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FIITJEE INTERNAL TEST IIT – JEE 2018

PHASE – VIII (Champions)_PAPER – I Time: 3 hours Maximum Marks: 183

INSTRUCTIONS:

A. General

1. This booklet is your Question Paper containing 54 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 & Marking Scheme

7. Each part has three sections as detailed in the following table:

Section Question Type

Number of Questions

Category wise Marks Each Question Maximum marks of the section

Full Marks Partial Marks Zero Marks Negative Marks

1

One or more correct option (s)

7

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

+1 For darkening a bubble corresponding to each correct option, provided NO incorrect option is darkened

0 If none of the bubbles is darkened

–2 In all other cases

28

2

Single digit integer (0–9)

5

+3 If only the bubble corresponding to the correct answer is darkened.

––– 0 In all other cases

––– 15

3

Single correct option

6

+3 If only the bubble corresponding to the correct option is darkened

––– 0 If none of the bubbles is darkened


18

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-VIII (Champions)-2018-P(I)–PCM-2

PAPER–I

PART I: PHYSICS SECTION 1 (Maximum Marks: 28)

This section contains SEVEN questions.

Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are) correct.

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

For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will get +4 marks; darkening only (A) and (D) will get +2 marks; and darkening (A) and (B) will get –2 marks, as a wrong option is also darkened.

1. A body is floating in a liquid in a beaker. If the whole system is projected at an angle with the

horizontal with initial velocity u, the upthrust on the body due to the liquid is (A) zero (B) equal to the weight of liquid displaced (C) equal to the weight of the immersed portion of the body (D) None of these 2. n drops of a liquid, each with surface energy E, join to form single drop (A) Some energy will be released in the process (B) Some energy will be absorbed in the process

(C) The energy released or absorbed will be 2/ 3E n n

(D) The energy released or absorbed will be 2/3nE 2 1

3. Photoelectric effect supports quantum nature of light because (A) There is a minimum frequency of light below which no photoelectrons are emitted (B) The maximum kinetic energy of photoelectrons depends only on the frequency of light and not on

its intensity (C) Even when the metal surface is faintly illuminated the photoelectrons leave the surface

immediately (D) Electric charge of the photoelectrons is quantised.

4. Which of the following is a incorrect statement ?

(A) particles are same as cathode rays

(B) - rays are high energy neutrons

(C) particles are singly ionized helium atom

(D) particles are same as cathode rays

Space for rough work




5. Consider a case of thin film interference as shown. Thickness of film is equal to wavelength of light in 2

.

(A) Reflected light will be maxima if 1 < 2

< 3

(B) Reflected light will be maxima if 1 < 2

> 3

(C) Transmitted light will be maxima if 1 > 2

> 3

(D) Transmitted light will be maxima if 1 > 2

< 3

6. The figure shows a ray incident at an angle i = / 3 . If the plot drawn shown the variation of | r – i |

versus 1 2/ = k, (r = angle of refraction)

(A) the value of k1 is 2/ 3 (B) the value of 1 / 6

(C) the value of 2 / 3 (D) the value of k2 is 1

. 7. In the figure shown a point object O is

placed in air on the principal axis. The radius of curvature of the spherical surface is 60 cm. If is the final image

formed after all the refractions and reflections

(A) If d1 = 120 cm, then the ‘If’ is formed on ‘O’ for any value of d2.

(B) If d1 = 240 cm, then the ‘If’ is formed on ‘O’ only if d2= 360 cm.

(C) If d1 = 240 cm, then the ‘If’ is formed on ‘O’ for all values of d2.

(D) If d1 = 240 cm, then the ‘If’ cannot be formed on ‘O’.

SECTION 2 (Maximum Marks: 15) This section contains FIVE 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 the ORS.

8. Consider a hypothetical atom having atomic number z= 2. It has two electrons each having mass m.

Assume that both electrons always lie diametrically opposite and nucleus of atom contains two

proton. Assume Bohr model is applicable. If the radius of first orbit of this atom is 15

pmn

(upto one

decimal place in pm), Find the value of n 2 0

0

2

hgiven 1.65A

me





9. A point source of source of light S is kept on

the axis of a cone of radius r and height h as shown in the figure. The inner surface of cone is made reflecting. If the minimum value of semi vertical angle in degrees of

the cone is n 15 , for which the rays

emitted from source (s) on the axis of the cone will be reflected from conical surface not more than once. Find the value of n.

