mock JEE ADVANCE PCM - 1.doc

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Physics Section – I Part – A Single Answer Questions 1. A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and its mass is M. it is suspended by a string in a liquid of density p where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is: (a) Mg (b) Mg-Vpg 2 2 (c) Mg  R hpg (d) pg  V  R h 

2. Heat

Q

3 RT is supplied to 4mol of an ideal diatomic gas at temperature T, which remains constant. How 2

many moles of the gas are dissolved into atoms? (a) 3 mol

(b) 2 mol

(c) 1 mol

(d)

3 mol 2

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2016

3. Three rods of same material and cross sectional area form the side of a triangle ABC Fig. The points A, B and C are maintained at temperatures

T , T 2, and



3T



2 1

, respectively. Assuming that only heat conduction

takes place and the system is in steady state, find the angle at B. The temperature difference per unit length along CB and CA is equal

(d) 90 0 4. Two wires A and B of the same cross sectional areas. Young’s moduli Y1 and Y2 and coefficients of linear expansion 1 and  2 respectively, are joined together and fixed between right supports at either ends. The tension in the compound wire (a)

30

(b)

45

(c)

when wire A is heated and wire B is cooled at different temperature is same when wire A alone is cooled at the same temporizer as wire B earlier. Find correct option (a)

1 Y2   2 2Y1

(b)

1 Y2   2 2Y1

(c)

1 2Y2   2 Y1

(d)

5. In the circuit shown, the ratio of magnetic energies in the 5mH & 10mH inductors in the stable state would be (a) 1:2 (b)1:4 (c) 3:2 (d) None of These

1 Y2   2 Y1 5 mH

10 mH 10V 2

6. The segment AB of wire carrying current I1 is placed perpendicular to a long straight wire carrying current I 2 as shown in figure. The magnitude of force experienced by the straight wire AB is II II (a) o 1 2 ln 3 (b) o 1 2 ln 2 2 2 2o I1 I 2 o I1 I 2 (c) (d) 2 2 

7. As shown in the figure, four identical loops are placed in a uniform magnetic field B . The loops carry equal current i. n$ denotes the normal to the plane of each loop. Potential energies in descending order are

(a) I, II, III, IV

(b) IV, II, III, I

(c) I, III, II, IV

(d) IV, III, II, I

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2016

8. Two ends of an inductor of inductance L are connected to two parallel conducting wires. A rod of length l and mass m is given velocity vo as shown. The whole system is placed in perpendicular magnetic field B. Find the maximum current in the inductor. (neglect gravity and friction) mvo m (a) (b) vo L L mv02 (c) (d) None of these L 9. The figure shows a non – conducting ring of radius R carrying a charge q. In a ur circular region of radius r, a uniform magnetic field B perpendicular to the plane of dB   . The torque acting on the ring is the ring varies at a constant rate dt 1 1 (a) qr 2  (b) qR 2  2 2 2 (c) qr  (d) zero 10. A thin circular ring of area A is held perpendicular to a uniform magnetic field of induction B. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is R. When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is BR AB B2 A (a) (b) (c) ABR (d) A R R2 More than one Correct Answer 11. An incompressible liquid flows in the tube array as shown. Then: 1 (a) a2  2  2a11 for a2  a1 (b) a2  2  a3 3  a11 2 (c) 2a2 v2  a1v1 for a2  a3 (d) a3 v3  a2 v2

2V0 is divided by a frictionless piston of area S and mass m into two equal parts A and B. Part A has an ideal gas at pressure P0 and temperature T0 and in part B is vacuum. A

12. A thermally insulated chamber of valueme

mass less spring of force constant K is connected with the piston and the wall of the container as shown in Fig. Initially the spring is unreformed. The gas in chamber A is allowed to expand. Let in equilibrium the spring is compressed by x0 Then

(a) Pressure of the gas at equilibrium is Kx0 (b) Temperature of the gas is decreased (c) Increase in internal energy of the gas is (d) Work done by the gas is

 1/ 2  Kx02

/S

 1/ 2  Kx02

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ur ur 13. A charged particle is moving along positive y – axis in uniform electric and magnetic fields E  Eo k$ and B  Bo $ i Here Eo and Bo are positive constants. Choose the correct options. (a) particle may be deflected towards positive z - axis (b) particle may be deflected towards negative z – axis (c) particle may pass undeflected (d) kinetic energy of particle may remain constant 14. Two long, thin, parallel conductors, separated by a distance d, carry currents i1 and i2 . The force acting on unit length of any one conductor is F. (a) F is attractive, if i1 and i2 flow in the same direction. (b) F is repulsive, if i1 and i2 flow in opposite directions. (c) F is the same for both conductors (d) F is different for the two conductors. 15. A wire of length l carreies s a current i along the X-axis. A magnetic field





B  B0 iˆ  ˆj  kˆ T exists in the

region. Then (a) magnetic force acting on wire is

2B0il .

