Sec: SR IIT Date: 20-02-21 Time: 3 Hrs Max. Marks: 300

Sec: SR IIT Date: 20-02-21 Time: 3 Hrs Max. Marks: 300 Name of the Student: ___________________ H.T. NO:

20-02-21_SR IIT_Jee-Main_GTM-11(AN)_Syllabus

PHYSICS: Total Syllabus CHEMISTRY: Total Syllabus MATHEMATICS: Total Syllabus

Narayana IIT Academy 20-02-21_OUTGOING.Sr.IIT_ JEE-MAIN_GTM(AN)_Q’P

SR.IIT_N-SC Page. No. 2

The important thing in life is not the triumph but the struggle.

PHYSICS MAX.MARKS: 100

SECTION – I (SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 1. In a verniercallipers 1 main scale division is 1 mm and there are 10 divisions on vernier

scale which match with 9 divisions on main scale. When there is no object between the

jaws (when they are in contact) the zero mark of the vernier scale is to the left of zero th

mark of main scale and 8th division of vernier scale coincided with one of the main scale

divisions. When a plate is kept between the jaws 0th mark of vernier scale crossed 12

mm mark on the main scale and vernier coincidence is 3. The correct thickness of the

plate is

A) 12.1 mm B) 12.5 mm C) 13.1 mm D) 11.5 mm

2. A uniform flexible chain of mass m is held vertical by holding one of it’s ends with

other end just touching the ground. If the chain is released it fall on the ground as a heap,

then find the force exerted by the chain on the ground at the instant when 2 3 rd of the

chain has been fallen on the ground (neglect height of the heap being formed).

A) 3

mg B) 23mg C) mg D) 2mg

3. Position vector of a particle moving in x-y plane at time t is ^ ^

1 cos sinr a t i a t j . The path of the particle is

A) A circle of radius a with its centre at ,0a

B) A circle of radius a with its centre at 0,0

C) An ellipse with its foci at ,0a and ,0a

D) A straight line

4. A tunnel is dug inside the Earth of radius R along the diameter as shown. A particle is

projected from a point 1P at a distance 2R from the centre of the earth with speed




v gR towards the centre as shown. Find the time taken by the particle to go to the

other end 2P of the tunnel. (g is acceleration due to gravity on the surface of Earth)

A) 1 11sin sin 12

Rg

B) 1 11 2sin sin

5 5Rg

C) 1 12 1sin sin5 2 5

Rg

D) 1 11 3sin sin

5 2 5Rg

5. An ideal fluid flows along a bent tube uniform cross-section located in horizontal plane

as shown in figure. The flow is steady 1 and 2 are two points in the tube. If 1 2,P P are

pressure and 1 2,V V are velocity of the fluid at points 1 and 2 respectively

A) 1 2P P B) 1 2P P C) 1 2V V

D) Total energy per unit volume at point 1 is less then at point 2

6. A metal sheet (whose is positive) has two circular holes as shown in figure. a is

distance between centres of the holes and b is distance between nearest edges of the

holes and c is distance between farthest edges of the holes as shown in figure. On

heating




A) a remains constant b and c increase

B) a remains constant b decreases and c increase

C) All distances , ,a b c increase

D) a remains constant, b increases, c decreases

7. If is the ratio of specific heats p

v

CC

of a perfect gas, the number of degrees of freedom

of a molecule of the gas is

A) )1( B) 1213

C)

12

D) )1(29

8. In a prism of angle A, critical angle and refractive index , the maximum deviation

does notoccur for which of the following situation.

A) The angle of incidence is

B) The angle of incidence is

C) The angle of emergence is

D) The angle of emergence is equal to the angle of incidence

9. A sinusoidal wave is propagating along a stretched string that lies along the x axis.

The displacement of the string as a function of times is graphed in figure for particles at

0x and 0.09x m. These two points are within one wave length of each other. The

speed of the wave, if the wave is moving in positive xdirection is [ Take

1 3sin 0.5894

radian]




A) 13 ms B) 13.8 ms C) 19.1 ms D) 12.2 ms

10. A point charge q is placed at a distance r from the center of a thin metallic spherical shell

of radius R as shown in fig. Electric potential at point A is

A)0

14

qR

B) 0

14

qr

C) 2 2

0

14

qR r

D) 0

1 14

qr R

11. The given R C circuit has two switches 1S and 2S . Switch 2S is closed and 1S is open till the capacitor is fully charged to 0q . Then 2S is open and 1S is closed simultaneously till the charge on capacitor decreases to 0 2q for which it takes time 1t . Now 1S is again opened and 2S is closed till charge on capacitor becomes 03 4q and it takes time 2t . The ratio 1 2t t is

