21-05-20 SR.N-SUPER CHAINA/N-CHAINA Jee-Adv …...string connecting the pulleys are essentially...

Sec: Sr.IIT_N-SUPER CHAINA/N-CHAINA Date: 21-05-20Time: 3hrs Max. Marks: 264

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

21-05-20_SR.N-SUPER CHAINA/N-CHAINA_Jee-Adv_PTA-1_SYLLABUS

PHYSICS: Unit Dimensions, Error Analysis, Kinematics,

laws of motion, Circular Motion

CHEMISTRY: Thermodynamics & Thermo chemistry, Gaseous State,

Atomic Structure, Solid State, Stoichiometry, Liquid Solutions

MATHEMATICS : Trigonometry (Equations, POT, ITF), Complex Numbers, Vectors

Narayana IIT Academy 21-05-20_Sr.IIT_N-SC/N-C_JEE-Adv_PTA-1_Q’P

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

Education is the key to unlock the golden door of freedom.

Time: 3:00 Hours IMPORTANT INSTRUCTIONS Max Marks: 264

PHYSICS:

Section Question Type +VeMarks

- VeMarks

No.ofQs

Totalmarks

Sec – I(Q.N : 1 – 8) Questions with Integer Answer Type 4 0 8 32Sec – II(Q.N : 9 – 18) Questions with Multiple Correct Choice 4 -2 10 40

Sec – III(Q.N : 19 – 20) Matrix Matching(+2/-1 for every match) 8 -4 2 16

Total 20 88

CHEMISTRY:Section Question Type +Ve

Marks- VeMarks

No.ofQs

Totalmarks

Sec – I(Q.N : 21 – 28) Questions with Integer Answer Type 4 0 8 32

Sec – II(Q.N : 29 – 38) Questions with Multiple Correct Choice 4 -2 10 40


Total 20 88

MATHEMATICS:Section Question Type +Ve

Marks- VeMarks

No.ofQs

Totalmarks

Sec – I(Q.N : 41 – 48) Questions with Integer Answer Type 4 0 8 32Sec – II(Q.N : 49 – 58) Questions with Multiple Correct Choice 4 -2 10 40


Total 20 88




PHYSICS Max Marks: 88SECTION – I

(SINGLE INTEGER ANSWER TYPE)This section contains 8 questions. The answer is a single digit integer ranging from 0 to 9 (both inclusive).Marking scheme +4 for correct answer, 0 if not attempted and 0 in all other cases.

1. For a man walking towards east with a velocity of 5 km/hr rain appears to fall vertically

down. When the man begins to walk towards west with a velocity of 3 km/hr the rain

appears to fall at an angle of 060 to the vertical. The magnitude of velocity of the rain

when the man stops walking is 139 Km /hrN

. Then N is equal to

2. The percentage error of a physical quantity m given by the relation tanm is

minimum when 15 ºn . Then n = ___

3. A rope rests on two platforms which are both inclined at an angle , as shown. The rope

has uniform mass density and its coefficient of friction with the platform is 1. The

system has left-right symmetry. The rope is arranged such that the largest possible

fraction of the rope does not touch the platform. The maximum value of which allows

this isn

, then ‘n’ is

4. The speed of a motorboat in still water is four times the speed of a river. Normally, the

motorboat takes one minute to cross the river to the port straight across on the other

bank. One time due to a motor problem, it was not able to run at full power, and it took

four minutes to cross the river along the same path. Speed of the motor boat in the

situation of motor problem is 314X

times of its usual speed. Find the value of X.(Assume

that the speed of the water is uniform throughout the whole width of the river)




5. Two objects. One sliding down from rest on a smooth (frictionless) slope. The otherbeing thrown from the point O, start their motion at the same instant. Both get to thepoint P at the same time and at the same speed. If is the angle of projection and is

the angle of inclination then find the value of 1sin sin

?

6. Consider the Atwood’s machine shown, It consists of three pulleys, a short piece ofstring connecting one mass to the bottom pulley, and a continuous long piece of stringthat wraps twice around the bottom side of the bottom pulley, and one around the topside of the top two pulleys. The two masses are m and 2m. Assume that the parts of thestring connecting the pulleys are essentially vertical, then the magnitude of acceleration

of 2m is 2g m /secn

g is acceleration due to gravity. Find the value of n.

