FIITJEE PET XV EXTENDED) - fiitjeehyderabad.com (EXTENDED) (MAIN… · 1 = 222 a b c a b c, ... cotx tanx ³ (A) 1 cos4x c 4 (B

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FIITJEE PET – XV (EXTENDED) MAINS

DATE: 09.12.2017 Time: 3 hours Maximum Marks: 360

INSTRUCTIONS:

Instructions to the Candidates 1. This Test Booklet consists of 90 questions.

Use Blue/Black ball Point Pen only for writing particulars and bubbling of OMR.

2. For each correct answer 4 Marks will awarded and for each wrong answer 1 Mark will be deducted.

3. Attempt all questions.

4. In case you have not darkened any bubble you will be awarded 0 mark for that question.

5. Use of calculator/logarithmic table is not permitted.

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.:



PET-XV (EXTENDED)-2018-MPC-2

1. If

a x a x

a x a x

a x a x

= 0, then x is

(A) 0 (B) a (C) 3 (D) 2a

2.

0 p q p r

q p 0 q r

r p r q 0

is equal to

(A) p + q + r (B) 0 (C) p – q – r (D) –p + q + r

3. If a b c such that

3 3 3

2 2 2

a 1 b 1 c 1

a b c

a b c

= 0, then

(A) ab + bc + ca = 0 (B) a + b + c = 0 (C) abc = 1 (D) a + b + c = 1

4.

1 x 1 1

1 1 x 1

1 1 1 x

is equal to

(A) x2 (x + 3) (B) 3x

3 (C) 0 (D) x

3

5. If x, y, z are integers in AP, lying between 1 and 9, x51, y41 and z31 are three-digit numbers then the

value of

5 4 3

x51 y41 z31

x y z

is

(A) x + y + z (B) x – y + z (C) 0 (D) none of these

6. If 1 = 2 2 2

1 1 1

a b c

a b c

, 2 =

1 bc a

1 ca b

1 ab c

, then

(A) 1 + 2 = 0 (B) 1 + 22 = 0 (C) 1 = 2 (D) none of these

Space for rough work




7. The determinant

xp y x y

yp z y z

0 xp y yp z

= 0 for all p R, if

(A) x, y, z are in AP (B) x, y, z are in GP (C) x, y, z are in HP (D) xy, yz, zx are in AP

8. The value of

2

2

2

x x yz 1

y y zx 1

z z xy 1

is

(A) 1 (B) –1 (C) 0 (D) –xyz

9. If f(x) =

2

1 x x 1

2x x x 1 x x 1

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

, then f(100) is equal to

(A) 0 (B) 1 (C) 100 (D) –100

10. If A2 = 8A + k I, where A =

1 0

1 7

, then k is

(A) 7 (B) –7 (C) 1 (D) –1

11. If f(x) =

cosx sinx 0

sinx cosx 0

0 0 1

, then f(x + y) is equal to

(A) f(x) + f(y) (B) f(x) – f(y) (C) f(x) . f(y) (D) none of these

12. If A =

0 c b

c 0 a

b a 0

and B =

2

2

2

a ab ac

ba b bc

ca cb c

, then AB is equal to

(A) 0 (B) I (C) 2 I (D) none of these

13. If A =

4 1 4

3 0 4

3 1 3

, then A2 is equal to

(A) A (B) I (C) AT (D) none of these





14. 2

x 3

x 2x 3

dx =

(A) 2 1 x 1x 2x 3 4sinh c

2

(B) 2 1 x 1

x 2x 3 4sinh c2

(C) 2 1 x 1x 2x 3 4sinh c

2

(D) 2 x 1

x 2x 3 4sin c2

15. 2

4

x 1dx

x 1

(A) 2

11 x 1tan c

2x2

(B)

211 x 1

tan c2x2

(C) 11 x 1

tan c2x2

(D) 11 x 1

tan c2x2

16.

3 2

x 1 dx

x 1 x x x

=

(A) 1 3 22tan x x x c (B) 1 22tan x x 1 c

(C) 1 12tan x 1 c

x

(D) 1 2 12tan x x c

x

17.

