09. rev full test-5 jee main-2020 q.prev_full+test-5... · 2020. 3. 21. · w p r î 1 ñ 1 Û 1 x...

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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-5

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

IV. Attempt all questions.

V. 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 Questions (01–20): 1. The number of ways in which nine boys & five girls can be arranged in two vans each having numbered

seat, three in the front and five at the back such that at least four girls always sit together is

(A) 11P9 5! . 46 (B) 11P9 . 5! (C) 11P9 6! .2 (D) 10P9 5!.38

2. A bag contains a large number of white and black marbles in equal proportions. Two samples of 5 marbles

are selected (with replacement) at random. The probability that the first sample contains exactly 1 black marble, and the second sample contains exactly 3 black marbles, is

(A)25

512 (B)

15

32 (C)

15

1024 (D)

35

256

3. The distance of the point (3, 4, 5) from the plane x + y + z = 2 measured parallel to the line 2x = y = z is.

(A) 4 3 (B) 6 (C) 5 2 (D) 12

4 Let a,b,c be three non-coplanar vectors and d be a non-zero vector, which is perpendicular to a b c .

Now, if d sinx a b cos y b c 2 c a , then the minimum value of 2 2x y is equal to

(A) 2 (B) 2

2 (C)

2

4 (D)

254

5. Each of the 'n' urns contain 4 white and 6 black balls. The (n + 1)th urns contains 5 white and 5 black balls. One of the urns is chosen at random and two balls are drawn from it without replacement. Both the balls

turn out to be black. If the probability that the (n + 1)th urn was chosen to draw the balls is 1

16 , then the

value of n is (A) 10 (B) 11 (C) 12 (D) 13 6. S – I : ~ ~ p ~ r p q

S – II : ~ p ~ q (pv ~ q) (qv ~p)

Which of the following is true about above two statements S – I and S – II. (A) Both S – I, S – II are true and S – II is a correct explanation of S – I. (B) Both S – I, S – II are true, but S – II is not a correct explanation of S – I. (C) S – I is true and S – II is false (D) S – I is false and S – II is true 7. R = {(1, 2), (2, 3), (3 4)} be a relation on the set of natural numbers. Then the least number of elements

that must be included in R to get a new relation S where S is an equivalence relation, is (A) 11 (B) 7 (C) 9 (D) 13

8. Domain of derivative of the function x , |x| 1

1 |x|f x x , |x| 11 |x|

is

(A) R 1,0,1 (B) R 1,1 (C) R 0 (D) R

9. If A is the area between the curve 76 1y x x and x - axis then the number of prime factors of 1A is

(A) 3 (B) 4 (C) 2 (D) 5

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10. The solution of the differential equation dy siny x

dx sin2y xcos y

is

(A)2x

sin y x siny C2

(B) 2x

sin y x siny C2

(C)2x

sin y x siny C2

(D) 2x

sin y x siny C2

11. For an ellipse 2 2

19 4

x y with vertices A and 1A , tangent drawn at the point P in the first quadrant meets

the y-axis in Q and the chord 1A P meets the y-axis in M. If 'O' is the origin, then 2 2OQ – MQ is equal to (A) 9 (B) 13 (C) 4 (D) 5

12. If the function 3 2 2f x x 3 a 7 x 3 a 9 x 1 has a point of maximum at positive values of x then

(A) 29

a ,7

(B) a ,7

(C) 29a , 3 3,

7

(D) a 3, , 3

13. The circum circle of ABC is 2 2x y 5x 4y 6 0 , if a parabola 21 k y x have sides AB,

BC, CA as tangents then the value of k is

(A) 7

8 (B)

11

13 (C)

2

3 (D)

4

7

14. Let and are the roots of 2x 10x 7 0 . If n nna for n 1then the value of 12 10

11

a 7a

2a

is

(A) 4 (B) –5 (C) 5 (D) –3

15. If f(x) is a continuous function in 0, such that f(0) = f( ) = 0 then the value of

/ 2

11

0

f 2x f 2x sinx.cos xdx

is equal to

(A) (B) 2 (C) 3 (D) 0

16. The value of 1

2n2

2n

xsin x dx

2

(where {x} denotes the fractional part of x),

n Z is

(A) n

(B)

n 1

(C) 2

1 2n

2

(D) 2

2n 1

17. Let f (x) = ax2 + bx + c with degree less than or equal to 2, f(0) = 0, f(2) = 2. The minimum value of 2 1

0( )f x dx

(A) 4 (B) 2 (C) 1 (D) 0

18. 2 4 2m

Lt dx(m 1,2,....)

m 1 x x ... x

(A) 4 (B) 4

3 (C)