7. A block of mass m 1Kg placed on a wedge of mass M 2Kg is attached at one end of

a light inextensible cord that passes over an ideal pulley affixed on the top of the wedgeas shown in the finger. The free end of the thread is pulled by a constant horizontal

force 3F N2

. if friction between the block and the wedge as well as between the

wedge and the floor is absent, find acceleration of the wedge (in 2m /sec ,to nearest

integer value)Acceleration due to gravity is 2g 10m /sec .




8. A bead of massm 1Kg , which can slide on a straight horizontal frictionless rod, is

being pulled with the help of a light inextensible thread of length 1m in such a mannerthat the end P of the thread, which is being pulled moves with a constant speed

2 / secu m always directed along the thread. Find the value of the tensile force T(in N) inthe thread at an instant when the thread makes angle 045 with the rod.

SECTION – II(ONE OR MORE CORRECT ANSWER TYPE)

This section contains 10 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for itsanswer, out of which ONE OR MORE than ONE option can be correct.Marking scheme: +4 for correct answer, 0 if not attempted and -2 in all other cases.

9. Two blocks of masses 2Kg and 4 kg are placed over each other as shown in theadjoining figure .The coefficient of kinetic and static friction are as shown in the figure.A variable force F=4t starts acting on the 4 kg block as shown .Choose the correctoption(s) from the following 4 2(a and a represents the accelerations of 4 kg and 2 kgblocks respectively)

A) B)

C) D)




10. The speed of a small object undergoing uniform circular motion is 4m/s. The magnitudeof the change in the velocity during 0.5 second is also 4m/s

A) the angular speed of object is 2rad / sec

3

B) the centripetal acceleration of the object is28

m / s3

C) the radius of the circle is 6metre

D) the radius of circle is 3metre

11. A man wants to reach directly at point B on the opposite bank of a river flowing at a

speed as shown in fig. RV Velocity of river with respect to ground .

Velocity of man with respect to riverMRV

A) minimum speed relative to water, the man should have so that he can reach point B

will be1

/ sec2

m

B) minimum speed relative to water, the man should have so that he can reach point B

will be 2 / secm

C) the time required for aman to cross the river in the above condition (when he travels

with minimum relative speed required) is 200 2 s

D) The angle, man has to maintain with the line perpendicular to river is 030 with

minimum speed condition




12. The velocity time graph of the fig. shows the motion of a wooden block of mass 1 kgwhich is given an initial push t = 0, along a horizontal table.( g = 10 m/s2)

A) The coefficient of friction between the blocks and the table is 0.1

B) The coefficient of friction between the blocks and the table is 0.2

C) If the table was half of its present roughness, the time taken by the block to completethe journey is 2 sec.

D) If the table was half of its present roughness, the time taken by the block to completethe journey is 8 sec

13. The dimensions of the quantities in one (or more) of the following pairs are the same.Identify the pair(s):

A) torque and work B) angular momentum and work

C) energy and Young’s modulus D) light year and wavelength

14. A wedge and a block system is released from rest in the given arrangement. If allsurfaces are smooth and acceleration of wedge with respect to ground is 22 /m s towardsleft, then choose CORRECT option(s).

60

22 /m s

A) Magnitude of acceleration of block with respect to ground is different from itsacceleration (magnitude) with respect to wedge

B) Magnitude of acceleration of block is same with respect to ground and with respect towedge

C) Magnitude of acceleration of block is 22 /m s with respect to wedge

D) Magnitude of acceleration of block is 22 /m s with respect to ground




15. A student uses a simple pendulum of length 1m to determine acceleration due to gravity

g. He uses a stop watch with least count of 0.5 s for this and records 40 s for 20

oscillations. For this observation, which of the following statements is/are true? Least

count of scale used for measurement of length is 1cm.

A) Percentage error in measurement of time period is 5 / 4 %

B) Percentage error in measurement of time period is 5 / 2 %

C) Percentage error in determination of g 2.5%

D) Percentage error in determination of g 3.5%

16. Three identical cylinders each of mass 10 3m kg are arranged on a horizontal floor as

shown in the figure with their axes horizontal. The floor as the cylinders is frictionless.

