05. REV FULL TEST-3 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-3

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 Type Questions (01–20): 1. If the terms of the A.P. a x, x, a x are all integers where a > x > 0 then the least composite odd

integral value of a is (A) 9 (B) 15 (C) 45 (D) 49

2. P is a variable point on the ellipse 2 2

2 2

x y2

a b whose foci are F1 and F2 then maximum area of 1 2PFF is;

Given (a > b)

(A) 2 22a a b (B) 2 22b a b (C) 2 2a 2a 2b (D) 2 2b 2a 2b

3. General solution of equation |sin x| = cos x is

(A) 2n , n I4

(B) n , n I

4

(C) 2n , n I

4

(D) n , n I

4

4. Distance of point P(–2, 3, 4) from the line x 2 2y 3 3z 4

3 4 5

measured parallel to the plane

8x 6y 9z 1 0 is

(A) 301

2 (B)

401

2 (C)

307

2 (D)

207

2

5. The point P ( 1, 1 ) is translated parallel to 2x = y in the first quadrant through a unit distance . The

coordinates of the point P in new position are

(A) 2 1

1 , 15 5

(B)

1 21 , 1

5 5

(C)

1 2,

5 5

(D) 2 1

,5 5

6. If nf x x , n N, then the value of nnf 1 f 1 f 1 f 1

f 1 .... 11! 2! 3! n!

is

(A) 1 (B) 2n (C) n 12 (D) 0 7. In a city, no two persons have identical set of teeth and there is no person without a tooth. Also no person

has more than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth then the maximum population of the city will be

(A) 232 (B) 232 + 1 (C) 232 – 1 (D) 232 – 2 8. If a (–20, 0) then the probability that the graph of the function 2y 16x 8ax 40x 7a 5 , is strictly

above the x–axis, is

(A) 14

20 (B)

14

21 (C)

13

21 (D)

13

20

9. If 1, z1, z2, …., zn – 1 are the nth roots of unity then the value of 1 2 n 1

1 1 1.....

3 z 3 z 3 z

is equal to

(A) n 1

n

n.3 1

23 1

(B) n 1

n

n.31

3 1

(C) n 1

n

n.31

3 1

(D) n 1

n

n.3 1

23 1

10. Let x

42

dtf x

1 t

and g be the inverse of f then the value of g 0 is

(A) 1 (B) 17 (C) 17 (D) 0

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11. The function 2x 1f x x cos ,

2

( where [ . ] denotes the greatest integer function) is discontinuous

(A) for each real x (B) for each integral point (C) no where (D) at each non–integral point

12. The range of the function 1 1f x 1 sec x 1 cos x is

(A) , (B) , 0 4, (C) 21, 1 (D) 20, 1

13. Consider the following equation in x and y : 2 2x 2y 1 4x 3y 4 x 2y 1 4x 3y 4 0. How

many solutions to (x, y) with x, y real, does the equation have (A) zero (B) exactly one (C) exactly two (D) more than two

14. If 2015 x

n0

ef n dx,

1 x

then nlim f n

is equal to

(A) e – 1 (B) e (C) 1 (D) 2e 1 15. Which of the following is NOT equivalent to p ~ q r

(A) ~ q ~ p r (B) ~ r ~ p q

(C) ~ p ~ q ~ r (D) ~ r ~ p q

16. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is

increased by 2, then the median of the new set (A) is increased by 2 (B) is decreased by 2 (C) is two times the original median (D) remains the same as that of the original set

17. In a ABC, if AB = 5 cm, BC = 13 cm and CA =12 cm, then the distance of vertex ‘A’ from the side BC is

(in cm)

(A) 25

13 (B)

60

13 (C)

65

12 (D)

144

13

18. A relation R is defined on the set of circles such that “C1 R C2 circle C1 and circle C2 touch each other

externally”, then relation R is (A) Reflexive and symmetric but not transitive (B) Symmetric only (C) Symmetric and transitive but not reflexive (D) Equivalence 19. If f(x) is a differentiable function satisfying f x 2 for all x R, f(1) = 2, then greatest possible integral

value of f(3) is (A) 2 (B) 3 (C) 5 (D) 7

20. a and b

are two non parallel vectors. The angles of the triangle, two sides of which are represented by

ˆ ˆ ˆ3 a b and b a.b a

.