A)1 2 B) 2 C) 1 3 D) 1 4

12. Consider parallel conducting rails separated by a distance l . There exists uniform magnetic field B perpendicular to the plane of the rails shown fig. Two conducting wires each of length l are placed so as to slide on parallel conducting rails. One of the wires is given a velocity 0v parallel to the rails. Till steady state is achieved, loss in kinetic energy of the system is




A) zero B) 20

34

mv C) 20

14

mv D) 20

38

mv

13. If the B H curve of two samples P and Q of iron are as shown below, then which one

of the following statements is correct.

A) Both P and Q are suitable for making permanent magnets

B) P is suitable for making permanent magnets and Q for making electromagnets

C) P is suitable for making electromagnets and Q is suitable for permanent magnets

D) Both P and Q are suitable for making electromagnets

14. A plane electromagnetic wave of angular frequency propagates in a poorly conducting

medium of conductivity and relative permittivity . The ratio of maximum values of

conduction current density and displacement current density in the medium is

A) 0

B) 0

C) 0

D) 0

15. Refer to the common emitter amplifier circuit shown below, using a transistor with

80 and 0.7BEV volt. The value of resistance BR is




A) 330 B) 330 k C) 220 D) 220 k

16. Two point charges +2q and –q are placed on x-axis at (0, 0, 0) and (3, 0, 0) respectively.

How many points of zero electric potential are there in the plane X = 5?

A) 0 B) 1 C) 2 D) many

17. Velocity time graph is shown for the motion of two cars A and B which are moving in

same direction on a straight road. Their initial position is same. Which of the following

statements is notcorrect?

A) Relative speed between the cars first increases for some time, and then decreases for

some time and then increases continuously.

B) At 0t t , car B is behind car A

C) Car B overtakes car A at 0t t

D) At 0t t , acceleration of B is greater than that of A

18. An ideal gas is enclosed in an insulating vessel with a light insulated piston as shown. By some mechanism, the piston is now removed and the gas is allowed to occupy the




full volume of the vessel. The initial pressure, volume and the final pressure and volume are 1 1 2,V ,P P and 2V respectively. Pressure and volume of the gas during the expansion are P and V respectively. Choose the correct statement

A) 1 1 2 2PV PV B) PV = constant

C) 1 1 2 2PV PV D) PV = constant

19. A thin uniform square plate of side 60 cm suspended by pivoting at a point on it’s

periphery and made to oscillate in the vertical plane coinciding the plane of square plate.

Which of the following cannot be the time period of small angular oscillations of the

plate? 2 2/take g m s

A) 223

lg

B) 2 lg

C) 423

lg

D) 2 22 lg

20. E-emissive power of a body, W-work done by a force, - coefficient of viscosity and V-

gravitational potential. Which of the following derived physical quantities doesnot give

the dimensional formula 1 2 3M L T ?

A) 7 8 5E V B)7 5 52 2 4W V

C) 3 2 2E W D)5 8 53 3 3E W V




SECTION-II

(Numerical Value Answer Type) This section contains 5 questions. The answer to each question is a Numerical value. If the numerical value has more than two decimal places, Truncate/Round-off the value of Two decimal places. Answer to each question will be evaluated according to the following marking scheme: Marking scheme: +4 for correct answer, 0 in all other cases. 21. In a photoelectric experiment a metal surface was irradiated with light of different

wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength of incident light and the corresponding stopping potential are given below:

Given that , what is the work function of the metal calculated from the above data (in electron volt)

22. A body is projected from the Earth’s surface with a velocity equal to half the escape velocity from that point at an angle 045 with horizontal. The maximum height attained by the body above the Earth’s surface is (nearly)nR. Find the value of n. (Where R is radius of the earth)

23. A beam of length 10m, width 20cm and depth 1m rests on two rigid pillars horizontally. When a load of 54 10 N acts on the middle of the beam, find the vertical deflection (in mm) of the middle point of the beam due to bending of the beam. (Young’s modulus of the beam is 11 22 10 Nm )

24. A point source of light is placed at a depth 0.5h m below the surface of a

liquid 54

. Then, find the fraction of light energy that escape directly from the liquid

surface.