(b) magnetic force acting on wire is

(c) magnetic force lies in Y – Z plane.

3B0il

(d) magnetic force lies in X – Y plane. Numerical

N1.

N2.

N3.

N4.

10 Magnetic field at point A B  x0  10 Calculate xo . a  3 metre I = 10 A Write the first digit of answer.

A square metal wire loop of side 10 cm and resistance 10 ohm is moved with a constant velocity Vo in a uniform magnetic field of induction B  2 weber / m 2 as shown in the figure. The magnetic field lines are perpendicular to the plane of the loop. The loop is connected to a network of resistors each of value 3 ohms. The resistances of the lead wires OS and PQ are negligible. What should be the speed of the loop so as to have a steady current of 1 milliampere in the loop? (in cm/s) Write the first digit of answer. 2 A wire carrying a current of 3A is bent in the form of a parabola y  4  x as shown in figure, where x and y are in metre. The wire is placed in a uniform ur $ , then x = magnetic field B  5k$ tesla. The force acting on the wire is 10 xiN

A body is cooled in 2 min in a room at temperature of 30C from 75C to 65C If the same body is cooled from 55C to 45C in the same room, find the time taken (in minute)

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N5.

2016

The resistance offered by the conductor shown given the resistively of the  r  material depends on the radius as   0 is 0 in N, the value of N is R R (Give (rxn)

Chemistry II

Section – Part – A Single Answer Questions

1.

2.

3.

The number of chiral centres present in glucopyranose and fructofuranose are (a) 4 and 3 (b) 5 and 4 (c) 4 in each

(d) 5 in each

Arrange the following amides according to their relative reactivity when treated with Br2 in excess of strong base. (i) Benzamide (ii) p Methyl benzamide (iii) p nitro benzamide (iv) p chloro benzamide (a) I  II  III  IV (b) II  IV  I  II (c) II  I  N  III (d) IV  I  II  III O

CH3 CF3CO3H

A+B

Product A and B are (b) Position isomer

(a) Enantioners 4.

O

1. H2C

CCl4

+

CH

(c) Diastereomers

CH2 Br

B.

+

2. H3O ,

N H

(a)

B is

O

(b) N

OH

(c )

CH 2

5.

(d) Functional isomers

(d)

CH 2

N

A monocarboxylic acid decolarise

Br2 / H 2O on heating with soda lime derivative of styrene is formed. With neutral

FeCl3 a buff coloured precipitate is formed. Acid could be (a)

O

COOH

O

(b)

OH

O

(c)

O

(d)

CH2

OH

O OH

OH

6. Ethyl iodide when treated with dry silver oxide gives FIITJEE Kochi Center Lakshmi Bai Towers, TD Road, North End, Kochi - 682035

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(A) Ethanol

7. The compound in which the number of (a) 8.

2016

(B) Diethyl ether

XeO4

(C) Ethylene

(D) Ethane

d   p bonds are equal to those present in ClO4  (b) XeO4 (c) XeO3

Among the following, density is maximum for (A) CH3Cl (B) CH2Cl2

(C) CHCl3

(d)

XeF4

(D) CCl4

9. BuNa N synthetic rubber is a co-polymer of (a) CH 2  CH  CH  CH 2 and

C6 H 5  CH  CH 2 . (b) CH 2  CH  CN and CH 2  CH  CH  CH 2 CH 2  CH  C  CH 2 CH  CH  CN | (c) and 2 CH 3 Cl | (d) CH 2  CH  C  CH 2 and CH 2  CH  CH  CH 2