You apply a constant horizontal force (directed to the right) on the leftbottom cylinder.

Consider acceleration of free fall is 210 /g m s

A)For 50F N ,bottom two cylinders will not be in contact

B)For 150F N ,all cylinders maintain contact

C)For any value of F ,upper cylinder and bottom left cylinder never loose contact

D)For 400F N ,contact force between upper cylinder and right bottom cylinder is zero

17. Seven pulleys are connected with the help of 3 light strings and two small strings with

roof as shown in the figure. Consider 1 2 3 4 5, , , ,P P P P P as light pulleys and pulleys 6P and

7P have mass m each. For this arrangement, choose the correct statements, if system is

released from rest.




1P2P

3P

4P

5P

6P

7P

A) Tension in the string connecting 1 3,P P and 4P is zero

B) Tension in the string connecting 1 3,P P and 4P is mg/3

C) Tension in all the strings are same and equal to zero

D) Acceleration of 6P and 7P is each equal to g downward

18. A ball is projected along smooth inclined plane in a direction perpendicular to line of

greatest slope with speed 8m/s as shown in figure at time 0t .choose the correct

option(s) from below at time 1sect (take 210 / secg m )

A) Speed of the ball is 10 / secm

B)Normal acceleration of the ball is 210 / secm

C)Tangential acceleration of the ball is23.6 / secm

D)Radius of curvature of trajectory is500

24m




SECTION - III(MATRIX MATCHING ANSWER TYPE)

This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and fourstatements (P, Q, R and S) in Column II. Any given statement in Column I can have correct matching with ONE orMORE statement(s) given in Column II.For example, if for a given question, statement B matches with the statements given in Q and R, then for theparticular question darken the bubbles corresponding to Q and R in the OMR sheet. For each correct matchingwill be awarded +2 marks ONLY and 0 if not attempted and -1 in all other cases.19. Find the accelerations of blocks A and B for the following cases ( g = 10 m/s2)

1 kg 1 kg

AB

1 2

10 N

ColumnI ColumnII(A) 1 = 0 and 2 = 0.1 (P) aA = aB = 9.5 m/s2

(B) 2 = 0 and 1 = 0.1 (Q) aA = 9 m/s2, aB = 10 m/s2

(C) 1 = 0.1 and 2 = 1.0 (R) aA = aB = g = 10 m/s2

(D) 1 = 1.0 and 2 = 0.1 (S) aA = 1, aB = 9 m/s2

20. Some physical quantities are given in List-I and some possible SI units in which thesequantities may be expressed are given in List-II. Match the physical quantities inList-I with the units in List-II and select the correct answer using the code given

below listsLIST-I LIST - II

(A)e sGM M ,Where G-universal gravitational

constant, Me-mass of the EarthMs-mass of the Sun

(P) (volt)(coulomb)(meter)

(B)3RT

M,Where R-universal gas constant,

T-absolute temperature, M-molar mass(Q) (kilogram) (meter)3(second)

(C)

2

2 2

F

q B, Where F-force q-charge

B-magnetic field

(R) (meter)2(second)-2

(D)

e

e

GM

R, where G-universal gravitational

constant, Me-mass of the Earth Re-radiusof the earth

(S) (farad)(volt)2(kg)-1




CHEMISTRY Max Marks: 88SECTION – I


21. If a mono atomic gas xPV constant. It possess molar heat capacity as1 1P

R RC

x

.

How much heat in calories is required to raise the temperature of one mole of that by02 C if it obeys P

V constant?

