03. rev full test-2 jee main-2020 q.prev_full... · w p r í 1 ñ 1 Û 1 x x , _ ] ð 1 1 ï w ð 1...

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KUKATPALLY CENTRE: # 22-97, Plot No.1, Opp. Patel Kunta Huda Park, Vijaynagar Colony, Hyderabad - 500 072. Ph.: 040-64601123 MIYAPUR CENTRE: Above Sai Motors Maruthi Showroom, Allwyn X Road, Miyapur, Hyderabad.

INTERNAL TEST

SECOND YEAR 2018-20

REVISION FULL TEST-2

Time: 3 hours Maximum Marks: 300

Instructions to the Candidates I. This Test Booklet consists of 75 questions.

Use Blue/Black ball Point Pen only for writing particulars and bubbling of OMR.

II. Each subject (Physics, Chemistry & Mathematics) have 25 Questions. Total 75 Questions

20 multiple Choice Questions, 5 Numerical value Questions.

III. Each subject have 20 Questions in Part–I and 5 Questions in Part–II like below table:

Multiple Choice Questions Numerical Value Questions

Mathematics 01 – 20 Mathematics 21 – 25

Physics 26 – 45 Physics 46 – 50

Chemistry 51 – 70

Chemistry 71 – 75

III. Attempt all questions.

IV. Use of calculator/logarithmic table is not permitted.

Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam.

NAME:

ENROLLMENT NO.:

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Multiple Choice Type Questions (01–20): 1. If f(x) is a quadratic expression with real coefficients, such that f(x) = x has no real roots then,

(A) f f x x will have four real roots (B) f f x x will have no real roots

(C) f f x x will have two real roots (D) none of these

2. If atleast one value of the complex number z = x + iy satisfies the condition 2z 2 a 3a 2 , then

range of values of ‘a’ is, (A) , 2 (B) , 1 2, (C) 3, (D) 3, 4

3. If m be the greatest value of k for which 100! is divisible by 3k, then the number of ways of distributing m

different things among 5 persons, so that two of them get 10 things each, two get 12 things each and the fifth one gets four things is

(A) 2 2

48! 5.410! 12!

(B) 2 2

48!

10! 12! 4! (C)

2 2

24!

10! 12! 4! (D)

2 2

24!5!

10! 12! 4!

4. The coefficient of 8 4 9 9a b c d in 10abc abd acd bcd is

(A) 10!

8! 4! 9! 9! (B) 2520 (C) 10! (D) 3000

5. If 2 2 2

2 2 2 3 3 31

cos a 1 and tan tan , then sin cos3 2

(Given that cos 0 & 02

)

(A)

1

32

a

(B)

2

32

a

(C)

4

32

a

(D) a

6. Range of values of for which the equation 4 4sin x cos x sin2x 0 has solutions, is

(A) 1

02

(B) 3 1

2 2 (C)

31

2 (D) 2 4

7. If 1 2 3I , I , I are excentre of the triangle with vertices 0, 0 , 5, 12 , 16, 12 then the orthocenter of 1 2 3I I I is

(A) 6, 9 (B) 7, 9 (C) 6, 7 (D) 9, 7

8. A tangent to the parabola 2y 4bx 0 meets the parabola 2y 4ax at P and Q, then locus of the

mid–point of PQ is

(A) 2227ay 2 x 2a (B) 2 2y 2a b 4a x

(C) 2y 2a b 4ax (D) none of these

9. A tangent to the hyperbola 2 2

2 2

x y1

a b cuts the ellipse

2 2

2 2

x y1

a b in P and Q. Then locus of midpoint of

PQ is

(A) 32 2 2 2

2 2 2 2

x y x y

a b a b

(B)

22 2 2 2

2 2 2 2

x y x y

a b a b

(C)22 2 2 2

2 2 2 2

x y x y

a b a b

(D)

22 2 2 2

2 2 2 2

x y x y

a b a b

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10. Let R be the set of real numbers. Then the relation S a, b : 1 ab 0 on R is

(A) Reflexive, symmetric but not transitive (B) Reflexive, transitive but not symmetric (C) Symmetric, but neither reflexive nor transitive (D) Symmetric, transitive but not reflexive