12 9 p

3 r5 3 5 3

2x 5x xdx c

x x 1 q x x 1

, then p – q – r =

(A) 6 (B) 8 (C) 10 (D) 14

18. If

2/7 k

9 /7

1 cosx xdx A tan c

21 cosx

, then AK =

(A) 11

7 (B)

121

49 (C)

49

121 (D) 1

19. 41 x

dx1 x

(A) 2 3 4x x x

x c2 3 4

(B) 2 3 4x x x

x c2 3 4

(C) 2 3 4x x x

2x c2 3 4

(D) 2 3 4

2 x x xx c

2 3 4





20. 5logx 4logx

3logx 2logx

e e

e e

dx =

(A) x + c (B) 3x2 + c (C)

3xc

3 (D)

2xc

2

21. 5

2

x

x 1 dx =

(A) 4 2

1x xtan x c

4 2

(B) 4 2

2x x 1log x 1 c

4 2 2

(C) 4 3

1x xtan x c

4 3

(D) 4 3

1x xtan x c

4 3

22. a x a x

a x a x

dx =

(A) 1 x2sin c

a

(B) 1 x

2asin ca

(C) 1 x

2cos ca

(D) 1 x

2acos ca

23. xloga xe e dx

(A) ex log a

. ex + c (B)

x

aec

logae (C)

xec

1 loga

(D)

xaec

loga

24. 1 cos4x

dxcot x tanx

(A) 1

cos4x c4

(B) 1

cos4x c8

(C) 1

sin4x c4

(D) 1

cos4x c8





25.

1log 1

xdx

x 1 x

(A)

2 2log x 1 logx

log x 1 logx c2 2

(B) 21 1log 1 c

2 x

(C) 2 21 1

log x 1 logx c2 2

(D) 2 21 1

log x 1 logx log x 1 logx c2 2

26. 1

dxxlogxlog(logx) =

(A) log |log (log x)| + c (B) log |log sin x| + c (C) 1

clogsinx

(D) none of these

27. sec2x cosec

4x dx =

1

3 cot

3x + k tan x – 2 cot x + c k =

(A) 4 (B) 3 (C) 2 (D) 1

28. 2

1

3 x 2x dx =

(A) 1 x 1sin c

2

(B) 1 x 1

cosh c2

(C) 1 x 1

sin c2

(D) 1 x 1

sinh c2

29. 2

2x 1dx

1 5x 6x

=

(A) 2 11 11 12x 51 5x 6x sin c

3 76 6

(B) 2 11 11 12x 5

1 5x 6x sin c3 76 6

(C) 2 11 11 12x 51 5x 6x sin c

3 76 6

(D) none of these





30.

dx

x 100 x 99 = f(x) + c f(x) =

(A) 2(x + 100)1/2

(B) 3(x + 100)1/2

(C) 12tan x 99 (D) 12tan x 100

31. An infinite long plate has surface charge density . As shown in the figure, a point charge q is moved from A to B along two semicircular paths of radius r each. Net work done by electric field is

(A) 1 2

o

qx x

2

(B) 2 1

o

qx x

2

(C) 2 1

o

qx x

(D)

o

q2 r r

B(x1,0) A(x2,0)

32. Potential of the points P and Q in the circuit shown in the

figure are (A) 6V and –2V (B) 6V and +2V (C) –6V and –2V (D) -6V and +2V

D 1 Q P

3

1 10V

33. For the given electric lines of force consider the

following statements (A) Flux through closed surface S is zero

(B) A BV V 0

(C)

B

A

E.dr is negative

(D) If a point charge particle is released at point C then its path will be straight line.

34. What should be the value of resistance R in

the circuit shown in Figure so that the electric bulb consumes the rated power ?

