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SAMPLE PAPER (JEE MAIN DIAMOND COURSE-2019-20)QUESTION PAPER

Time : 3 Hours Maximum Marks : 216Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONSA. General :

1. This booklet is your Question Paper containing 72 questions. The booklet has__ pages.

2. The question paper CODE is printed on the right hand top corner of this sheet andon the back page (page no. __) of this booklet.

3. The question paper contains _ blank pages for your rough work. No additional sheetswill be provided for rough work.

4. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers andelectronic gadgets in any form are not allowed to be carried inside the examination hall.

5. Fill in the boxes provided below on this page and also write your Name andUID. No. in the space provided on the back page (page no. __) of this booklet.

6. The answer sheet, a machine-readable Objective Response Sheet (ORS), is providedseparately.

7. DO NOT TAMPER WITH / MUTILATE THE ORS OR THE BOOKLET.

8. Do not open the question-paper booklet before being instructed to do so by the invigilators.

B. Question paper format Read the instructions printed on the back page

C. Marking scheme (page no. __) of this booklet.

Name of the candidate UID Number

I have read all the instructions and I have verified all the information filled shall abide by them. in by the candidate.

.......................................................... ............................................................ Signature of the Candidate Signature of the invigilator

VIBRANT ACADEMY(India) Private Limited

A-14(A), Road No.1, Indraprastha Industrial Area, Kota-324005 (Raj.)Tel.: 06377791915 Fax: (0744) 2423405

Email: [email protected] Website : www.vibrantacademy.comWebsite : dlp.vibrantacademy.com

CODE - A

USEFUL DATAAtomic weights: Al = 27, Mg = 24, Cu = 63.5, Mn = 55, Cl = 35.5, O = 16, H = 1, P = 31, Ag = 108, N = 14, Li = 7,I = 127, Cr = 52, K=39, S = 32, Na = 23, C = 12, Br = 80, Fe = 56, Ca = 40, Zn = 65.5, Ti = 48, Ba = 137, U = 238,Co= 59, B =11, F = 19, He = 4, Ne = 20, Ar = 40 , Mo = 96, g = 10 m/s2

Vibrant Academy (I) Pvt. Ltd. "A-14(A)" Road No.1, IPIA, Kota (Raj.) Ph. 06377791915 (www.vibrantacademy.com) [2]

PART I : MATHEMATICSSingle Correct Choice Type

This section contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.

1. Let P be a variable point on the ellipse 2 2x y 1

25 16 with foci at S1 and S2. If A is the area of tirangle PS1S2,

then the maximum value of A is(A) 12 (B) 24 (C) 36 (D) 48

2. For the hyperbola 2 2

2 2

x y1

a b , distance between the foci is 10. From the point 2, 3 perpendicular tangents

are drawn to the hyperbola, then eccentricity of the hyperbola is

(A) 54

(B) 113

(C) 53

(D) 53

3. The expression (4cos29º – 3) (4cos227º – 3) equals(A) tan9º (B) cot9º (C) cosec9º (D) sec9º

4. If the coefficients of x7 and x8 in the expansion of nx2

3

are equal, then the value of n is :

(A) 15 (B) 45 (C) 55 (D) 56

5. Let f(x) = sin3x + x5 ; then 1

2 4

–1

3 | x | f(x) . cos x dx2

is equal to

(A) 0 (B) 1 (C) 2 (D) None of these

6. A common tangent to x2 – 2y2 = 18 and x2 + y2 = 9 is

(A) 53x2y (B) 33x2y (C) 73x2y (D) 53x2y

7. The number of ways in which we can get atleast 6 successive tails when a coin is tossed 10 times in a rowis :(A) 10C6 (B) 27 – 26 (C) 40 (D) 48

8. If a, b, c R and a + b + c = 0, then the quadratic equation 3ax2 + 2bx + c = 0 has(A) at least one root in [0, 1] (B) at least one root in [1, 2](C) at least one root in [3/2, 2] (D) none of these

9. If 1 x x 1

f(x) 2x x(x 1) (x 1)x3x(x 1) x(x 1)(x 2) (x 1)x(x 1)

then f(500) is equal to

(A) 0 (B) 1 (C) 500 (D) – 50010. In which one of the following functions, Rolle's theorem applicable?