22. Degeneracy of 2nd exicited state of 2Li ion is x, and degeneracy of 4th exicited state ofLi ion is y then x/y is

23. Vander waal’s gas equation may be expressed as2

1 ...m m

B CZ

V V where mV molar

volume of gas. If 10.105B Lmol and 4 24 10C L 2mol at 0127 C , the value of Vanderwaal constant ‘a’(in atm 2 2L mol ) is 0.08 /R L atm K mol :

24. 5 mL of gaseous hydrocarbon was exposed to 30 mL of 2O . The resultant gas, on cooling

is found to measure 25 mL. of which 10 mL was absorbed by NaOH and the remainderby pyrogallol. All measurements are made at constant pressure and temperature. Thesum of number of carbon and hydrogen atoms in the hydrocarbon is___

25. A compound AB has zinc blende structure with ‘A’ atoms at corners and face centre ofthe unit cell. If all the atoms present in one body diagonal are removed, the formula ofthe compound becomes x yA B . The sum x y is:

26. Work done in chemical reaction (in k cal): 3A s B g c g at 0227 C , 1 atmosphere

in closed vessel with movable piston is

27. For the redox reaction : 2 24 2 4 2 2MnO C O H Mn CO H O , the correct coefficients of

the reactants for 4MnO ,2

2 4C O , H in the balanced reaction are X,Y,Z respectively. Then

find (Z-X-Y)

28. If the freezing point of a 0.01 molal aqueous solution of cobalt(III) chloride-ammoniacomplex (which behaves as a strong electrolyte) is 00.0558 C , the number of chloride(s)in the coordination sphere of the complex is

[ fK of water 11.86K kg mol ]






29. One mole of O2(g), initially at a temperature of 120 K and under a pressure of 4 atm is

expanded adiabatically to 1 atm in such a way that the temperature of the gas falls to 90

K (just above its normal boiling point). Cpof O2(g) is 28.2 JK-1 mol-1 and is constant

over the required temperature range. O2(g) is supposed to behave ideally. Choose the

correct options: (log2=0.3010, log3=0.4771)

(A) q = 0 (B) w = + 597J (C) H = - 846 J (D) Ssys = 3.416 JK-1

30. When 5 mL of a 1.0 M HCl solution is mixed with 5 mL of a 0.1 M NaOH solution,temperature of solution increases by 0t C . Which of the following can be predicted fromthis observation:

(A) If 5 mL of 0.1M HCl is mixed with 5 mL 0.1 M 3NH solution, the temperature rise

will be less than 0t C

(B) If 5 mL of 0.1 M 3CH COOH is mixed with 5 mL 0.1 M NaOH, the temperature rise

will be less than 0t C

(C) If 10 mL of 1.0 M HCl mixed with 10 mL of 0.1 M NaOH, the temperature rise willbe 02t C .

(D) If 10 mL of 0.1 M HCl is mixed with 10 mL of 0.1 M NaCl, the temperature risewill be 0t C

31. In an universe other than earth all the quantum numbers have same value

as on earth except ‘’ and ‘s’. Azimuthal quantum number can have values

from 0 to (n + 1) in integral step and ‘s’ (spin quantum number) has values of

1 1– ,0&2 2

. If all rules like Aaufbau rule, Hund’s rule and Paulis exclusion

rule follow in other universe also. Then which of the following are true?




(A) No. of elements in third period of another universe will be 27

(B) Configuration of element with atomic number 29 will be, 1s3, 2s3, 2p9, 3s3, 3p9, 4s2

(C) Configuration of element with atomic number 29 will be, 1s3, 1p9, 2s3, 1d14

(D) Atomic number of element in 4th period and 5th column will be71

32. A balloon blown up with 1 mole of a gas, has a volume of 480 ml to 05 C . If the balloon

is filled to 7

8

th of its maximum capacity, then which of the following options is/are

correct?

(A) The balloon will burst at 030 C

(B) The pressure of the gas inside the balloon at 05 C is 47.5 atm

(C) The minimum temperature at which the balloon will burst is 044.71 C

(D) The pressure of gas when balloon burst at minimum temperature is 50 atm

33. 8.7gm of pure 2MnO is heated with an excess of HCl and the gas evolved is passed into a

solution of KI. The amount of iodine liberated is ( 55 35.5 127 16) Mn Cl I O

2 2 2 2

2 2

MnO HCl MnCl H O Cl

Cl KI KCl I

(A) 25.4gm (B)12.7gm (C) 0.1mole (D)0.05mole

34. For a mixture of two volatile liquid of A and B, Boiling point curve is given as

0

AT0

BT

1Ax 1Bx

Then identify true statement(s)




