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FIITJEE INTERNAL TEST IIT – JEE 2018

PHASE – VI (CHAMPIONS)_PAPER – I

Time: 3 hours Maximum Marks: 264 INSTRUCTIONS:

A. General

1. This booklet is your Question Paper containing 60 questions.

2. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed to be carried inside the examination hall.

3. Fill in the boxes provided for Name and Enrolment No.

4. The answer sheet, a machine-readable Objective Response (ORS), is provided separately.

5. DO NOT TAMPER WITH / MULTILATE THE ORS OR THE BOOKLET.

B. Filling in the OMR:

6. The instructions for the OMR sheet are given on the OMR itself.

C. Question paper format:

7. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of two sections.

8. Section I contains 8 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

9. Section II contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

10. Section III contains 2 Match the following type questions and you will have to match entries in Column I with the entries in Column II

D. Marking Scheme

11. For each question in Section I, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect answers in this section.

12. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –2 marks will be awarded for incorrect answers in this section.

13. For each question in Section III, you will be awarded 2 marks for each entry in Column I; if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –1 marks will be awarded for incorrect answers in this section.

Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam.

NAME:

ENROLLMENT NO.:



PH-VI (Champions)-2018-P(I)-PCM-2

PAPER–I PART I: PHYSICS

SECTION 1 (Maximum Marks: 32) This section contains EIGHT questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. Marking scheme:

+4 If the bubble corresponding to the answer is darkened. 0 In all other cases.

1. A rectangular loop PQRS made from a uniform wire has length a,

width b and mass m . It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y –axis (see figure). Take the vertically upward direction as the z–axis. A

uniform magnetic field 0ˆ ˆB 3i 4k B

exists in the region. The

loop is held in the x–y plane and a current I is passed through it. The loop is now released and is found to stay in the horizontal

position in equilibrium. Find the ratio 0

mg

IB b

2. The current in the outer coil is varying with time as 2I 2t . If the resistance of the inner coil is R and b>>a then the heat developed

in the inner coil between t= 0 and t seconds is 2 2 4 30

2

4 a t

kb R

. Find k

3. A resistance circuit is constructed such that 12 resistance are to form a cube. Each resistor is of 2 . A battery of 30 volt is applied across the body diagonal of the cube. Find the current flowing through DC.

Space for rough work




4. Two resistance are measured in Ohm. 1R 3 1% , 2R 6 2%

When they are connected in parallel, maximum percentage error in equivalent resistance is . Find 3

5. Consider a cell of emf E and internal resistance r. The current drawn (i) from cell can be varied. Output power from cell is same when current drawn is 1i 2A and 2i 8A . For what value of current

the output power will be maximum. For question 6 and 7 Consider a hexagonal pyramid OABCDEF made by 12

straight wires each of resistance R. Centre of base of pyramid is P. 7 straight wires each of resistance R are connected between each vertex of pyramid and P. Whole arrangement is shown in figure. Answer the following two questions.

6. Equivalent resistance between vertex E and F is 1BR

A 5where B and A are positive integer then

find B–A

7. A battery of emf and internal resistance r is connected between P and O. The ratio between R and r

will result in maximum heat production from pyramid

8. A wire having current 3A is lying is x-y plane along curve 3x = y2. Find the magnitude of the force (in Newton) acting on the part of the wire

(OA) due to uniform magnetic field of magnitude B = 1 T directed at an angle 30° with x-axis.





SECTION 2 (Maximum Marks: 40)

This section contains TEN questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)

is (are) correct. For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS. Marking scheme:

+4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. 0 If none of the bubbles is darkened. –2 In all other cases

9. ABC is an equilateral triangle, of side length 0 and resistance 0R

at temperature 00 C , kept in uniform magnetic field 0B as shown

Temperature coefficient of linear expansion of wire is and

temperature coefficient of resistance of wire is R . Now the

temperature of the wire is slowly changed according to the equation

0T T sin t , where 0T is in 0 C . Given that R and

R 0 0T 1 & T 1 ). Choose the correct options (s).

(A) Amount of charge flown through the wire in the first quarter

cycle of temperature starting from t 0 is 2

0 00

0

3BT

2R

(B) Amount of charge flown through the wire in the first quarter

cycle of temperature starting from t = 0 is 2

0 00

0

3BT

4R

(C) Rate of heat production from wire at any time ‘t’ is 2 2 4 2 2

3 T 20 0 0

0

B T3e cos t

4 R

(D) Rate of heat production wire at any time

‘t’2 2 4 2 2

3 T 20 0 0

0

B T3e cos t

2 R





10. Four batteries of EMF 1 2 3E 4V,E 8V,E 12V and 4E 16V ,

four capacitors with the same capacitance 1 2 3 4C C C C 1 F ,

and four equivalent resistors each of resistanceR 1 are connected in the circuit shown in figure. The internal resistance of the batteries is negligible choose the correct option(s)

(A) In steady state current from the resistance connected between D and H is 3A

(B) In steady state current from the resistance connected between D and H is 2 A

(C) Total energy W accumulated on the capacitors when a steady of the system is established, will be 26 J

(D) Total energy W accumulated on the capacitors when a steady state of the system is established, will be 36 J

11. A parallel – plate capacitor is connected to a cell. Its positive plate A and its negative plate B have charges +Q and –Q respectively. A third plate C, identical to A and B, with charge +Q, is now introduced midway between A and B, parallel to them. Which of the following is/are correct ?

