batch: otg sr iit mpc sgtm 03 mains date: 26.06.2021 time

Batch: OTG SR IIT MPC SGTM_03 MAINS Date: 26.06.2021

Time: 03:00 Hrs JEE MAIN Max. Marks: 300

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.

01. In a large room, a person receives direct sound waves from a source 120 metres away from him. He also receives waves from the same source which reach him, being reflected from the 25 metre high ceiling at a point halfway between them. The two waves interfere constructively for wavelength of

1) 20, 2/3, 20/5 etc 2) 10, 5, 2.5 etc 3) 10, 20, 30 etc 4) 15, 25, 35 etc

02. A train has just completing a U-curve in a track which is a semicircle. The engine is at the forward end of the semi circular part of the track while the last carriage is at the rear end of the semicular track. The driver blows a whistle of frequency 200 Hz. Velocity of sound is 340 m/sec. Then the apparent frequency as observed by a passenger in the middle of a train when the speed of the train is 30 m/sec is

1) 209 Hz 2) 288 Hz 3) 200 Hz 4) 181 Hz

03. In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. when this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction

1) 0.012m 2) 0.025m 3) 0.05m 4) 0.024m

04. The difference between the apparent frequency of a source of sound as perceived by an observer during its approach and recession is 2% of the natural frequency of the source. If the velocity of

NARAYANA IIT ACADEMY

sound in air is 300 m/sec, the velocity of the source is (It is given that velocity of source<<velocity of sound)

1) 6 m/sec 2) 3 m/sec 3) 1.5 m/sec 4) 12 m/sec

05. Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously. On changing the tension in one of them, the beat frequency remains unchanged. Denoting by 1 2, ,T T the higher and the lower initial tensions in the strings, then it could be said that while making the above change in tension

1) 2T was decreased 2) 2T was increased 3) 1T was increased 4) 1T was kept constant

06. A wire of 3 19.8 10 kgm passes over a frictionless light pulley fixed on the top of a frictionless

inclined plane which makes an angle of 030 with the horizontal. Masses m and M are tied at the two ends of wire such that m rests on the plane and M hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of 1100ms . Chose the correct option

1) m = 20 kg 2) m = 5kg 3) m = 2kg 4) m = 7kg

07. Two glass slabs of same thickness are joined to form an L as shown. A ray is incident on the combination as shown (in the plane of paper). The final emergent ray will

1) Come out at point A in the same direction as that of the original ray

2) Come out at point A but not in the same direction as that of the original ray

3) Does not come out at point A but is in the same direction as that of the original ray

4) Does not come out at point A and is not in the same direction as that of the original ray

08. A convex lens of focal length 20 cm and another plano cnvex lens of focal length 40 on are placed coaxially as shown in the diagram. The plano convex lens is silvered at plane surface. If final image of object O is formed on itself, then find the value of d.


1) 10 cm 2) 40 cm 3) 20 cm 4) 80 cm

09. Mirror is moving towards the particle with speed 2 cm/sec. speed of A and B are 10 2 and 5 cm/sec respectively in the direction shown in figure. Magnitude of velocity of image of the particle B with respect to image of A.

1) 325 / seccm 2) 15 / seccm 3) 13 / seccm 4) 269 / seccm

10. Radius of curvature of a concave spherical surface separating air-glass medium is R. A point object is placed on the principal axis in the glass 1.5g . For the image to be real seen by observer in air,

distance of the object from P should be

1) 2 3R u R 2) 2u R 3) u R 4) 3u R

11. A light ray incident along vector ˆˆ ˆ2 4 5i j k strikes on the x-z plane from medium of refractive

index 3 and enters into medium II of refractive index is 2 . The value of 2 for which the value of

angle of refraction becomes 090 , is

1) 4 35

2) 3 35

3) 2 35

4) 35

12. For the same objective, the ratio of the least separation between two points to be distinguished by a microscope using electrons accelerated through 100 V and light of 5500 o A used as the illuminating substance is

1) 42 10 2) 32 10 3) 22 10 4) 44 10

13. Two coherent waves represented by 1 21 2

2 2sin ωt+ sin -ωt+λ 6 λ 8x xy A and y A

are

superposed. Find the path difference 1 2x x to produce constructive interference n I .