(A) Vapor pressure of pure liquid B is more than A

(B) Liquid A is more volatile than B

(C) If it is non-ideal solution then it has –ve deviation

(D) If it is non-ideal solution then inter molecular attraction force between

A and B in the mixture is less than the individual attraction in A and B

35. The data given below is used to find the type of cubic lattice to which the crystal belong.

Ag Al Cu Cr

a (pm) 407.7 405 361 287

(g cm-3) 10.5 2.7 8.92 7.31

At. mass (gm) 108 27 63.5 52

Which of the above crystallizes in FCC unit cell

(A) Ag (B) Al (C) Cu (D) Cr

36. A salt MX has NaCl type lattice in which r is the minimum distance between 2M and2X . Each 2M ion is surrounded by

(A) 26X ions, each at a distance r

(B) 212M ions, each at a distance 2r

(C) 28X ions, each at a distance 3r

(D) 212M ions, each at a distance 4r

37. Which of the following is(are) correct statement(s)?

(A)Schottky defect have no effect on the physical properties of solid

(B) Greater is the number of F-centres, greater is the intensity of color developed

(C)Frenkel defect is a dislocation defect

(D)A compound may have both Frenkel and Schottky defect




38. 4CCl and acetone form a non-ideal solution at room temperature in a copper container.

For this process, the true statement(s) is (are):

(A) G is positive (B) systemS is positive

(C) 0surroundingS (D) 0H


This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and fourstatements (P, Q, R and S) in Column II. Any given statement in Column I can have correct matching with ONE orMORE statement(s) given in Column II.For example, if for a given question, statement B matches with the statements given in Q and R, then for theparticular question darken the bubbles corresponding to Q and R in the OMR sheet. For each correct matchingwill be awarded +2 marks ONLY and 0 if not attempted and -1 in all other cases.39.

Column – I(Solute)

Column – II(van’t Hoff Factor)

(A) K4[Fe(CN)6] (aq) (p) 12

(B) Al2(SO4)3 in aqueous solution (q) Greater than 1

(C) C6H5COOH in benzene solution (r) 1 + 4

(D) NH2CONH2 in benzene solution (s) 1

40. Which of thermodynamic processes given under column I with the expressions givenunder column II

Column-I Column-II(A) Freezing of water at 273 K and 1 atm (P) q=0

(B)Expansion of 1 mol of an ideal gas intovaccum under isolated conditions

(Q) w=0

(C)Mixing of equal volumes of two idealgases at constant temperature andpressure in an isolated container

(R) 0sysS

(D)

Reversible heating of 2H g at 1 atm

from 300 K to 600 K, followed byreversible cooling to 300 K at 1 atm

(S) 0U




MATHEMATICS Max Marks: 88SECTION – I


41. Let a, b and c be three distinct complex numbers satisfying 1a b c and 0a b c ,

then 2 2 2a b c is equal to

42. If x satisfies the equation1 2 1

1 2 1

sin cos3

cos sin

x x

x x

, then find the value of

1 1

1 1

sec tan

cot cos ec

.

43. In a triangle XYZ , let a, b, c be the length of the sides opposite to the angles X, Y and

Z respectively and T denotes ( ) ( ) ( )s s a s b s c . If3

3 6

3

a b c b a b c

a b c b a b c

a b a b c b c

,

2 2 2 2 2 2 2 2 2, ,b c a a b c a c b , then sum of all possible integral values of 1

T

, where

2

a b cs

is

44. Number of solution(s) of equation sec(sin ) (cos ) (cos ), 0,2

xn x ec x n x x

is

45. In a triangle ABC, 090 , 1, 3CAB AB AC

and a point P inside the ABC satisfies

0PA PB PC

PA PB PC

, then

PC PB

PA

is equal to

46. Let C be the set of complex numbers, z C satisfies 3 1 8z z , then minimum value

of2

1

2

z is

47. Let x and y be two real numbers such that 2sin sin 3cos 6cos sin 7x y y x y , then2 2tan 2 tanx y is equal to

48. Let 1z and 2z are two distinct roots of the equation 101 1z and2

a

b

is the probability

that 1 2 2 3z z where a and b are relatively prime natural numbers then a b is






49. If 1, 1, ,

2

zw z z w C

z

, then

A)min

73

3w B)

max3 3w

C) max( ) ( )

