09-04-20 sr.n-super chaina/n-chaina jee-adv uta-3

Sec: Sr.IIT_N-SUPER CHAINA/N-CHAINA Date: 09-04-20Time: 3HR Max. Marks: 183

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

09-04-20_SR.N-SUPER CHAINA/N-CHAINA_Jee-Adv_UTA-3

PHYSICS: Gravitation, Electrostatics, Current Electricity, Capacitors, Magnetics,Electromagnetic Induction, Alternate Current

CHEMISTRY: Liquid solution, Chemical kinetics, Surface chemistryCarbonyl compounds, Polymers, Acid & DerivativesGroup-17 and Group-18, D-block, Compound of heavy metals

MATHEAMTICS : Logarithms, Quadratic Equations, Sequence & series, Matrices &Determinants, Complexnumbers

Narayana IIT Academy 09-04-20_Sr.IIT_N-SC _JEE-Adv_UTA-3 Q’P

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

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

IMPORTANT INSTRUCTIONSPHYSICS:

Section Question Type +VeMarks

- VeMarks

No.ofQs

Totalmarks

Sec – I (Q.N : 1 – 7) Questions With Multiple Correct Choice(partial marking scheme) (+1,0) +4 -2 7 28

Sec – II (Q.N : 8 – 12) Questions With Integer Answer Type +3 0 5 15

Sec – III (Q.N : 13 – 18) Questions With Matching Answer Type(Two Tables x 3Q = 6Q) +3 -1 6 18

Total 18 61

CHEMISTRY:Section Question Type +Ve

Marks- Ve

MarksNo.of

QsTotalmarks




Total 18 61

MATHEMATICS:Section Question Type +Ve

Marks- Ve

MarksNo.of

QsTotalmarks




Total 18 61




PHYSICS Max. Marks: 61SECTION – I

(MULTIPLE CORRECT ANSWER TYPE)This section contains 7 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of which ONE ORMORE than ONE option can be correct.Marking scheme: +4 for all correct options & +1 partial marks, 0 if not attempted and -2 in all wrong cases

1. A capacitor of capacity ‘C’ is charged to a steady potential difference ‘V’ and connectedin series with an open key and a pure resistor ‘R’ (Battery disconnected). At time 0t ,the key is closed. If I Current at time ‘t’, a plot of log ‘I’ against ‘t’ is as shown in (1)the graph. Later one of the parameters i.e., V, R or C is changed keeping the other twoconstant, and the graph (2) is recorded. Then

A) C is reduced B) C is increased C) R is reduced D) R is increased

2. The capacitance of a parallel plate capacitor is ‘C’ when the region between the plate hasair. This region is now filled with a dielectric slab of dielectric constant ‘k’. Thecapacitor is connected to a cell of emf E. Choose the correct options when the slab ismoved out slowly in the presence of battery.

A) Charge 1CE k flows through the cell

B) Energy 2 1E C k is absorbed by the cell

C) The energy stored in the capacitor is reduced by 2 1E C k

D) The external agent has to do 211

2E C k amount of work to take the slab out

3. A sample circuit that can be used for multi-meter (with A and B as terminals) is shownin figure-1. It consists of a galvanometer coil ‘G’ of resistance 48 and two resisters

952R and 2r and two switches 1k and 2k as shown in figure-1. It can be used as

ammeter or voltmeter. Figure-2 shows another circuit with battery of emf 10V andinternal resistance 0 2r .




A student uses this multi-meter to measure current in the circuit shown in figure-2 andpotential difference across 0R

A) Current measured by the student is 50

105A

B) Voltage measured by the student is 9V

C) Current measured by the student is 500

1096A

D) Voltage measured by the student is418 10

20036V

4. In the given potentiometer circuit, the resistance of the potentiometer wire AB is 0R . ‘C’is a cell of internal resistance ‘r’. The galvanometer ‘G’ does not give zero deflection forany position of the jockey ‘J’. Which of the following cannot be a reason for this?

A) 0r R B) 0R R

C) emf of C > emf of D

D) The negative terminal of ‘C’ is connected to ‘A’




5. The two diagram A and B below give the field lines near a current carrying large sheethaving uniform current. Which of the following options are correct.

A) In A the external field applies a force towards right on the sheet.

B) In A the external field applies a force towards left on the sheet.

C) In B force having rightward and out of the plane components.

D) In B force having downward and out of the plane components.

