Fitjee AITS PT 3 paper 1+2

AITS-PT-III (Paper-2)-PCM-JEE(Advanced)/14

Physics

PART-i

SECTION - A Single Correct Choice Type This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which O N L Y O N E is correct. 1.

A thin hemispherical shell of mass M and radius 'R' is placed as shown in the figure. The magnitude of gravitational field at 'P' due to thin hemispherical shell is l . The magnitude of gravitational field at 'Q' duelo thin hemispherical shell is given by TA) lc/2 (B) l 0

0

( C )

™ ( D )

2.

9R 2

G

2

'°

M +

,

-9R^ °

A person sitting at a large distance from a point source of sound writes down the following equation for the waves received by him. y = Asin(27ix + 7007it), where x is in metre and t in sec. If the Bulk modulus of air = 1.40 x 10 Nm" , then the density of the medium is (A) 39/35 kg/m (B) 7/5 kg/m (C) 8/7 kg/m (D) 10/7 kg/m 5

2

3

3

3

3

Space for Rough work

FITTJCC Ltd., FIITJEE

House,

29-A, Kalu

Sarai, Sarvapriya website:

Vlhar, New Delhi -110016, www.fiitjee.com

Ph 46106000,

26569493,

Fax

26513942

AITS-PT-lll(Paper-2)-PCM-JEE(Advancedyi4

3.

Three identical isosceles right angled prism (ABC, BCD and CDE) are placed as shown in the figure. ZABC, ZBCD and ZCDE are 90° in the given prism respectively. A ray is incident along line AB. Refraction takes placed at BC and CD and then it emerges along the line DE. ix-t, n and ^ are the refractive index of prism ABC, BCD and CDE respectively. The relatior between \i and p. is (A) r x + u - r x + 2 = 0 (B) n | - n f - u | + 2 = 0 2

3

2

2

2

2

3

2

2

(C) n + u - 2 ^ + 2 = 0

(D) u

2

2

u -u§+2 =0

Two identical, thin rods, each with mass m and length L, are joined at right angles to form an L-shaped object. This object is balanced on top of a sharp edge as shown in the figure. If the L-shaped object is deflected slightly, it oscillates. The frequency of oscillation is ( A ) ± S 2TIVV2 L (B)

1

v 4a/2 L

~2x

(C)

3g

1

3g

2TTV2V2L

A 2.71 gm sample of KCI from the chemistry stockroom is found to be radioactive, and it is decaying at a constant rate of 4490 Bq. The decays are traced to the element potassium and in particular to the isotope * ° K . which constitutes 1.17% of normal potassium. The half life of nuclide is (A) 1.25 x 10 year (B) 5.5 x 10 year (C) 5.5 x 10 year (D) 1.25 x 10 year jGiven J^MK^219/102^gm/mole, MQ = 35.453 gm/mole, Avogadro number N = 6.02 x 10 ) 9

9

8

8

23

A

Space for Rough work

unite

Ltd., FIITJEE

Bouse,

29-A, Kutu

Sural, Sarvaprtya Vlhar, New Delhi website: www.fiitjee.com

-110016,

Ph 461060OO,

26569493,

Tax

26513942

5 AITS-PT-lll(Paper-2)-PCM-JEE(Advanced)/14

Two liquids of density 2p and p are filled in a vertical U-tube as shown in the figure. The vertical height of liquid of density 2p is h. If we accelerate the tube towards right till the heights of liquid columns will be same. The acceleration of tube is 3g (A) 5 o (D)

(C) 7.

4g

A circular spring of stiffness constant k = 30 N/m is cut and then welded with two blocks of masses 2 kg and 4 kg such that ratio of length of spring between the blocks is 1 : 3. The angular frequency of oscillation of blocks in a smooth horizontal rigid tube, if the blocks are slightly displaced form equilibrium position is (A)

r£

rad/sec (D) ^60 rad/sec In the given figure, a string of linear mass density m and length L, is stretched by a force F = (F -kt)N, where F & k are constant and t is time. At the time t = 0, a pulse is generated at the end P of the string. As the pulse reaches the point Q, the force vanishes. The value of k in the above equation is 0

51

0

T F = (F -kt)N 0

Space for Rough work

FHIJK LUL, FIITJEE

House,

29-A, Kalu

Sural,

Sarvaprtya Vthar, New Delhi -110016, website: www.fittjee.com

Ph 46106000,

26S69493, •

Fax

26S13942

I

AITS-PT-lll(Paper-2)-PCM-JEE(Advanced)/14 Multiple Correct Answer(s) Type

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (I out of which ONE or MORE are correct.

9.

at some angle from the vertical

A body is thrown from the surface of earth with velocity

the maximum height reached by the body is — . Then choose the correct option(s) (R = Radi 4 of earth) e

(A) the angle of projection from the vertical is sin-1 v

4

(B) the velocity of the body at maximum height is v • (C) the angleof projection from the vertical is sin

, gR 10

e

1

(D) the velocity of the body at maximum height is zero.

10.