(A) The charge on the inner face of B is now 3Q

2

(B) There is no change in the potential difference between A and B. (C) The potential difference between A and C is one – third of the

potential difference between B and C

(D) The charge on the inner face of A is now Q

2





12. In the circuit shown in the figure, which one of following statement is correct ?

(A) If the switch S is closed, the time constant during charging is RC (B) IF the switch S is closed, the time constant during charging is

RC/2 (C) If the switch is opened again, the time constant during

discharging is 3RC (D) If the switch is opened again, the time constant during

discharging is RC /2

13. The conductor AB of mass 1 kg is sliding over two parallel

conducting rails separated by a distance of 1 m and is in a region

of inward uniform magnetic filed 0ˆB 0.1 k

. At time t=0, AB is

projected towards right with speed 0v .

(A) The velocity of AB as a function of time is given as t

6000v v e

(B) The velocity of rod becomes 0v

2 at t 600 n 2

(C) The induced current is 0vA

120 at t= 600 n 2

(D) The induced emf as a function of time is given as t

0 600v

e10





14. A charge Q is distributed over two concentric hollow spheres of radii r and R R r such that their surface densities are equal. Find the

potential a the common centre. (Given 0

1k

4

)

(A) kQ

R r (B)

2 2

kQ R r

R r

(C) kQ

r (D)

kQ

R

15. Electric and magnetic field are directed as 0ˆE i and 0

ˆB k , a particle

of mass m and charge +q is released from position (0,2,0) from rest.

The velocity of that particle at (x,5,0) is ˆ ˆ5i 12 j the value of x can

be

(A) 0

169m

2qE (B)

0

25m

2qE

(C) 25m

12qE (D)

0

144m

12qE

16. Two uniform concentric coil of radii 1r and 2r 1 2r r carry currents 1 2i and i respectively. if the

smaller coil is rotated slightly about one of its diameter it starts oscillating. Then choose the correct

statements

(A) The oscillations are simple harmonic in nature

(B) The frequency of oscillation is directly proportional to product 1 2i i

(C) The frequency of oscillation is directly proportional to square root of 2r

(D) The frequency of oscillation is independent of radius 1r





17. A vertical conducting ring of radius R falls vertically in a

horizontal magnetic field of magnitude B. The direction of B is perpendicular to the plane of the ring. When the speed of the ring is v,

(A) no current flows in the ring . (B) A and D are at the same potential

(C) C and E are at the same potential

(D) the potential difference between A and D is 2BRv, with D at a higher potential

18. A rectangular frame ABCD made of a uniform metal wire has a straight connection between E and F made of the same wire, AEFD is square of side 1 m and EB = FC = 0.5 m. The entire circuit is placed

in a steadily increasing uniform magnetic field directed into the plane of the paper and normal to it.

The magnetic field is cylindrical and perpendicular to the plane of frame ABCD with its centre lying on line EF. The rate of change of the magnetic

field is 1 TS–1 .The resistance per unit length of the wire is 1Ώm–1.

(A) Current in segment AE is 7/22 A from E to A

(B) Current in segment AE is 1/22 A from A to E (C) Current in segment BE is 6/22 A from B to E (D) Current in segment EF is 1/22 A from F to E





SECTION 3 (Maximum Marks: 16) This section contains TWO questions. Each question contains two columns, Column I and Column II Column I has four entries (A), (B), (C) and (D) Column II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column I with the entries in Column II One or more entries in Column I may match with one or more entries in Column II. The ORS contains a 4 5 matrix whose layout will be similar to the one shown below:

(A) (P) (Q) (R) (S) (T) (B) (P) (Q) (R) (S) (T) (C) (P) (Q) (R) (S) (T) (D) (P) (Q) (R) (S) (T)

For each entry in Column I, darken the bubbles of all the matching entries. For example, if entry (A) in Column I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS. Similarly, for entries (V), (C) and (D). Marking entry in Column I.

+2 If only the bubble(s) corresponding to all the correct match (s) is (are) darkened. 0 If none of the bubbles is darkened. –1 In all other cases.





19. Column I gives certain situations involving two thin conducting shells connected by a conducting wire via a key K. In all situations one sphere has net charge +q and other sphere has no net charge. After the key K is pressed, column II gives some resulting effect. Match the figures in column I with the statements in column II.

Column – I Column – II

(A)

Initially no net charge

K +q

Shell I Shell II

(p) Charge flows through connecting

wire

(B)

Initially no net charge

K

+q

Shell I

Shell II

(q) Potential energy of system of sphere

decreases.

(C)

K

+q

Initially nonet charge

Shell I

(r) No heat is produced

(D)

K

Initially nonet charge

Shell I

+q

Shell II

(s) The sphere I ahs no charge after

equilibrium is reached.

(t) None.





20. For the circuit shown in fig. cells are arranged . In column I, the cell number is given while in column II, some statement related to cells are given. Match the column I with column II.

10

Cell I

Cell II 2v 10

Cell III

Cell IV

1v 1 3v 3

2v 2

Column – I

Column – II

(A) Cell –I (p) Chemical energy of cell is decreasing

(B) Cell –II (q) Chemical energy of cell is increasing

(C) Cell –III (r) Work done by cell is +ve

(D) Cell –IV (s) Thermal energy developed in cell is +ve

(t) can’t be determined





PART II: CHEMISTRY

SECTION 1 (Maximum Marks: 32) This section contains EIGHT questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. Marking scheme:


21. Which o the following carboxylic acid on heating gives carbon dioxide?

O

COOH

O

COOHHOOCO

COOHCH3

COOH

O

COOHHOOC

HOC COOH

O

COOH

CH3

, ,,

,CN

COOH

COOH

COOH

CCl3 COOH

NO2

COOH

,,

,

22.