3

4 (D) 0

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19. Two circles passing through the points A(1, 2) and E(2, 1) touch the line 4x + 8y – 7 = 0 at B and D. The possible coordinates of point C such that ABCD is a parallelogram are

(A) 15 9

,2 2

(B) (0, 3) (C) 1 5,

2 2

(D) 5 3,

2 4

20. If 1 2z ,z are complex numbers such that 1 1 2 2Re(z ) | z 2 |,Re(z ) | z 2 | and 1 2Arg(z z ) / 3 , then

Im 1 2(z z )

(A) 2 / 3 (B) 4 / 3 (C) 2 3 (D) 3 Numerical Type Questions (21–25): 21. If 'a' is a real constant and A, B, C are variable angles and

2 2a 4 TanA aTanB a 4 TanC 6a , then the least value of 2 2 2Tan A Tan B Tan C is____

22. The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls

combined is 50. The percentage of boys in the class is

23. The value of m m nm 0 n 0

m n mn

2 (2 2 )

is equal to

24. A and B are two square matrices such that 2A B BA and if 10 k 10AB A B then k is

25. If 1 2 3 4001x ,x ,x ,....x are in an AP such that 1 2 2 3 4000 4001

1 1 1.... 10

x x x x x x and 2 4000x x 50 then

1 4001x x

Multiple Choice Type Questions (26–45): 26. The photon radiated from hydrogen corresponding to the second line of Lyman series is absorbed by a

hydrogen like atom X in the second excited state. Then, the hydrogen like atom X makes a transition of nth orbit

(A) X He , n 4 (B) X Li , n 6 (C) X He , n 6 (D) X Li , n 9

27. 238U decays with a half–life of 4.5 × 109 years, the decay series eventually ending at 206Pb , which is

stable. A rock sample analysis shows that the ratio of the number of atoms of 206 238Pb to U is 0.0058.

Assuming that all the 206Pb is produced by the decay of 238U and that all other half–lives on the chain are

negligible, the age of the rock sample is 3in 1.0058 5.78 10

(A) 838 10 years (B) 638 10 years (C) 819 10 years (D) 619 10 years

28. In Young’s double slit experiment, 12 fringes are observed to be formed in a certain segment of the screen

when light of wavelength 600 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 is given by

(A) 12 (B) 18 (C) 24 (D) 30 29. An equilateral prism is placed on a horizontal surface. A ray PQ is incident

onto it. For minimum deviation. (A) PQ is horizontal (B) QR is horizontal (C) RS is horizontal (D) any one will be horizontal

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30. In the circuit of figure, the source frequency is 12000 rad s .

The current in the circuit will be (A) 2A (B) 3.3 A

(C) 2

A5

(D) 5 A

31. A uniform but time varying magnetic field B(t) exists in a circular region of

radius a and is directed into the plane of the paper as shown in figure. The magnitude of the induced electric field at point P at a distance r from the center of the circular region (A) is zero (B) decreases as 1/r (C) increases as r (D) decreases as 1/r2

32. In the following electrical network at t < 0 (figure), key is placed on (1) till the

capacitor got fully charged. Key is placed on (2) at t = 0. Time when the energy in both the capacitor and the inductor will be same for the first time is

(A) LC2

(B)

3LC

4

(C) LC3

(D)

2LC

3

33. Two infinitely long straight parallel wires are 5 m apart perpendicular to

the plane of paper. One of the wires, as it passes perpendicular to the plane of paper, intersects it at A and carries current i in the downward direction. The other wire intersects the plane of paper at point B and carries current i in the outward direction O in the plane of paper as shown in figure. With x and y axes as shown, magnetic induction at O in the component form can be expressed as

(A) 0î 3 jˆB i

2 5

(B) 0

î 7 jˆB i5 24

(C) 0î 7 jˆB 3i

4 18

(D) 0

î 3 jˆB 2i7 5

34. Current I flows through the circuit, as shown in figure. Find the magnetic

moment of the figure, if AB = BC = CD = DE = EF = FG = GH = HA :

(A) 2 27I a

2 (B) 25

I a2

(C) 24 I a (D) 25I a

3

35. A battery of internal resistance 4 is connected to the network of

resistance as shown in figure. In order that the maximum power can be delivered to the network, the value of R in should be

(A) 4

9 (B) 2

(C) 8

3 (D) 18

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36. In the potentiometer arrangement (figure), the driving cell a has emf and internal resistance r. The emf of the cell B to be rechecked has emf / 2 and internal resistance 2r. The potentiometer wire CD is 100 cm long. If balance is obtained, the length CJ l is (A) 50 cml (B) 50 cml >

(C) 50 cml < (D) Balance cannot be obtained

37. In the circuit as shown, VA – VB = V. The resistance of each wire

AB, AC, etc are shown in the figure. Find the current in AC.