10. An aqueous solution of ethanol has a density 1.025 g/ml and it is 8.0M. The molality of this solution is (a) 12.17 (b) 11.72 (c) 10.27 (d) 13.58 One or more than one option correct questions 11. A narrow tube of negligible volume connects two evacuated bulb of 1L capacity each. One bulb is placed in a 200K thermostat bath and other in a 300K thermostat bath and then 1.0 mole of an ideal gas is injected into the system. Which of the following is correct regarding the above system? (a) The pressure in the flask A is 9.8 atm (b) The pressure in the flask B is 8.7 atm (c) The number of moles is coled flask is 3/5 (d) The number of moles in hot flask is 6/8. 12. A mixture of KMnO4 and K 2Cr2O7 weighing 0.24g on being treated with KI in acid solution liberates sufficient react with 60 ml of 0.1N hypo. Select the wrong statement (a) % of Mn in the sample is 20.83% (b) % of Cr in the same is 14.17% (c) wt., of KMnO4 is 0.034g. (d) wt., of K 2Cr2O7 is 0.050g. 13. Which of the following compound has Fe only in +3 oxidation state? (a) Fe2O3 (b) FeO (c)

Fe3O4

14. Which reagents gives oxygen as one of the product during oxidation with ozone? (a) H 2 S (b) PbS (c) SO2 15. Which of the following are correct for glucose? (a) It gives positive test with Schiff’s reagent.

(b) It reacts with

(c) Pentaacetate derivative of glucose does not react with (d) It gives positive test with Benedicts solution.

(d)

Fe4 [ Fe(CN )6 ]3

(d)

SnCl2 / HCl

I 2 to

NaHSO3 and NH 3 .

1/ 2N  OH

Numerical N1.

How many of the following compounds will show higher rate of nucleophillic addition than p methyl benzaldehyde? FIITJEE Kochi Center Lakshmi Bai Towers, TD Road, North End, Kochi - 682035

KOPA56A01, A02 PHASE - 3 JEE ADVANCE PCM - 1 CHO

CHO

CHO

;

;

;

OCH 3

NO 2

Cl

N2.

Br n.

+

CHO

CHO

;

;

N(CH 3) 2

CH2

Br

2016

CHO

CN

OH

COOC2H5

C2H5ONa C2H5OH

COOC2H5

At what value of n, the formation of six membered ring takes place. N3.

How many of the following are more basic than aniline. CONH2

NH

NH2

NH2

H ;;3C

;

;

NH2

NH

C NH2 ; CH3

C

NH2 ;

NO2 NH2

;

;

Cl

N4.

NH 2

NH2

OCH3

; CHO

6. A 0.127g of an unsaturated oil was treated with 25ml of 0.1m Icl solution. The unreacted ICl was then treated with excess of KI. 40 ml of 0.1M hypo was required to titrate the liberated I 2 . Determine mass of iodine that would have been required by 5g oil if

N5.

NH2

I 2 were used in the place of ICl.

n factor for Br2 in the following reaction is ---Br2 + NaOH  NaBr + NaOBr + H2O

Mathematics Section – III Part – A Single Answer Questions x 2

1. Let x x (A) 0 (C) 16

2 x x 6  Ax 4  Bx 3  Cx 2  Dx  E , then the value of 5A + 4B + 3C + 2D + E = x 6 (B) 6 (D) none of these

2. If a matrix A is such that 3A3 + 2A2 + 5A + I = 0, then A–1 is equal to (A) –(3A2 + 2A + 5) (B) 3A2 + 2A + 5 (C) 3A2 – 2A – 5 (D) –3A2 – 2A – 5I FIITJEE Kochi Center Lakshmi Bai Towers, TD Road, North End, Kochi - 682035

KOPA56A01, A02 PHASE - 3 JEE ADVANCE PCM - 1  1

3

  2

 2

4

8 



3. If the matrix  

 3

5

  

2016

is singular, then  is equal to

10 

(A) –2 (C) 2

(B) 4 (D) –4

1   4. The number of terms in the expansion of  a3  3  1 a   (A) 201 (B) 300 (C) 200 (D) 100C3 5.

6.

7.

8.

is

r r r r r r r r r r r r r r Let a = 2i - j + k, b = i + 2 j - k, c = i + j - 2k be three vectors. A vector in the plane of b and c, whose r 2 projection on a is of magnitude is 3 r r r r r r r r r r r r (a) 2i + 3j - 3k (b) 2i + 3j + 3k (c) - 2i - j + 5k (d) 2i + j + 5k r r r r r r r r r r If a, b, c are three non-coplanar vectors, then ( a + b + c) ×é (ëa + b) ´ ( a + c) ùúû= ê (a) [ abc ] (b) 2 [ abc] (c) - [ abc]

(d) 0

r r r r r r r If a and b are two unit vectors such that a + 2b and 5a - 4b are perpendicular to each other, then angle between a r and b is 1÷ 2÷ - 1 æö - 1 æö ÷ ÷ (a) 450 (b) 600 (c) cos ç (d) cos ç ç ç ÷ ÷ ç ç è3 ø è7 ø 2 2 2 ‘P’ is any arbitrary point on the circumcircle of the equilateral  ABC of side length l units then PA  PB  PC is always equal to (a) 2 l 2

9.