A vertical U-tube contains a liquid of density 'p'. Now it moves with a constant horizontal acceleration 'a' Let fn & h are the heights of liquid column in left and -right limbs and n and r are the radius of curvature of menisceus are respectively as shown in the figure. 2

2

_ f hi

Assume 'P ' is the atmosphere pressure and 'S' is the surface tension of liquid. point 'A' is / are 0

(AJpgrM + Po-

25

2S

(B)pgh + P 2

2S

(C) pgh! + P + — i

0

(D) pgh + P +

0

2

r

+ pae

2S

0

The pressui

P

a£

h Space for Rough work

FHTJCC Ltd., rUTJEE

House,

29-A, Kalu

Sural,

Sarvaprtya Vlhar, Sew Delhi -110016, website: www.filtjee.com

Ph 461O600O,

26569493,

Fax

26513:

7 A1TS-PT-III (Paper-2)-PCM-JEE(Advanced)/14 In YDSE, intensity of light wave passing through slits Si and S are U and l respectively as shown in figure (1). The pattern of intensity distribution on the screen is givenin figure (2) where x is distance measured from the point O. In this case which of the following statement(s) is/are true (Given d « D) 2

2

Screen Figure-2

Figure-1

(A) The intensity of light passing through Si and S is the same. (B^Thrphase difference between the light waves passing through Si and S to a fixed point on the screen is independent of time. (C) The phase difference between the light waves passing through Si and S to a fixed point on the screen varies with time. (D) Light waves passing through Si and S have the same wavelength. 2

2

2

2

12

In the shown figure mass of the pulley is m and radius 2R. A light concentric spool of radius R is rigidly attached with the pulley. Two blocks A and B having masses m & 4m respectively are attached with the pulley by means of light strings. Lower surface of the block B is attached to a spring of stiffness k and block B rests on a smooth inclined plane inclined 30° with horizontal. Other end of the spring is fixed to the ground. Initially the blocks are held at a height such that spring is in relaxed position. The block A is streatched a small distance and released. The strings do not slip on the pulley and spool. (A) In equilibrium the extension in the spring is zero (B) In equilibrium the extension in the spring is 2mg/k

10m

(C) The time period of oscillation of block B is T = 2n V (D) The time period of oscillation of block B is T = 2n

Space for Rough work

F1FTJC6 Ltd., FIITJEE

House,

29-A, Kulu

Sural,

Sarvaprlya website:

Vlhar, Hew Delhi -110016, www.flltjee.com

Fh 461O6OO0, 26S69493,

Fax

26S13942

8 AITS-PT-III (Paper-2)-PCM-JEEjAdvanced)/14

SECTION - B Matrix - Match Type This section contains 2 questions. Each question contak^stalsmeets gnen in two columns, which have to be matched. The statements in Cotumm I are labelled A, B, C and D, while the statements in Column II are a.:-'-?-: : z r, s and t. Any given statement in Column I can have corrmA H k l i g **?» OWE OR MORE statement(s) in Column II. The appropriate M * H corresponding to the answers to these questions have to be dBkened am illustrated in the following example: If the correct matches are A-p, s and t; B-q and r: C-p and q: and D-s and t; then the correct darkening of bubbles will look like the fotomng: 1.

p

q

*»©©©©

I 00©O 0 0000 5®©©©

Some physical quantities~are given in column -I and their j ~e-.s--o.TS • DBhmn h -> (Planck's constant) S -» (Surface tension) G -> (Gravitational constant) r| ->• (Coefficient of viscosity) P—^ (Power) Match the following. Column - If

Column-I (A)

The dimension of — r|

(P)

M-l r

(B)

GS The dimension of — P

(q)

MLT"

(C)

The dimension of — S

(0

M~ LT~

(D)

The dimension of — G

(s)

M-l r

3

2

2

-

1

1

6

2

(t) Space for Rough work

FOTJCC Ltd., FIITJEE

House,

29-A, Kalu

Sural, Sarvapriya website:

Vihar, Sew Delhi www.flitjee.com

llXie.

Ph 46106O00,

26569493,

Fax

26513942

9 AITS-PT-lll(Paper-2)-PCM-JEE(Advanced)/14

2.

A particle of mass 2 kg is moving on a straight line under the action of force F = (8 - 2x) newton along the x-axis, where x is the coordinates on x-axis. If a particle is released from x = 7 m, then for the subsequent motion match the following (all values in Column II are in S.I. units)

Column 1

Column il

(A)

Amplitude of SHM is

(B)

Time taken to move directly from x = 2.5 m to (q)

(P)

0.52 3

x = 4 m (approx) (C)

Maximum kinetic energy of SHM system

(r)

6

(D)

Velocity of particle at x = 4m

(s)

9

0)

4.5

SECTION - C Integer Answer Type This section contains 6 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1.

A uniform rod of mass m and length L is clamped at one end, vibrates in the third harmonic, with the frequency of 300 Hz7 The Young's modulus of the rod is X x 10 N/m . Given that length of rod is 1 m and density of rod is 5 x 10 kg/m . Find the value of X. 10

5

2.