1) nλ 2) 148

n

3) 48n 4) / 2n


14. Two coherent point sources of frequency ( 10vfd

where v is speed of light) are placed at a distance

d apart as shown in figure. The receiver is free to move along the dotted line shown in the figure. Find total number of maxima observed by receiver.

1) 6 2) 7 3) 5 4) 8

15. A parallel beam of light of wavelength 5000 o A is incident on slit S. another two slits 1 2S and S are

illuminated at a distance 2 meter as shown in the figure. The minimum distance between 1 2S and S such that maximum intensity will occur at O is

1) 10 mm 2) 1 mm 3) 12

mm 4) 5mm

16. Light of wavelength 6328 o A is incident normally on a slit having a width of 0.2 mm. the distance of the screen from the slit is 0.9 m. The angular width of the central maximum is

1) 0.09 degree 2) 0.72 degree 3) 0.18 degree 4) 0.36 degree

17. A plane wavefront AB is incident on a concave mirror as shown. Then, the reflected wavefront will be

1) 2) 3) 4) None


18. A person lives in a high rise building at a height 30m on the bank of a river. Across the river is a well lit tower of height 60m. when person looks through a polarizer at an appropriate angle at light from top of tower reflecting from the river surface, he finds intensity of light is least. If refractive index of

water is 4 ,3

width of river is

1) 120m 2) 80m 3) 60m 4) 40m

19. A cube of green jelly rests on a table. You push the jelly laterally with a force 1003NF at its top

surface and find that instead of sliding across the table it takes the shape of a parallelogram (as shown in the diagram) where the lateral displacement is 0.116m. The modulus of rigidity of the jelly is

1) 22500 /N m 2) 21170 /N m 3) 21250 /N m 4) 22340 /N m

20. An agent applies force of constant magnitude 0F always in the tangential direction as shown in the figure. Find the speed of the bob when string becomes horizontal, assuming that it is at rest at its lowest point.

1) 0 2l F mgm

2) gl 3) 0 4l F mgm

4) 0l Fm


SECTION-II (Numerical Value Answer Type)

This section contains 10 questions. The answer to each question is a Numerical values comprising of positive or negative decimal numbers. 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.

_________________________________________________________________________

21. A uniform vertical cylinder of cross-sectional area ‘a’ floats, 90% submerged, in an unknown liquid

inside a tank with cross-sectional area four times that of cylinder. When cylinder is pushed down

gently and released it performs SHM. The maximum possible amplitude (in cm) for this SHM is.

22. A rope whose mass is not negligible supports a block of mass three times that of rope. A pulse is

generated in string near lower end, the pulse moves up with acceleration 2/in m s .

23. A biconvex thin lens of focal length 30 cm and aperture diameter 10 cm is broken into four identical

pieces. Two of the pieces are placed in a coordinate system as shown in the diagram. Find the

magnitude of the y coordinate of the image if an object is placed at origin.


24. A glass sheet 312 10 mm thick is placed in the path of one of the interfering beams in a Young’s

double slit interference arrangement using monochromatic light of wavelength 0

6000 A . If the central

bright fringe shifts a distance equal to width of 10 bands. What is the thickness of the sheet (in m )

of diamond of refractive index 2.5 that has to be introduced in the path of second beam to bring the

central bright fringe to original position?

25. A rod of mass 2kg is placed at rest on a horizontal smooth surface. An impulse 10 Ns is applied at

one end of the rod perpendicular to the rod as shown. After that, point A of the rod moves

rectilinearly. Find the acceleration in 2/ ,m s of the point B just after the application of impulse. The

moment of inertia of the rod about vertical axis through B is 13 2kg m

26. A particle is projected with an initial velocity of 200m/s in a direction making an angle of 30 with

the vertical. The horizontal distance covered by particle in 3s is (in SI)

27. Current i = 2A flows through the resistance 10R . With what constant speed v (in m/s), must the

piston move in upward direction so that temperature of ideal gas may remain unchanged.

210 /g m s .

