14-12-20 SR CO-SUPER CHAINA Jee-Main CTM-15 SYLLABUS€¦ · thin tube of radius 5cm is filled in Piston as shown in figure. Assuming that the Piston is in equilibrium, the height

Sec: Sr.IIT_CO-SUPER CHAINA Date: 14-12-20

Time: 3HRS Max. Marks: 300

Name of the Student: ___________________ H.T. NO:

14-12-20_ SR_CO-SUPER CHAINA_Jee-Main_CTM-15_SYLLABUS

PHYSICS: PT-15 SYLLABUS (40%) + PT-1 T0 PT-14 SYLLABUS (60%)

CHEMISTRY: PT-15 SYLLABUS (40%) + PT-1 T0 PT-14 SYLLABUS (60%)

MATHEMATICS: PT-15 SYLLABUS (40%) + PT-1 T0 PT-14 SYLLABUS (60%)

Narayana IIT Academy 14-12-20_Sr.IIT_CO-SC _JEE-MAIN_CTM-15_Q’P

SR.IIT_CO-SC/ N-C Page. No. 2

Education consists mainly of what we have unlearned.

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. Water from a pipe is coming at rate of 100 liters per minute. If the radius of the pipe is

5cm, the Reynolds number for the flow is of the order of (density of water = 31000 / ,kg m

coefficient of viscosity of water =1mPa-s).

1) 310 2) 410 3) 210 4) 610

2. A carnot heat engine (with high temperature reservoir of temperature 800 )HT K and low

temperature reservoir of temperature LT is 50% efficient. Now a new intermediate source

of temperature 2

H LT T

is used & heat engine is divided into two parts (i.e., one between

HT and 2

H LT T other between

2

H LT T and LT ). Heat rejected by 1st part of heat engine is

send as heat input to 2nd part of heat engine calculate the overall percentage efficiency of

the new heat engine.

1) 50% 2) 66.67% 3) 33.3% 4) 75%

3. Free surface of liquid present in cylindrical tank A(radius = 10cm) is fully covered by a

frictionless thin Piston (B) of mass 20kg and external radius 10cm, internal radius 5cm A

thin tube of radius 5cm is filled in Piston as shown in figure. Assuming that the Piston is

in equilibrium, the height of water column in the tube (C) above the level of the Piston is

nearly

1) 85cm 2) 105cm 3) 54cm 4) 38cm




4. An ideal liquid having total length of liquid column L is contained in V-shaped tube as

shown. The system is in lift which is moving in upward direction with constant

acceleration a. If liquid is displaced, then its time Period is

1)

2cos cos

LT

g a

2)

2sin cos

LT

g a

3)

2sin sin

LT

g a

4)

2sin cos

LT

g a

5. A spherical shell of copper is completely filled with a liquid of bulk modulus B and

coefficient of volume expansion 3 . The temperature of the liquid and the shell is

increased by . If the expansion in shell is only due to temperature increase and not due

to the pressure of liquids, then the outward pressure P on the shell that result from the

temperature increases is given by

( = coefficient of linear expansion of copper)

1) 3B 2) 3B 3) 3B 4) 4B

6. An observer looks at a distant building of height 20m with a telescope of magnifying

power of 18. To the observer the building appears.

1) 18 times nearer 2) 20 times taller 3) 20 times nearer 4) 18 time taller

7. Two strings of linear mass densities and 9 are stretched under same tension. A wave

travelling on the lighter string towards the heavier string gets partially reflected and

transmitted at the junction. Then fraction of incident wave energy getting transmitted to

the heavier is

1) 1

4 2)

1

2 3)

3

4 4)

9

16




8. An object of weight W has a uniform rectangular cross section of ax2a and density of 0.25 3/g cm . Part of it is immersed in water and the rectangle is tilled by 45 ,o while one of its

corners is just at the water surface. Find the torque of the buoyancy force with respect to

center of mass of the object

1) 2 2aw 2) 2

aw 3)

2

aw 4)

2 2

aw

9. A solid conical bar of circular cross –section is suspended vertically as shown in figure.

The vertical length of the bar is L the diameter of its base is D, the young’s modulus Y

and mass density . The elongation of the bar due to its own weight will be

1) 2

2

L g

Y

2)

2

6

L g

Y

3)

2

8

L g

Y

4)

2

12

L g

Y

10. A current carrying wire having current ‘ I = 30A ’ is of the shape of a sin curve given by the

function sin 3 xy here x and y are in meter, there exists a constant external magnetic

field B 5 3 cos 3 Xi j k

in the region. Find the force (in Newton) from magnetic

field on the length of the wire between x=0 and 2

3x .