4Arg w Arg w

D) min

( ) 0 ( )Arg w Arg w

50. The value of the expression 0 0 0 0 0 0

0

sin 36 cos36 2 sin 27 sin 36 cos36 2 sin 27

2sin 54

is less than

A) 0cos36 B)01

cos 672

C) 0cos9 D) 0cos15

51. If 2 4 7 1cos . cos . cos . cot

9 9 9 32 9b a

where a, b N then

A) 3a B) 2a C) 2b D) 1b

52. In a tetrahedron OABC, the edges are of lengths,, ,OA BC a OB AC b OC AB c . Let 1G and 2G be the centroids of the triangle

ABC and AOC such that 1 2OG BG , then the value of2 2

2

a c

b

is (O being origin)

A) 2 B) 3 C) 6 D) 9

53. Which of the following is (are) correct ?

A) The value of 1 110 1sin sec cot

3 3

is a rational number

B) Number of solution of the equation 1 1cos sin ( )3

x x is one

C) Number of solution of the equation 1 1cos sin ( )3

x x is infinite

D) Let :g R R be defined as ( ) sgn 4 xg x e then 1( )g x is not defined (sgn x denote

the signum function of x)




54. Given that a and b

are two unit vectors such that angle between a

and b

is 1 1cos

4

. If

c be a vector in the plane of a

and b

, such that 4, 2c c b a b and c a b

then

A) 2

B) sum of possible values of is -1

C) Product of possible values of is -12

D) number of distinct values of is three

55. Let P, Q is circum centre of ABC and PBC respectively. In , 3, 2ABC AB AC , S

is perimeter of ABC and Q is midpoint of BC, then which can be true

A) circum radius of 5

2ABC B) circum radius of 5ABC

C) [S] = 6 D) [S] = 8

(where [S] denotes greatest integer less than or equal to S)

56. Let 1 2 3 ...... 22 n

and 1 20 ........ 2m are values of and

respectively such that 2cos 2 3 2cos(2 ) 2cos , then which of the following

is(are) true?

A) 2n > 3m B) n > m C)1

2m

ii

D)1 1

m m

i ii i

57. Let 1 2 3 4, , ,z z z z are roots of equation 6 4 3 2 1 0z z z z such that 3 1 0rz for

1, 2, 3, 4r . Area of quadrilateral made by joining 1 2 3 4, , ,z z z z on the argand plane is

A) 02sin18 B) 02cos36 C) 02sin 72 D) 3 02cos 18

58. If2016

1 1

1

2 tan 2 cot 22

r r

r

(where

20182

), then identify correct option

A) 2 B) 1

C) D)





This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and fourstatements (P, Q, R and S) in Column II. Any given statement in Column I can have correct matching with ONE orMORE statement(s) given in Column II.For example, if for a given question, statement B matches with the statements given in Q and R, then for theparticular question darken the bubbles corresponding to Q and R in the OMR sheet. For each correct matchingwill be awarded +2 marks ONLY and 0 if not attempted and -1 in all other cases.59. Let P be a point inside a triangle ABC. The lines PA, PB and PC are drawn so that

,PAB PBC PCA then

List-I List-II

A) The value of max

is lesser than P)1

6

B) The value of cot cot cot

cot

A B C

is greater than Q)1

3

C) The value of2 2 2

2

cos cos cos

cos

ec A ec B ec C

ec

is R) 1

D)The value of

3

sin( ) sin( ) sin( )

sin

A B C

is lesser

thanS) 3

T) 6

60. The complex numbers 1 21

, ....... , 0n

n ii

z z z z

, represents the vertices of a regular polygon

of n sides in order, is inscribed in a circle of unit radius and 3 1 2nz z Az Az . Then the

values of A for prescribed values of n in column-I(where[x] be the greatest integer x).

Column-I Column-II

A) 4 P) 0

B) 6 Q) 1

C) 8 R) 2

D) 12 S) 3

T) 7

21-05-20 SR.N-SUPER CHAINA/N-CHAINA Jee-Adv …...string connecting the pulleys are essentially...

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