF

(2)  20 μF

(3)  10 μF

(4)  30 μF

17. An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true?

(A) the mean free path of the molecules decreases.

(B) the mean collision time between the molecules decreases.

(C) the mean free path remains unchanged.

(D) the mean collision time remains unchanged.

(1)  (B) and (C)

(2)  (A) and (B)

(3)  (C) and (D)

(4)  (A) and (D)

18. A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm–1, density = 667 kg m–3) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60° with one another. Then h is close to (g=10 ms–2).

(1)  0.172 m

(2)  0.049 m

(3)  0.087 m

(4)  0.137 m

19. The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected):

(1)

(2)

(3)

(4)  R/2

20. The figure shows a region of length ‘l’ with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 ×105 ms–1 making an angle 60° with the field. If the proton completes 10 revolution by the time it cross the region shown, ‘l’ is close to (mass of proton = 1.67 × 10–27 kg, charge of the proton = 1.6 × 10–19 C)

(1)  0.11 m

(2)  0.22 m

(3)  0.44 m

(4)  0.88 m

21. A light ray enters a solid glass sphere of refractive index μ= √3 at an angle of incidence 60°. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is ________.

22. An ideal cell of emf 10 V is connected in circuit shown in figure. Each resistance is 2Ω. The potential difference (in V) across the capacitor when it is fully charged is _______.

23. A square shaped hole of side l =a/2 is carved out at a distance d = a/2 from the centre ‘O’ of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is –a/X, value of X (to the nearest integer) is _________.

24. A particle of mass m is moving along the x-axis with initial velocity  It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If sinθ1 = √n sin θ2 then value of n is

25. A wire of density 9 × 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4.9 × 10–4. The lowest frequency of the transverse vibrations in the wire is (Young’s modulus of wire Y = 9 ×1010 Nm–2), (to the nearest integer), _______.

Chemistry

1. Cast iron is used for the manufacture of :

(1)  Wrought iron and steel

(2)  Wrought iron and pig iron

(3)  Wrought iron, pig iron and steel

(4)  Pig iron, scrap iron and steel