1) 80N 2) 100N 3) 120N 4) ZERO




11. In the given figure ABC is a right –angled isosceles prism kept in air. A ray of light is

incident on it normally as shown in figure. Refractive index of the Prism is varying with

time t as 1 0.4 ,t here t is in seconds. The angular velocity of the emergent ray at time

t = 1 sec is

1) 1.2 rad/sec 2) 1 rad/sec 3) 2 rad/sec 4) 1.5 rad/sec

12. A flat circular coil having N turns (tightly wounD) is placed in a time varying magnetic

field sin .oB B t The outer radius of the coil is R. Determine the maximum value of the

induced emf in the circuit.

1) 2

oR NB 2) 23 oR NB 3) 2

oR NB

4)

2

3

oR NB

13. In equilibrium, find the ratio of compression in the left spring to the compression in the

right spring

1) 4:3 2) 4 :1 3) 40:33 4) 50:33

14. A wooden plank of length 1m and uniform cross-section is hinged at one end to the

bottom of a tank as shown. The tank is filled with water up to a height of 0.5m. The

specific gravity of the plank is 0.5. The angle (in degrees) made by the plank in

equilibrium position is




1) 45o

2) 30o

3)15o

4) 60o

15. Young’s double slit experiment is performed inside a liquid. The 35th bright fringe in

liquid lies where 28th dark fringe lies in vacuum. The refractive index of the liquid is

1) 14/13 2)14/11 3) 35/22 4) 11/7

16. A disc of radius R = 1 m is kept on the surface of viscous liquid having thickness ‘h’ as

shown in the figure then external power required to rotate the disc with constant angular

velocity 2 /o rad s is P, then (take coefficient of viscosity of the liquid

2

.S I

units, h = 2 mm).

1) P = 6 KW 2) P = 4 KW 3) P = 2 KW 4) P = 5 KW

17. A basket ball of radius R is spun with an angular speed k and it’s center of mass

moves with a speed V. Assume that the pressure over the entire upper half of ball is same

as the pressure at top most point of ball and pressure over the entire lower half is same as

pressure at the lowest point of the ball. Density of air is . Assuming pressure difference

over the ball due to height is negligible, the aerodynamic lift force experienced by the ball

can be expressed as.

1) 3R V 2) 34 R V 3) 33 R V 4) 32 R V




18. Two balls of radii r and 2

r are released inside a deep water tank. Their initial accelerations

are found to be 2 4

g gand respectively. Find the velocity of smaller ball relative to the larger

ball, a long time after the two balls are released. Coefficient of viscosity is and density

of water is .

1) 211

54

r gdownwards

2)

211

54

r gupwards

3) 25

27

r gdownwards

4)

25

27

r gupwards

19. A large open tank is filled with water upto a hight H. A small hole is made at the base of

the tank. It takes 1T time to decrease the height of water to 1H

nn

and it takes 2T time to

take out the remaining water. If 1 2 ,T T then the value of n is:

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

20. A container filled with viscous liquid is moving vertically downwards with constant speed

3v .o At the instant shown, a sphere of radius r is moving vertically downwards (in liquid)

has speed vo . The coefficient of viscosity is . There is no relative motion between the

liquid and the container. Then at the shown instant, the magnitude of viscous force acting

on sphere is

1) 6 rvo 2) 12 rvo 3) 18 rvo 4) 24 rvo




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 certain hypothetical radioactive decay process, Species A decay into species B and

species B decays into species C according to the reactions.