N(CH 3)3

CH3

+OH

-

major hydrocarbon product is

‘X’. number of hyperconjugable hydrogen atom in ‘X’ is? 23. The total number of tetrahedral voids in the face-centred unit cell is x . Find x .

24. ,235 207

8092x yP Qa b . Find the value of y .





25. A hydrogenation reaction is carried only at 500K. If the same reaction is carried out in presence of a catalyst at the same rate, the temperature required is 400K. If the catalyst lowers the activation barrier

by 20 kJ 1mol then the activation energy of the uncatalysed reaction is 1aE kJ mole . Find aE

20 value.

26. The rate constant for the thermal decomposition of 2 2H O aqueous solution is 3 13 10 min . At

what molar concentration of 2 2H O the rate of the reaction will be 4 12 10 ms .

27. The half life for a zero order reaction is equal to o

o

a

xk. Find ‘x’.

28. How many enantiomeric pairs are possible for glucose ?

SECTION 2 (Maximum Marks: 40) This section contains TEN questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)



29. Which of the following can give carbylamine test ?

(A) 256 NHHC (B) 223 CHNHCH (C) NHCH 23 (D) 23 NHCH

30. Select the correct statement(s): (A) the ionic crystal of AgBr has Schottky defect

(B) the unit cell having crystal parameters, a b c= ¹ , 90a=b= , 120g = is hexagonal

(C) in ionic compounds having Frenkel defect the ratio r r+ - is high

(D) the coordination number of Na+ ion in NaCl is 6 31. Choose correct statement(s) (A) no. of octahedral voids in fcc unit cell is 4 (B) units for rate constant of zero order are mol L–1 sec–1 (C) packing fraction of fcc is 0.74 (D) The numerical value of rate constant is unaffected by temperature.





32. In the nuclear transmutation, 8944Be X Be Y (X, Y) is (are)

P : Proton ; D : Deuterium; n : neutron (A) ,n (B) (p, D) (C) (n, D) (D) (, P)

33. A metal crystallizes into two cubic system FCC and BCC whose unit cell lengths are x and y Å

respectively. The ratio of densities of FCC and BCC is

(A) 3

3

2y

x (B)

3

3

4x

y (C)

2

2

2x

y (D)

3

2

4x

y

34. Distance between layers in FCC packing of edge length 7 3 Å :

(A) 7

Å3

(B) 7 3

Å2

(C) 7Å (D) 14

Å3

35. Which of the following statements are correct ? (A) D–Mannose is a C–2 epimer of D–glucose (B) D–Mannose is a C–3 epimer of D–glucose. (C) D–Gallactose is a C–4 epimer of D–glucose. (D) –D (+) glucopyranose and –D (+) glucofuranose are anomers. 36. Which of the following statements are correct ? (A) One mole of pHNHNH2 reacts with 3 mol glucose to form osazone. (B) One mole of D–fructose reacts with 3 mol PhNHNH2 to form osazone. (C) One mole of D–2–deoxy glucose reacts with 1 mol PhNHNH2 to form phenylhydrazone. (D) One mole of D–3–deoxy glucose reacts with 3 mol of PhNHNH2 to form osazone. 37. Which of the following are D–sugars ?

(A) HO

CHO

H

CH2OH

(B) HOH2C

H

CHO

OH

(C) H

OH

CH2OH

CHO

(D) HO H

CH2OH

CHO

HO H





38. For a reaction X Y, the rate law is Rate = k[A]1/2 which of the following statements are correct (A) Half life of the reaction is inversely proportion to the initial concentration. (B) Half life of the reaction is directly proportional to the square root of the initial concentration. z (C) The rate constant of the reaction is constant at a particular temperature for this reaction. (D) On increasing the concentration of the reactant 9 times ,the rate of reaction increases by 3 times

SECTION 3 (Maximum Marks: 16) This section contains TWO questions. Each question contains two columns, Column I and Column II Column I has four entries (A), (B), (C) and (D) Column II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column I with the entries in Column II One or more entries in Column I may match with one or more entries in Column II. The ORS contains a 4 5 matrix whose layout will be similar to the one shown below:




39. Match the following

Column – I(reduction) Column – II(atomicity of the main product)

(A) C6H5NO2 AcidSn (P) 15

(B) 2C6H5NO2 4LiAlH (Q) 24

(C) 2C6H5NO2 KOH.alcZn (R) 14

(D) C6H5NO2 ZnClNH4 (S) 26





40. In a Fcc unit cell of edge length A

Column – I (distance from a lattice point)

Column – II (No. of neighbours)

(A) A

2 (P) 12

(B) 3

A2

(Q) 6

(C) 2A (R) 8

(D) 3A (S) 24

PART III: MATHEMATICS SECTION 1 (Maximum Marks: 32)

This section contains EIGHT questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. Marking scheme:


41. Let d

dx(x2y) = x – 1, where x 0 and y = 0 when x = 1. Find the smallest natural x for which

dy

dx is

positive.

42. Suppose 2

7 2 7

1 7cos x g(x)dx C

sin xcos x sin x

, where C is an arbitrary constant of integration. Then find the

value of g(0) + g4

.





43. Let f(x2) = 1

x for x > 0, f(1) = 1 and g(sin2x – 1) = cos2x + p x R, g(–1) = 0. If h(x) =

f(x), x 0

g(x), 1 x 0

is a continuous function, then find the absolute value of 2p.

44. If F(x) = 2 2 2

2 3 4 5 6

1 x 1 x x 1 x x x

1 2x 3x 4x 3x 2x x

dx, then find the value of [F(99) – F(3)].