25. The count rate from 100 3cm volume of a radioactive liquid is c . Some of this liquid is now discarded. The count rate of the remaining liquid is found to be 10c after three half-lives. Find the volume of the discorded liquid (in 3cm ).

26. The total electrostatic energy stored in both the capacitors (in J ) is




3V3 F 6 F

27. A body released from a great height falls freely towards the earth. Another body is released from the

same height exactly one second later. The separation (in m) between the two bodies two seconds after the release of the second body is ( 29.8g ms )

28. A 3m long straight metal rod is moving with a constant velocity ^ ^ ^

2 3 /v i j k m s

in a

uniform magnetic field ^ ^ ^

3 2B i j k T

. The length of rod is oriented along the vector

^ ^ ^2 2i j k . The potential difference (in volts) between the ends of rod is

29. A, B, C and D are four heat reservoirs at temperatures 800 K, 400K, 200K and 100K are

respectively. Now 4 joules of heat is transferred from A to B, 2 joules of heat is

transferred from B to C and 1 joule of heat is transferred from C to D. What will be the

change in entropy of the system of A, B, C and D? (in SI units) __

30. A lift ascends with constant acceleration -2a=1ms , then with constant velocity and finally,

it stops under constant retardation21a ms . If total distance ascended by the lift is 7m,

in a total time of the journey is 8s. Find the time (in second) for which lift moves with

constant velocity.

CHEMISTRY MAX.MARKS: 100 SECTION – I

(SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.

31. A gaseous mixture contains 4 2 6CH and C H in equimolecualar proportion. The weight of 2.24 liters of this mixture at NTP is

A) 4.6 g B) 2.3 g C) 1.6 g D) 23 g

32. A hydrogen like species in fourth orbit has radius 1.5 times that of Bohr’s orbit. In neutral state, its valence electron is in

A) 3d B) 3s C) 2p D) 1s




33.

Cl

dipole moment value is x debey. What is dipole moment value of

Cl

Cl is ___ debey

A) x B) 2x C) 2x D) 2x

34. 3NH is liquefied more easily than 2N . Hence,

A) 3 2a and bof NH that of N B) 3 2 3 2a NH a N but b NH b N

C) 3 2 3 2a NH a N but b NH b N D) None

35. The quantity of electricity required to liberate 3112cm of hydrogen at STP from acidified water is

A) 0.1 faraday B) 96500 C C) 965 C D) 10 faraday 36. Addition of lyophilic sols to lyophobic colloid ,forms A) Protective film around the dispersed phase B) A protective film around the dispersion medium C) An aerosol D) True solution 37.

2NH

2Ph N Cl

AColoured compound (Major product)

The coloured major product formed in above reaction is :




A)

2NH

N N

B)

2NH

N N

C)

2NH

N N

D)

NH N N

38. A cell is containing two H electrodes .The negative electrode is in contact with a

solution of 610 M H ions .The e.m.f of cell is 0.118V at 025 C .what is the H at

positive electrode ?

A) 410 M B) 610 M C) 210 M D) 810 M

39. The addition of a catalyst during a chemical reaction alters which of the following

quantites ?

A) Enthalpy B) Activation energy C) Entropy 4) Internal energy

40. Which of the following have identical bond order?

I) CN II) 2O III) NO IV) CN

A) I, III B) II, IV C) I, II, III D) I, IV

41. The energy of an electron in the first Bohr orbit for hydrogen is 13.6eV . Which one of the following is a possible excited state for electron in Bohr orbit of hydrogen atom?

A) 3.4eV B) 6.8eV C) 1.7eV D) 13.6eV




42. The magnetic moment of nCr is 3.87 BM . The ratio of number of paired e and

unpaired e in nCr is equal to

A) 4 B) 5 C) 6 D) 7

43. At high pressure, the van der Waals equation gets reduced to

A) 2aP V RT

V

B) P V b RT

C) PV RT D) 2aP V b RT

V

44. Which among the following pairs are not isostructural with each other

A) 4 4SiF and SF B) 3 310 and XeO

C) 4 4BH and NH D) 6 6PF and SF

45. When aqueous solution of sodium ethanoate is electrolysed, the product which is not obtained at anode is

A) Ethane B) methyl ethanoate C) Hydrogen D) carbon dioxide

46. Which of the following is the most reactive towards aqueous KOH?

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

47. The time for half life period of a certain reaction A products is 1 hour. When the initial

concentration of the reactant ‘A’, is 2.0 mol L–1, how much time does it take for its

concentration to come from 0.50 to 0.25mol L–1 if it is a zero order reaction?