(A) 12

(B) 4.5

(C) 6

(D) 9

0.5 W

3V

4

R

6V 0.5,





35. The length of a potentiometer wire is 10 m. The distance between the null points on its wire

corresponding of two cells comes out to 60 cm. If the difference of emf’s of the cell is 0.6 V, then the potential gradient on potentiometer wire will be

(A) 0.67 V/m (B) 0.5 V/m (C) 2.5 V/m (D) 1 v/m 36. Two bars of radius r and 2r are kept in contact as shown. An electric current I is passed through the

bars. Which one of following is correct? (A) Heat produced in bar BC is 4 times the heat produced in bar AB (B) Electric field in both halves is equal (C) Current density across bar AB is double that of across BC (D) Potential difference across AB is 4 times that of across BC

37. 600 identical cells each of emf 20V and internal resistance ‘r’ are arranged in a mixed grouping circuit

across an external resistance R = 30 such that 60 cells are in series in row and there are 10 such rows in parallel and for this arrangement, current through R (and hence the power dissipation) is found to be maximum. Value of r in ohms is

(A) 5 (B) 1 (C) 10 (D) 2 38. A galvanometer having 30 divisions has a current sensitivity of 20 A / division. It has a resistance of

25 ohm. To convert it into ammeter measuring upto 1.0 A, a shunt should be connected in parallel to it of resistance

(A) 0.001 (B) 0.015 (C) 0.025 (D) 0.035 39. Consider the potentiometer circuit arranged as in figure. The

potentiometer wire is 500 cm long. At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer ?

(A) 150 cm (B) 133.3 cm (C) 100 cm (D) None

/4

40. In a meterbridge, the wire consists of two parts left part of length 30 cm and of radius ‘r’ and right of

radius ‘2r’. Where well null point occur from left end, if the resistance in the left and right gaps are 5 ohms and 8 ohms respectively? Given that material of the wires is the same.

(A) 18.3 cm (B) 20.2 cm (C) 25.2 cm (D) 40 cm





41. A source of constant P.D is applied across a conductor of irregular cross section as shown. Then,

(A) Electric field intensity at “p” is more than that of Q (B) Rate of electrons crossing per unit area of cross section at ‘P’ is more than that at Q (C) The rate of generation of heat per unit length at P is less than that at Q (D) The drift velocity at “P” is greater than that at Q 42. In a potentiometer experiment, two cells connected in series get balanced at 9 m length on the wire.

Now the connections of terminals of cell of lower emf are reversed, then the balancing length is obtained at 3 m. The ratio of emf of two cells will be

(A) 3 : 1 (B) 2 : 1 (C) 4 : 1 (D) none

43. A potentiometer contains a cell of emf E0, internal resistance 0r , a series resistance Rs and a

uniform wire of length L and resistance R0 in its primary circuit. Its secondary circuit contains a cell of

emf E and internal resistance 0r

2. sR varies with time (t) according to s 0R =R 1+ αt

isa +ve constant . The speed of jockey to keep the galvanometer of secondary circuit remain

undeflected is

(A)

0

ELα

E. (B)

0

ELα

2E (C)

0

0 0 0

rE Lα

2

E r +R

d

0

0 0 0

E2r Lα

E r +2R

44. A meter bridge contains zero error. Its balancing length against an unknown resistance with a known

resistance of 10 in right gap and left gaps are 34.33cm and 67.67 cm respectively. The unknown

resistance is

(A) 5.1 (B) 4.9 (C) 5 Ω (D) 10 Ω





45. Identify the correct statement (A) Principle of potentiometer is balancing resistances against known resistance (B) Sensitivity of potentiometer can be increased by increasing emf in primary circuit (C) Potentiometer can be used to measure only “emf” but not P.D. in a circuit (D) Potentiometer can be used for measuring internal resistance and PD in any circuit also

46. Circuit shown in figure is an arrangement which can be used to

measure the resistance R though the reading may not be linear. In the circuit “G” is a galvanometer, R0 is a known resistance and R is the resistance which is to be measured. If A and B are short circuited by a resistance-less wire; (G) gives full scale deflection. Then to read a resistance “R” directly from (G), its scale should be like:

(A) (B) (C) (D) 47. An electrical circuit is given. Calculate the current flowing in the

resistor of 400 , if voltmeter resistance is 400

(A) 1

60A (B)