A→2B + particles + energy

B→3C + particles + energy

The decay constant for the species A is

1

1 1secA and that for the species B is

1

2 100secA . Initially 410 moles of the species of A were present while there was none of

B and C. It was found that species B reaches its maximum number at a time to = 2

ln(10)sec. The value of the maximum number of moles of B is 2.303 10e

22. A rectangular metal plate has dimensions of 10 cm x 20 cm. A thin film of oil separates

the plate from a fixed horizontal surface. The separation between the rectangular plate and

the horizontal surface is 0.2 mm. An ideal string is attached to the plate and passes over

an ideal pulley to a mass m. When m = 125 gm, the metal plate moves at constant speed

of 5 cm/s across the horizontal surface. The coefficient of viscosity of oil in

2 2adyne-s/cm is .Find a. Useg=1000cm/s

2




23. The velocity of liquid (v) in steady flow at a location through cylindrical pipe is given

2

2v=v 1 ,o

r

R

where r is the radial distance of that location from the axis of the pipe and R

is the inner radius of pipe. If R = 10 cm. volume rate of flow through the pipe is

2 3 1/ 2 x 10 m s and the coefficient of viscosity of the liquid is 0.75 N sm-2, find the

magnitude of the viscous force per unit area, in Nm-2 at r = 4 cm.

24. A closed loop of the shape in the figure is placed in a horizontal magnetic field of 2T

perpendicular to field. Give 0.01 A current is flowing in closed loop. It is free to rotate

about axis AB. The movement of inertia of this arrangement about AB axis is

4 21.0224X10 kgm what will be its magnitude of angular acceleration 2/in rad s at this

position?

25. Two immiscible liquid are filled in conical flask as shown in figure. The area of cross

section is shown a hole of area ‘a’, is made in lower end of the cone. Find the speed of

liquid flow from the hole (consider 2

2

2

2, 8 , 10 / .

17

ah m g m s

A Express answer in the units

of cm/s)




CHEMISTRY MAX.MARKS: 100 SECTION – I



26. The order of decreasing Sn1 reactivity for the following compounds

Br

I

Br

II

Br

III

1) I>II>III 2) I>III>II 3) II>III>I 4) III>I>II

27. In the reaction given below which is the incorrect consideration

3 2 2/ . / /

3 3

Na liq NH Ag O NaOH H OCH C C CH X Y Z

1) Y is a racemic mixture while Z is achiral

2) Both Y and Z are racemic mixture.

3) A diastereomer of Y gives racemic Z

4) X shows diastereomerism but not enantiomerism

28. The enthalpy change under standard conditions for which of the reaction below would

be equal to the o

fH of NaOH(s)

1) (s) 2 (l) (s) 2(g)

1NaOH

2Na H O H 2) (s) 2(g) 2(g) (s)

1 1NaOH

2 2Na O H

3) (s) 2 2(l) (s)

1

2Na H O NaOH 4) (aq) (aq) (s)Na OH NaOH

29. 0.01 M CH3COOH is 4.24% ionized. What will be the percentage ionisation of 0.1M

CH3COOH?

1) 1.33% 2) 4.24% 3) 5.24% 4) 0.33%




30. The value of Kp for the reaction, 2 2 (g) 2Cl2(g)H O 24 (g) O (g)HCl is 0.03 atm at 427o C,

then the value of Kc for the same reaction is

1) 45.23 10 2) 47.34 10 3) 33.2 10 4) 55.43 10

31. The volume X of H2 gas effuses through a hole in a container in 5seconds. The time

taken for the effusion of the same volume of the specified gas under identical

conditions is

1) 10 seconds: He 2) 20 seconds: O2 3) 25 seconds: CO 4) 55 seconds: CO2

32. For a chemical reaction A B, the rate of the reaction increases by a factor of 1.837

when the concentration of A is increased by 1.5 times. The order of reaction with

respect to A is

1) 1 2) 1.5 3) 2 4) -1

33. Given below are some standard reduction potentials:

2 2 ; 0.14oSn e Sn E V 2

2 2 2 ; 0.79oHg e Hg E V

Which of the following statements is correct?

1) Hg can reduce Sn+2 to Sn 2) Sn+2 can oxidize Hg to Hg2+2

3) Hg2+2 can oxidize Sn to Sn+2 4) Sn+2 is stronger oxidising agent than Hg2

+2

34. For the reaction 2 3 3X Y Z , the combination of 2 moles of X with 2 moles of Y

produces 1.75 moles of Z. What is the percent yield of this reaction?