11. The value of 2 3 2

tan x4

dxcos x tan x tan x tan x

is

(A) 12tan tanx cot x 1 c (B) 12tan tan x co tx 1 c

(C) 1 22tan tan x tanx 1 c (D) 12tan tanx cot x 1 c

12. Let 2 2

0 0

tanx sinxI dx and J dx

x x

(A) I , J2 2

(B) I , J

2 2

(C) I , J

2 2

(D) I , J

2 2

13. If p : It rains today q : I go to school r : I shall meet my friend s : I shall go for a movie Then, which of the following is the proposition. If it does not rain today or I do not go to school, then I shall

meet my friend and go for a movie. (A) p q r s (B) p q r s

(C) p q r s (D) p q r s

14. In a binomial distribution 1

B n, p4

, if the probability of at least one success is greater than or equal to

9,

10 then n is greater than or equal to

(A) 10 10

100

log 4 log 3 (B)

10 10

9

log 4 log 3 (C)

10 10

4

log 4 log 3 (D)

10 10

1

log 4 log 3

15. Expression of a non zero vector r

as a linear combination of a non–zero vector a

which is non–collinear

with r

and another vector perpendicular to a

and coplanar with r and a

is given as

( r and a

are non collinear)

(A) r .a 1r r a a r

a.a a.r

(B) a.a 1

r a a a rr .a a.a

(C) r .a 1r a a a r

a.a a.a

(D) a.a 1

r r a a rr .a a.a

16. The distance of point (0, 0, 0) from the plane x + y + z + 1 = 0 in the direction parallel to the line

x 1 y z

2 1 1

is equal to

(A) 3

2 2 (B)

1

2 2 (C)

1

3 (D)

3

2

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17. Statement–1 : The mean of the distribution given as

Variable (x) 1 2 3 4 5

Frequency (y) 4 5 f 1 2 is 2.6 then f = 8

and

Statement–2 : The mean of the values xi with their respective frequencies fi is given by

n

i ii 1

n

ii 1

f x

f

.

(A) Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1 (B) Statement–1 is true, Statement–2 is true, Statement–2 is NOT a correct explanation for statement–1 (C) Statement–1 is true, Statement–2 is false (D) Statement–1 is false, Statement–2 is true

18. The solution of 2 2 2x xy dy x y dx is

(A) e e

ylog x log x y c

x (B) e e

ylog x 2log x y c

x

(C) e e

xlog x log x y c

y (D) None of these

19. The general solution of the differential equation dy x y x y

sin sindx 2 2

is

(A) y

n tan 2sin x c2

l (B) y x

n tan 2sin c2 2

l

(C) y x

n tan 2sin c4 2

l (D) None of these

20. The area of region bounded by 2 2 2 2 2a y x a x is

(A) 2a

3 (B)

22a

3 (C)

24a

3 (D)

28a

3

Numerical Type Questions (21–25):

21. If there are n harmonic means between 1 and 1

31 and the ratio of 7th and (n – 1)th harmonic means is 9 : 5,

then the value of n will be

22. If 1 3

sin2 sin2 and cos2 cos2 ,2 2

then 2cos

23. The sides of triangle ABC are in A.P. If the angles A and C are the greatest and the smallest angles

respectively & if 1 cosA 1 cosC cos A cosC, then is

24.

x

02008x 0

x cos2008t dt

limx 2008x

25. Richa applied for a post of manager in a company and Monika applied for the post of assistant manager.

There are 10 candidates for manager and 6 candidates for assistant manager. If Monika is selected then the probability of Richa’s selection is

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Multiple Choice Type Questions (26–45): 26. For a person with normal hearing the faintest sound that can be heard at a frequency of 400Hz has a

pressure amplitude of about 56.0 10 atm. Calculate the corresponding intensity in w/ 2m . Take speed of

sound in air as 344 m/s and density of air 1.2 kg/ 3m . (A) 3 24.4 10 W m (B) 2 24.4 10 W m (C) 4 24.4 10 W m (D) 1 24.4 10 W m

27. A point charge q is placed inside a neutral conducting spherical shell of inner radius 2R and outer radius

3R at a distance of R from the centre of the shell. The electric potential at the centre of shell will be 0

1

4

times

(A) q

2R (B)

4q

3R (C)

5q

6R (D)

2q

3R

28. A substance of mass m kg requires a power input of ‘P’ watts to remain in the molten state at its melting

point. When the power is turned off the sample completely solidifies in time ‘t’ sec. What is the latent heat of fusion of the substance?