100

(b)

2 3 l2

(c)

l2

(d) 3 l 2

2 x3  3x2  12 x  3  0 . Then the centroid of the  ABC, where A  ( ,  , ), B  (  , , ), C  (  , ,  ) is 1 1  1 1 1  1 (a)  , ,  (b)  1, 1, 1 (c)   ,  ,   (d)  1,  1,  1 2 2  2 2 2  2

If  ,  ,  are the roots of the equation

10. The line

 

r



 a  ( b X

   (a)  aX cbX c



c)

 



 (b)  a.c 



and

 will intersect if

r  b  ( c X a ) b.c



(c) b

X

 



acXa

(d) None

One or more than one correct option questions r r r r r r r r r r r 11. Let a and b be two non-collinear unit vectors. If u = a - ( a ×b) b and v = a ´ b, then v is r r r r r r r r r r r (a) u (b) u + u ×a (c) u + u ×b (d) u + u × ( a + b)

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2016

ur 12. Let A be vector parallel to line of intersection of planes P 1 and P2 through origin. P1 is parallel to the vectors 2$ j + 3k$ u r $ then the angle between vectors A and 2i$+ $ and 4$ j - 3k$ and P2 is parallel to $ j - k$ and 3i$+ 3j, j - 2k$ is

(a)

π 2

(b)

π 4

(c)

π 6

(d)

3π 4

r r r 13. The vector i + x j + 3k is rotated through an angle 'θ ' and doubled in the magnitude, then it becomes r r r 4i +( 4x - 2) j + 2k. The value of ‘x’ are (a)

- 2 3

(b)

1 3

(c)

2 3

(d) 2

a b aα + b b c bα + c = 0. Then 14. If aα + b bα + c 0 (a) a, b, c are in AP (a) a, b, c are in GP é1 w ê 2 ê A = w w 15. The matrix ê êw 2 1 ê ë (a) symmetric

(b) a, b, c are in HP (b) ( xα- ) is a factor of ax 2 + 2bx + c = 0 w2 ù ú 1ú ú is wú ú û (b) skew symmetric

(c) singular

(d) orthogonal

Numerical

N1. N2.

N3.

é1 a 2ù ê ú 1 2 5úis not invertible if ‘a’ is equal to _______. The matrix ê ê ú ê ê2 1 1 ú ú ë û éx 1ù 2 ú If A = ê ê1 0ú and A is identity matrix, then ‘x’ = _______. ë û é4 5 ê ê5 6 If x, y, z are in AP., then the value of det ( A ) is, where A = ê ê6 7 ê êx y ê ë

6 7 8 z

xù ú yú ú; _______. zú ú 0ú ú û

N4.The sum of the factors of 7!, which are odd and are of the form 3t + 1 where t is a whole number, is _____. N5.

Six identical coins are arranged in a row. The total number of ways in which the number of heads is equal to the number of tails, is 4k, then ‘k’ is _______.

KOPA56A01, A02 PHASE - 3 JEE ADVANCE PCM - 1 ANSWER KEYS

Physics 1. C

2.A

3.D

4.B

5.D

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KOPA56A01, A02 PHASE - 3 JEE ADVANCE PCM - 1

2016

6. B

7.D

8.D

9.D

10.B

11. B, C, D

12.A, B

13.B, D

14.A, C

15.A, B

N1.2

N2.3

N3.8

N4.4

N5. 4

Chemistry 1. B

2.C

3.B

4.A

5.D

6. B

7.C

8.D

9.B

10.A

11. AC

12.AB

13.A

14.AB

15.CD

N1.3

N2.3

N3.5

N4.5

N5.1

Mathematics 1.

D

2.D

3.B

4. A

5. A

6. C

7.B

8. A

9.C

10.B

11. A, C

12.B, D

13.A, D

14.C, D

15.A, C

N1.1

N2.0

N3.0

N4.8

N5.5

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