2

3

A particle of mass m is placed at a distance of 4R from the centre of a huge uniform sphere of mass M and radius R. A spherical cavity of diameter R is made in the sphere as shown in the figure. If the gravitational interaction potential energy of the system of mass m and the remaining sphere after making the cavity is _

: > t G M m

28R

p j j the value of X. n c

Space for Rough work

»

niJCC

Ltd., FIITJEE

House,

29-A, Kalu

Saral,

Sarvaprtga Vlhar, New Delhi -110016, website; www.fiitfee.com

Ph 46106000,

26569493,

Fax

26513942

10 AITS-PT-lll(Paper-2)-PCM-JEE(Advanced)/14

Two strings AB and BC of equal length are connected as shown to a 10kg block through an inextensible string QP. AB and BC both are made of same material, whose density is 8000 kg / m . The entire arrangement is kept in an elevator accelerating upwards with acceleration 2 m/s . Find the minimum number of loops in the string AC if joint B is a 25 , node. Cross sectional area of BC is —mm and that of AB 24 is 25/6 m m .

B

3

4 t 4 I I t I

2

Ip

2

2

A fixed container having area of cross-section 1 m contains water. The initial height of Water in container is 1m. The container has an orifice of small cross section area near its bottom. Find the ratio of i / 2 > where Pm and R are the rates of change of height of the R

R

2

liquid in the container when the heights of liquid in container are 1 m and 0.25 m respectively. Area of orifice is 0.001 m . 2

V-t

A rectangular tank of height 6 nufilled with water, is placed near the bottom of an incline of angle 30°. At height x from bottom a small hole is made (as shown in figure) such that the stream coming out from hole, strikes the inclined plane normally. Find x in metre. A ray PO is incident on the mirror AC at an angle 30° as shown in the figure. Ray PO is reflected by mirror AB and AC. The deviation of ray P O after its final reflection from mirror AC is Kn . Find the value of K.

Space for Rough work

nnJCC Ltd.. FIITJEE

House,

29-A, Kalu

Saral,

Sarvapriya Vlhar, New Delhi website: www.Jiitjee.com

-110016,

Ph 46106000,26569493,

Tax

26513942

11

Chemistry

AITS-PT-III (Paper-2)-PCM-JEE(Advanced)/14

PART-II SECTION - A Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1.

How many of the following reactions/statements are correct? (i) Cr0 shows blue colour in organic solvent but in aq. solution blue colour fades because C r 0 decomposes to Cr and 0 . (ii) [Co(SCN) ] ~ shows blue colour is aq. solution. (Hi) The pink ppt. of Co(OH) converts slowly to brown ppt. Co(OH) on exposure to air while green ppt. of Ni(OH) can^e oxidised to black, Mi(OH)3 with an oxidising reagent like NaOCI only. (A) (i) only (B) (i) and (ii) only (C) (Hi) only (D) (i), (if) and ("0 all are correct 5

5

3+

2

2

4

2

3

2

2.

The wrong statement about NH is: (A) NH3 is oxidised with oxygen at 700°C in the presence of platinum. (B) NH gives black precipitate with calomel. (C) NHs can be dried by P 0 , H S0 and CaCI . (D) NH gives white fumes with HCI. 3

3

2

5

2

4

2

3

3.

Nitrogen cannot be obtained by heating: (A) Pb(N ) (s) (C) (NH ) Cr 0 (s) 3

4

4.

2

2

2

7

(B) KN03(s) (D)NH N0 (s) 4

2

If aq. NaCI is electrolysed using graphite as anode and Hg as cathode, than products are: (A) Cl gas at anode and Na at cathode. (B) Cl gas at anode and H gas at cathode. (C) 0 gas at anode and H gas at cathode. (D) Cl gas at anode and 0 gas at cathode. 2

2

2

2

2

2

2

Space for Rough work

FlirJCC Ltd., FHTJEE

House, 29-A, Kalu

Saral,

Sarvaprtya Vthar, New Delhi -110016, Ph 461060OO, website: www.flltjee.com

26S69493, '

Fax

26513942

12 AITS-PT-lll(Paper-2)-PCM-JEE(Advanced)/14

5.

Which of the following is true when a gas moves freely from one part to another part of a rigid system? (A) Work is zero because the external pressure is zero (B) Work is zero because AV of the system is zero (C) Work is zero only if the temperature is held constaM (D) Work is zero only if the external pressure is hekj constant

6.

Select the correct statements among the following: 1. Complexes [Cu(NH ) ] , [MnCI ] -, [Fe(CN) ] . | T l f U J " are all paramagnetic. 2. Complexes [Cu(NH ) ] , [Ni(CN) ] ~, [Ni(DMG)-] are afl square planner. 3. The correct stability order of the complexes will be [Fe(H20) ] < [Fe(C 0 ) ] " < [Fe(CN) ] ". 4 . [Cr(en) ] exist in three isomeric forms. (A) Only 1 is correct (B) 1, 3 and are correct (C) 2 and 4 are correct (D) 1, 2 and 3 are conect 2+

3

2

4

3

3_

4

e

2+

2

4

4

3+

6

3

2

4

3

3

6

3+

3

7.