(Note: [k] denotes the greatest integer less than or equal to k)

45. Given that Un = (x (1 – x))n and n 2 and 2

n2

d U

dx= n(n – 1)Un – 2 – 2n (2n – 1)Un – 1, further if Vn =

1x

n0

e U dx , then for n 2, we have Vn + K1n (2n – 1) . Vn – 1 + K2 n(n – 1) Vn – 2 = 0. Find (K1 + K2)

46. If the value of the definite integral

21

1 1

2 x21

a b1 xcot cot dx

c1 x 1 x

, where a, b,

c N in their lowest form, then find the value of (a + b + c).

47. Let f: (0, 1) (0, 1) be a differentiable function such that f(x) 0 for all x (0, 1) and 1 3

f2 2

. If

f(x) =

t x

2 2

0 0

t x

1 f s ds 1 f s ds

limf(t) f(x)

, then the value of

1f

4

equals m

4 where m N. find the

value of m.

48. Let I = 1

9950 100

0

1 x x dx and J = 1

10050 100

0

1 x x dx . If I

J is equal to

m

n where m and n are co-

prime then find the value of m n 1

20

.





SECTION 2 (Maximum Marks: 40) This section contains TEN questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)



49.

1tan x 221 2 1

22

e 1 xsec 1 x cos

1 x1 x

dx (x > 0)

(A) 1tan x 1e tan x C (B)

1 2tan x 1e tan xC

2

(C) 12

tan x 1 2e sec 1 x C

(D) 12

tan x 1 2e cosec 1 x C

50. Let f(x) be a cubic polynomial with leading coefficient unity such that f(0) = 1 and all the roots of f(x) =

0 are also roots of f(x) = 0. If f(x) dx = g(x) + C, where g(0) = 1

4 and C is constant of integration, then

g(3) – g(1) is equal to (A) 27 (B) 48 (C) 60 (D) 81 51. sin x . cos x . cos 2x . cos 4x . cos 8x . cos 16x dx equals

(A) sin16x

C1024

(B) cos32x

C1024

(C) cos32x

C1096

(D) cos32x

C1096

52. Which of the following definite integral (s) has / have their value equal to atleast one of the remaining

three ?

(A) 4

0

xdx

1 x

(B)

/ 4

0

xdx

cos x cosx sinx

(C)

1 522

4 21

x 1 1ln 1 x dx

xx x 1

(D) 1 1

0

sin xdx

x





53. Let f(x) = 2

x 1, 0 x 1

2x 6x 6, 1 x 2

and g(t) =

t

t 1

f(x) dx for t [1, 2]. Which of the following hold(s)

good ?

(A) f(x) is continuous and differentiable in [0, 2] (B) g(t) vanishes for t = 3

2 and 2

(C) g(t) is maximum at t = 3

2 (D) g(t) is minimum at t = 1

54. Let f(x) = x

t t

0

e dt (x > 0), where [x] denotes greatest integer less than or equal to x, is

(A) continuous and differentiable x (0, 3] (B) continuous but not differentiable x (0, 3] (C) f(1) = e (D) f(2) = 2(e – 1)

55. Let I = 1

0

1 x

1 x

dx and J = 1

0

1 x

1 x

dx, then the correct statement is

(A) I + J = 2 (B) I – J = (C) I = 2

2

(D) J =

4

2

56. Let f: R (0, ) be a real valued function satisfying x

0

tf x t dt = e2x – 1, then which of the following

is (are) correct ?

(A) The value (f–1) (4) equals 1

8

(B) Derivative of f(x) with respect to ex at x = 0 is equal to 8

(C) The value of x 0

f(x) 4lim

x

equals 4

(D) The value of f(0) is equal to 4





57. Which of the following definite integral vanishes ?

(A) 2 3 4 5cos2x cos2 x cos2 x cos2 x cos2 x dx

(B) 1

2

1

ln x x 1 dx

(C) 1

12

0

2x 1tan dx

1 x x

(D) / 2

0

ln tanx dx

58. If f() = |||3 cos – sin | + 2 cos | + cos | where ,2

, then

(A) / 2

f( ) d 1

(B) 5 3

f6 2

(C) 2

/ 2

f4

(D)

2 1f

3 2


This section contains TWO questions. Each question contains two columns, Column I and Column II Column I has four entries (A), (B), (C) and (D) Column II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column I with the entries in Column II One or more entries in Column I may match with one or more entries in Column II. The ORS contains a 4 5 matrix whose layout will be similar to the one shown below:








59. Let fn(x) + fn(y) = n n

n n

x y

x y

for all x, y R – {0} where n N and g(x) = max {f2(x), f3(x),

1

2}, x R –

{0}. Column I Column II

(A) The possible value (s) of 2k 2k

k 1 k 1

f cosec f sec

where

k

2

, k I is/are

p. 1

(B) The value(s) of n for which h(x) = fn(x) sgn x is even, is/are q. 2 (C)

Values of consecutive integers between which, 2

1/ 2

g(x) dx lie are r. 3

(D) Number of values of x for which the function y = g(x) x R – {0} is non-differentiable, is/are

s. 4

60.