(A) 4 h (B) 0.5 h (C) 0.25 h (D) 1 h




48. Increased concentration of CO2 in the atmosphere is responsible for

(A) green house effect (B) Acid rain

(C) Lack of photosynthesis (D) Death of aquatic organisms

49. In which of the following arrangements, the sequence is not strictly according to the

property written against it ?

(A) CO2 < SiO2 < SnO2 < PbO2 : increasing oxidising power

(B) HF< HCl < HBr < HI : increasing acid strength

(C) NH3 < PH3 < AsH3 < SbH3 : increasing basic strength

(D) B < C < O < N : increasing first ionization enthalpy.

50. Among the following, the compound that produces least stable ketone on hydrolysis

with dil. 2 4H SO is

(A)

O

O (B)

OH

OH (C) 3 2 2( )CH C OH (D)

O

O

SECTION-II

(Numerical Value Answer Type) This section contains 10 questions. The answer to each question is a Numerical value. If the numerical value has more than two decimal places, Truncate/Round-off the value of Two decimal places. Have to Answer any 5 only out of 10 questions and question will be evaluated according to the following marking scheme: Marking scheme: +4 for correct answer, 0 in all other cases.

51. Count the mixtures showing negative deviations 6 6 7 8 3 6 6, ,C H C H CHCl C H 4 7 8 ,CCl C H

2 3 3 3 6 5 2 3 5 5 2 2 5 3 3 3, ,H O HNO CH COCH C H NH CH COOH C H N H O C H OH CHCl CH COCH are showing negative deviation

52. Number of amines formed by 4 11C H N which reacts with alcoholic potash and chloroform [Carbylamine test]

53. Count the amino acids are reacts with ceric ammonium nitrate to give yellow or red colour Lysine, Tyrosine, Threonine, Arginine, Proline, Serine, Cysteine, Isoleuline, Valine




54. Equanil is used in controlling depression and hypertension; how many non bonding electrons present in equanil

55. The total number of alkenes possible by dehydrobromination of 3-bromo -3-cyclopentylhexane using alcoholic KOH is

56. The number of resonance structures for N is

OH

NaOH N

57. The number of water molecule (s) directly bonded to the metal center in 4 2.5CuSO H O

58. The number of total lone pairs present in 4XeF molecule

59. A weak filed complex of 2Ni has magnetic moment value of 2.82B.M the number of electrons in the 2gt level of 2Ni is

60.

2 1 /H mole PtA

Double bond equivalent (degree of unsaturation) of (A) is

MATHEMATICS SECTION – I

(SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 61. The value of such that the sum of the absolute values of the roots of quadratic

equation 2x 1 x 2 x has the least value

A) 0 B) 1 C) 12

D) 32




62. Value of 2 8tan tan ....... tan9 9 9 is

A) 81 B) 9 C) 512 D) 64

63. Let f : R R be a function defined by f x max x 1 , x 1 min x 1 , x 1 . If K is

the set of all points at which f is not differentiable, then number of elements in the

power set of K is

A) 2 B) 3 C) 4 D) 8

64. The number of values of ,2 2

for which the system of linear equations

sin x cos tan z 0

cos x tan sin z 0

tan x sin cos z 0 has a non-trivial solution is

A) 0 B) 1 C) 2 D) 3

65. Let 1 a 1 b

and 23 1 a 6 b

be two non zero vectors where a

and b

are non -collinear . The value of for which

and

are collinear is

A) 1 B) - 5 C) 4 D) 3

66.

23

4 23 3

dx 3f x & f 4 ,2x 1 x 3

then f 5

A) 145

3 B)

342

3 C)

233

4 D) 4

3

3

2

67. Consider the following statements

p : 3 is the smallest prime number

q : units digit of 1! 2! 3! 4! ........ 10! is 3




r : 7 is the greatest prime factor of 91.

Then the truth value of which one of the following statements is true ?