28. A piece of ice (heat capacity 1 0 12100 J kg C and latent heat 5 13.36 10 J kg ) of mass m grams

is at 05 C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally

when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there

is no other heat exchange in the process, the value of m in gm is


29. A long flexible inextensible rope of uniform mass density is being pulled on a rough floor with

horizontal force F in such a way that the lower part is at rest and upper part moves with constant

speed v as shown, the magnitude of F will be (in N). 1kg m v 2m s/ , /

30. A constant tangential force of 0.02N is acting on a large wooden plate of area 210m floating on the

surface of river and plate moves with the constant speed 2m/s on the river surface. The river is 1 m

deep and the water in contact with the river bed is stationary. Assuming constant speed gradient,

coefficient of viscosity of water is n10 poise. Find the value of n.

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. The maximum electrical work done by standard Daniell cell is

2 20 0

/ /0.76 , 0.34

Zn Zn Cu CuE V E V

(1) 212kJ (2) 424 Kj (3) 106 KJ (4) 318 KJ

32. On adding 3AgNO solution into KI solution , a negatively charged colloidal sol is obtained when they are in :

(1) 50 ml of 0.1 M 3AgNO + 50 ml of 0.1 M KI

(2) 50 ML of 0.1 M 3AgNO + 50 ml of 0.2 M KI

(3) 50 ML of 0.2 M 3AgNO + 50 ml of 0.1 M KI

(4) 50 ML of 0.2M 3 25 mL 0.4 M KIAgNO

33. Bredig’s arc method cannot be used for the preparation of colloidal sol of :

(1) platinum (2) gold (3) silver (4) sodium


34. Which of the following is correct about lyophilic sol?

(1) They are irreversible

(2) They are formed by inorganic substance

(3) They are readily coagulated by addition of electrolytes

(4) They are self-stabilised

35. Which of the following is required in lowest concentration for coagulating a sol having positively charged colloidal particle?

(1) KCl (2) K2SO4 (3) K3[Fe(CN)6] (4) K4[Fe(CN)6]

36. Which of the following molecule has zero dipolemoment?

(1) PBr3Cl2 (2) PF3Br2 (3) CH2Cl2 (4) Hydroquinone

37. The correct bond order for NO and NO are respectively

(1) 3,7/2 (2) 5/2,3 (3) 3,5/2 (4) 3,2

38. In solid state 5PCl exist as an ionic solid. Hybridisation of phosphorous in cation and anion are respectively

(1) 3 3 2,sp sp d (2) 3 2 3,sp d sp (3) 3 3,sp sp d (4) 3 3,sp d sp

39. The maximum number of 090 angles between bond pair-bond pair electrons is observed in 3 2sp d hybridization are

(1) 4 (2) 8 (3) 12 (4) 10

40. Which of the following has minimum bond length ?

(1) B2 (2) C2 (3) F2 (4) 2O

41. Which of the following arrangements represents the increasing order(smallest to largest) of ionic radii of the given species 2 2 3 3, , , ?O S N p

(1) 2 3 2 3O N S P (2) 2 3 3 2O P N S

(3) 3 2 3 2N O P S (4) 3 2 2 3N S O P 42. For a first order reaction, the plot of log K against 1/T is a straight line. The slope of the line is equal

to

1) aER

2) 2.303

aE R 3)

2.303aE

4) 2.303

EaR

43. The correct order of ionisation potentials of coinage metals

(1) Cu Ag Au (2) Au Ag Cu (3) Cu Au Ag (4) Au Cu Ag 44. One mole of magnesium in the vapour state absorbed 1300kJ of energy . If the first and second

ionization energies of Mg are 750 and 1450 kJ /mol respectively, the final composition of mixture is

(1) 59% Mg2+ and 41% Mg+ (2) 38% Mg2+ and 62% Mg+


(3) 41% Mg2+ and 59% Mg+ (4) 62% Mg2+ and 38% Mg+

45.

2CH COCl

2CH COCl

AlCl3X ; X is

(1)

CH2

CH2

C

O

Cl

C

O

(2)

CH2

CH2

C

O

CO

(3)

CH2

CH2

C

O

C

O

(4)

CH2

CH2

C

O

C

O

46.

CH3

4KMnOA

3 2 4/ .HNO conc H SO

B(Major Product)

, the product B is

(1)3-Nitorbenzoic acid (2)3-Nitrotoluene

(3)4-Nitrotoluene (4)4-Nitrobenzoic acid

47.