6. A conducting loop in the shape of a right angled isosceles triangle of height 10cm is keptsuch that the 090 vertex is very close to an infinitely long conducting wire (see thefigure). The wire is electrically insulated from the loop. The hypotenuse of the triangle isparallel to the wire. The current in the triangular loop is in counterclockwise directionand increased at a constant rate of 110 As . Which of the following statement(s) is (are)

true?

A) There is a repulsive force between the wire and the loop

B) If the loop is rotated at a constant angular speed about the wire, an additional emf of

0

volt is induced in the wire

C) The magnitude of induced emf in the wire is 0

volt

D) The induced current in the wire is in opposite direction to the current along thehypotenuse




7. At a moment 0t when charge on capacitor 1C is zero, the switch is closed. If 0I be

the current through inductor at that instant, for 0t

A) Maximum current through inductor equals 0

2

I

B ) Maximum current through inductor equals 1 0

1 2

C I

C C

C) Maximum charge on 1 0 11

1 2

C I LCC

C C

D) Maximum charge on 1 0 11 2

LC I C

C C

SECTION-II(INTEGER ANSWER TYPE)

This section contains 5 questions. The answer is a single digit integer ranging from 0 to 9 (both inclusive).Marking scheme +3 for correct answer , 0 if not attempted and 0 in all other cases.

8. In the circuit shown in the figure, 6 , 3L CX X and 8R . If the current through the

voltage source is ‘ I ’ (in amp). Find2

I.




9. The circuit shown consists of two capacitors of capacitances ‘C’ and ‘2C’, a resistance‘R’ and an ideal battery of terminal voltage ‘V’. Initially the switch is open and thecapacitors are fully charged. The total heat dissipated in the circuit after the switch is

closed is 2

3

nC V . Find ‘n’.

10. A solid non-conducting sphere has charge ‘Q’ uniformly distributed over its surface andis rotated uniformly about its diameter (which coincides with z-axis) as shown. The

value of the integral B d l

along the entire z-axis (where ‘B’ is due to moving charges

on the sphere) is of magnitude 0Q

n

. Find the value of ‘n’.

11. A non-conducting uniform rod AB of mass ‘m’ and charge ‘Q’ uniformly spread over itslength rotated uniformly in a conical pendulum motion forming a constant angle 030 with its axis of rotation. The magnetic moment of the rod is . The angular momentum

of the rod about ‘A’ has a magnitude ‘L’. Find the value of QL

min SI units?




12. A conducting medium is the form of a quarter of an annulus of radii ‘a’ and b a with

uniform thickness ‘h’ as shown in figure. The conductivity ‘ ’ of the material of themedium is uniform. The resistance of the specimen between the pair of opposite faces in

the direction ˆpe isln

bX

ah

. Then ‘X’ is

( ˆpe is unit vector along radial direction of annulus)

SECTION – III(THREE COLUMN MATRIX MATCHING TYPE)

This section contains 6 questions of matching type. This section contains two tables (each having 3 columns and 4 rows). Based on Eachtable there are 3 questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of which ONLY ONE option can becorrect.Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.

Answer Q.13, 14 &15 by appropriately matching the information given in the threecolumns of the following table.

A particle of mass ‘m’ is projected at a radial distance ‘r’ r R from the centre of a

planet of radius ‘R’ and mass ‘M’ at an angle ‘ ’ with a speed ‘v ’ as shownColumn – 1: Corresponds to speed of projection.

Column – 2: Corresponds to trajectory of particle

Column – 3: Corresponds to the energy at the point of projection.

r

M

v

(P.E. – represents gravitational potential energy; E – represents total energy)




Column-1 Column-2 Column-3

I) GMv

r

i) Circular P) P.E. is +Ve

II)4

GMv

r

ii) Elliptical Q) E is +Ve

III) 2GMv

r

iii) Parabolic R) P.E. is ve

IV) 3GMv

r

iv) Straight line S) E is ve

13. Choose appropriate combination for 00

A) (I) (ii) (P) B) (I) (i) (S) C) (II) (i) (R) D) (III) (iii) (P)

14. Choose appropriate combination for / 2

A) (III) (iii) (Q) B) (III) (iv) (Q) C) (IV) (iv) (Q) D) (IV) (iv) (P)

15. Choose appropriate combination for 030

A) (I) (i) (S) B) (III) (iii) (Q) C) (II) (ii) (R) D) (II) (i) (R)

Answer Q.16, 17 &18 by appropriately matching the information given in the three

columns of the following table.