Column I Column II(A) Let f(x) is a continuous function. If f(1) = 1 and

x

1 2

0

1t f 2x t dt tan x

2 , then the value of

2

1

4 f(x) dx is equal to

p. 1

(B) Let f(x) =

2009

r 1

x r

, then the value of the definite integral 2009

1

f(x) dx

is equal to

q. 2

(C) If

ln10 x x

x0

e e 1

e 8

dx has the value equal to (a – b), then

a

b equals

r. 3

(D) Suppose g is the inverse function of a differentiable function f and

G(x) =1

g(x). If f(4) = 2 and f(4) =

1

16, then (G(2))2 equals

s. 4






PHASE – VI (CHAMPIONS)_PAPER – II

Time: 3 hours Maximum Marks: 240

INSTRUCTIONS:

A. General

1. This booklet is your Question Paper containing 60 questions.

6. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed to be carried inside the examination hall.

7. Fill in the boxes provided for Name and Enrolment No.

8. The answer sheet, a machine-readable Objective Response (ORS), is provided separately.

9. DO NOT TAMPER WITH / MULTILATE THE ORS OR THE BOOKLET.

B. Filling in the OMR:

6. The instructions for the OMR sheet are given on the OMR itself.

C. Question paper format:

7. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of two sections.

8. Section I contains 8 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

9. Section II contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

10. Section III contains 2 paragraphs type questions. Each paragraph describes an experiment, a situation or a problem. Two multiple choice questions will be asked based on this paragraph. One or more than one option can be correct.

D. Marking Scheme

11. For each question in Section I, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect answers in this section.

12. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –2 marks will be awarded for incorrect answers in this section.

13. For each question in Section III, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –2 marks will be awarded for incorrect answers in this section.

Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam.

NAME:

ENROLLMENT NO.:




PAPER – II PART I: PHYSICS

SECTION 1 (Maximum Marks: 32) This section contains EIGHT questions The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive

For each question, darken the bubble corresponding to the correct integer in the ORS Marking scheme:

+4 If the bubble corresponding to the answer is darkened

0 In all other cases 1. Two cells of emf 1 2 2 1and are joined as shown in figure

When a potentiometer is connected between X and Y it balance for 300 cm length against 1 . On connecting the same potentiometer

between X and Z it balance for 100 cm length against 1 2and .

Find possible number of integer value(s) of 2

1

2

.

2. Magnetic field at point P is zero. If current 1I is equal to XA.

Then find the value of X.





3. Twelve infinite long wire of uniform linear charge density () are passing along the twelve edges of a cube. If electric flux through

any force of cube is 0n

. The value of n is

4. A conducting loop made of thin, light thread has a soap film inside and outside it. Length of thread is , total resistance is R, and initially area enclosed by it is

2

A8

. It is kept in a uniform magnetic

field B directed inwards and than a small puncture is made in inner film. If total charge flown through the loop after the

puncture is 2B

n R

. Then value of n is

5. A point charge +q is placed on the axis of closed cylinder of radius

R and length 25R

12 as shown. If electric flux coming out from the

curved surface of cylinder is 0

xq

10, then calculate x.





6. Given circuit is in steady state. Potential energy stored in the capacitors is U. now switch S is closed. Heat

produced after closing the switch S is H. Find U

H

7. Gravitational acceleration is ˆg gj

. Uniform magnetic field

exists in the region given by 0ˆB B k

. A charge particle

having mass 0m and charge 0q is fixed at one end of the

string of length . Another end of the string is fixed at point O. Particle can perform circular motion in vertical plane with respect to O. The particle is given a velocity 0v

perpendicular to the length of the string at the bottom most position. Minimum value of 0v so that particle performs

complete vertical circle is given by 35 m/ s . Here is

an integer. Find (given 0 0

0

q B3SI unit, g 10 SI unit

m

)

8. If a point charge q is placed at origin, then flux through a triangle with corners at 0,0,2 ; 0,3,0 and

(1,0,0) is found to be 0

q

2k. Find k.






This section contains EIGHT questions Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)

is(are) correct For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS

Marking scheme: +4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened

0 If none of the bubbles is darkened

–2 In all other cases

9. Consider a perfectly conducting uniform disc of mass m and radius

‘a’ hinged in vertical plane from its centre and free to rotate with respect to hinge. A resistance R is connected between centre of the disc and periphery by using two sliding contact 1 2C & C . A long non

conducting massless string is wrapped around the disc, whose another end is attached with a block of mass m. There exist a uniform horizontal magnetic field B. Whole arrangement is shown in the figure.

Given system is released from rest at t=0. Assume friction between string and disc is sufficient so that there is no slipping between them . Let at any time t, velocity of block is v, angular velocity of disc and current in resistance is i.

(A) From the energy equation 2dv dmgv mv I i R

dt dt

(B) The work done by the magnetic field is zero but it converts some part of the mechanical energy into heat

(C) The velocity v, of the block a function of time is tv 1 e

(D) The acceleration of the block is tge

3





10. Consider the given arrangement of resistance and on ideal

battery on shown Choose the correct option(s) regarding current through resistance

3R

(A) If 31

2 4

RR

R R , current in 5R will be from A to B

(B) If 31

2 4

RR

R R , current in 5R will be from B to A

(C) If 31

2 4

RR

R R , current in 5R will be from A to B

(D) If 31

2 4

RR

R R , current in 5R will be from B to A

11. Consider a uniformly charged sheet ABCD, which is a part of an equilateral triangular sheet of side a as shown in figure.

Choose the correct option(s) regarding the intensity of

electric E

at point O due to this sheet

(A) Magnitude of E

, increase with the increase in a (keeping charge density same)

(B) Magnitude of E

, decreases with the increase in a (keeping total charge same)

(C) if charge density is and a = 1m, magnitude of E is

equal to 0

7n 2

44

(D) If charge density is and a= 2m magnitude of E is

equal to 0

7n 2

22





12. A charged particle (+q) is moving simple harmonically on the x– axis with its mean position at origin. Amplitude of the particle is A and its angular frequency is

(A) The magnitude of magnetic field at (2A,0) will change periodically with period 2 /

(B) The maximum magnitude of the magnetic field at (0,A) is

0 q.