(A) 30, 60 and 90 (B) 15, 75 and 90 (C) 20, 60, 100 (D) none of above

Numerical Type Questions (21–25): 21. The number of ways of forming seven digit numbers with distinct digits of the form a1 a2 a3 a4 a5 a6 a7

ia 0 i 1, 2,.....,7 be present in decimal system, such that 1 2 3 4 5 6 7a a a a a a a

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22. A function f from integers to integers is defined as n 3 , n is odd

f x n, n is even

2

. If k is an odd integer and

f f f k 27 , then the sum of digits of k is

23. The number of values of k, for which the system of equations : kx + (3k + 2) y = 4k (3k – 1) x + (9k + 1) y = 4 (k + 1) has no solution, are

24. If 1 1 1

adj BA 0 2 3 , B adj A and C 5A, then

C2 1 0

25. For a certain curve y f x satisfying 2

2

d y6x 4,

dx f(x) has a local minimum value 5 when x = 1. Then

global maximum value of f(x) if 0 x 2, is

Multiple Choice Type Questions (26–45): 26. Two blocks of equal masses (M) are connected by a string

and are kept on rough horizontal surface as shown in figure. The coefficient of friction between the blocks and the surface is . If 1 20 F F 2 Mg , then choose the

correct statement.

(A) The direction of friction on block A is towards right. (B) The direction of friction on block B may be towards left or right (C) Tension in the string must be zero (D) Friction force on block B must be zero 27. A small block of mass m is lying at rest at point P of a stationary

wedge having a smooth semi circular track of radius R. The maximum value of horizontal acceleration a0 that can be given to the wedge so that block does not leave the track is

(A) g

2 (B) g (C) g (D) 2g

28. A car is moving towards a huge wall with a speed =c/10 , where c = speed of sound in still air. A wind is also blowing parallel to the velocity of the car in the same direction and with the same speed as car. If the car sounds a horn of frequency f , then what is the frequency of the reflected sound of the horn heard by driver of the car?

(A) 10f

9 (B)

11f

10 (C)

11f

9 (D)

10 f

11

29. The temperature at the bottom of a water pond of depth L is maintained at 4°C . The temperature of air,

just above the layer of ice frozen at the pond’s surface, is 2 C for the past many days. Assume that the thermal conductivity of ice is three times that of water. The thickness of the frozen layer of the ice in equilibrium must be (Neglect the expansion due to freezing of water)

(A) 2L

3 (B)

L

2 (C)

L

3 (D)

3 L

5

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30. The internal energy of an ideal gas is related as U=a + b (PV) (where P is the pressure of gas, V is the volume of gas, ‘a’ and ‘b’ are constants of appropriate dimensions. Then of the gas is

(A) a/b (B) 1 + (b/a) (C) 1+ (1/a) (D) 1 + (1/b) 31. A cavity of radius r is made inside a solid sphere. The volume charge density of

the remaining sphere is . An electron (charge e, mass m) is released inside the

cavity from point P on the surface of cavity as shown in figure. The centre of sphere C1 and centre of cavity C2 are separated by a distance a. The time after which the electron again touches the sphere is

(A) 06 2 r m

e a

(B) 02 r m

e a

(C) 06 r m

e a

(D) 0r m

e a

32. A wire carrying a current i from O to A is placed inside a uniform

magnetic field 0B B k

. The shape of the wire is parabolic and has

equation 2Y 2x x . The force on the wire will be (y-axis is along vertical) (A) F = 2B0i, upwards (B) F = 2B0i, downwards (C) F = 4B0i, upwards (D) F = 4B0i, downwards

33. Two resistors with resistances R1 and R2 are connected in series and

so are two capacitors with capacitances C1 and C2, these two systems are connected to a battery as shown in figure. Potential difference between a and b is zero in steady state if (A) 1 2 1 2R R C C (B) 1 2 1 2R R C C

(C) 1 2 2 1R C R C (D) 1 1 2 2R C R C

34. In the circuit shown switch is connected to 1 for a very long time. At a particular instant t = 0, switch is suddenly shifted to 2, the current in

the circuit after a time gap of L

R is (use 1/e = 0.37)

(A) E

1.74R

(B) E

0.63R

(C) E

1.11R

(D) E

R

35. When a thin transparent sheet of refractive index 3

2 is placed near one of the slits in Young’s double

slit experiment; the intensity at the centre of the screen reduces to half of the maximum intensity. The minimum thickness of the sheet should be

(A) 4

(B)

8

(C)

2

(D)

3

36. The x–z plane separates two media A and B of refractice indices 1 21.5 and 2 . A ray of light travels

from A to B. Its directions in the two media are given by unit vectors 1 2u ai bj and u ci dj . Then

(A) a 4

c 3 (B)

a 3

c 4 (C)

b 4

d 3 (D)

b 3

d 4

37. A radioactive isotope is being produced at a constant rate X. Half-life of the radioactive substance is Y.

After some time the number of radioactive nuclei become constant. The value of this constant is

(A) XY

n 2l (B) XY (C) XY log 2 (D)

X

Y

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38. In a junction transistor operating under common emitter connections in active region, the base current is changed by 20 A . Due to this, base-emitter voltage is changed by 0.02 volt and collector current

changed by 2mA. Find the voltage gain of amplifier if load resistance RL is 5000 . (A) 100 (B) 300 (C) 400 (D) 500