(A) f(x) = |x|, in – 2 x 2 (B) f(x) = tanx, in 0 x (C) f(x) = 1 + (x – 2)2/3, in 1 x 3 (D) f(x) = x(x – 2)2 in 0 x 2


MATHEMATICS11. The real value of a for which the value of m satisfying the equation (a2 – 1)m2 – (2a – 3)m + a = 0 gives the

slope of a line parallel to the y-axis is

(A) 32

(B) 0 (C) 1 (D) ± 1

12. The area of the region bounded by y = ex, y = e–x, x = 0 and x = 1 is

(A) 1ee

(B) log(4/e) (C) 4 log (4/e) (D) 1e 2e

13. If m and n are the order and degree of the differential equation 3

5 (y )(y ) 4. y sin xy '''

, then

(A) m = 3, n = 5 (B) m = 3, n = 1 (C) m = 3, n = 3 (D) m = 3, n = 2

14. If 1 1cos x cos y2

and tan–1 x – tan–1 y = 0 then x2 + xy + y2 is equal to :

(A) 0 (B) 12 (C)

32

(D) 18

15. The distance between the origin and the normal to the curve y = e2x + x2 at x = 0 is

(A) 15 (B)

25 (C)

23 (D)

12

16. If h denote the A.M. k denote G.M. of the intercepts made on axes by the lines passing through (1, 1) then(h, k) lies on(A) y2 = 2x (B) y2 = 4x (C) y = 2x (D) x + y = 2xy

17. If the function f(x + 3y, x – 3y) = 12 xy, then f(x, y) is :(A) 2xy (B) 2(x2 – y2) (C) x2 – y2 (D) None of these

18. If the pair of tangents drawn from origin O to the circle x2 + y2 – 6x – 8y + 21 = 0, meets the circle at A andB, then the length of AB is

(A) 11 (B) 4

215

(C) 173

(D) 215

19. If x is real, and 2

2

x x 1kx x 1

then

(A) 1/3 k 3 (B) k 5 (C) k 0 (D) 2/3 k 1

20. If A is a square matrix such that 4 0 0

A(adj.A) 0 4 00 0 4

, then | adj.(adj.A) |

| adj.A | is equal to

(A) 256 (B) 64 (C) 32 (D) 16


MATHEMATICS

21. 1–xlim |x|–x

x2cos–2cos2 =

(A) 2cos2 (B) –2cos2 (C) 2sin2 (D) –2sin2

22. The solution of the differential equation 2 2 2 2dyx xy y xy 0

dx is

(A) x 1 1log cy x y

(B) y 1 1log cx x y

(C) 1 1log xy cx y

(D) 1 1log xy cx y

23. If two circles (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then(A) 2 < r < 8 (B) r < 2 (C) r = 2 (D) r > 2

24. The common tangent of parabola y2 = 4x and hyperbola 2 2x y 1

4 3 touches them at P and Q respectively,,

then Q can be(A) (4, 3) (B) (3, 4) (C) (–4, –3) (D) (4, –3)

PART II : PHYSICSSingle Correct Choice Type


25. The work done in joules in increasing the extension of an elastic spring of stiffness 500 Nt/m from 6 cm to20 cm is :(A) 11.0 J (B) 9.1 J (C) 2.7 J (D) 3.2 J

26. In the situation shown, the string connecting both the masses is extensible having force constant k. InitiallyB is held with string just taut and released. What can be maximum value of coefficient of friction so that Amay start moving ?