10. A radioactive sample has decay constant . The rate of production of nuclei in the given sample as

2

09 N

N

, where

0N is the number of radioactive nuclei in the sample at t= 0 and N is the number of

radioactive nuclei in the sample at time t= t sec. If the number of nuclei present in the radioactive

sample at t is 6m 10 nuclei then find the value of m (Given 6

0N 10 nuclei )

11 In the figure shown S is a monochromatic point source

emitting light of wavelength = 500 nm . A thin lens of circular shape and focal length 0.10 m is cut into two identical halves L1 and L2 by a plane passing through

a diameter . The two halves are placed symmetrically about the central axis SO with a gap of 0.5 mm . The distance along the axis from S to L1 and L2 is 0.15 m,

while that from L1 & L2 to O is 1.30 m . The screen at

O is normal to SO . If the third intensity maximum occurs at the point A on the screen, find the distance OA in mm.

12 A concave mirror of focal length 20 cm is cut into

two parts from the middle and the two parts are moved perpendicularly by a distance 1 cm from the previous principal axis AB. Find the distance between the images formed by the two parts?





SECTION 3 (Maximum Marks: 18) This section contains SIX questions of matching type.

This section contains TWO tables (each having 3 columns and 4 rows)

Based on the table, there are THREE questions

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.

For each question, darken the bubble corresponding to the correct option in the ORS.

In Bohr’s atomic model for hydrogen like atoms

Column – 1 Column –2 Column –3

I If electron jumps from n = 4 to n = 2

p Time of electron will become 1/27 times

i speed of electron will become 2 times

II If electron jumps from n = 6 to n = 2

q Time of electron will become 1/8 times

ii speed of electron will become 3 times

III If electron jumps from n = 3 to n = 1

r Time of electron will become 1/9 times

iii speed of electron will become 1/2 times

IV If electron jumps from n = 6 to n = 3

s Time of electron will become 1/4 times

iv speed of electron will become 1/3 times

Answer the Following Questions

13. For wave length of emitted radiation is 16

3R

(A) I, q ,iii (B) II, p iii (C) I, q ,i (D) II, r,i


8R

(A) II, p ,iv (B) I, s, ii (C) II, p ,ii (D) I, q, iv


8R

(A) III, p, ii (B) II, q, iv (C) III, p ,iii (D) II, s ,ii





A lens is made up of a material of

refractive index 2 and is placed in

medium of refractive index 1. Radii of

curvature of lens are 1 2R and R for the

surfaces shown in figure.

2 1

R2

R1

Column – 1 Column –2 Column –3

I 2= 1.5 i 1= 1.3 p R1 = +20 cm

II 2= 1.3 ii 1= 1.3 q R1 = –20 cm

III 2= 2 iii 1= 1.3 r R1 = +

IV 2= 1 iv 1= 1.3 s R1 = –

Answer the Following Questions 16. For R2 = + , the combination will be diverging for (A) I,i,p (B) II, i,r (C) III,i,r (D) IV,i,p 17. For R2 = +20 cm, the combination will be diverging for (A) I,i,p (B) II, ii,q (C) III,iii,r (D) IV,iv,p 18. For R2 = + , the combination will be converging for (A) I,i,p (B) II, ii,q (C) III,iii,r (D) IV,iv,s

PART II: CHEMISTRY SECTION 1 (Maximum Marks: 28)





19. The normal boiling point of a liquid ‘X’ is 400 K. Which of the following statement is true about the

process X (I) (X)(g)?

(A) at 400 K and 1 atm pressure G = 0 (B) at 400 K and 2 atm pressure G = + ve

(C) at 400 K and 0.1 atm pressure G = ve (D) at 410 K and 1 atm pressure G = + ve





20. The value of Htransition of C (graphite) C (diamond) is 1.9 kJ/mol at 250C entropy of graphite is

higher than entropy of diamond. This implied that (A) C (diamond) is more thermodynamically stable then C (graphite) at 25

0C

(B) C (graphite) is more thermodynamically stable then C (graphite) at 250C

(C) diamond will provide more heat on complete combustion at 250C

(D) Gtransition of C (diamond) C (graphite) is ve 21. Consider 0.1 M solutions of two solutes X & Y. the solute X behaves as an univalent electrolyte while

the solute Y undergoes dimerization in solution. Select the correct statement(s) regarding these solutions:

(A) The boiling point of the solution “X” will be higher than that of “Y” (B) The osmotic pressure of the solution “X” will be higher than that of “Y” (C) The freezing point of the solution “X” will be lower than that of “Y” (D) The relative lowering of vapour pressure of both the solutions will be the same 22. When a lead storage battery is discharged (A) SO2 is evolved (B) lead sulphate is produced at both electrodes (C) sulphuric acid is consumed (D) water is formed 23. The correct statement(s) about O3 is (are) (A) O–O bond lengths are equal (B) Thermal decomposition of O3 is endothermic (C) O3 is diamagnetic in nature. (D) O3 has a bent structure. 24. The azeotropic solution of two miscible liquids: (A) Can be separated by simple distillation (B) May show positive or negative deviation from Raoult’s Law (C) Behaves as a supersaturated solution (D) Behaves like a single component and boils at a constant temperature at a given pressure. 25. Which of the following statement(s) is/are correct?

(A) SbH3 > NH3 > ASH3 > PH3 (boiling point)

(B) H3PO4 > H3PO3 > H3PO2 (reducing character)

(C) N2O < NO < N2O3 < N2O5 (oxidation state on nitrogen atom)

(D) NH3 > PH3 >ASH3 > SbH3 > BiH3 (basic strength)








26. For the reaction at 298 K, 2A + B C

H = 100 kcal and S = 0.050 kcal K1. If Hand S are assumed to be constant over the

temperature range, above what temperature will the reaction become spontaneous in kilokelvin 27. A sample of 4.0 mol O2 is originally confined in 20L at 270 K and then undergoes adiabatic expansion

against a constant pressure of 600 Torr until the volume has increased by a factor of 3.0. Calculate the value of q

28. The no. of P–O–P bonds in P4O10 is : 29. Find the current in amperes required to deposit 2.977 g of Pd by the electrolysis of an aqueous

solution of 4Pd salt per 1 hour (At. Wt. of Pd = 106.4)

30. The difference of the effective atomic number and the number of unpaired electrons of Fe in

4 6K Fe CN x

. Find the value of

x

4.






Column 1 Column 2 Column 3

(I) Acetone + Ethyl

alcohol

(i) Hmix = 0 (P) Ideal solution

(II) H2O + HNO3 (ii) Hmix > 0 (Q) Non Ideal solution with + ve

deviation

(III) Chlorobenzene +

Bromo benzene

(iii) Hmix < 0 (R) Non – Ideal solution with the

deviation

(IV) CCl4 + CuCl3 (iv) Stotal > 0 (S) Do not obey Raoult’s law





31. For the mixture of solution HNO3 and H2O, correct combination is (A) II–iv–Q (B) II–iii–R (C) II–ii–R (D) II–i–P

32. For the mixture of solution

Cl Br

and

, correct combination is (A) I–ii–Q (B) III–i–P (C) III–iv–R (D) III–i–S 33. Identify the incorrect combination is (A) II–iii–S (B) III–i–P (C) I–i–R (D) IV–ii–Q 2.


(I)

Isothermal

reversible

expansion P1,

V1, T1 p2 , V2

T1

(i)

V = + ve

T = 0

p = –ve

(P)

U = 0

H = 0

S = +ve

(II)

Adiabatic

reversible

expansion p2,

V2, T1 p3, V3,

T2

(ii)

V = + ve

T = – ve

p = – ve

(Q)

U = –ve

H = –ve

S = 0

(III)

Isothermal

reversible

compression

p3, V3, T2 p4,

v4, T2

(iii)

V = – ve

T = 0

p = + ve

(R)

U = 0

H = 0

S = – ve

(IV)

Adiabatic

reversible

compression

p4, V4, T2 p1,

V1, T1

(iv)

V = –ve

T = + ve

p = + ve

(S)

U = +ve

H = +ve

S = 0





34. Correct Combination is (A) II–ii–S (B) I–i–P (C) III–iii–Q (D) IV–iii–S 35. Correct combination is (A) II–ii–Q (B) I–iii–P (C) III–i–S (D) IV–iv–P 36. Correct combination is (A) I–iv–S (B) II–ii–P (C) III–iii–R (D) IV–ii–S

PART III: MATHEMATICS SECTION 1 (Maximum Marks: 28)





37. Given that n is the odd, the number of ways in which three numbers in AP can be selected from

1,2,3..,n is

(A)

2n 1

2

(B)

2

n 1

4

(C)

2

n 1

2

(D)