The values of critical pressure (P ) and critical temperature (T ) for O ^ C b , H jand He are given below. The gas which has smallest value of van der Waal's constant 'b' is: c

Name of the gas

c

P (Nm )

T c (K)

c

2

0 0

5 8 1 2

2

2

H He 2

(A) 0 (C) H

x 10 x 10 x 10 x10

3

3

s

b

153 412 33.9 5.12

(B) Ch (D) He

2

8.

2

2

The entropy change for the isothermal expansion of an ideal gas at 3 0 0 K from a particular state A to state B is 50 JK" . When an expansion was performed, the work done by the system was 6 kJ. The process is (A) Reversible (B) Irreversible (C) It can be both (D) Cannot be calculated 1

Space for Rough work

FHTJCC Ltd., rOTJXE

House, 29-A, Kalu

Saral,

Sarvapriya Vihar, Sew Delhi -110016, website: www.flitjee.com

Ph 46106000,

26569493,

Fax

26513942

13 AITS-PT-III (Paper-2)-PCM-JEE(Advanced)/14

Multiple Correct Answer(s) Type This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. ' _____ 9.

Which of the following reactions are correctly balanced (A) 2CuS0 +2Na C0 + H 0 4

2

3

>CuC0 .Cu(OH) +2Na S0 + C 0

2

3

(B) 4Ag+8CN" + 0 +2H 0 2

2

2

4

2

>40H" +4[Ag(CN) J

2

2

4

3

(C) 4[Co(CN) ] ~ + O + 2H 0>4[Co(CN) ] " +40H" (D) 3CuC\ 2Hp ^ >CuO + Cu CI + 2HCI + CL, + H 0 6

z

2

6

2

10.

2

2

2

2

(CN) +20HT 2

2

2

2

Products are (B) OCN" (D) All are correct

(A) CN~ (C) H 0 2

12.

2

Which of the following cell representations4s/are correct? (A) Pt, H (1 bar) | HCI (aq) | Cl (1 bar), Pt (B) Hg | Hg2CI (s) | HCI (aq) | H (1 bar), Pt (C) Ag | AgCI (s) | KCI (aq) | Hg CI (s) | Hg (D) Pt, H (1 bar) | HI | Aul(s) | Au 2

11.

2

Which of the following statement(s) is/are correct? (A) At Boyle's temperature a real gas behaves as ideal gas for a wide range of temperature and pressure. (B) At Boyle's temperature van der Waal's constant 'a' and 'b' compensate each other. (C) The area under the maxwell distribution molecular speed curve remains same irrespective of temperature^f-gas. (D) The fraction of molecules with most probable speed increases with increase of temperature. Space for Rough work

MTJCC Ltd., FirTJEB

Bouse,

29-A, Kulu

Sural,

Sarvaprtya website:

Vthar, New Delhi www.flttjee.com

110016,

Ph 46106000,

26569493,

Fax

26513942

14 AITS-PT-lll(Paper-2)-PCM-JEE(Advanced)/14

SECTION - B Matrix - Match Type This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles B corresponding to the answers to these questions have to be darkened as C illustrated in the following example:

p

q

r

s

t

A|@®0©© ©

©

©

©

®@©0© -©600©

If the correct matches are A- p, s and t; B-q and r; C-p and q; and D- s and t; then the correct darkening of bubbles will look like the following: 1.

©

Match the Column - I with Column - II:

Column - II

Column - 1 (A) (B) (C) (D)

Na B O7Tl0H2O Na C0 K S0 -AI (S0 ) .24H 0 NH CI 2

4

2

2

3

4

2

4

3

2

4

FOTJCC Ltd., FIITJEE

House, 29-A, Kalu

Sarai,

(P) (q) (r) (s) (t) Space for Rough work

Basic solution Acidic solution Can react with NaOH Swell up on treating Neutral solution

Sarvapriya Vihar, New Delhi -110016, website; www.Jtitjee.com.

\

Ph 46106000,

26569493,

Fax

26513942

15 AITS-PT-lll(Paper-2)-PCM-JEE(Advanced)/14

2.

Match the Column - I with Column - II:

Column -1 (A)

(B)

(C)

(D)

Column - II

Melting points of the dioxides of the group 14 elements carbon, silicon, germanium, tin

The stability of monochlorides of group 13 elements boron, aftrminium, gallium, indium

Boiling point of the hydrides of the 16 group elements oxygen, sulphur, selenium, tellurium

Bond energies of the hydro acids of the halogen fluorine, chlorine, bromine, iodine

(P)

2

3 4 (Period No.)

2

3 4 (Period No.)

2

3 4 (Period No.

(q)

(0

(s)

3 4 (Period No.)

(t)

2 I^MMMBMMmaflBisasflaaaBfiaagflaaafiafifl

3 4 (Period No.)

.w.wwvvwvvvv%v.%v^^^

Space for Rough work

mutt Ltd., FIITJEE

House,

29-A, Kulu

Sural,

Sarvaprhja Vlhar, New Delhi -110016, website: wutw.fiitjee.com

Ph 461060OO,

26S69493,

Fax

26S13942

16 AITS-PT-III (Paper-2)-PCM-JEE(Advanced)/14

"SECTION - C Integer Answer Type This section contains 6 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1.