A charged particle (electron or proton) is introduced at the origin 0, 0, 0x y z with a

given initial velocity v. A uniform electric field E

and a uniform magnetic field B

exist

everywhere. The velocity v, electric field E

and magnetic field B

are given in columns

1, 2 and 3 respectively. The quantities 0E , 0B are positive in magnitude. ( ˆ ˆ ˆ, &x y z are

units vectors along x, y and z axis)




Column-1 Column-2 Column-3

I) Electron with

0

0

ˆ2E

v xB

i)0 Ê E z

P)

0 ˆB B x

II) Electron with

0

0

Êv y

B

ii)0 Ê E y

Q)

0 ˆB B x

III) Proton with 0v

iii)0 Ê E x

R)

0 ˆB B y

IV) Proton with

0

0

ˆ2E

v xB

iv)0 Ê E x

S)

0 ˆB B z

16. In which case will the particle move in a straight line with constant velocity?

A) (III) (ii) (R) B) (IV) (i) (S) C) (III) (iii) (P) D) (II) (iii) (S)

17. In which case will the particle describe a helical path with axis along the positive ‘z’

direction?

A) (IV) (i) (S) B) (II) (ii) (R) C) (III) (iii) (P) D) (IV) (ii) (R)

18. In Which case would the particle move in a straight line along the negative direction of

y-axis (i.e., move along - y )

A) (II) (iii) (Q) B) (III) (ii) (R) C) (IV) (ii) (S) D) (III) (ii) (P)




CHEMISTRY Max. Marks: 61SECTION – I


19. The freezing point of 0.20 M solution of weak acid HA is 272.5 K. The molality of thesolution is 0.263 mol kg-1. Find the pH of the solution on adding 0.25 M sodium acetatesolution (Kf of water = 1.86 k kg/mol)

(A)5.4 (B)3.2 (C)6.1 (D)4 .11

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

(A)During electrophoresis, colloidal particles move under influence of electric field.

(B)Suspensions are opaque and they do not show tyndell effect.

(C)Higher is the coagulating power of an electrolyte, higher is its coagulation value.

(D)50 ml of standard gold sol needs 0.05 mg of gelation or 125 mg of starch, for itsprotection from coagulation by 1 ml, 10% Nacl solution, it means gold number of starchis more than that of gelation and is better protective agent than gelation.

21. Which of the following products is/are obtained when Cl2O reacts NH3.

(A) NO2 (B) N2 (C) NCl3 (D) NH4Cl

22. Incorrect order is/are

(A) He > Ar > Kr > Ne > Xe (Abundance in air)

(B) He < Ne < Ar < Kr < Xe (Boiling point)

(C) XeF6> XeF4> XeF2 (melting point)

(D) XeF6< XeF4< XeF2 (Xe –F bond length)

23. 603 2

Product(s)CKClO COOH , Products is/are

(A) 2ClO (B) 2 3K CO (C) 2CO (D) 2Cl O

24. Which of the following reaction is/are correct

(A) 5-Aminohept -3-en-2-one /H 2,5-Dimethyl pyrole

(B) 3,4-Epoxycyclohexanone /H Cyclohexane -1,4-dione

(C) Cyclohex -2-enone 2 2

2

1. /

2. /

H O NaOH

H O H Trans -2,3-dihydroxy cyclohexanone

(D) Phenol 2 /

1CH O NaOH

eqMajor product Polymerisation Novolac




25.

Correct statement (s) is /are

(A)Acidic hydrolysis of product ‘S’ is 4-Hydroxybutanal

(B)Product ‘R’ give dihydrofuran on heating with conc. H2SO4

(C)Product ‘S’ can reduce tollens reagent(D)Product R is a olefinichydrated product of compound T



26. Nitrogen gas adsorb on charcoal to the extent of 0.921 cm3 gm-1 at a pressure of 16 atmand 190k temp. But at 250k the same amount of adsorption was achieved only when thepressure was increased to 32 atm. What is the molar enthalpy of adsorption of N2 oncharcoal in Kcal.