2

n 1

4

38. If ‘a’ denotes the number of permutations of x+2 things taken all at a time, ‘b’ the number of

permutations of x things taken 11 at a time and ‘c’ the number of permutation of x – 11 things all at a

time such that a = 182 bc, then the value of x is

(A) 15 (B) 12 (C) 10 (D) 18

39. The number of ways of arranging seven persons (having A, B, C and D among them) in a row so that

A, B, C and D are always in order A-B-C-D (not necessarily together) is

(A) 210 (B) 5040 (C) 46 7C (D) 7

3P





40. Let h(x) = min 2x,x for every real number x. Then

(A) h is continuous for all x

(B) h is differentiable for all x

(C) h' x 1 for all x > 1

(D) h is not differentiable at two values of x

41. A card is selected at random from cards numbered as 00, 01,02,…,99. An event is said to have

occurred. If product of digits of the card number is 16. If card is selected 5 times with replacement

each time, then the probability that the event occurs exactly three time is

(A)

2 3

5

3

3 97C

100 100

(B)

3 2

5

3

3 97C

100 100

(C)

3 3

5

3

0.3 9.7C

100 100

(D) 3 2

10 0.03 0.97

42. If a b sin a b sin and atan btan c,2 2

then,

(A) btan atan (B) atan btan

(C) 2 2 2

2bcsin

a b c

(D)

2 2 2

2acsin

a b c

43. A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or

tests I and III. The probabilities of the student p[assign in tests I, II, III are p, q and 1/2 respectively. If the probability that the student is successful is 1/2, then

(A) p = 1, q = 0 (B) p = 2/3, q = 1/2 (C) p = 3/5, q = 2/3 (D) there are infinitely many values of p and q








44. If k be the value of x at which the function x 3 5t

1f x t e 1 t 1 t 2 t 3 dt

has maximum

value and sinx cosecx k , then for n N, , n nsin x cosec x ....

45. Let n 1 na 2 a n 1,2,3..... and

1a 3 , then the value of n

nlim a

is ……..

46. The number of positive integral solutions of x2 – y

2 = 352706.

47. There are three piles of identical red, blue and green balls and each pile contains at least 10 balls.

The number of ways of selecting 10 balls if twice as many red balls as green balls are to be selected

is …

48. The value of ‘a’ for which the area of the triangle included between the axes and any tangent to the

curve a ax y k is constant is ……..










(49 – 51): Column-1 (Complex equation), Column-2 (Greatest value of |z|) and Column-3 (Least value of |z|)


(I) 1

z 2z

(i) 8 (P) 1 2

(II) 2

z 4z

(ii) 2 6 (Q) 3 2 3

(III) 3

z 6z

(iii) 3 2 3 (R) 1

(IV) 8

z 7z

(iv) 1 2 (S) 2 6

49. Which of the following option is the correct combination?

(A) I ii S (B) II iii Q (C) III iv P (D) IV i R 50. Which of the following options is the only correct combination?

(A) I iv P (B) II iii S (C) III i Q (D) IV ii R 51. Which of the following options is the only incorrect combination?

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





(52 – 54): Let f(x) = x

2 – 5x + 6, Column-1 contains information about f(x). Column-2 contains information

about f(|x|) and Column-3 contains information abut |f(|x|)|


(I) Vertex of 5 1

f x ,2 4

(i) f(|x|) is non differentiable at x = 0 (P) |f(|x|)|= 1 has 8 real and distinct

solution

(II) Vertex of 1 5

f x ,4 2

(ii) f(|x|) is differentiable at x = 0 (Q) |f(|x|)|= 1 has 4 real and distinct

solution

(III) f(x) increasing in 5

,2

(iii) f(|x|) = 1 has 4 real and distinct solutions

(R) |f(|x|)| is non differentiable at 5 points

(IV) f(x) decreasing in 5

,2

(iv) f(|x|) = 1 has 2 real and distinct solutions

(S) |f(|x|)| is non differentiable at 6 points

52. Which of the following options is the only CORRECT combination?

(A) IV i S (B) I ii R (C) III iv P (D) I iii Q 53. Which of the following options is the only CORRECT combination?

(A) III iii R (B) I i P (C) IV iv S (D) II ii Q 54. Which of the following options is the only INCORRECT combination?