(A) = 0.5 (B) = 1 (C) = 2 (D) = 0.25

27. A 1 Horse power motor is used to lift load at vertically constant speed of 0.1 m/s. The maximum load that itcan lift at this speed is (approx.)(A) 375 kg (B) 750 kg (C) 1000 kg (D) 500 kg

28. A car of mass 100 kg is moving on level ground around a circular stadium of radius 50 m with constant speedof 10 m/s. Which of following statement is correct when car is located south of centre ?(A) Friction = 500 N in West direction (B) Friction = 500 N in North direction(C) Friction = 200 N in West direction (D) Friction = 200 N in North direction


29. A pendulum bob is projected horizontally with velocity g5 from lowermost point as shown. When the

velocity of bob becomes ,g its acceleration is :

(A) Vertically downward (B) Vertically upward(C) Horizontal (D) Zero

30. A hole is punched in the side of a bucket so that water flows out and follows a parabolic trajectory. If thecontainer is dropped from a height, falls freely accelerating under gravity, and air resistance can be ignored,the water flow:(A) Stops(B) Follows a straight line trajectory relative to the falling bucket(C) Follows an upward curving trajectory relative to the bucket(D) Follows a downward curving trajectory relative to the bucket

31. An incompressible liquid flows through a horizontal tube as shown in the figure. Then the velocity ‘v’ of thefluid is:

(A) 3.0 m/s (B) 1.5 m/s (C) 1.0 m/s (D) 2.25 m/s32. Three objects A, B and C all individually float on top of water. A and B have identical masses and densities but

different shapes while B and C have identical sizes and shapes but C has less mass and density than B. Ifthree identical weights are then tied to the objects and all three are pulled completely beneath the surface ofthe water, which object will displace the greatest volume of water?(A) object A only (B) object C only(D) objects A and B only (D) All three displace equal volumes of water

33. You dip a capillary tube into a beakers of different fluids, and from observation of the shape of the fluid surfacededuce that in which figure cohesive forces dominate over adhesive forces.

(A) (B) (C) (D)

34. Why do raindrops fall with constant speed during the later stages of their descent ? (Neglect buoyancy of air)(A) All drops fall from the same height.(B) The gravitational force is negligible for objects as small as raindrops.(C) The gravitational force cannot increase the speed of a falling object to more than 9.8 m/s.(D) Air resistance balances the gravitational force on a drop.

35. 10 gm of ice at 0°C is mixed with ‘m’ gm of water at 50°C. What is minimum value of m so that ice meltscompletely. (Lf = 80 cal/gm and sw = 1 cal/gm-°C)(A) 32 gm (B) 20 gm (C) 40 gm (D) 16 gm


PHYSICS36. The distribution of relative intensity I() of blackbody radiation from a

solid body versus the wavelength is shown in the figure. If the Wiendisplacement law constant is 2.9 × 10-3 mK, what is theapproximate temperature of the object? (A) 50 K (B) 250 K(C) 1450 K (D) 6250 K

37. In the figure shown a particle P strikes the inclined smooth plane horizontally and

rebounds vertically. If the angle is 60°, then the coefficient of restitution is:

(A) 1/3 (B) 31 (C) 1/2 (D) 1

38. If a calculation reveals that the net force on the rod is zero, then which one of the following can be concluded(A) the rod is definitely in rotational equilibrium(B) the rod is in rotational equilibrium only if the net torque about any one point is found to be zero(C) the rod might be in the rotational equilibrium even if the net torque about centre of mass is not zero(D) None of the above

39. If a circular concentric hole is made in a disk then about its axis(A) Moment of inertia remains same (B) Moment of inertia increases(C) Radius of gyration increases (D) Radius of gyration decreases

40. A horizontal platform is rotating with uniform angular velocity about the vertical axis passing through itscentre. At some instant of time, a viscous fluid of mass m is dropped at the centre and is allowed to spreadout and finally fall. The angular velocity during this period(A) Decreases continuously(B) Decreases initially and increases again(C) Remains unaltered(D) Increases continuously

41. If the weight of a body in vacuum is W and W1 and W2 are weights when it is fully immersed in liquids ofspecific gravities 1 and 2 respectively, then the relation among W, W1 and W2 is

(A) 21

1221

WWWWW

(B) 12

1221

–W–WW

(C)

21

1221 WWW

(D)