1

3A

(C) 20

3A (D)

10

3A

V

400

100 100 200

100

10V

48. In the figure shown, the potentiometer wire of length

L 100cm and resistance 9 is joined to a cell of

emf 1E 10V and internal resistance

1r 1 . Another

cell of emf 2E 5V and internal resistance

2r 2 is

connected as shown. The Galvanometer G will show no deflection when the length AC is

(A) 50 cm (B) 55.55 cm (C) 45.55 cm (D) None

r =11

E =10V1

E =5V2

r =22

A BC

G





49. In the shown meter-bridge arrangement if AC corresponding to

null deflection of the galvanometer is x , what would be it’s value if the radius of the wire AB is doubled ?

(A) x (B) x / 2

(C) 4x (D) 2x

G

A BCx

R1R2

50. Current in the wire varies according to equation I 15sin50 t where I is in ampere, t is in second

and 50 t is in radian. How much net charge will passed a cross-section of the wire in the interval

t 0 to t 40 ms :

(A) 0.080 C (B) 0.80 C (C) 0.030 C (D) Zero 51. Figures show two squares, X and Y, cut from a sheet of metal, of uniform thickness t. X and Y have

sides of length L and 2 L, respectively. The resistance RX and RY of the square are measured

between the opposite faces shaded in the first figure. What is value of X

Y

R

R?

(A) 1

4 (B)

1

2 (C) 1 (D) 2

52. In potentiometer experiment a cell of emf 1.5 V connected in the secondary circuit gives a balancing

length of 165 cm of the wire. If a resistance of 5 is connected parallel to the cell, the balancing length of the wire is 150 cm. The internal resistance of the cell is

(A) 5 (B) 1.5 (C) 1 (D) 0.5 53. A cell of emf E volt with negligible internal resistance is connected to a

wire whose cross-section changes. The wire has three sections of equal length. The middle section has a radius a whereas the radius of the outer two sections is 2a. The ratio of the potential difference across the section AB to the potential difference across the section CA is

(A) 5 (B) 4 (C) 1

2 (D)

1

4





54. Read the following statement carefully Y : The resistivity of semiconductor decreases with increase of temperature. Z : In a conducting solid, the rate of collisions between free electrons and ions increases with increase

of temperature. Select the correct statement from the following (A) Y is true but Z is false (B) Y is false but Z is true (C) both Y and Z are true (D) Y is true and Z is the correct reason for Y 55. The galvanometer G in the following circuit reads

zero. Find the value of R. Batteries are resistance less.

(A) 100 (B) 50 (C) 250 (D) None 56. The resistance of a metallic conductor increases with temperature due to (free electrons are the

charge carriers): (A) change in carrier density (B) change in the dimensions of the conductor (C) decrease in average speed of the carrier (D) increase in the rate of collisions between the carriers and the vibrating atoms of the conduct 57. Two resistances connected in parallel across a cell of negligible internal resistance, use 4.5 times the

power that they would use, when in series across the same cell. If one of the resistances is 8 ohm, the other can be

(A) 8 (B) 12 (C) 16 (D) 36

58. Two identical batteries each of emf E = 2V and internal resistance r = 1 are available to produce heat in an external circuit with variable resistance ‘R’. What is the maximum rate of production of heat that can be obtained in the external circuit?

(A) 1 W (B) 2 W (C) 4 W (D) 8 W 59. How many 60 W lamps may be safely run on a 230 V circuit fitted with a 5 A fuse? (The fuse would

melt when the current passing through it exceeds 5(A). Lamps are connected in parallel to mains. (A) 2 (B) 19 (C) 20 (D) 4

60. To get maximum current through a resistance of 2.5 , one can use m rows of cells, each row having

n cells. The internal resistance of each cell is 0.5 . What are the values of n and m if the total number of cells is 45?