4 A

(C) The magnitude of magnetic field at (A,A) at the moment the

particle passes through A

,0 ,2

will be 03. q

5 5 A

(D) The magnitude of magnetic field at (0,A) and (0,–A) will be same at any time.

13. A point charge having mass m charge +q is revolving around a fixed point –Q in elliptical orbit of semi major axis ‘a’ under the action of their mutual electrostatic interaction force only choose the correct option(s).

(A) Total energy of the system is kQq

a

(B) Total energy of the system is kQq

2a

(C) Time period of one revolution is 3

2m

2 akQq

(D) Time period of one revolution is 3

2m

akQq





14. A long co–axial cable carries a uniform volume charge density on inner cylinder and uniform surface charge

density on outer cylinder. If radius of inner cylinder is ‘a’ and radius of outer cylinder is ‘b’. It is found that this infinite cable is electrically neutral then which of the following is/are correct.

(A) 2

02ab

(B)

20

2ba

(C) Electric field outside the cable increases linearly with radial distance (D) Electric field will be zero outside the cable

15. Consider an imaginary cube of side ' ' as shown in figure. An infinite large sheet of surface charge density passes through

PQGF. P and Q are mid points of AB and DC respectively. Out of six faces of cube he electric flux linked.

(A) is zero with three faces (B) with face ADHE and face BCGF are equal (C) is minimum (non zero) with FGHE (D) is zero with two faces

16. Two point charges 1q and 2q , each of same mass are kept on x and y

– axis respectively in gravity free space, such that they are constrained to move on x–axis and y –axis respectively. They are released from their initial position as shown in fig. (Given that 0 0y x )

Considering only electrostatic interaction between the charges at any instant, (neglect gravity) choose the correct option(s).

(A) Magnitude of net external force acting on the system of 2 charges at any instant is equal to the magnitude of electrostatic force between the charges

(B) Magnitude of net external force acting on the system of 2 charges at any instant is greater than the magnitude of electrostatic force between the charges

(C) Both the charges will reach at origin simultaneously (D) 1q will reach at origin first.





SECTION 3 (Maximum Marks: 16) This section contains TWO paragraphs

Based on each paragraph, there will be TWO questions Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)

is(are) correct For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS

Marking scheme: +4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened

0 If none of the bubbles is darkened

–2 In all other cases

Paragraph – 1 Consider a long conducting rail, separation

between track is , fixed in uniform magnetic field B directed normal to the plane of rail tracks and shunted by an uncharged capacitor of capacitance C. A conducting rod of mass m, given velocity 0V and then kept

gently and symmetrically on tracks as shown. Neglect any resistance (i.e. of track and conducting rod) and any friction between rod and track. (Use: 2 2B C 2m )

Answer the following 2 questions based on the given arrangement.

17. Final velocity of rod is

(A) 0V (B) 0V

2 (C) 0V

3 (D) 0V

4

18. Total energy loss is

(A) 0 (B) 20

1mV

8 (C) 2

0

1mV

3 (D) 2

0

13mV

32





Paragraph – 2

Consider the given arrangement of vary large no. of identical capacitors, each of capacitance c.

All the switches are initially opened and all capacitor are initially uncharged

All the switches are closed simultaneously Answer the following question based on the

above arrangement

19. The equivalent capacitance between the points A and B is

(A) 5 1

C2

(B) 5 1

C2

(C) 5 1 C (D) 5 1 C

20. Total heat loss after closing all the switches is

(A) 20

5 1CV

2

(B) 20

5 1CV

4

(C) 20

5 1CV

4

(D) 205 1 CV

PART II: CHEMISTRY SECTION 1 (Maximum Marks: 32)

This section contains EIGHT questions The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive For each question, darken the bubble corresponding to the correct integer in the ORS Marking scheme: +4 If the bubble corresponding to the answer is darkened 0 In all other cases 21. The number of esters formed in the following reaction is

OH

O

+ CH3

H

DOHCon.H2SO4





22.

H

OBr2 (1 eq)/OH-

Product.

Find the total number of products. (Including stereoisomers)

23. HO

3 2CH CH O PhCH CH O

mixture of aldols fractional distillation (A) products. What

is A.

24. The total number of carboxylic acid groups in the product P is

O

O

O

O

O

1. H3O+,

2. O3

3. H2O2

P

25. A compound with molecular mass 180 is acylated with CH3COCl to get a compound with molecular

mass 390. The number of amino groups present per molecule of the former compound is : 26. The concentration of R in the reaction R P was measured as a function of time and the following

data is obtained : [R] (molar) 1.0 0.75 0.40 0.10 t(min.) 0.0 0.05 0.12 0.18

The order of the reaction is

27. The number of neutrons emitted when 23592 U undergoes controlled nuclear fission to 142

54 Xe and 9038 Sr is

28. Number of optical active primary amines are possible for the formula C4H11N?

SECTION 2 (Maximum Marks: 32) This section contains EIGHT questions Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)

is(are) correct For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS Marking scheme: +4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened 0 If none of the bubbles is darkened –2 In all other cases





29. A mixture of two aromatic compounds (A) and (B) was separated by dissolving in chloroform followed

by extraction with aqueous KOH solution. The organic layer containing compound (A), when heated with alcoholic solution of KOH produced a compound (C) (C7H5N) associated with an unpleasant odour. The alkaline aqueous layer on the other hand, when heated with chloroform and then acidified, gives a mixture of two isomeric compounds (D) and (E) of molecular formula C7H6O2. Identify the compounds (A), (B), (C), and (D)

NH2

(A) :

OH

(B) :

N = C

(C) :

OH

CHO

(D) :

30. Which of the following statements is correct? (A) Replacement of halogen by NH2 in alkyl halide is a nucleophilic substitution reaction (B) Ary halides show more reactivity as compared to alkyl halides in the replacements of halogen by

the NH2 group (C) During the replacement of halogen by —NH2 group, ammonia is taken in large excess so as to

avoid the formation of 2° and 3° amines (D) Tertiary alkyl halide generally produces alkene instead of the replacement of halogen by NH2

group. 31. Identify compound (A) in the following oxidation reaction.