(A) Pm

t (B)

Pt

m (C)

m

Pt (D)

t

Pm

29. A point P moves in counter-clock wise direction on a circular path

as shown in below mentioned figure. The movement of ‘P’ is such that it sweeps out a length 3s t 5 , where‘s’ is in metre and ‘t’ is in seconds. The radius of the path is 20 m. The magnitude acceleration of ‘P’ at t = 2 s is nearly: (A) 214ms (B) 213ms

(C) 212ms (D) 27.2ms

20 m

P(x,y)

A X

B

Y

O20 m

20 m

30. A coil having 100 turns and area of 0.001 2m is free to rotate about an axis; the coil is placed with its plane

perpendicular to magnetic field of2

Wb1.0

m. If the coil is rotated rapidly through an angle of 0180 , how

much charge will flow through the coil ? The resistance of the coil is 10

(A) 0.02 coulomb (B) 0.04 coulomb (C) 0.08 coulomb (D) 0.07 coulomb 31. ‘n’ identical light bulbs, each designed to draw P power from a certain voltage supply are joined in series

and that combination is connected across that supply. The power consumed by one bulb in the combination will be

(A) nP (B) P (C) P/n (D) P/n2

32. To decrease the cut-off wavelength of continuous X-rays by 25%, the potential difference across X-ray

tube

(A) must be increased by 100

%3

(B) must be decreased by 100

%3

(C) must be increased by 25% (D) must be decreased by 25% 33. A plank P is placed on a hollow cylinder C, which rolls on a

horizontal surface as shown. No slippage is there at any of the surfaces in contact. Both have equal mass say M (each) and if v is the velocity of centre of mass of the cylinder C, then the ratio of the kinetic energy of plank P to the cylinder C is

P

C

(A) 1 : 1 (B) 2 : 1 (C) 3 : 8 (D) 8 : 3

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34. A cubical wooden block of side 10 cm floats at the interface between oil and water with its lower face 2 cm below the interface. If the density of oil is 0.6 gcm-3, the mass of the block is (A) 200 g (B) 340 g (C) 480 g (D) 680 g

35. If two soap bubbles of different radii are in communication with each other, then (A) air flows from the larger bubble into the smaller one until their sizes become equal (B) the sizes of the bubbles remain unchanged (C) air flows from the smaller bubbles into the larger one and the larger bubble grows at the expense of the

smaller one (D) air flows from the larger into the smaller bubble until their radii interchange 36. A closed cubical box made of perfectly insulating material has walls of thickness

8 cm and the only way for heat to enter or leave the box is through two solid metal plugs A and B, each of cross – sectional area 12 cm2 and length 8 cm fixed in the opposite walls of the box as shown in the figure. Outer surface A is kept at 100 0C while the outer surface B is kept at 4 0C. The thermal conductivity of the material of the plugs is 0.5 cals-1 cm-1 (0C)-1. A source of energy generating 36 cals-1 is enclosed inside the box. The equilibrium temperature of the inner surface of the box (assuming that it is same at all points on the inner surface) is

(A)380C (B) 570C (C) 760C (D) 850C 37. In the given circuit, the potential difference across the 7 F

capacitor is 6 V. Then incorrect statement among (A) the potential difference across the 12 F capacitor is 10 V

(B) the potential difference across the 3.9 F capacitor is 10 V

(C) the charge on the 3 F capacitor is 42 C

(D) the emf of the battery is 30 V 3.9μF

3 F

12μF

7μF 38. A convex lens of focal length 40 cm is held coaxially 12 cm above a concave

mirror of focal length 18 cm. An object held x cm above the lens gives rise to an image coincident with it. The x is equal to (A) 12 cm (B) 15 cm (C) 18 cm (D) 30 cm

x cm

12 cm

39. In Young’s experiment using monochromatic light, the fringe patterns shifts by a certain distance on the

screen when a mica sheet of refractive index 1.6 and thickness 1.964 micron is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the slits and the screen is doubled. It is found that the distance between successive maxima now is the same as the observed fringe shift upon the introduction of the mica sheet. The wavelength of light is

(A) 0

5762 A (B) 0

5825 A (C)0

5892 A (D) 0

6500 A

40. A metal disc of radius a rotates with a constant angular velocity about its axis. Assuming, m and e to be

the mass and charge of electron, the potential difference between the centre and the rim of the disc is

(A) 2 21 m a

2 e

(B) 2 2m a

e

(C)

2 22m a

e

(D)

2 24m a

e

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41. The number of undecayed nuclei N in a sample of radioactive material as a function of time is shown in the graph. Which of the following graphs correctly shows the relationship between N and the activity A?

N

t

(A)

A

N

(B)

A

N

(C)

A

N

(D)

A

N

42. A metal bar of mass 1 kg is heated at atmospheric pressure 5 2atmP 10 N/m from 0 020 C to 70 C . The

coefficient of linear expansion, the specific heat and the density of metal are 6 020 10 per C , 0400 J/kg / C

and 4 310 kg/m respectively. Choose the correct statement

(A) The fraction of heat energy that is used to do work against the atmospheric pressure is 61.5 10

(B) The fraction of heat energy that is used to do work against the atmospheric pressure is 31.5 10 (C) The quantity of heat supplied to the metal is 18 kJ (D) The increase in internal energy of the metal is 16kJ

43. A block of mass M is placed on a surface with a vertical cross section given by3x

y6

.