(A) m = 3, n = 15 (B) m = 5, n = 9 (C) m = 9, n = 5 (D) m = 15, n = 3





61. Only one bromoether is obtained from the reaction of the alkyl halide

Br

Br with methanol. The structure of the ether is

(A)

Br

OCH3

(B)

OCH3

Br

(C) OCH

3

Br

(D)

Br

OCH3 62. Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so

obtained is diazotised and then heated with cuprous bromide. The reaction mixture is formed contains (A) mixture of o–and p–bromotoluenes (B) mixture of o–and p–dibromobenzenes (C) mixture of o– and p–bromoanilines (D) mixture of o– and m–bromotoluenes 63. Which of the following gives a precipitate with moist silver oxide (A) CH2=CH-Cl (B) C6H5Cl

(C)

Cl

(D)

Cl

64. The treatment of CH3MgX with CH3CC–H produces

(A) 3 2CH CH CH (B) 3 3CH C C CH

(C) 3 2 3CH CH CH (D) CH4

65. Which of the following reactions will yield 2, 2–dibromopropane ?

(A) 3CH C CH 2HBr (B) 3CH CH CHBr HBr

(C) CH CH 2HBr (D) 3 2CH CH CH HBr





66. Which of the following will react easily with conc. NaOH

(A)

Cl

NO2

(B)

Cl

NO2

(C) NO

2

NO2

Cl

(D)

NO2

ClO2N

67. Reaction of one molecule of HBr with one molecule of 1, 3–butadiene at 40C gives predominantly (A) 3–bromobutene under kinetically controlled conditions (B) 1–bromo–2–buttene under thermodymically controlled conditions (C) 3–bromobutene under thermodynamically controlled conditions (D) 1–bromo–2–butane under kinetically controlled conditions 68. The correct order of reactivity of the following compounds towards SN1 reactions is,

I II

IIIIV

CH2BrH3CO CH2BrO2N

CH2BrCH2BrH3C

(A) I > IV > III > II (B) II > I > III > IV (C) I > IV > II > III (D) II > III > IV > I 69. When 2-butanol is treated with SOCl2 in presence of ether the product formed will be, (A) a recemic mixture (B) optically inactive (C) with retention of configuration (D) with complete inversion 70. The product of the reaction given below is :

1. NBS/ hv

2. H2O / K2CO3

(A)

OH

(B)

OH

(C)

CO2H

(D)





71. The synthesis of alkyl fluorides is best accomplished by : (A) Sandmeyer’s reaction (B) Finkelstein reaction (C) Swarts reaction (D) Free radical fluorination 72. The major organic compound formed by the reaction of 1, 1, 1–trichloroethane with silver powder is : (A) 2–Butyne (B) 2–Butene (C) Acetylene (D) Ethene

73. NS 1reaction is are favoured in

(A) Polar solvents (B) Less no. of alkyl group on the carbon atom attached to the halogen atom (C) Small alkyl groups on the carbon attached to the halogen atom (D) None of these

74. 3 3CH Br Nu CH Nu Br

The decreasing order of the rate of the above reaction with nucleophiles (Nu–) A to D is

Nu A PhO , B AcO , C HO , D EtO

(A) D > C > A > B (B) D > C > B > A (C) A > B > C > D (D) B > D > C > A 75. Fluorobenzene (C6H5F) can be synthesized in the laboratory (A) by heating phenol with HF and KF (B) from aniline by diazotization followed by heating the diazonium salt with HBF4 (C) by direct fluorination of benzene with F2 gas (D) by reacting bromobenzene with NaF solution 76. The structure of the major product formed in the following reaction

Cl

I

NaCN

DMF

(A)

CN

CN

(B)

Cl

I

NC

(C)

Cl

CN

(D)

CN

I





77. Reaction of trans–2–phenyl–1–bromocyclopentane on reaction with alcoholic KOH produces (A) 4–phenylcyclopentene (B) 2–phenylcyclopentene (C) 1–phenylcyclopentene (D) 3–phenylcyclopentene

78. Tertiary alkyl halides are practically inert to substitution by 2NS mechanism because of

(A) insolubility (B) instability (C) inductive effect (D) steric hindrance 79.