(A) 2 2 7 2 4K Cr O , H SOO O

(A)

NH2

NH2

(B)

NH2

OH

(C)

OH

OH

(D) None of these

32. Rate constant k varies with temperature by eqn:

log k (min–1) = 5– 2000 K

T. We can conclude

(A) pre-exponential factor A is 5 (B) Ea is 2000 kcal (C) pre-exponential factor A is 105 (D) Ea is 9.212 kcal





33. Which of the following statements is/are correct

(A) I– is a weaker base than F– (B) HO

is a stronger base H2N

(C) HONH2 is a weaker base than NH3 (D) F3C:– is a stronger base than Cl3C:– 34. Which of the following statements is/are not correct? (A) Maleic acid is a stronger acid than fumaric acid but maleate monoanion is a weaker acid than

fumarate monoanion (B) Maleic acid is a stronger acid than fumaric acid and also maleate monoanion is a stronger acid

than fumarate monoanion (C) Maleic acid is a weaker acid than fumaric acid but maleate monoanion is a stronger acid than

fumarate monoanion (D) Maleic acid is a weaker acid than Fumaric acid and also maleate monoanion is a weaker acid

than fumarate monoanion. 35. An organic compound A upon reacting with NH3 gives B. On heating, B gives C. C in presence of

KOH reacts with Br2 to give CH3CH2NH2. A is : (A) CH3CH2CH2COOH (B) CH3–CH(CH3)–COOH (C) CH3CH2COOH (D) CH3COOH 36. Which of the following is/are weaker base(s) than aniline in aqueous solution?

(A) NH2

F

(B)

NH

CH3

O

(C) NH2

CH3

(D) CH2NH2

SECTION 3 (Maximum Marks: 16) This section contains TWO paragraphs Based on each paragraph, there will be TWO questions Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)






Paragraph–1 Consider the two sequence of reaction

(H2C)5

NH2

NH2

A BI. SeH+

2NaNO / HClNaOH

D E COOH

NH2

II.

37. The compound B may be (A) Pyridine (B) Piperidine (C) Pyrrole (D) All 38. The product E is

(A) (B)

OH

(C) Acetone (D)

Paragraph–2 Ozone is prepared in laboratory by passing silent electric discharge through pure and dry oxygen in an apparatus known as ozoniser. This conversion from oxygen to ozone is a reversible and endothermic reaction. When oxygen is subjected to an ordinary electric discharge, most of the O3 produced will get decomposed. When any insulating material such as glass, is inserted in the space between the two electrodes and high current density is applied, silent electric discharge passes on between the two electrodes. By this process no spark is produced and much less heat is generated, and as a result the decomposition of the produced ozone is much retarded. The decomposition of ozone is believed to occur by the following mechanism:

K f

3 2KbO O O (fast step)

K13 2O O 2O (slow)

39. Order of the reaction is (A) 1 (B) 2 (C) 3 (D) 0 40. When the concentration of O3 is increased, for the same concentration of oxygen, its rate (A) increases (B) decreases (C) remains the same (D) cannot be answered





PART III: MATHEMATICS SECTION 1 (Maximum Marks: 32)

This section contains EIGHT questions The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive For each question, darken the bubble corresponding to the correct integer in the ORS Marking scheme: +4 If the bubble corresponding to the answer is darkened 0 In all other cases

41. (logex) sin–1x dx = P(x) 2

2 xe e 2

1 1 x1 x log 1 Qlog C

1 1 x

, then Q +

3

2=

42. 1 1 13 x x xsin 2tan dx Pcos Qsin 2cos C

3 x 3 3

, then P + 2Q is

43.

7 / 6 17 / 6 3 2

1/ 2 1/ 31/ 3 1/ 22 2

tan tan d y yP y Qlog 1 y C

3 2tan sec tan tan sec tan

, where y =

1/ 61

tan 1tan

, then find P + Q.

44. If 1 2

4 22

d

1

= I and the value of

11 2

23 22 1

2

x dx dx

1x 1 x x 11 xx

= –k I, then k =

45. If I1 = 7 / 25 / 21

0

x 1 xdx

12

, I2 =

7 / 25 / 21

80

x 1 xdx

3 x

, and I1 = k 108 3 I2, then k =

46. If x x x x

0 x x x

logsin dx log cos sin d log cos sin d log cos2 sin2 d2 2

+ 3x log 2 =

0, then x

0

logsin8 d =





47. Let g be a differentiable function satisfying x

4 2

0

x t 1 g(t) dt x x for all x 0. The value of

1

0

8 12dx

g (x) g(x) 10 =

48. The value of t for which

/ 2

0

/ 22

0

sinx tcos x dx

sinx tcos x dx

is


This section contains EIGHT questions Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)

is(are) correct For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS Marking scheme: +4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened 0 If none of the bubbles is darkened –2 In all other cases 49. Let g(x) be non–constant twice differentiable function defined such that y = g(x) is symmetric about

the line x = 2 and I1 = g x 2

sin x dx; I2 = 1

g (x)0

1

1 e dx

(A) I1 = 0 (B) I1 < I2 (C) I1 > I2 (D) I2 = 2

50. For 0 < a < 1, –1 < x < 1. Let f(x) = a x

1 ax

and If 6a

20

1 f(x)