27. The pyrolysis of an ester follows a first order process and its rate constant can be

expressed as42075

78.09InKT

where K is given in the min-1. The time required for

25% reaction to complete at 227 will be Z hr. Find Z (Use e-6.06 = 0.0023)

28. How many of the following statements are correct

(a) FeCl3, 6H2O actually exist as 2 2 25Fe H O Cl Cl .H O

(b) FeCl3 dissolves in H2O, ether & NH3

(c) Phosphine reduces AgNO3 to metallic Ag

(d) VO2 is an amphoteric oxide and in acidic medium it forms VO2+

(e) When H2O2 is added to alkaline solution of K2Cr2O7solution turns to yellowdue to formation of K2CrO4

(f) 22 8S O Oxidise Ag+ in presence of pyridine and give red colour compound

(g) 24MnO disproportionate to yield 4 2MnO & MnO in presence of H

ions

(h) Ti3+ is purple while Ti4+ is colourless

(i) The yellow colour of aqueous CuCl2 is due to 24CuCl

(j) TiCl4 gives white fumes in moist air




29. How many of the following give silver mirror with

Tollers reagent or AgNO3

Ph − CH = 0,Ph C CH PH

O OH, ,

Ph – NH − OH

PH3, Dihydroxyacetone, HCOOH, Zn, Heating only

30.

Degree of unsaturation in the product is


This section contains 6 questions of matching type. This section contains two tables (each having 3 columns and 4 rows). Based on Eachtable there are 3 questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of which ONLY ONE option can becorrect.Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.


Columns 1 contains integrated rate equation, Column 2 contains half-life andColumn 3 I contain graph corresponding to different order reactions, ‘a’ is initialconcentration of reactant and a - x is the concentration at time ‘t’

COLUMN-I COLUMN-II COLUMN-III

(I)1 1 1

kt a x a

(i) 1/2

at

2k (P)

(II)x

kt (ii) 1/2

0.693t

k (Q)

(III)2.303 a

k logt a x

(iii) 1/2

1t

ka (R)




(IV) 2 2

1 1 1k

2t aa x

(iv) 1/2 2

3t

2ka (S)

31. For the decomposition of HI on the surface of gold the only correct combination is

(A)(lll)(ii)(R) (B) (ll)(i)(P)

(C)(IV) (i) (P) (D) (I) (iii) (z)

32. For the reaction 2 5 2 2

12

2N O NO O , the only correct combination is

(A)(III) (ii) (Q) (B) (l)(iii) (P)

(C)(ll)(i)(S) (D) (IV)(i)(P)

33. For the reaction 2A→ Product. the rate equation is

r = k[A]2

Which of the following is the only correct combination for the reaction?

(A)(II) (iii) (P) (B) (ll)(iii)(S)

(C)(III) (i) (S) (D) (l)(iii)(R)


Column I Column II Column III

(I) (i) KBr/KOBr (P) Racemisation

(II) (ii) Heat (Q) Redox reaction

(III) (iii) Conc.H2SO4 (R) Dehydration

(IV) Phenol (iv)CH2= O excess

NaOH(S) Substitution




34. The only correct combination in which reaction proceeds through carbanion is

(A)(IV) (i) (S) (B) (III) (ii) (P)

(C)(I) (iv) (Q) (D) (II) (iii) (R)

35. The only correct combination that given two carboxylic acid

(A)(I) (i) (Q) (B) (III) (ii) (P)

(C)(II) (iv) (Q) (D) (IV) (iii) (S)

36. For the synthesis of polymer the only correct combination is

(A)(II) (iii) (R) (B) (IV) (i) (S)

(C)(IV) (iv) (S) (D) (I) (i) (Q)

MATHEMATICS Max. Marks: 61SECTION – I


37. Consider the system of equations:

log log 48a ax xyz ,

log log 12a ay xyz ,

log log 84, 0, 1a az xyz where a a ,

Then, which of the following may be correct?

A) 12xyz a B) 12xyz a C) 2x yz D) 2z a xy

38. Let N be the number of ordered pairs (p, q) of real numbers such that 2020p qi p qi ,

then sum of the digits of N is greater than or equal to

A) 1 B) 3 C) 5 D) 7

39. Let 1 2 3,z z and z be distinct complex numbers of equal modulus, such that

1 1 2 3z z z z , then

A) 2 3 0z z B) 2 32 0z z

C) 2 1

3 1

arg2 2

z zor

z z

D) 2 3

1 3

arg2 2

z zor

z z




40. Let 2 21 1,y x x x x x , then y may be equal to

A)2

B)