C—OH NHC in

SOCl

55

2

H

Ph

Me

Which statement is true for the above reaction? (A) Retention of configuration (B) Inversion of configuration (C) Inversion and Retention both (D) None

80. The nucleophilicities of 3 2CH ,NH ,OH and F decrease in which order ?

(A) 3 2CH NH OH F (B) 2 3OH NH CH F

(C) 2 3NH OH CH F (D) 3 2CH OH F NH

81. Correct order of leaving group tendency is :

(A) I Br Cl F (B) F Cl Br I

(C) Cl F Br I (D) I Cl Br F





82. Which of the following will not undergo nucleophilic aromatic substitution ?

(A)

Cl

D

(B) Cl

D

D

(C)

CH3

Cl

D

CH3

(D)

CH3

Cl

CH3

CH3 (A) I, II and III (B) II and IV (C) III and IV (D) only IV 83.

O

Ph2 Cu Li

H3OProduct :

Identify the structure of product :

(A)

O

Ph

(B)

HO Ph

(C)

OH

Ph

(D)

Ph OH

Ph





84. In the given reaction

O

H3CMgBr

H / H2O

Product

Find the product of reaction :

(A) OH

(B)

(C)

OH

(D)

OH

85. In the reaction

2 5

NaOH HBr AlC KOH3 2 2 C H OH

CH CH CH Br A B C;C is

(A) Propene (B) Propyne (C) 1-Propanol (D) 2-Propanol 86. Which of the following is the correct order of reactivity of arylhalies towards nucleophilic substitution

reactions.

F Cl Br I

< < < (A)

F Cl Br I

> > > (B)

Cl F Br I

> > > (C)

Br I Cl F

> > > (D)





87. The order of relative reactivity of the given halides towards NS 2 reaction is

(A) Ph 2 3 3 2CH Cl PhCHCl(CH ) PhCCl(CH ) (B) 2 3 3 2PhCH Cl PhChCl(CH ) PhCCl(CH )

(C) 3 2 3 2PhCHCl(CH ) PhCH Cl PhCcl(CH ) (D) 3 3 2 2PhCHCl(CH ) PhCCl(CH ) PhCH Cl

88. Ethylidene chloride on treatment with aqueous KOH gives (A) acetaldehyde (B) ethylene glycol (C) formaldehyde (D) none of them 89. In the reaction

2 6

2 2

1.B H3 2 2.H O /OH

CH CH CH 3PBr AgCNA B C;C is

(A) 3 2 2CH CH CH NC (B) 3 2CH CH CN

(C) 3 2 2CH CH CH CN (D) 3 2CH CH COOH

90. The compound 2 4 2C H Cl has following number of isomers and they can be distinguished by the

reaction with (A) 2, Aq KOH (B) 2, Alc KOH (C) 3, Bromine water (D) 3. Alc KOH





FIITJEE PET – XV (EXTENDED) MAINS_ANSWERS

DATE: 09.12.2017

MATHEMATICS

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

5. C 6. A 7. B 8. C

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

13. B 14. BONUS 15. BONUS 16. C

17. A 18. D 19. B 20. C

21. B 22. B 23. B 24. D

25. B 26. A 27. D 28. A

29. B OR C 30. C

PHYSICS

31. A 32. A 33. A 34. C

35. D 36. A 37. A 38. B

39. B 40. A 41. C 42. B

43. A 44. BONUS 45. BONUS 46. A

47. A 48. B 49. A 50. D

51. C 52. D 53. B 54. C

55. A 56. D 57. C 58. B

59. B 60. A

CHEMISTRY

61. B 62. A 63. C 64. D

65. A 66. D 67. B 68. A

69. C 70. A 71. C 72. A

73. A 74. A 75. B 76. D

77. D 78. D 79. B 80. A

81. A 82. D 83. A 84. C

85. A 86. B 87. A 88. A

89. A 90. A

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FIITJEE PET XV EXTENDED) - fiitjeehyderabad.com (EXTENDED) (MAIN… · 1 = 222 a b c a b c, ... cotx tanx ³ (A) 1 cos4x c 4 (B