1 x

dx = f(a), then

(A) f(a) is an even function (B) f(a) is an odd function

(C) f(1) = 23

15 (D) f(1) =

8

15

51. I1 = e

100

e1

1 x x log x dx and I2 = 1

/ 2101

e1

sine

1 esinx log sinx cos x

dx. If I1 +

101

2

e 1 e keI

101 101

, then k is greater than or equal to

(A) 0 (B) 1 (C) 2 (D) –1





52. I = 1

0

k x cos x dx where k is any real number, then the value of I is

(A) 2

2

, if k 0 (B) 2

2

if k 1 (C) 0 if 0 < k < 1 (D)

2

2

if k = 1

53. If I =

/ 2

20

dx

1 tanx

, then

(A) I < 1 (B) I is a rational number (C) I is irrational number (D) none of these

54. I1 = / 4

cot x

0

tanx dx

, I2 = / 4

tanx

0

cot x dx

, I3 = / 4

tanx

0

tanx dx

, I4 = / 4

cot x

0

cot x dx

(A) I1 < I3 (B) I2 < I4 (C) I1 < I4 (D) I3 < I2

55. The value of

2 /3

34 / 3

1 sinxd sinx

1 sinx

(A) 1 3sin 1 sinx c (B) 1 3sin sinx c

(C) 3 2

1

3

1 sin x 1tan c

2 2 sinx

(D) 3

11 sinxtan c

2 2

56. 3 22 x logx 2xe dx Ae c

, then the value of A is

(A) 1

2 (B)

1

6 (C)

1

3 (D)

1

5





SECTION 3 (Maximum Marks: 16) This section contains TWO paragraphs Based on each paragraph, there will be TWO questions Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s)


Paragraph–1 L1 is a line intersecting x and y axis at P(a, 0) and Q(0, b). L2 is a line perpendicular to L1 intersecting x and y

axis at R and S respectively 57. Locus of the point intersection of the line PS and QR is a circle with

(A) centre at a b

,2 2

(B) ax + by = 0 as a tangent

(C) a and b as the intercepts on x-axis and y-axis respectively

(D) radius equal to 2 21a b

2

58. Common chord of the circles on QS and PR as diameters passes through the point (a, b) if (A) a = 2b (B) 2a = b (C) a = b (D) a = –b

Paragraph–2 A(3, 7) and B(6, 5) are two points, C: x2 + y2 – 4x – 6y – 3 = 0 is a circle. 59. The chords in which the circle C cuts the members of the family S of circles through A and B are

concurrent at

(A) (2, 3) (B) 23

2,3

(C) 23

3,2

(D) (3, 2)

60. Equation of the member of the family S which bisects the circumference of C is (A) x2 + y2 – 5x – 1 = 0 (B) x2 + y2 – 5x + 6y – 1 = 0 (C) x2 + y2 – 5x – 6y – 1 = 0 (D) x2 + y2 + 5x – 6y – 1 = 0






PHASE – VI (CHAMPIONS)_PAPER – I

ANSWERS

PHYSICS

1. 6 2. 3 3. 3 4. 4

5. 5 6. 5 7. 4 8. 3

9. A,C 10. A,C 11. A,B,C,D 12. A,C

13. A,B,C,D 14. B 15. A 16. A,D

17. A,C,D 18. ACD 19. A–p,q, B– p,q , C– p,q,s, D– r,s

20. A–q,s,B–p,r,s, C–p,r,s, D– q,s

CHEMISTRY

21. 7 22. 1 23. 8 24. 2

25. 5 26. 4 27. 2 28. 8

29. A, B, D 30. A, B, D 31. A, B, C 32. A, B

33. A 34. C 35. A, C 36. B, C, D

37. A, B, D 38. B, C, D

39. A r; B q ; C s ; D p

40. A p ; B s ; C p ; D r

MATHEMATICS

41. 2 42. 5 43. 3 44. 3

45. 2 46. 5 47. 6 48. 7

49. C 50. C 51. B 52. BC

53. BCD 54. BD 55. BD 56. ABD

57. ABCD 58. ABCD 59. A q,r,s; B p, r; C q, r; D r

60. A r; B Bonus; C s; D p





PHASE – VI (CHAMPIONS)_PAPER – II

ANSWERS

PHYSICS

1. 0 2. 2 3. 1 4. 8

5. 5 6. 0 7. 9 8. 1

9. A,B,C 10. B,C 11. A 12. A, B

13. C 14. ABCD 15. BCD 16. B

17. C 18. C 19. Bonus 20. Bonus

CHEMISTRY

21. 1 22. 2 23. 6 24. 2

25. 5 26. 0 27. 3 28. 2

29. A,B,C,D 30. A, C, D 31. A,B,C 32. C,D

33. A, C, D 34. B,C,D 35. C 36. A, B, C

37. A 38. B, D 39. A 40. A

MATHEMATICS

41. 2 42. 0 43. Bonus 44. Bonus

45. 8 46. 0 47. 2 48. Bonus

49. AB 50. Bonus 51. ABD 52. Bonus

53. AC 54. ABCD 55. C 56. Bonus

57. ABCD 58. CD 59. B 60. C

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