A) r q p B) p ~ q r C) p ~ q r D) p q ~ r

68. The length of the chord of the parabola 2y 8x having equation 3y 4x 8 0 is

A) 8 2 B) 10 C) 12.5 D) 25

69. Variance of the 50 number in A.P whose first term is 992 and common difference is

" 2" is ( rounded upto two decimal digits )

A) 208. 25 B) 14.43 C) 833.00 D) 28.86

70. Let f x be a differentiable function defined from 0, R such that

2f xf ' x 4x 0

x & f 1 2, then 2x

1 1lt fx x

A) 0 B) 1 C) 2 D) 12

71. Locus of a point ,P x y satisfying the equation 2 2 2 224 144 13 10 25x y y x y x

is

A) a line segment B) hyperbola

C) part of a circle with finite radius D) ellipse

72. If the vectors a and b are linearly independent and satisfying

3 tan 1 3 sec 02a b then the most general values of are

A) ,6

n n Z B) 112 ,

6 n n Z

C) ,6

n n Z

D) 112 ,

6 n n Z

73. If two events A and B are such that P(A) = 0.3, P(B) = 0.4 and

P(A B) = 0.5, then

'BABP =




A) 53 B)

52 C)

41 D)

51

74. Solution of 2 3dysec y + xtany = xdx

is

A) 22 -xtany = x + ce B) 22 -xtany = x - 2 + ce dx

C) 22 -x 2tany = x - 2 + ce D) 22 -xtany = x + 2 + ce

75. The Coefficient of 10x in 21 21 21 210 1 2 10........ x C x C x C x C is

A) 20 12 B) 202 C) 21 1

22 D)

21 12

2

76. In a sequence of (4n+1) terms, the first (2n+1) terms are in A.P., whose common difference is 2, and the last (2n+1) terms are in G.P whose common ratio is 0.5 if the middle terms of the A.P and G.P are equal then the middle term of the sequence is

A) 12

2 1

n

nn

B) 2

1.22 1n

nn

C) .2nn D)

122 1

n

nn

77. Suppose Rolle’s Theorem holds in

[1, 2] for the function 3 2f x x bx cx , at the point 43

x . Then the values of b, c

are respectively are given by

A) 5, 8 B) 5,8 C) 5, 8 D) 8, 5

78. If the straight line 3x + 4y + 1 = 0 is a tangent to the parabola y2 + x = 0, then distance between focus and directrix of the parabola is

A) 38

B) 3223

C) 1613

D) 43

79. Angle between &a b is ;4

| | 2 2a , | | 3b . Length of longer diagonal of the

parallelogram having adjacent sides represented by 5 2a b and 3a b is

A) 593 B) 26 C) 15 D) 25




80. The tangent at any point to the circle 2 2 2x y r meets the coordinate axes at A and B. If the lines drawn parallel to the coordinate axes through A & B intersect at P. Then the locus of P is

A) 2 2 2x y r B) 2 2 2x y r C) 2 2 2x y r D) 2 2 2x y r

SECTION-II (Numerical Value Answer Type)

This section contains 10 questions answer any five questions. The answer to each question is a Numerical values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases.

81. If the three distances of the vertices of a triangle ABC from the points of contact of the

incircle with sides are 3, 4 & 4, then inradius of the triangle ABC is 2K, then K

82. A bird is flying along the curve 2 2x y 1

9 1 . A hunter positioned at the point 17 ,0

6

wants to shoot down the bird when it's nearest to him, then this nearest distance is

83. If z 2i 1 and 1z 6 3i then the maximum value of 1iz z 4 is equal to

84. Mean of 5 observations is 7. If four of these observations are 6, 7, 8, 10, then the

variance of all the five observations is

85. The total number of three – letter words that can be formed from the letters of the word

“SAHARANPUR” is

86. A circular ring of radius 3 cm is suspended horizontally from a point 4 cm vertically

above the centre by 4 strings attached at equal intervals to its circumference. If the

angle between two consecutive strings be ‘ ’ then cos is

87. If 30

1 cos sinlim 1x

x a x b xx

, then the value of ab is equal to

88. If the solution of the differential equation 2 2 sinx dy xydx xdx is coskx y x C (where C is an arbitrary constant), then the value of k is equal to




89. If a,b,c, N then the least possible value of

2

2

2

a ab acba b bcca cb c

is

90. The image of the line 1 12 5 3x y z in the plane 2 3x y z meets the xz-plane at the

point (a,b,c), then the value of c is equal to

Documents

Sec: SR IIT Date: 20-02-21 Time: 3 Hrs Max. Marks: 300