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






PHASE – VIII (Champions)_PAPER – I

ANSWERS

PHYSICS

1. A,B,C 2. A,C 3. A,B,C 4. B,C,D

5. A,D 6. BCD 7. AB 8. 2

9. 4 10. 3 11. 1 12. 2

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

17. C 18. A

CHEMISTRY

19. A, B, C 20. B, C, D 21. A, B, C 22. B, C, D

23. A, C, D 24. B, D 25. A, C, D 26. 8

27. 0 28. 6 29. 3 30. 9

31. B 32. B 33. C 34. B

35. A 36. C

MATHEMATICS

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

41. B,D 42. B,C,D 43. A,B,C,D 44. 2

45. 2 46. 0 47. 4 48. 1

49. D 50. A 51. D 52. D

53. A 54. C




FIITJEE INTERNAL TEST

IIT – JEE 2018

PHASE – VIII (Champions)_PAPER – II Time: 3 hours Maximum Marks: 183

INSTRUCTIONS:

A. General

1. This booklet is your Question Paper containing 54 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 & Marking Scheme

21. Each part has three sections as detailed in the following table:

Section Question Type

Number of Questions

Category wise Marks Each Question Maximum marks of the section

Full Marks Partial Marks Zero Marks

Negative Marks

1 Single Correct Option

7


––– 0 If none of the bubbles is darkened


21

2 One or more correct option(s)

7

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

+1 For darkening a bubble corresponding to each correct option, provided NO incorrect option is darkened.

0 If none of the bubbles is darkened.

–2 In all other case.

28

3 Comprehension

4


––– 0 In all other case.

––– 12

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: 28)



For each question, darken the bubble corresponding to all the correct option in the ORS.

1. For a right angled prism PQR immersed in water,

the incident and emergent rays are parallel as shown in figure. The minimum value of refractive index of the prism is

(A) 3

22

(B) 4

23

(C) 3

4 (D) 2

2. Suppose potential energy between electron and proton at separation ‘r’ is given by U= K In r, where k

is constant. For such hypothetical hydrogen atom, the ratio of energy difference between energy levels (n=1 and n=2) and n=2 and n=4 is

(A) 1 (B) 2 (C) ½ (D) 3 3. Along a stream line (A) the velocity of fluid particle remain constant (B) The velocity of all fluid particle crossing a given position is constant (C) The velocity of all fluid particle at a given instant is constant (D) The speed of a fluid particle remains constant





4. Electromagnetic radiation whose electric component varies with time as 1 2 3 0E c c c cos t cos t ,

here 1 2c ,c and

3c are constants, is incident on lithium and librates photoelectrons. If the kinetic

energy of most energetic electrons be 190.592 10 J. Given that 15

0 3.6 10 rad/ sec and 146 10 rad /sec. The work function lithium is (take planks constant h = 346.6 10 MKS )

(A) 1.2 eV (B) 1.5 eV (C) 2.1 eV (D) 2.39 eV 5. A cylindrical vessel with its axis vertical is filled

with a liquid of negligible viscosity to a height z on one side is small orifice at a height y, both z and y being measured from the base. The jet of liquid strikes the horizontal plane through the base at a distance x from base, the maximum value of x, as y is varied, will be

(A) 2z (B) z

(C) z

2 (D)

z

4

6. In a Young's Double slit experiment, first maxima is observed

at a fixed point P on the screen. Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity at point O (centre of the screen)

(A) remains constant (B) keeps on decreasing (C) first decreases and then increases (D) First decreases and then becomes constant





7. In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the

slits then the variation of resultant intensity at mid-point of screen with ‘ ’ will be best represented by

( 1).[Assume slits of equal width and there is no absorption by slab]

(A) (B)

(C) (D)

SECTION 2 (Maximum Marks: 15) This section contains SEVEN questions.


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


8. If the potential difference of Coolidge tube producing X –ray is increased, then choose the correct

option(s)

(A) the interval between k kand

increases

(B) the interval between k 0and

increases

(C) the interval between k 0and

increases

(D) 0 does not change





9. If the wave length of light in an experiment on photo electric effect is doubled (A) the photoelectric emission will not take place (B) the photoemission may or may not take place (C) the stopping potential will increase (D) the stopping potential will decrease under the condition that energy of photon of doubled

wavelength is more than work function of metal 10. If a rod of length , very small area of cross section A,

Young’s modulus of elasticity Y is acted upon by two parallel forces 3F and F respectively (as shown) and placed on a smooth horizontal plane. If the elastic limit is not crossed and then to study the change in length of rod ( ) and it’s elastic potential energy (U) the rod is segmented into four equal parts where magnitude of

change in lengths are 1 ,

2 3 4, , and elastic

potential energy stored in each segment are

1 2 3 4U ,U ,U ,U respectively as shown then which is/are

correct ?