1) 43.8 2) 58.3 3) 66.7 4) 87.5

35. 2 3 3 3 2 22 22 2 2 22 10KI I HNO HIO KIO NO H O .If 3 mole of KI and 2 moles of I2 are

reacted with excess of HNO3. Volume of NO2 gas evolved at STP is

1) 749.1 2) 1089.6 3) 45.4 4) 68.1




36. Which molecule will give the following dicarboxylic acid upon treatment with acidic

solution of KMnO4?

COOH

O

OCOOH

1) 2) 3) 4)

37. The following reactions are carried out

COOCH3

CH2CONH2

Br2/NaOH(A)

heat (B)

The product B is

1)

NH

O

O

2) O

O

O

3) O

O

4)

NH

O

38.

Br2

CCl4

(i) alc.KOH

(ii) NaNH2

(A)

Product A is

1) 1,3-Butadiene 2) 2-Butyne 3) 1-Butyne 4) 1,2- Butadiene

39. The ratio of packing density in fcc, bcc and cubic structure is respectively

1) 1:0.92:0.70 2) 0.7.:0.92:1 3) 1:0.70:0.92 4) 0.92:0.70:1

40. A binary solid AB has a rock salt structure. If the edge length is 400pm and radius of

cation is 75pm the radius of anion is

1) 100pm 2) 125pm 3) 250pm 4) 325pm

41. In which of the following systems interfacial angles 90o but 90o

1) Monoclinic 2) Rhombohedral 3) Triclinic 4) Hexagonal

42. A crystal is made up of X,Y and Z. X forms fcc packing. Y occupies all octahedral

voids of X and Z occupies all tetrahedral voids of X. If all the particles along one body

diagonal are removed, then the formula of the crystal would be

1) XYZ2 2) X2YZ2 3) X8Y4Z5 4) X5Y4Z8




43. The debroglie wavelength of a neutron at 927o C is . What will be its wavelength at

27o C?

1) 2) 2

3) 2 4) 4

44. The number of waves made by a Bohr electron in an orbit of maximum magnetic

quantum number+2 is

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

45. The first ionisation energy of Cs is 6.24x10-19 J/atom. What is the minimum frequency

of light that is required to ionise a Cs atom?

1) 1.06x10-15 s-1 2) 4.13x1014 s-1 3) 9.42x1014 s-1 4) 1.6x1018 s-1

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




46. How many of the following compounds show reactivity with LiAlH4, Aldol

condensation & I2/NaOH?

CH3CHO, 2CH 2CH ,

CHO

,3 2 2 3CH CH CO CH CH ,

COCH3

CHO

, COCl

CHO

, 3 2 3CH CO CH CO CH

47. The number of moles of HI required when O

O

is treated with HI

48. When a solution of CuSO4 is electrolysed for 10min with a current of 1.5A. What is

the mass of Cu deposited at cathode? (accurate to 3 decimals)

49. A metallic crystal crystallises into a lattice containing a sequence of layers

ABABAB…. Any packing of spheres leaves out voids in the lattice. What percentage

by volume of this lattice is empty space?

50. What is the difference in the wavelengths of 4th and 5th lines of Balmer series in the

spectrum of hydrogen atom?




MATHEMATICS MAX.MARKS: 100 SECTION – I



51. Let f : R R be 4 4f x sin x sin x cos x cos x . The range of f is

1) 9

0,8

2) 1 5

,2 8

3) 7

0,4

4) 1 7

,2 4

52. 1

lim [ ] | | .x

x x where

indicates the greatest integer, indicates modulus

1) 0 2)1

2 3)

3

4 4) does not exist

53. Given

2 12

2

0 1

cos 2 2 1 2

xx e x

f xa x bx x

f x is differentiable at 1x provided

1) 1, 2a b 2) 1, 2a b 3) 3, 4a b 4) 3, 4a b

54. 4/42 )x1(x

dx is equal to

(1) cx

)x1( 4/14

(2) cx

)x1( 4/14

(3) cx

)x1( 4/34

(4) 4 5/4(1 )x

cx

55. 1 2

2 2

0 1

| x x | dx | x 3x 2 |dx

(1) 1

2 (2)

1

3 (3)

1

4 (4)

1

8

56. The area bounded by x = x1, y = y1 and y = (x + 1)2 where x1, y1 are the values of x, y

satisfying the equation sin–1x + sin–1y = will be, (nearer to origin).