(A) 2V

3R

(B) 4V

11R

(C) V

6R

(D) None of these

38. The effective capacitance between points A and B is (the

capacitance of each of the capacitors is C)

(A) C (B) C

2

(C) 36C

17 (D)

42C

17

39. A block of mass m containing a net negative charge –q is placed on

a frictionless horizontal table and is connected to a wall through an unstretched spring of spring constant k. If the horizontal electric field E parallel to the spring is switched on, then the maximum compression of the spring is

(A) qE

k (B)

2qE

k (C)

qE

k (D) zero

40. A train moves towards a stationary observer with a speed of 34 m/s. The train sounds a whistle and its

frequency registered by the observer is f1. If the train’s speed is reduced to 17 m/s, the frequency

registered is f2. If the speed of sound is 340 m/s, then the ratio 1

2

f

f is

(A) 18

19 (B)

1

2 (C) 2 (D)

19

18

41. Find the amount of work done to increases the temperature of 1 mol of an ideal gas by 30°C if it is

expanding under the condition 2 / 3V T . (A) 166.2 J (B) 136. 2 J (C) 126.2 J (D) none of these 42. When at rest, a liquid stands at the same level in the tubes as

shown in the figure. But as indicated, a height difference h occurs when the system is given an acceleration a towards the right. Then h is equal to

(A) aL

2g (B)

gL

2a

(C) gL

a (D)

aL

g

43. Two discs, each having moment of inertia 5 kg m2 about its central axis, rotating with speeds 10 rad s–1

and 20 rad s–1, are brought in contact face to face with their axes of rotation coincided. The loss of kinetic energy in the process is

(A) 2 J (B) 5 J (C) 125 J (D) 0 J

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44. Figure shows an arraignment of masses hanging from a ceiling.

In equilibrium, each rod is horizontal, has negligible mass and extends three times as far to the right of the wire supporting it as to the left. If mass m4 is 48 kg, then mass m1 is equal to (A) 1 kg (B) 2 kg (C) 3 kg (D) 4 kg

45. When the string of a conical pendulum makes an angle of 45°

with the vertical, its time period is T1. When the string makes an

angle of 60° with the vertical, its time period is T2. Then 2

122

T

T is

(A) 2

(B) 2 (C) 0.5 (D) none of these

Numerical Type Questions (46–50): 46. In figure, find the horizontal velocity u (in ms–1) of a projectile so

that it hits the inclined plane perpendicularly. Given H = 6.25 m.

47. Two soap bubbles A and B are kept in a closed chamber where the air is

maintained at pressure 8 N/m2. The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap water used to make bubbles is

0.04 N/m. Find the ratio nB

nA, where nA and nB are the number of moles of air

in bubbles A and B, respectively. (Neglect the effect of gravity)

48. A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches its

maximum height, its acceleration due to the planet’s gravity is 1/4th of its value at the surface of the planet.

If the escape velocity from the planet is escv v N, then the value of N is __________.

(Ignore energy loss due to atmosphere) 49. Consider the zener diode circuit shown in figure

where two ideal zener diodes with break down voltage

1 2z zV 10 V and V 15 V are connected

in series. The series current sI flowing through the

resistance SR 3k in mA ?

Source voltage BV 40 V .

50. An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation

between the objective and eye–piece is 36 cm and the final image is formed at infinity. Determine the focal length eye–piece in cm.

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Multiple Choice Type Questions (51–70): 51. The IP1, IP2, IP3, IP4 and IP5 of an element are 7.1, 14.3, 34.5, 46.8, 162.2 eV respectively. The element is

likely to be: (A) Na (B) Si (C) F (D) Ca

52. The orbit and orbital angular momentum of an electron are 3h

2 and

h6

2respectively. The number of

radial and angular nodes for the orbitals in which the electron present are (A) 3, 2 (B) 1, 2 (C) 2, 2 (D) 0, 2 53. Choose the correct statement. (A) In a period noble gases have the lowest ionisation energy.