(A) 31

3 8

(B) 1 4

UU U

4

(C) 42

5 8

(D) 2 3 4U U U

11. A luminous point object is placed at O, whose image is

formed at I as shown in the figure. Line AB is the optical axis. Which of the following statement is / are correct ?

(A) If a lens is used to obtain the image, then it must be a diverging lens and its optical centre will be the intersection point of line AB and OI

(B) If a lens is used to obtain the image, then it must be a converging lens and its optical centre will be the intersection point of line AB and OI

(C) If a mirror is used to obtain the image then the mirror must be concave and object and image subtend equal angles at the pole of the mirror.

(D) I is a real image





12. In an interference arrangement similar to Young's double- slit

experiment, the slits S1 & S2 are illuminated with coherent

microwave sources, each of frequency 106 Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance d = 150.0 m . The intensity I( ) is

measured as a function of at a large distance from S1 & S2,

where is defined as shown . If I0 is the maximum intensity then

I( ) for 00 90 is given by :

(A) I( ) = for = 30º

(B) I( ) = for = 90º

(C) I( ) = I0 for = 0º

(D) I( ) is constant for all values of

13. Point A(0, 1) and B (12, 5) are object – image pair (one of the point acts as object and the other point

as image) x-axis is the principal axis of the mirror. Then this object image pair is: (A) due to a convex mirror of focal length 2.5 cm (B) due to a concave mirror having its pole at (2, 0) (C) real virtual pair (D) data is insufficient for options (A) and (B) 14. In the diagram shown, a ray of light is incident on the interface between 1 and

2 at angle slightly greater than critical angle. The light suffers total internal reflection at this interface. After that the light ray falls at the interface of 1 and 3, and again it

suffers total internal reflection. Which of the following relations should hold true?

(A) 1 < 2 < 3 (B) 2 2 2

1 2 3

(C) 2 2 2

1 3 2 (D) 2 2 2

1 2 3





SECTION 3 (Maximum Marks: 18) This section contains TWO paragraphs.

Based on each paragraph, there are TWO questions.



Paragraph–1 An electron is orbiting in a circular orbit of radius r under the influence of a constant magnetic field B. Assuming that Bohr’s postulate regarding the quantisation of angular momentum holds good for this electron [ii = Planck’s constant, e = charge on electron and m = mass of electron] 15. Radius of nth orbit of the electron will be:

(A) 2nh

Be (B)

2

2

nh

Be (C)

2

n eh

Be (D)

2n eh

Be

16. Kinetic energy of the electron in nth orbit will be:

(A) 4

nhBe

m (B)

2

nhBe

m (C)

2

nhB

em (D)

4

nhB

em

Paragraph–2

A liquid flow through a horizontal tube. The

velocities of the liquid in the two sections, which

have areas of cross –section 1A and

2A , are

1 2v and v respectively. The difference in the levels

o f the liquid in the two vertical tubes is h.

17. The volume of the liquid flowing through the tube in unit time is

(A) 1 1A V (B)

1 2A V (C) 2 1A V (D)

2 12A V

18. The magnitude of 2 2

2 1v v is

(A) gh (B) 2gh (C) 3gh (D) 4 gh





PART II: CHEMISTRY SECTION 1 (Maximum Marks: 28)




19. Ice Water mass ratio is maintained as 1 : 1 in a given system containing water in equilibrium with ice

at constant pressure. If CP (ice) = CP (water) = 4.18 J mol1 K1

molar heat capacity of such a system is

(A) zero (B) infinity (C) 4.182 JK1 mol

1 (D) 75.48 JK1

mol1

20. 1 mole of NH3 gas at 270C is expanded in reversible adiabatic condition to make volume 8 times ( =

1.33). Final temperature and work done respectively are (A) 150 K, 900 cal (B) 150K, 400 cal (C) 250 K, 1000 cal (D) 200 K, 800 cal 21. Two moles helium gas undergo a reversible cyclic process as showing in

figure. Assuming gas to be ideal. What is the net work involved in the cyclic process c?

(A) 100 Rn4 (B) + 100 Rn4

(C) + 200 Rn4 (D) 200Rn4

22. Which of the reaction defines molar 0

fH ?