A, C, D are

48. Most basic one is :

(1)

NHCH3

(2)

3

O

NH C CH

(3)

2

O

C NH

(4)

NH2

49. Most acidic one is:

(1)

OHCOOH

(2)

OH

2NO

(3) OH

COOH

(4) 2NO

OH

50. NH4Cl crystallizes in a body-centred cubic lattice with edge length of unit cell equal to 387 pm.

If the radius of the Cl ion is 181 pm, diameter of NH4+ ion is (assume all ions are spherical in shape)

(1) 154.1 pm (2) 92.6 pm (3) 308.3 pm (4) 206 pm


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.


51. 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

52. Electrolysis of an acetate solution produces ethane according to the Kolbe reaction : 3 2 6 22 2 2CH COO C H CO e What volume (in L)of ethane is produced at 270C and 760 mm Hg, if a current of 0.500 A were passed through the solution for 10 hours and the electrode reaction is 96.5% efficient?

53. The molar conductivity ( 2 1S cm mol ) for 4NH OH , when the molar conductivity for

22,Ba OH BaCl and 4NH Cl are 523.28, 280.0 and 2129.8 cmS 1mol respectively.

54. A current of 10.0 A flows for 2.00 h through an electrolytic cell containing a molten salt of metal X. This results in the decomposition of 0.250 mol of metal X at the cathode. The oxidation state of X in the molten slt is : 96,500F C

55. Molar conductance of saturated BaSO4 solution is 400 ohm–1 cm2 mol–1 and its specific conductance

is 5 1 14 10 ohm cm . Hence solubility product value of BaSO4 can be concluded as x 10–8 M2. Identify x.

56. The oxidation potential of half cell Pt, H2/H2SO4 is 0.3 V, then what will be pH of cell?(2.303RT\F=0.06)_______

57. On addition of 1 mL of 10% NaCl solution to 10 mL gold sol in the presence of 0.025 g of starch, the coagulation is just prevented. Starch has gold number:________


58. Graph between log / logx m and p is a straight line at angle 045 with intercept OA as shown in

figure. Then /x m at a pressure of 2 atm is

045

log xm

A

log 2

log pO

59. 100 mL of 0.6M acetic acid is shaken with 2g activated carbon. The final concentration of the solution after adsorption is 0.5M. What is the amount of acetic acid(in grams) adsorbed per gram of carbon ?

60. 2SO and He are kept in a container at partial pressure 1P and 2P . A thin perforation is made in the

wall of the container and it is observed that gases effuse at the same rate. The ratio of 1P and 2P will be_____

MATHEMATICS 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.

61. If 1 2 3 nx ,x , x ,...,x are the roots of nx ax b 0 , then the value of

1 2 1 3 1 4 1 nx x x x x x .... x x is equal to

(1) 1nx b (2) n 11nx a (3) n 1

1nx (4) n 11nx

62. Let g be the inverse function of a differentiable function f and G(x) = 1

g x. If f(4) = 2 and

' 1f 416

, then the value of 2'G 2 equals to

(1) 1 (2) 4 (3) 16 (4) 64

63. If the difference between the roots of 2x ax b 0 is same as that of 2x bx a 0,a b, then

(1) a + b + 4 = 0 (2) a + b – 4 = 0 (3) a – b – 4 = 0 (4) a – b + 4 = 0


64. Let rT be the rth term of an AP whose first term is 12

and common difference is 1, then

n

r r 1 r 2 r 3r 1

1 T T T T

(1) n n 1 2n 1 5n6 4

(2) n n 1 2n 1 5n 1

6 4 4

(3) n n 1 2n 1 5n 16 4 2

(4) n n 1 2n 1 5n 1

6 8

65. Let ab = 1,

2 2

2 2

2 2

1 a b 2ab 2b2ab 1 a b 2a2b 2a 1 a b

then the minimum value of is

(1) 3 (2) 9 (3) 27 (4) 81

66. It is given that complex numbers 1z and 2z satisfy 1z 2 and 2z 3 . If the included angle of their

corresponding vectors is 60°, then 1 2

1 2

z zz z

can be expressed as n7

, where ‘n’ is a natural number

then n =

(1) 126 (2) 119 (3) 133 (4) 19

67. Let matrix x y z

A 1 2 31 1 2

where x, y, z N. If det(Adj(Adj .A)) = 8 42 .3 then the number of such

matrices A is (Adj. A denotes adjoint of square matrix A)