21

1221

–W–WW

42. The electric field inside a sphere which carries a charge density proportional to the distance from the origin = r( is a constant) is

(A) 0

3

4r

(B)

0

2

4r

(C)

0

2

3r

(D) None of these

43. A solid sphere rolls down two different inclined planes of the same height but of different inclinations.(A) In both cases the final speeds and time of descent will be same(B) The final speeds will be same but time of descent will be different(C) The final speeds will be different but time of descent will be same(D) The final speeds and time of descent both will be different


PHYSICS44. A particle is acted upon by a force whose component's variations with time are shown in diagrams. Then the

magnitude of change in momentum of the particle in 0.1 sec will be

(A) secmkg2

(B) secmkg10

x y

z

(C) secmkg12

(D) secmkg25

45. A cubical block of wood of side 'a' and density floats in water of density 2. The lower surface of the cubejust touches the free end of a massless spring of force constant k fixed at the bottom of the large vessel. Theweight w put over the block so that it is completely immersed in water without wetting, the weight is :

(A) a(a2 g + k) (B) a(ag + 2k) (C) a g

a 2k2 (D) 2 k

a a g2

46. Four equal charges of magnitude q each are placed at four corners of a square with its centre at the originand lying in y-z plane. An external charge +Q is moved along x-axis. The electrostatic potential energy. Uvaries on x-axis as

(A) (B) (C) (D)

47. The mass per unit length of a non uniform rod is given by = 2a xL

where a is a constant, L is length of the

rod and x is distance of any point from one end. The distance of the COM of the rod from the same end is

(A) L2

(B) 2L3 (C)

3 L5 (D)

3 L4

48. A particle is projected with velocity u along x-axis. The acceleration of the particle is proportional to thesquare of the distance from the origin i.e., a = kx2, the distance at which the particle stops is

(A) 3u2k

(B) 1/33u

2k

(C) 22u

3k(D)

1/323u2k


PART III : CHEMISTRYSingle Correct Choice Type


49. Which of the following statement is cause of more acidic nature of HNO3 than HNO2.(A) Oxidation state of nitrogen in HNO3 > HNO2 (B) Conjugate base of HNO3 is more stabilized(C) O – H bond is more polar in HNO3 than HNO2 (D) All

50.

If A is total number of alkenes formed (Including stereoisomers), find A.(A) 5 (B) 3 (C) 2 (D) 4

51. Which can act as buffer ?(A) NH4Cl + NH4OH (B) CH3COOH + CH3COONa(C) 40 mL of 0.1 M NaCN + 20 mL of 0.1 M HCl (D) All of above

52.

(A) will be

(A) (B) (C) (D)

53. For the equilibrium, PCl5 PCl3 + Cl2, KC = 2/(1–)V, temperature remaining constant :

(A) KC will increase with the increase in volume(B) KC will increase with the decrease in volume(C) KC will not change with the change in volume(D) KC may increase or decrease with the change in volume depending upon its numerical value

54. Which set of properties has same value for D2 & H2

(I) Bond length (II) Bond energy (III) Boiling point(A) Only I (B) Only I & II (C) Only II, III (D) Only (II)

55. Predict the product of the following reaction sequence.

ethyne

(A) 6-iodo-1-hexyne (B) 1-hexyne (C) 5-decyne (D) 1-iodo-1-hexene


CHEMISTRY56. Thermodynamic parameters for : HX + H2O H3O

+ + X¯ are given for HF, HCl, HBr and HI. Which acidwill show the forward reaction?

HF HC HBr HIG° +16 –46 –59 –61G° –13 –59 –63 –57TS° –29 –13 –4 +4

(A) Only HF (B) Only HI (C) Only HCl and HBr (D) HF, HCl, HBr and HI

57. Final product B is

(B)

(A) Ph – CH2 – O – SO2 – Ph (B) CH3 – CH2 – O – SO2 – Ph(C) (D) Ph – CH2 – O – CH3

58.