1

2 C)

2

3D)

5

4

41. Consider two real sequences 1 2 1 2, ,........and , ,.......x x y y defined as:

21 13 , 1n n nx x x x and 1 1 2

3 ,1 1

nn

n

yy y

y

for all 1n , then

A) Greatest integer less than or equal to n nx y is 1 for all n > 1

B) Greatest integer less than or equal to n nx y is 2 for all n > 1

C) Least integer greater than or equal to n nx y is 3 for all n > 1

D) Least integer greater than or equal to n nx y is 2 for all n > 1

42. Let A and B are two square idempotent matrices such that AB BA is a null matrix,

then the value of the det A B can be equal to

A) –2 B) –1 C) 0 D) 1

43. Let3 3ijA a

be a matrix. Given 21 12 23 32

31 13

6 4 4

10

4 8

TA A a a a a

a a

,

where 12 23 31, anda a a are the positive roots of the equation 3 26 8 0,x x px p R .

If k = det(A), then

A) A is a symmetric matrix B) A is a skew symmetric matrix

C) Number of prime factors of k is 2 D) Exponent of 10 in k is 6

[Note: TA denotes the transpose of matrix A]






44. If80

1

1( , ) ,

k

a b where a N b Nk

, then sum of digits of the sum Max Mina b is

45. Consider the sequence2 2

1 11 1 1 1 , 1nT n

n n

. The greatest prime

number less than or equal to the sum20

1

1

r rT is

46. Consider 2

2

4 10P t ,

4 5

t tt R

t t

and 2 2 6 41Q x x mx m , where x, m R .

If 54Q x P t x R , then number of integral values of m is

47. The smallest integral value of for which the inequality

2 25 51 log 1 log 4x x x holds true for all x R , is

48. If2

2

3 4,

3 4

t tt R

t t

, then the number of solutions of the system of equations

3 4 3, 2 3 2,6 5 3x y z x y z x y z for a particular value of is


This section contains 6 questions of matching type. This section contains two tables (each having 3 columns and 4 rows). Based on Eachtable there are 3 questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of which ONLY ONE option can becorrect.

Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.

Answer Q.No:49, Q.No:50, Q.No:51 by appropriately matching the information given inthe three columns of the following table.

Column 1 contain equation in terms of complex number zColumn 2 represents the sum of principle values of argument (in radian) of all possibleroots of equations given in Column 1Column 3 represents the modulus of possible roots of equations given in Column 1




Column– 1 Column– 2 Column– 3

(I) 2 1 0z z (i)2

(P) 2

(II) 4 , 0z iz z (ii)2

(Q) 1

(III) 3 2 2 0z iz i (iii) 0 (R) 2

(IV) 25 3 32 1,whereRe( ) 1z z z z z z (iv)

5

2

(S)

4

1

249. Which of the following is the only correct combination?

A) II-i-Q B) I-ii-Q C) III-i-P D) IV-ii-Q


A) II-iii-R B) I-iii-R C) III-iii-Q D) IV-iii-S


A) II-iii-S B) III-ii-Q C) III-i-S D) IV-i-S

Answer Q.No:52, Q.No:53, Q.No:54 by appropriately matching the information given inthe three columns of the following table.

Column 1 gives value of .Column 2 contain multiples of .Column 3 contain numbers, which are less than or equal to .

Column– 1 Column– 2 Column– 3

(I) The value of expression

227 32 625 9 4 4

log 9log 8 log 243 log 81 log 25 log 25 log 93 2 5 3 2 3 5 is (i) 12 (P) 2

(II) The value of x satisfying the equation

log 8 31010log7log 75ln52log

2 29, is

x

e

(ii) 45 (Q) 3

(III) The number2 6

1 1

log log

(where [.] is GIF) (iii) 30 (R) 4

(IV) Let 2 2

3 2 3 2log 4 log 9 log 4 log 9l and

653

log 5log 8m 0.8 1 9 then 1l

m

(iv) 20 (S) 5




52. Which of the following is the only incorrect combination?

A) II-i-S B) I-ii-P C) III-iv-P D) IV-ii-Q

53. Which of the following is the only incorrect combination?

A) II-iv-P B) I-i-P C) III-ii-Q D) IV-iv-S


A) II-ii-R B) I-iii-Q C) III-iv-R D) IV-i-S

09-04-20 sr.n-super chaina/n-chaina jee-adv uta-3

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