(A) 2 3CaO s CO g CaCO s (B) 2 2

1 1Br g H g HBr g

2 2

(C) 2 2 2 4 3

3N g 2H g O g NH NO s

2 (D) 2 2I s H g 2HI g

23. 2 2C s O g CO , g ; H = 94.3 kcal/mol

2 2

1CO g O g CO g ;

2 H = 67.4 kcal/mol

2O g 2O g H = 117.4 kcal/mol

CO g C g O g ; H = 230.6 kcal/mol

Calculate H for C (s) C (g) in kcal/mol (A) 171 (B) 154 (C) 117 (D) 145





24. Which of the following reactions is associated with the most negative change in entropy?

(A) 2 2 32SO g O g 2SO g (B) 2 4 2 2 6C H g H g C H g

(C) 2 2C s, graphite O g CO g (D) 2 2 6 63C H g C H

25. For the gas – phase decomposition, 5 3 2PCl g PCl g Cl g

:

(A) H 0, 0 (B) H 0, S 0 (C) H > 0, S < 0 (D) H < 0, S > 0





26. For which of the following substance(s), the standard enthalpy of formation is/are zero? (A) C (graphite) (B) O3(g) (C) I2(g) (D) Br2(I)

27. At 25C the equivalent conductance at infinite dilution for HCl solution is 4250 ohm–1

cm2 equivalent

–

1, while its specific conductance is 3.825 ohm

–1 cm

–1. If the apparent degree of dissociation is 90%,

the normality of the solution is (A) 0.90 N (B) 1.0 N (C) 1.1 N (D) 1.2 N 28. Which of the following is a correct statement ? (A) Cassiterite is the ore of tin (B) Galena is the ore of lead (C) Calamine is the ore of zinc (D) Cryolite is the ore of aluminium

29. For the cell 2 2Zn s Zn aq Cu aq Cu s . The cell potential cellE can be increased

(A) by increasing 2Cu

(B) by increasing 2Zn

(C) by decreasing 2Cu

(D) by decreasing 2Zn

30. Which of the following reaction can evolve phosphine ?

(A) (white) 2P + Ca(OH) (B) 2Al P + H O

(C) 3 4H PO

(D) 4PH I + NaOH





31. Which of the following salts on heating liberate nitrogen gas? (A) (NH4)3PO4 (B) NH4NO2 (C) (NH4)2Cr2O7 (D) NH4NO3 32. The cell reaction of an electrolyte cell is given as :

3 2Fe 2Fe 3Fe with E = 0.404 V

and G = –2.424 J. if the cell reaction is to be written as :

2Fe + 4Fe3+

6Fe2+

, Then which of the following statements will be correct :

(A) E can be given by 0.404 V (B) G can be given by –4.848 V

(C) E and G are 0.404 V and – 2.424 J respectively (D) the value of ‘n’ changes from 6 to 12





Paragraph–1 All oxyacids of P have P–OH groups whre the H atom is ionisable. Hydrogen atoms in P–H bonds are not ionized. 33. The basicity of H3PO2 ? (A) 1 (B) 2 (C) 3 (D) 4

34. 0 0220 C` 320 C

3 4H PO X Y Y is

(A) (HPO3)n (B) H4P2O7 (C) H3PO3 (D) H3PO4





Paragraph–2 The Ellingham diagram for zinc, magnesium and carbon converting into corresponding oxides is shown below

35. At what temperature, zinc and carbon have equal affinity of oxygen?

(A)1000 C (B)1500 C (C) 500 C (D) 1200 C

36. At1100 C , which reaction is spontaneous to a maximum extent?

(A)MgO C Mg CO (B) ZnO C Zn CO

(C)MgO Zn Mg ZnO (D) ZnO Mg MgO Zn





PART III: MATHEMATICS




37. If the mean and variance of a binomial variate X are 7/3 and 14/9 respectively. Then probability that

X takes value 6 or 7 is equal to

(A) 1

729 (B)

5

729 (C)

7

729f (D)

13

729

38. One ticket is selected at random from 100 tickets numbered 00, 01, 02, ...., 99. Suppose X and Y are

the sum and product of the digit found on the ticket P(X = 7 / Y = 0) is given by (A) 2/3 (B) 2/19 (C) 1/50 (D) none of these 39. A wire of length l is cut into three pieces. What is the probability that the three pieces form a triangle? (A) 1/2 (B) 1/4 (C) 2/3 (D) none of these 40. Of the 25 questions in a unit, a student has worked out only 20. In a sessional test of that unit, two

questions were asked by the teacher. The probability that the student can solve both the questions correctly, is