A sample containing 4 moles of l-fe gas and 2 moles of He gas have most probable velocity of 50 m/sec. Find the average translational kinetic energy per mole of the given gas mixture (in Joules)?

If the number of effective number of molecules in each unit cell is x and coordination number of oxygen in each unit cell is y. What is the value of x + y? In the figure given above dark ball represents oxygen atoms and grey ball represents titanium atoms. Space for Rough work

•

FIITJCC Ltd., FIITJEB

House, 29-A, Kalu

Sarai,

Sanapriya Vihar, New Delhi website: www.JUtJee.com

-110016,

Ph 46106O0O,

26569493,

Fax

26513942

17 AITS-PT-JII (Paper-2)-PCM-JEE(Advanced)/14

3.

x g of sample containing NaHC0 and Na C0 consumes 2 g equivalents of HCI for complete neutralisation, x g of the same sample is heated strongly, then cooled and the residue is treated with HCI. Find out the number of g equivalents of HCI that will be required for complete' neutralization of residue obtained after heating?

4.

How many of following statement(s) are correct? (A) Hardy schulz rule is related to coagulation (B) Brownian motion and Tyndall effect are the characteristic of colloids. (C) In gel, the liquid is dispersed in liquid. (D) Lower the gold number, more is the protective power of lyophilic sols. (E) All colloidal dispersion give very low osmotic pressure and show very small freezing point depression or boiling point elevation. (F) When negatively charged smoke comes in contact with positively charged clouds, rain fall takes place. (G) For a positive sol, flocculation values are in the order: NaCI > K S 0 > Na^PO, > K [Fe(CN) ].

3

2

4

2

4

3

6

5.

How many diastereoisomers are possible for the compound [Co(NH ) (N0 ) CI]?

6.

How many of the following compounds are possible products when chlorine is passed through hypo solution? S, HCI, Na S, Na S0 , NaCI, H S0

3

2

2

3

2

3

2

2

4

Space for Rough work

FIITJCC Ltd., FIITJEE

House,

29-A, Kolu

Saral,

Sarvapriya website;

Vihar, New Delhi -110016, wwwjlitfee.com

Ph 46106000,

26569493,

Fax

26513942

18 AITS-PT-lll(Paper-2)-PCM^JEE(Advanced)/14

Mathematics

PARTSECTION - A Single Correct Choice Type

section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

This

1.

How many quadrilaterals are there in the following diagram?

(A) 36 (C) 42

(B) 40 (D) 44

Define a sequence of complex numbers by how far from the origin is Zm (A) 1 (C) V3

= 0, z • 1 = t\ +i for n > 1. In the complex plane, n

(B) 72 (D) ^/TT0

Number of complex number z such that |z| = 1 and _z + z— = 1 is z z (A) 4 (B) 6 (C)8 (D)10 4.

2

2

2

Given that 8x + y + z = 1 and 4x + 4y + 5z = c then the value of [c] greatest integer function) (A) 5 (B) 6 (C) 7 (D) 8

max

is, (where [.] denote

Space for Rough work

FIITJtt- Ltd., FIITJEE

House, 29-A, Kalu

Saral,

Sarvapriya website:

Vthar, Hew Delhi www.fiitjee.com

110016,

Fh 46106000,

26569493,

Fax

26513942

AITS-PT-III (Paper-2)-PCM-JEE(Advanced)/14 5.

Find out the probability when we throw 4 distinct dice the minimum number appears on the dice is 2 and maximum is 5 (A) (C)

6.

-

648

(B)-^638

628

618

Let a, b, c e R such that abc = p and qa - b = 0, where p and q are fixed positive numbers, then the minimum distance of the point (a, b, c) from origin in the three dimensional coordinate system, is \1/3 / / „2 n1/3 2 (A)

V3

fp(q +l)l

p(q +l) x

2q

(cj V5(p)1/3

(B)

73

(D)

y/2

Find the number of common terms in the following sequences (each of which is an A.P.) which are less than 10,000 37,103,169 17,82,147, (A) 5 (B)2 (C) 3 (D) 4 3.

2

Let A (co ), B (2ico) and C (- 4) be three points lying on the Argand plane. Now a point P is taken on the circumcircle of the triangle ABC such that PA • BC = PC • AB, (where P; A, B, C are in order). If z is the complex number associated with the mid-point of PB, then the value of |z| is, (co is a non-real cube root of unity) (A) 0 (B) 1 (C) 2 (D) 3 Space for Rough work

FIITJCC Ltd., FIITJEE

House, 29-A, Kalu

Sarat,

Sarvaprhja website:

Vthar, New Delhi -110016, www.fiitfee.com

Ph 46106000,

26569493,

Fax

26513942

20 AITS-PT-IIMPaper-2)-PCM-JEE(Advanced)/14

Multiple Correct Answer(s) Type This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE'br MORE are correct. 9.

Determine the number of subsets of {1, 2, 3, 4 50} whose sum of elements is larger than or equal to 638 (A) 2 (B) 2 ^ (C) 2 (D) 2 49

47

10.