(1) 1

3 (2)

2

3 (3) 1 (4)

3

2




57. The solution of the initial value problem 2 2 2 22 , 1 0x y dx xy dy y is f x x y where

f(x) is

1) 1

x 2) x 3)

3

1

x 4) 3x

58. The number of points of local extrema of the function 2008 2009 2010( ) ( 1) ( 2) ( 3)f x x x x is

1) 2 2) 3 3) 4 4) 5

59. If a line with direction ratios 2 : 2: 1 intersects the line x 7 y 5 z 3

3 2 1

and

x 1 y 1 z 1

2 4 3

at A and B then AB=.

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

60. A and B are square matrices such that A B AB . Then

(1) AB = BA (2) AB – BA = I (3) AB + BA = 0 (4) AB + BA = I

61. If A is a skew–symmetric matrix of order 3, then the matrix A4 is

(1) skew symmetric (2) symmetric (3) diagonal (4) scalar matrix

62. Equation of the line passing through (4, 6) and making an intercept 3

5 between the lines

x+ 2y + 7 = 0 and x + 2y + 10 = 0 is

1) 2x – y – 2 = 0 2) 2x – y + 2 = 0 3) 2x – y + 4 = 0 4) x + 2y – 2 = 0

63. The equation of line joining midpoints of the tangents OP, OQ drawn from origin O to

the circle 2 2 4 6 8 0x y x y is

1) 3 2 4 0x y 2) 2 3 2 0x y 3) 3 2 4 0x y 4) 2 3 4 0x y

64. Minimum distance between the parabolas y2 – 4x – 8y + 40 = 0 and x2 – 8x – 4y + 40 =

0 is

(1) 0 (2) 3 (3) 2 2 (4) 2




65. Minimum distance between y2 = 4x and x2 + y2 – 12x + 31 = 0

(1) 21 (2) 26 5 (3) 20 5 (4) 28 5

66. The locus of point of intersection of two tangents to the parabola 2 4y x such that their

chord of contact subtends a right angle at the vertex is

1) 4 0 x 2) 4 0 y 3) 4 0 x 4) 4 0 y

67. The tangent and normal at the point P(4, 4) to the parabola, y2 = 4x intersect the x–axis

at the points Q and R respectively. Then the cirucmcentre of the PQR is

(1) (2, 0) (2) (2, 1) (3) (1, 0) (4) (1, 2)

68. The mirror image of the parabola 2y 4x in the tangent to the parabola to the point (1,2)

is

(1) 2

x 1 4 y 1 (2) 2

x 1 4 y 1

(3) 2

x 1 4 y 1 (4) 2

x 1 4 y 1

69. Let (2, 3) be the focus of a parabola and x + y = 0 and x - y = 0 be its two tangents, then

equation of its directrix will be

(1) 2x - 3y = 0 (2) 3x + 4y = 0 (3) x + y = 5 (4) 12x - 5y + 1 = 0

70. If the locus of a point which divides a chord of slope ‘2’ of the parabola

2 4y x internally in the ratio 1:2 is a parabola. Then the vertex of this parabola is

1) 1 4

,9 9

2) 2 8

9, 9

3) 2 4

,9 9

4) 2 4

9, 9




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




71. Let :f R R be given by 3sin 6f x a x b x where a and b are real numbers. If

10 5log log 10 7f then the value of 10 10log log 5f

72. Normals 1 2, ,AO AA AA are drawn to 2 8y x from point ,0A h . If triangle 1 2OA A is

equilateral then / 7h =

73. If 2 3 5 0a b c then the area of the triangle whose sides are represented by the vectors

,a b and c is

74. The slope of the line which belongs to family of these

(1 + )x + ( – 1)y + 2(1 – ) = 0 and makes shortest intercept on 2x 4y 4 is

75. The number of distinct normals, which can be drawn from the point (2, 8) to the

parabola y2 = 6x is equal to

Documents

14-12-20 SR CO-SUPER CHAINA Jee-Main CTM-15 SYLLABUS€¦ · thin tube of radius 5cm is filled in Piston as shown in figure. Assuming that the Piston is in equilibrium, the height