39. Sand is deposited at a uniform rate of 20 kg/s and with negligible

kinetic energy on an empty conveyor belt moving horizontally at a constant speed of 10 meters per minute. Find the force required to maintain constant velocity of the conveyor belt. (A) 10/3 N (B) 10/4 N (C) 1/4 N (D) 5/4 N

40. The radiation of intensity I is falling obliquely on a surface. Area of

surface exposed to radiation is A. Select correct alternative

(A) If surface is perfectly reflecting surface then force experienced due to radiation is 2IA cos

c

(B) If surface is perfectly absorbing surface then force experienced due to radiation is 2IA cos

c

(C) If surface is perfectly absorbing surface then force experienced due to radiation is IA cos

c

(D) If surface is partially reflecting surface then force experienced due to radiation is 2IA cos

c

Where is a constant and depends upon nature of surface.

41. A plane electromagnetic wave travelling along the X-direction has a wavelength of 3 mm. The variation in

the electric field occurs in the Y-direction with an amplitude 66 Vm–1. The equations for the electric and magnetic fields as a function of x and t are respectively

(A) 11 7 11y z

x xE 66 cos 10 t , B 1.1 10 cos 10 t

c c

(B) 11 7 11y z

x xE 11 cos2 10 t , B 11 10 cos2 10 t

c c

(C) 11 7 11x z

x xE 33 cos 10 t , B 11 10 cos 10 t

c c

(D) 11 7 11y z

x xE 66 cos2 10 t , B 2.2 10 cos2 10 t

c c

42. A shell is fired at a speed of 200 m/s at an angle of 37° above

horizontal from top of a tower 80m high. At the same instant another shell was fired from a jeep travelling away from the tower at a speed of 10 m/s as shown. The velocity of this shell relative to jeep is 250 m/s at an angle of 53° with horizontal. Find the time (in sec) taken by the two shells to come closest.

(A) 1 (B) 2 (C) 3 (D) 4 43. A glass rod has ends as shown in figure. The refractive

index of glass is . The object O is at a distance 2R

from the surface of larger radius of curvature. The distance between apexes of ends is 3R. The range of

for which the image is real is given by (A) 2 – 2.5 (B) 2 – 2.25 (C) for any value of 1 (D) for any value of 2.25

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44. In a uniform electric field, a cube of side 1 cm is placed. The total energy stored in the cube is 8.85 J .

The electric field is parallel to four of the faces of the cube. The electric flux through any one of the remaining two faces is.

(A) 1

V /m5 2

(B) 100 2 V /m (C) 5 2 V /m (D) 10 2 V /m

45. Suppose that two heat engines are connected in series, such that the heat

exhaust of the first engine is used as the heat input of the second engine as shown in figure. The efficiencies of the engines are 1 2and , respectively.

The net efficiency of the combination is given by

(A) net 2 1 21 (B)

2net

1 21

(C) net 1 1 21 (D)

1net

2 2

1

1

Numerical Type Questions (46–50): 46. A uniform body of mass M and radius R has a small mass m attached at edge as

shown in the figure. The system is placed on a perfectly rough horizontal surface such that mass m is at the same horizontal level as the centre of body. It is assumed that there is no slipping at point A, If IA is the moment of the inertia of combined system about point of contact A then the normal reaction at point A just after the system is released from rest is (In N) (M = 6kg, m = 2kg, IA = 4 kg m2, R = 1 m, g = 10 m/s2)

47. A ball of mass 10kg and density 1 g/cm3 is attached to the base of a container

having a liquid of density 1.1 g/ cm3, with the help of a spring as shown in the figure. The container is going up with an acceleration 2 m/s2 .If the spring constant of the spring is 200 N/m, elongation in the spring is (in cm) (ball is in equilibrium as seen by container)

48. If the molar heat capacity of a gas in the process PT = constant is 5R, the number of degrees of freedom of

molecules in the gas is 49. A mixture of plane polarised and unpolarised light falls normally on a polarizing sheet. On rotating the

polarizing sheet about the direction of the incident beam, the transmitted intensity varies by a factor of 4. Find the ratio of the intensities IP and I0, respectively of the polarized and unpolarized components in the incident beam.