46

If n distinct objects are distributed randomly into n distinct boxes, (A) then the probability that no hox is empty is J=|n "C (B) then the probability that exactly one box is empty is — n" n

n

r

C (n-1) " (C) then the probability that a particular box get exactly r objects is — n" (D) none of these r

1

20

11.

30

S = (150 - 3x) (2x - 50) , 25 < x < 50 which of the following could be the possibl^value of S (A)4 x i o (B^xio^ (C) 2 x i o (D) 3 x 10 50

5 0

50

5 0

0

50

40

2

12.

If the curve y = ax + 2bx + c, (a, b, c e R, abc* 0) never meet x-axis, then a, b, c can't be in (A) A.P. (B) G.P. (C)H.P. (D) all of these Space for Rough work

tmiU

Ltd., FIITJEE

House,

29-A, Kalu

Saral,

Sarvapriya website:

Vihar, New Delhi -110016, www.fayee.com

Ph 46106000,

26569493,

Fax

26513942

21

AITS-PT-lll(Paper-2)-PCM-JEE(Advanced)/14

SECTION - B Matrix - Match Typt__ This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with B ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened asC illustrated in the following example: If the correct matches are A- p, s and t; B-q and r; C- p and q; and D-s and t; then the correct darkening of bubbles will look like the following:

p

q

r

s

t

®

®

#

©

©

®

@

®

®

©

*®®QBB

1.

Match the following Column-I with Column-ll We have to chose a, b, c, d and e from set of numbers {1, 2, 3 Column -1 (Conditions) a>b>c>d>e (A) (B)

ab>c>d>e

(s) (t)

2.

Match the following Column-I with Column-ll. Column -1 (When we throw) (A) 6 distinct dice (B) (C)

6 alike dice 3 distinct and 3 alike dice

(D)

4 distinct and 2 alike dice

c

100

p

104

o

U

104

n

u

5

99

103 ~

99

u

99

10V

Column-ll (Number of outcomes) (P)

(q) (r) (s) (t)

6 x C 6" x 21 6 x C 3

4

8

5

7

5

•.v.viSViSvi

Space for rough work

FIITJK Ltd., FIITJEE

House, 29-A, Kalu

Sarxzi, Sarvapriya Vihar, New Delhi website f'www.fiitjee.com

-110016,

Ph 46106000,

26569493,

Fax

26513942

22 AITS-PT-III (Paper-2)-PCM-JEE(Advanced)/14

SECTION - C Integer Answer Type This section contains 6 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). "1 -1 1.

A =

2 1

"4

2

2

and 10B = -5

0 -2

a

1"

1 1

-3 1

1

If B is the inverse of matrix A, then a is.

3

2.

Number of A.P. that can be formed from the set of numbers {1, 2, 3, term of A.P. is always 1 and last term is 1000

3.

Let f ( ) = 7 e

s i n 2 x

X

-e

c o s 2 x

+ 2, then the value of 7 min + 7f

max »

f

i s

, 1000} such that first

.

2

The exhaustive set of values of m for which f(x) = — + (m-1)x +(m+5)x + 7 is increasing 3 function V x > 0, is [k, a>) then the value of |k| is 5.

4

2

3

If the coefficient of x in the expansion of the polynomial p(x) = (1 + x + x + x + then the value of n/10 is Let

A =

2 1 be a matrix. If A 0 3

+x

100

5

) is n

a b then the last digit of a is. c dSpace for Rough work

H I T J E e Ltd., FIITJEE

House,

29-A, Kalu

Sand, Sarvaprlya Vlhar, New Delhi -110O16, website: www.fiitjee.com

Ph 46106000,

2 6 5 6 9 4 9 3 , Fax

26513942

3 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

Physics

PART - I

SECTION - A Single Correct Choice Type This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1.

A cubical block of wood 2.0 m on a side is weighted so that its centre of gravity is at point as shown in the figure -1 and it floats in water with half its volume submerged. If the block is hinged about point O at an angle of 45° as shown in the figure-2 with completely submerged in water. 1m

%m

figure-1

figure-2

Now the net torque about horizontal axis perpendicular to the block and passing through its geometrical centre (g = 10 m/s ) (A) 2^2x104 N-m (B) >/2*10 N-m (D) 4x10 N-m (C) 2x10 N-m 2

4

4

4

2.

A hemispherical tank of radius 'R' is completely filled with water. Now an orifice of small area 'a' is made at the bottom of tank. The time required to empty the tank is (A)

14TCR 5/2

(B)

15V2 a^g

(C)

14TIR

14TCR 5/2 -J2

a^/g

4nR5/2 (D) "' 15^2 a-TgL. !