If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is

(A) 1

m6

(B) 2

m3

(C) 1

m3

(D) 1

m2

44. The speed of flow of water through a long cylindrical pipe of diameter 2cm so that flow become turbulent is….(Assume density of water as 3 310 kg /m ,

viscosity 31 10 Pa.s , Reynold’s number=3000)

(A) 1.5 1ms (B) 0.15 1ms (C) 2 1ms (D) 1 1ms 45. In determining resistance of a galvanometer by using half deflection method, the following readings are

noted down S.No. Resistance (R ohm) Deflection div Shunt for 2

1 200 80 40

2 280 60 42

3 300 50 43

4 450 40 45

5 620 30 46.3

S

G

R

1K

2K

2V

The circuit diagram is as shown here. Galvanometer has a total of 100 divisions and it can measure

current up to 10 mA. The least count of the galvanometer is (A) 10 mA (B) 1mA (C) 0.1mA (D) Information insufficient

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Numerical Type Questions (46–50): 46. A cavity of radius R/2 is made in a solid sphere of radius R and

density at the periphery as shown in fig. A particle of mass

m=37 R

6

placed at A is inside the cavity. The time taken by the

particle to reach the point O is n

2 G . Find the value of n.

(The sphere is placed on a smooth horizontal surface)

47. Two bobs of different metals but of same mass are suspended from different metal wires of same cross

sectional area but of different length L1 and L2. Thus, the released heat is absorbed by the bobs and they get heated by different temperature 1 2and . The specific heats of two bobs are related as

1 2

2 1

C

C

. If the ratio of the strains in two wires is n times 2

1

L

L, find n.

48. Consider a situation shown in the figure. A source is moving with a

velocity Vs 35 m / s towards the wall and an observer is moving with a

velocity 0V 25 m / s away from the wall. The wall is moving with a

velocity u = 15 m/s towards the source. The wind is blowing with velocity 5 m / s towards the wall. The frequency of the sound emitted by the

source is f0= 310 Hz and the velocity of sound with respect of air is v = 330 m/s. The frequency of the reflected waves from wall received by the observer is (in Hz)

49. A cylindrical piston of mass M slides smoothly inside a long cylinder

closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be (in sec) (h = 0.5 m, M = 10.13 kg, A = 0.5 × 10–4 m2, 1 atm = 1.013×105 Pa)

50. A photon with an energy of 4.9eV ejects photoelectrons from tungsten. When the ejected electron enters a

constant magnetic field of strength B = 2.5mT at an angle of 600 with the field direction, the maximum pitch of the helix described by the electron is found to be 2.7 mm. Find the work function of the metal in electron volts. (Given that specific charge of electron is 1.76 1011 C/kg.)

Multiple Choice Type Questions (51–70): 51. In a solid, oxide ions are arranged in ccp. One sixth of the tetrahedral voids are occupied by the cations A

while one third of the octahedral voids are occupied by the cations B. The formula of the compound is (A) ABO3 (B) A2B3O4 (C) ABO2 (D) A3B2O4 52. Electrode potential data are given below : (A) 3 2Fe aq e Fe aq ; 0E 0.77V

(B) 3Al aq 3e Al s ; 0E 1.66V

(C) 2Br aq 2e 2Br aq 0E 1.08V

which combination would give a cell with a largest cell voltage (A) A and B (B) B and C (C) A and C (D) All are equal

53. In the equation 4M + 8CN– + 2H2O + O2 2

4 M CN 4OH identify the metal ‘M’.

(A) copper (B) Iron (C) Gold (D) zinc

M

h

Gas

P A

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54. On heating a colourless solid A, Vapours of B (liquid at room temp) and gas ‘C’ are formed. ‘A’ is decomposed by NaOH on heating to form gas D giving white fumes with HCl. Gas ‘C’ occupies 800 ml/gm at STP. Then ‘A’ is

(A) NH4NO3 (B) NaNO2 (C) NH4Cl (D) NH4NO2 55. If ‘n’ and ‘’ are the principal and azimuthal quantum number respectively, then the expression for

calculating total number of electrons in any energy level is

(A) n

1

2 2 1

(B)

n 1

1

2 2 1

(C)

n 1

0

2 2 1

(D)

n 1

0

2 2 1

56. Gas O2 N2 NH3 CH4

2 2lit atmmola

1.36 1.39 4.17 2.253

The gas that has highest critical temperature ? (A) O2 (B) N2 (C) NH3 (D) CH4 57. In the titration of mixture of NaHCO3 and Na2CO3, volume of HCl required is ‘x’ ml with phenolphthalein

indicator and ‘y’ ml with methyl orange indicator for the same. Hence volume of HCl for complete reaction of Na2CO3 is