(1) 220 (2) 45 (3) 55 (4) 110

68. Number of zero’s at the ends of 30

n 1

n 5

n

is

(1) 111 (2) 147 (3) 137 (4) None

69. If ra is the coefficient of xr in the expansion of n21 x x n N . Then the value of

1 4 7 10a 4a 7a 10a ... is equal to

(1) n 13 (2) 2n (3) n1 .23

(4) n 1n.3

70. The arithmetic mean of a set of observations is X . If each observation is divided by and then is increased by 10, then the mean of the new series is


(1) X

(2) X 10 (3) X 10

(4) X 10

71. If sin A 3sin B 2

and cos A 5cos B 2

, 0 < A, B < 2 then tan A + tan B is equal to

(1) 35

(2) 53

(3) 3 55 (4) 3 5

3

72. The number of solutions of the equation 2 2 2 24sin x tan x cot x cosec x 6 in 0,2

(1) 1 (2) 2 (3) 3 (4) 4

73. If 1 1 1 1sin cos sin tan x 1 , where [.] denotes greater integer function, then complete set of

values of x is

(1) tan sin cos1 , tan cos sin1 (2) tan sin cos1 , tan sin cos sin1

(3) tan cos sin1 , tan sin cos sin1 (4) tan sin cos1 ,1

74. The negative of the compound proposition p p q is

(1) p q p (2) p q p (3) p q p (4) p q q

75. Le 2

x xe ef x

. If f g x x x R then

1002

501

1 ____2

ege

(1) 1002 2) 501 3) 2004 4) 0

76. : , 5, 6f a b be defined as 3 22 9 12 1f x x x x . If the minimum value of a for which

f x is onto is 12

then maximum value of b for which f x is surjective on ,a b to 5,6

(1) 5 (2) 4 (3) 52

(4) 72

77. 38 3f x x x and 1f x be the inverse of f x then

1/ 3

1 1 _____8x

xLtf x f x

(1) 1 (2) 2 (3) 3 (4) 4

78.

0

0

1

tan (89.999............9)

______

2 tan (89.999............9)

n times

n

n times

Lt


(1) 1 (2) 3 (3) 5 (4) 7

79. If f is twice differentiable function and ,f x f x f x g x , 2 2h x f x g x

and if 1 8h then 11 ____h

(1) 11 (2) 8 (3) 6 (4) 1

80.

2 5

1| |

log

3

x xxx

ax

af x a x x

a

if 0, 0x a

= 0 if 0x

Then

(1) f is continuous but not differentiable at 0x

(2) f is differentiable at 0x

(3) f is differentiable at 0x if a e only

(4) None of the above

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.


81. Number of real roots of the equation ( ) 0P P x where 3 3 1P x x x ____________

82. If the normal to ( ) 0 3 3 0y f x at x is x y then the value of

2

2 2 20

1lim( ) 5 4 4 7x

x iskf x f x f x

then = __________

83. A man of 1.6 m height walks at the rate of 30 m per minute away from a lamp which is 4 m

above ground. If K is the rate at which the man’s shadow is lengthening then 4k _______

84. The least value of ‘a’ for which the equation 4 1sin 1 sin

ax x

has at least one solution in 0,

2


85. Let 3( ) 30 2f x x x then find number of positive integral values of ‘x’ which satisfies

f f f x f f x

86. :f R R is a function such that 2 3 ,f x y f x f y xy x y R and 0 1f .

Then 5f _____________

87. Let 1a and 2a be two distinct values of a for which

2 2

ln 1 ln 1. , 1,0

sec cos( )3 1 sin , 0,

x xx x

x xf xa a x x x

is differentiable at x = 0, then the value of 2 21 2a a is

88. If the range of 4 2

4 2

2 14 8 497 4 23

x x xf xx x x

is ,a b then a b is ___________

89. No. of solution for 12

2x 3sin1 x 2

is___________

90. If the function 3 2f x ax bx 11x 6 satisfies the conditions of Rolle's theorem in

[1, 3] and 1f ' 2 03

, then value of a+b=___________

batch: otg sr iit mpc sgtm 03 mains date: 26.06.2021 time

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