5/2

572 a^/g

K

_ja______a__aa^

Space for rough work

FinjC* Ltd.,

FIITJEE

House,

29-A, Kalu

Sural,

Sarvaprtya Vlhar, New Delhi website: www.flltjee.com

-110016,

Ph 461060OO,

26569493,

Fax

26513942

4 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

A metal wire, with density p and Young's modulus Y. is stretched between rigid support. At temperature T, the speed of transverse wave is found to be v-. When temperature is increased to T + AT, the speed decreased to v < V|. If the change in cross section area of the wire is ignored then, the coefficient of linear expansion of the wire is 2

(A)

(v?-vf)p 4YAT

(B)

(C)

(v?-v!)p YAT

(D)

2

(^ YAT

(Vl-V2)P

2YAT

A square metal frame in the vertical plane is hinged at O at its centre as shown in the figure. A bug moves along the rod PN which is at a distance I from the hinge, such that the whole frame is always stationary, even though the frame is free to rotate in the vertical plane about the hinge. Then, the motion of the bug will be simple harmonic, with time period, (A)

17

2TIJ-

(g (C)

/__

2TI

J —

g 5.

Wavelength of the k characteristics X-ray of iron and potassium are 1.931 : and 3.737 x 10~ cm respectively. The atomic number (approximately) of the element for which characteristic k wavelength is 2.289 x 10" cm is (atomic number of iron is 26 and atomic number is potassium is 19) (A) 24 (B) 28 (C) 41 (D) 30 a

8

8

a

6.

Four identical mirrors are made to stand vertically to form a square arrangement as shown in the top view. A ray starts from the midpoint M of mirror AD and after two reflections reaches corner D. Then, angle 9 must be (A) tan" (0.75) (B) cor (0.75) (C) sin" (0.75) (D) cos" (0.75) 1

1

1

1

Space fotxQugh work

H I T J « Ltd., FIITJEE

House,

29-A, Kalu

Sarai,

Sarvapriya Vihar, New Delhi -110016, website: www.fiitjee.com

Ph 46106OOO,

26569493,

Fax

26513942

5 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

The figure shows graph between stopping potential (along y-axis) and incident frequency (along x-axis) for different target metal A, EL.C and D. Let (j> (j> , c and §o are the work function of different target metals A, B, C and D respectively. Then the correct rank of work function of different target metals is A>

(A)

((.A >fo

> 4C >

B

(B) (j) < B < C < $D

D

A

(D) can not be predict from the given data

(C) A = B = §0 = D

Multiple Correct Answer(s) Type This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 8.

Choose the correct alternative(s) regarding standing waves in a string. (A) particles near the antinode have lesser potential energy than the particles near the node when they reaches at its extreme position (B) AHthe particles crosses their mean position simultaneously (C) Energy and momentum can transmitted through node (D) Particles near the antinode have lesser kinetic energy than the particles near the node when they crosses their mean position.

9.

Four identical sphere of radius R/4 are taken out from a uniform sphere of mass M and radius R as shown in the figure. The density of sphere is uniform. Choose the correct option(s). (A) Gravitational field at the origin is zero. (B) Gravitational potential at the centre of the spherical cavity is GM (81-2V2 r

64R

(C) The work done by gravitational field in moving-ai^oint mass from centre of third cavity to centre of second cavity is zero. (D) Gravitational potential at the centre of second cavity is

-^(75-272-) 64R

Space for rough work

FltTJtC Ltd., FHTJEE

House,

29-A. Kalu

Sarai,

Sarvapriya website:

Vihar, New Delhi -110016, www.fiitjee.com

Ph 46106000,

26569493,

Fax

26513942

6 AITS-PT-lll(Paper-1)-PCIVWEE(Advanced)/14

10.

A liquid of density p and surface tension S rises in a capillary tube upto its equilibrium position. Let '9' is the angle of contact bejween the liquid and capillary tube. Choose the correct option(s) regarding capillary rise. (A) The magnitude of work done by surface tension force during complete rise is

P.

4TLS C O S 9 2

2

P9 2TCS C O S 6 2

(B) The work done by gravity force during complete rise is 2TIS C O S 2

(C) The heat liberates during complete rise is

2

2

pg

9

pg 6TCS cos 9 2

(D) The heat liberates during complete rise is

2

pg 11.

A uniform ring of diameter a =0.03 m is free to rotate about a hinge at point P in the vertical plane as shown in figure. A source S is fixed at another end of diameter passing through P. The ring is released from rest from the position shown. When the ring becomes horizontal, the source emits^-pntee^ of frequency f . (g = 10 m/s ). Assume v to be velocity of sound in air. Choose the correct option(s).

: - ; s

2

0

(A) the frequency of this pulse observed by an observer at point O vertically below P is 5v fn 5v-4 (B) the angular velocity of the ring when it reaches horizontally is (C) velocity of source when it emits the pulse is 2 ^ | ^ . (D) the frequency of this pulse observed by an observer at point O vertically below P is In

(

5v

,5v + 4, Space for rough work

FIITjee Ltd., FHTJEE

House, 29-A, Kalu

Sarai,

Survaprtya website:

Vihar, New Delhi -110016, www.fiitjee.com

Ph 46106000,

26569493,

Fax

26513942

7 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

Comprehension Type This section contains 2 paragraphs. Based upon the paragraph 2 multiple choice questions and based upon the paragraph ^multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Question Nos. 12 to 13 A convex lens of focal length U is placed infront of a luminous point object. The separation between the object and the lense is 3f . A glass slab of thickness t is placed between object and the lens. A real image of the object is formed at the shortest possible distance from the object. 1

12.