For above reaction x, y, z are respectively(A) H2O2 / H

+ , H2O2 / OH– , H2O2 / OH– (B) H2O2 / OH– , H2O2 / OH– , H2O2 / H+

(C) H2O2 / OH– , H2O2 / H+ , H2O2 / H

+ (D) H2O2 / H+ , H2O2 / H

+ , H2O2 / OH–

59. Equal volume of 1 M HCl and 1 M H2SO4 are neutralized by dilute NaOH solution and x and y kcal of heat areliberated respectively. Which of the following is true?(A) x = y (B) x = 0.5y (C) x = 0.4y (D) None of these

60. Find IUPAC name of the hydrate isomer of CrCl36H2O, which is having lowest electrical conductivity.(A) Hexaaquachromium(III)chloride(B) Tetraaquadichloridochromium(III)chloridedihydrate(C) Pentaaquachloridochromium(III)chloridemonohydrate(D) Triaquatrichloridochromium(III)trihydrate

61. NH4Cl crystallises in bcc crystal. x gm NH4Cl is dissolved in 500 ml H2O to make a solution of pH = 5. Howmany bcc unit cell can be constructed by x g of NH4Cl ? (Kb of NH4OH = 4 × 10–6, NA = 6 × 1023)(A) 12 × 1021 (B) 12 × 1023 (C) 6 × 1021 (D) 6 × 1023

62. A compound has the empirical formula CoCl3·5NH3. When an aqueous solution of this compound is mixedwith excess silver nitrate, 2 mol of AgCl precipitate per mol of compound. On reaction with excess HCl, no

4NH is detected. Hence, it is:

(A) [Co(NH3)5Cl2]Cl (B) [Co(NH3)5Cl]Cl2 (C) [Co(NH3)5Cl3] (D) [Co(NH3)4Cl2]Cl·NH3


CHEMISTRY63. Which of the following will not give yellow colour with NaOI ?

(A) (B)

(C) (D)

64. Calculate molar mass of A+B– having NaCl type closed packed structure. Closest distance between cationsis 282.88 pm and density of unit cell is 2.71 g/cm3.(A) 48 g/mol (B) 60 g/mol (C) 96 g/mol (D) None of these

65. Which of the following flux is used to remove acidic impurities in metallurgical process ?(A) Silica (B) Lime stone (C) Borax (D) Sodium carbonate

66.OH)2(

HCl/NaNO)1(

2

2 (P) KOH/CHCl3 (Q)

Product (Q) is :

(A) (B)

3

(C)

3

2

(D)

67. The haemoglobin from the red blood corpuscles of most mammals contains approximately 0.33% of iron bymass. The molar mass of haemoglobin as 67,200. The number of iron atoms in each molecule of heamoglobinis (atomic mass of iron = 56) :(A) 2 (B) 3 (C) 4 (D) 5

68. KMnO4 + HCl H2O + X(g), X is a(acidified)

(A) red liquid (B) violet gas(C) greenish yellow gas (D) yellow-brown gas

69. Major product of the below reaction?

(A) (B) (C) (D)


CHEMISTRY70. The value of Kƒ for water is 1.86°, calculated from glucose solution. The value of Kƒ for water calculated for

NaCl solution will be :(A) = 1.86 (B) < 1.86 (C) > 1.86 (D) zero

71. Which of the following is the correct order of ionisation energy ?(1) Be+ > Be (2) Be > Be+ (3) C > Be (4) B > Be(A) 2, 3 (B) 3, 4 (C) 1, 3 (D) None of these

72. Which compound will not give silver mirror test with Tollen’s reagent (AgNO3 + NH4OH) ?

(A) (B) HCOOH (C) HC CH (D)

B. Question paper format :9. The question paper consists of 3 parts (Physics, Chemistry and Mathematics).

10. Parts contains 30 multiple choice questions. Each question has 4 choices (A), (B),(C) and (D) for its answer, out of which only one is correct.

C. Marking Scheme :

11. For each question in Parts, you will be awarded 4 marks if you have darkened onlythe bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus one (–1) mark will be awarded.

Name of the candidate UID Number

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