(A) 8/25 (B) 17/25 (C) 9/10 (D) 19/30 41. Dialing a telephone number, a man forgot the last two digits and remembering only that they are

different, dialed them at random. The probability of the number being dialed correctly is (A) 1/2 (B) 1/45 (C) 1/72 (D) 1/90

42. The point of intersection of the curves arg (z – 3i) = 3 / 4 and arg (2z + 1 – 2i) = /4 (where i 1 )

is (A) 1/4(3 + 9i) (B) 1/4(3 – 9i) (C) 1/2 (3 + 2i) (D) no point

43. For all complex numbers z1, z2 satisfying 1z 12 and 2z 3 4i 5 , the minimum value of

1 2z z is

(A) 0 (B) 2 (C) 7 (D) 17









44. The common roots of the equations 3 2z 1 i z 1 i z i 0 , (where i 1 ) and

1993 1994z z 1 0 are

(A) 1 (B) (C) 2 (D)

981

45. If cos + cos + cos = sin + sin + sin = 0, then

(A) cos 2 cos 2 cos 2 0 (B) sin 2 sin 2 sin 2 0

(C) cos cos cos 0 (D) sin sin sin 0 si

46. If 1, , 2, ........,

n-1 are the n, nth roots of unity, then (2 - ) (2 -

2) ..... (2 -

n-1) equals

(A) 2n – 1 (B) n n n

1 2 nC C ..... C

(C) 1/ 2

2n 2n 1 2n 1 2n 1

0 1 2 nC C C ...... C 1 (D) n2 1

47. Triplet (x, y, z) is chosen from the set {1, 2, 3, ......, n}, such that x y < z. The number of such triplets is

(A) 3n (B) n 1

3C (C) n

2C (D) n n

2 3C C

48. If 1 2 3x x x and

1 2 3y y y be two three digits number, the number of pairs of and can be

formed so that can be subtracted from without borrowing is (A) 2! 10! 10! (B) (45) (55)

2 (C) 3

2. 5

3. 11

2 (D) 136125

49. In a plane, there are two families of lines y = x + r, y = –x + r, where r {0, 1, 2, 3, 4}. The number of squares of diagonals of length 2 formed by the lines is

(A) 2

4!3

(B) 3

3!2

(C) 16 (D) 9





50. The value of the determinant

6 2i 3 6

12 3 8i 3 2 6i

18 2 12i 27 2i

, where i 1 is

(A) complex (B) real (C) irrational (D) rational





Paragraph–1

If a particular experiment be given n (a finite) independent trials. If the probability of success in one

trial (say) p We get probability of failure, q = (1 – p). The probability of r success in n trials = n r n r

rC p q

51. The probability of a man hitting a target in one fire is 1

4. Atleast n times he must fire at the target that

the chances of hitting the target at least once will exceed 2

3, then n is

(A) 2 (B) 4 (C) 6 (D) 8 52. A coin is tossed 4 times whose faces are marked with the numbers 5 and 3. The odds in favour of

getting a sum less than 15 is

(A) 5

16 (B)

5

11 (C)

16

5 (D)

11

5

Paragraph–2

Different words are being formed by arranging the letters of the word “SUCCESS”. All the words obtained by

written in the form of a dictionary. 53. The number of words in which the two C are together but no two S are together is (A) 120 (B) 96 (C) 24 (D) 420 54. The number of words in which the consonants appear in alphabetic order is (A) 42 (B) 40 (C) 420 (D) 280






PHASE – VIII (Champions)_PAPER – II

ANSWERS PHYSICS

1. B 2. A 3. B 4. B

5. B 6. C 7. C 8. B,C

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

13. BCD 14. BCD 15. B 16. A

17. A 18. B

CHEMISTRY

19. B 20. A 21. A 22. C

23. D 24. D 25. B 26. A, D

27. B 28. A, B, C, D 29. A, D 30. A, B, D

31. B, C 32. A, B, D 33. A 34. A

35. A 36. D

MATHEMATICS

37. B 38. B 39. B 40. D

41. D 42. D 43. B 44. B,C

45. A,B,C,D 46. A,B,C 47. B,D 48. B,C,D

49. B,D 50. B,D 51. B 52. B

53. C 54. A

fiitjee internal test second year que… · fiitjee internal test iit ... 12 a concave mirror of...

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