(A) 2x (B) y (C) x

2 (D) y x

58. The sulphur present in organic compound is oxidized by fuming HNO3 into (A) H2S (B) H2SO4 (C) SO2 (D) H2SO3 59. Which of statement does not explain fibers? (A) Fibers are made of linear long chains which permit side-by-side alignment. (B) Structures of fibers are controlled by enthalpy instead of entropy. (C) There exist strong intermolecular forces to prevent slipping between chains. (D) Nylon and rubbers are typical examples of fibers. 60. Which of the following is the correct order of dipole moments of the molecules (A) NH3 > NF3 > BF3 (B) NF3 > BF3 > NH3 (C) BF3 > NF3 > NH3 (D) NH3 > BF3 > NF3 61. Which of the following plots correctly represent the variation of bond energies of halogen with atomic

numbers ?

(A)

Z

BE

(B)

Z

BE

(C)

Z

BE

(D)

Z

BE

62. The general formula of cyclic or ring silicates is

(A) 2n

2 5 nSi O

(B) 6

2 7Si O (C) 23 n

SiO (D) 6n

4 11 nSi O

63. In which of the following reactions. H2O2 acts as oxidizing agent ?

(A) 3 ( ) 2 2H OFe / OH (B) 2 2H O

4MnO /H

(C) 2 2H OHOC (D) 2 2H OHCHO 64. The sparingly soluble salt, Ag2CrO4 is expected to be the most soluble in (A) Pure water (B) 0.10 M K2CrO4 (C) 0.10 M AgNO3 (D) 0.10 M KNO3

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65. In which of the following reactions nucleophilic addition is involved?

(A) H5C6 C

O

CH3

NH2NH2, H+

H5C6 C

NNH2

CH3

(B) H5C6 C

O

CH3

LiAlH4

H5C6 CH

OH

CH3 (C) Both (A) and (B) (D) None of the two

66. Which of the following will not give yellow coloration with NaOI?

(A) CH CH3

OH

(B) C CH3

O

(C) H3C C C CH3

O CH3

CH3

(D) C CH2

O

67. Consider the following ions.

(I) Me2 N N N

(II) O2N N N

(III) H3C O N N

(IV) CH3 N N

The reactivity of these ions towards azo–coupling reaction under similar conditions is (A) I < IV < II < III (B) I < III < IV < II (C) III < I < II < IV (D) III < I < IV < II 68. A compound of molecular formula (C3H6O) reacts with CH3MgI followed with hydrolysis forming secondary

alcohol. The compound doesn’t reduce Benedict’s solution. The compound is (A) CH3–CO–CH3 (B) CH3CH2CHO

(C) CH3 CH CH2

O (D) CH3CH2–CH2OH

69. A compound A has molecular formula C2Cl3OH. It reduces Fehling’s solution and on oxidation gives a

monocarboxylic acid. A is obtained by the action of Cl2 on ethyl alcohol. The compound A is (A) chloroform (B) chloral (C) trichloro ethanol (D) trichloro acetic acid 70. Which of the following phrases are correctly associated with an SN1 reaction?

1. Rearrangement is possible. 2. Rate is affected by solvent polarity. 3. The strength of the nucleophile is important in determining rate. 4. The reactivity series is tertiary > secondary > primary alkylhalides. 5. Proceeds with complete inversion of configuration, (A) 3, 5 (B) 1,2,4 (C) 2, 3, 5 (D) 1,2,3,4 Numerical Type Questions (71–75): 71. A Hypothetical reaction, A2 +B2 2AB follows the mechanism as given below:

eqk

2A A A fast

1k2A B AB B slow

2kA B AB fast

the theoretical order of overall reaction is

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72. A weak acid 5aHX K 10 on reaction with NaOH gives NaX. For 0.1 M aqueous solution of NaX, the

percentage hydrolysis is 73. The oxidation state of inert gas element, in the first inert gas compound prepared by Bartlett is 74. 100 ml of 0.12 M aqueous ammonia solution is titrated with 0.12 M H2SO4 solution. The pH value at

equivalence point is [Given pKb for ammonia = 4.74, log2 = 0.3]

75. 0.01M aqueous solution of 3 6K Fe CN freezes at – 0.062C. What is the percentage dissociation of

complex 1f 2K H O 1.86K Kgmol

Space for rough work

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