(B) According to Bohr’s theory, the angular momentum of an electron in 2nd orbit is h

(C) The two electrons of a given orbital can be distinguished by magnetic quantum number

(D) The orbital angular momentum of an electron in 2s orbital is

2

h

2

1

54. The compressibility factor for 1 mole of a van der Waal’s gas at o0 C and 100 atmospheric pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the constant ' 'a

(A) 2.53 2 2L mol atm (B) 1.253 2L atm (C) 1.253 2 2L mol atm (D) 2.506 2 2L mol atm 55. Which of the following statement is correct: (A) Both O2 and C2 are paramagnetic (B) O2 is paramagnetic where as C2 is diamagnetic

(C) Both B2 and C2 are paramagnetic (D) Both O2 and 22O are diamagnetic

56. Which of the following statements are incorrect about silicones. (A) the repeating structural unit in all types silicones is 2R SiO

(B) Hydrolysis of 3 22CH SiCl followed by condensation polymerisation yields straight chain polymer

(Linear silicone) (C) silicones are organo silicon polymer. (D) silicones are water repelling in nature. 57. Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that

graphite (A) is an allotropic form of diamond (B) has molecules of variable molecular masses like polymers (C) has carbon atoms arranged in large plates of rings of strongly bound carbon atoms with weak interplate

bonds (D) is a non-crystalline substance 58. NH2

A B C (major)CH3COCl Br2 - H2O H3O

+

(A)

NH2

Br

(B)

NH2

Br (C)

NH2

Br

(D) None

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59. X ml of 2H effuse out through a hole in container in 5 seconds, the time taken for the effusion of same

volume of gas specified below under identical conditions is

(A) 10 sec; 2H (B) 20 sec; 2O (C) 25 sec; CO (D) 55 sec; 2CO

60. Which pair of species given below have different bond order

(A) 2 2,O N (B) 2 2,F N (C) 2 2, O N (D) 2 2,F O

61.

The above decarboxylation is fastest if “Z” is

(A) 3OCH (B) 2NO (C) 2NH (D) CN

62. What is the relation between the following pairs of molecules?

Et

MeH

HCl

Me

Me

MeH

HCl

Et

(A) enantiomers (B) Diastereomers (C) identical (D) position isomers 63. The following equilibrium is established when hydrogen chloride is dissolved in acetic acid

3 3 2HCl CH COOH Cl CH COOH

The set that characterises the conjugate acid-base pairs is

(A) 3 3 2, ,HCl CH COOH and CH COOH Cl

(B) 3 2 3, ,HCl CH COOH and CH COOH Cl

(C) 3 2 3, ,CH COOH HCl and Cl CH COOH

(D) 3 2 3, ,HCl Cl and CH COOH CH COOH

64. A compound contains 50% of X(atomic mass 10) and 50% of Y (at.mass 20). Which formula/e certain to

above data? (Given % is by mass)

(A) XY (B) 2X Y (C) 4 3X Y (D) 2 3X Y

65. An organic compound shows the following characteristics reaction/tests: (i) +ve : 2, 4-DNP (ii) -ve : Schiff’s (iii) -ve : Tollens (iv) –ve: Fehillings

(v) +ve : 3NaHSO

(vi) +ve: Iodoform

Which compound is fit for these facts? (A) Acetone (B) Benzaldehyde (C) Acetaldehyde (D) Acetophenone

66. (+) 2-methyl cyclohexanone on treatment with dilute aqueous alkali produces 2-methyl cyclohexanone

is due to formation of: (A) Carbocation (B) Enolate ion (C) Carbene (D) Radical anion.

67. 4-oxopentanoic acid upon reaction with 4NaBH followed by boiling under acidic (catalytic quantity)

condition produces mainly

(A) OCH3

(B) O OCH3

(C)

CH3

CH2

(D)

CH3

OH

O

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68. Readucing sugar among the following is:

(A)

(B)

(C)

(D)

69. Among following ions which one has highest paramagnetism?

(A) 3

2 6Cr H O

(B) 2

2 6Fe H O

(C) 2

2 6Cu H O

(D) 2

2 4Zn H O

70. Which of the following is correct about lyophilic sol? (A) They are irreversible (B) They are formed by inorganic substance (C) They are readily coagulated by addition of electrolytes (D) They are self-stabilised Numerical Type Questions (71–75): 71. In a flask of volume ‘V’ litres, 0.2 moles of oxygen, 0.4 moles of 2N , 0.1 mole of 3NH and 0.3 moles of

He are enclosed at 27°C . If the total pressure exerted by these non-reacting gases is one atmosphere, the partial pressure exerted by 2N is (in atm)

72. In a hydrogen atom, if the energy of an electron in the ground state is -13.6 eV, then that in the 2nd excited

state is (in eV)

73. The enthalpy of vaporization of liquid is 30 kJ 1mol and entropy of vaporization is 1 175JK mol . The boiling point of the liquid at 1 atm is (in K)

74. 0.5 molal aqueous solution of weak acid HX is 20% ionized. If fK for water is 1.86 K kg 1mol , the

lowering in freezing point of solution is (in K) 75. Given

2 02 ; 0.337Cu e Cu E V

2 0; 0.153Cu e Cu E V

0E value for the reaction, Cu e Cu will be (in V)

Space for rough work

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