50. The plot given below is of the average power delivered to an

LRC circuit versus frequency. The quality factor of the circuit is : (approximately)

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Multiple Choice Type Questions (51–70): 51. Which of the following is non–narcotic analgesic ? (A) Heroin (B) Morphine (C) Aspirin (D) Equanil 52. Primary aliphatic or aromatic amines can be distinguished from secondary and tertiary amines by reacting

with : (A) chloroform and alcoholic KOH (B) methyl iodide (C) chlofoform alone (D) zinc dust 53. The standard oxidation potentials for the half-cell reactions are

Zn → Zn2+ + 2e , E0 = 0.76 V

Fe → Fe2+ + 2e , E0 = 0.41 V The emf of the cell reaction, Fe2+ + Zn → Zn2+ + Fe is (A) -0.35 V (B) +0.35 V (C) +1.17 V (D) -1.17 V 54. Consider the following reactions,

2Ca OH Heat

3CH COOH A B

Compound B is : (A) an ether (B) an alcohol (C) an aldehyde (D) a ketone 55. The momentum of a particle having de Broglie wavelength of 0.1 nm is (A) 6.626 x 10–21 kg ms–1 (B) 6.626 x 10–22 kg ms–1 (C) 6.626 x 10–23 kg ms–1 (D) 6.626 x 10–24 kg ms–1 56. The value of observed and theoretical molecular masses of certain electrolyte XY are 65.4 and 114.45

respectively. The electrolyte XY in the solution has dissociation to the extent of (A) 75% (B) 80% (C) 50 % (D) 90%

57. For the process NH3(g) + HCl(g) NH4Cl(s) (A) Both H and S are +ve (B) H is – ve and S is +ve (C) H is +ve and A is – ve (D) Both H and S is – ve 58. Aspirin is an acetylation product of (A) p–Dihydroxybenzene (B) o–Hydroxybenzoic acid (C) o–Dihydroxybenzene (D) m–Hydroxybenzoic acid 59. An azeotropic solution of two liquids has as boiling point lower than either of the boiling points of the two

liquids, when it : (A) shows negative deviation of from Raoult’s law (B) shows positive deviation from Raoult’s law (C) shows no deviation from Raoult’s law (D) become saturated. 60. Consider the following nucleophiles :

(I) H2O (II) CH3COO– (III) OH– (IV) 3CH O

The correct order of decreasing nucleophilicity is (A) I > II > III > IV (B) IV > II > III > I (C) IV > III > I > II (D) III > IV > II > I 61. Which of the following species has the shortest bond length ?

(A) N2 (B) 2N (C) 2N (D) 22N

62.

i hydroborationZn dust3 2 ii oxidation

CH CHBr CH Br A B.

The compound B is :

(A) CH4CH(OH)CH3 (B) CH3CH(OH)CH2(OH) (C) CH3–CH2–CH2OH (D) CH3–CH2–CH(OH)2

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63. Given 17 2

sp AgIK 8.5 10 M . The solubility of AgI in 0.1 M KI solution is :

(A) 8.5 x 10–15 M (B) 8.5 x 10–16 M (C) 8.5 x 10–17 M (D) 8.5 x 10–18 M

64. Standard electrode potentials of three metals A, B & C are respectively +0.5V, –3.0V and –1.2 V. The reducing powers of these metals are :

(A) A > C > B (B) B > C > A (C) A > B > C (D) C > B > A 65. In the brown–ring test of nitrate ion, the compound formed is :

(A) 2

2 5Fe H O NO

(B)

3

2 5Fe H O NO

(C) 2

2 25Fe H O NO

(D)

2

2 3 3Fe H O NO

66. 2 20

NaNO HCl Brwarm water6 5 2 aq0 5 C

C H NH A B C.

The product C in this reaction sequence is :

(A) o–bromo phenol (B) p–bromo phenol (C) m–bromo phenol (D) 2, 4, 6–tribromophenol. 67. Kolbe’s electrolysis of potassium succinate gives : (A) Ethane (B) ethene (C) ethyne (D) methane 68. In which of the following complexes, metal utilises 2 3d sp hybrid orbital?

(A) 36CoF (B) 3

2 6Ti H O

(C) 3 2 3

CoF H O (D) 2

2 6Ni H O

69. A mixture of acetone and carbon tetrachloride can be separated by (A) fractional crystallization (B) fractional distillation (C) steam distillation (D) vacuum distillation 70. Aniline can be separated from phenol using (A) NaHCO3 (B) dilute HCl (C) NaCl (D) conc. HNO3

Numerical Type Questions (71–75): 71. How many litres of chlorine gas will be obtained by electrolysis of molten NaCl at 1.8 atm and 270C? The

electrolysis examined for 9.65 sec.using 1000 amp current. (in L) 72. The electron affinity of chlorine is 349 kJ mol–1. How much energy in joules must be released when 1mg of

chlorine is converted to Cl– (g) ions ? (in J) 73. In rock salt structure what percentage of the octahedral voids are occupied by cations ? 74. A solvent of molar mass 84.2 g mol–1 and boiling point 81.4C has boiling point elevation constant equal to

2.79 K Kg mol–1. Its molar enthalpy of vaporization will be about (in kJ mol–1) 75. For a first order reaction, the half life period is 4 minutes. Then the time take for 99.9% completion of the

reaction is : (in min)

Space for rough work

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