The refractive index of the slab is t (A) -t +Vf, (C)

13.

t _ t - f,

—

2t (B) t - f i 2t (D) — t + f,

Now, if a concave lens of very large focal length f is placed in contact with the convex lens, then the shifting of the image is 2

2

2

f, (A) f f

„ . 4f (B) i_ f

2

(C) ^ f

2

(D) J 4f

2

2

Paragraph for Question Nos. 14 to 16 A photocell is operating in saturation mode with a photo current 4.8 mA. When a monochromatic radiation of wavelength 3000 A and power 1W is incident. When another monochromatic radiation of wavelength 1650 A and power 5 mW is incident, it is observed that maximum velocity of photoelectron increases to two times. Assuming efficiency of photo-electron generation per incident photon to be same for both the cases, calculate 14.

15.

16.

Threshold wavelength for the cell is (A) 4125 A (C) 5525 A

(B) 6925 A (D) 4825 A

Saturation current in second case is (A)9.2uA (C) 15.1 uA

(B)13.3pA (D) 19.4 uA

Efficiency (in %) of photo-electron generation per incident photon is (A) 1 (B) 2 (C) 3 (D) 4 Space for rough work

FlirJCC Ltd., FITTJEE

Ho-^e. 29-A. Kalu

Sarai,

Sarvapriya Vihar, New Delhi website: www.fiitjee.com "

-110016,

Ph 46106000,

26569493,

Fax

26513942

8 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

SECTION - C Integer Answer Type This section contains 7 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). Consider a plane inclined at an angle 45° with the horizontal has two slits (S, and S ) separated by a distance d = ^ 2 mm. The screen is placed at a distance of D = 10 m. A parallel monochromatic light beam of wavelength 5000 A is incident on the slits as shown. If the fringe width of interference pattern on the screen is k x 10 meter, then find the value of k. 2

10 meter

3

2L

45°

A point source of sound radiates energy at the rate of 3.14 watts. Find the intensity level of loudness at a distance of 15.8 m from the source in dB(approximately)? (take n = 3.14) A rod of length L is rotated on a frictionless surface at an angular speed of 0 rad/s. The mass of the rod is M^nd is uniformly distributed over the entire length of the rod. A pulse of frequency 'n' is generated at -fixed point 'P' of the rod. Let ti is the time taken by pulse to reach from C to P' and t is the time taken by pulse to reach from P to C, where C 2

is the centre of the rod, then find the ratio of — . t, A frictionless tunnel is dug inside the uniform spheres as shown in the figure-1 and figure-2. A particle of mass m is to be projected from point P in both sphere so that it can escape from the influence of sphere. Let is the velocity given to the particle in figure-1 and v is the velocity given to the particle in figure-2. Find the ratio of Vi/v . (Given: R is radius of sphere and M is mass of sphere.) 2

2

Figure-1

Figure-2

Space for rough work

Unlit

Ltd., FIITJEE

House,

29-A, Kalu

Sural, Sarvaprlya website:

Vlhar, New Delhi www.flltfee.com

-110016,

Ph 46106000,

26569493,

Fax

26513942

9 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

A thin square plate of side i = 10cm is

5.

dragged with constant velocity v = 3cm/s in an oil. The width 'd' of the oil column is 2mm. Square plate is placed symmetrically as shown in the figure. Assumed velocity of layer of oil at the end is negligible. The coefficient of viscosity is 150 poise. Find the horizontal force (in Newton) required to move the square plate with constant velocity. 6.

-dtz-

Three point masses m, m and 2m are placed on the vertex of an equilateral triangle of side 'a'. Another point mass'm' is placed at the centroid of the triangle as shown in the figure. If the magnitude K Grn of net force on the point mass placed at centroid is —-—- then a find the value of K. (G = universal gravitational constant) 2

2

7.

The percentage error in the measurement of a quantity Z which is related to two other quantities as Z= x y , is due to the percentage error in the measurement of x and y, which are 2% and 1% respectively. Find the maximum fractional error in Z (in %) _1

+1

Space for rough work

mittf

Ltd., FIITJEE

House,

29-A, Kalu

Saral,

Sarvapriya Vlhar, New Delhi -110016, website: www.flltjee.com

Ph 46106000,

26569493,

Fax

26513942

10 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

Chemistry

PART - n SECTION - A

Single Correct Choice Type This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1.

Given the following half reactions, Ag (aq) + e" > Ag(s) +

E° = +0.799 V

AgCI(s) + e>Ag(s) + Cr(aq) E° =+0.222 V What is the molar solubility of AgCI? [Given antilog (- 9.758) = 1.743 * 10~ ] (A) 4.46 x 10" M (B) 1.32 x 10" M (C) 1.79 x i o - M ~ (D) 0.577 M 10

9

5

1tr

2.

Which of the following reaction is/are correct? (A) 4NO + 2NaOH >2NaN0 + ^ 0 + ^ 0

(B) KN0 + P b — ^ K N 0 +PbO

(C) 2RbN0 + C — M 2RbNQ + CQ

iD^thaTexorrect

2

3

3.

3

2

2

(B) Na2C0 .H 0(s) (D) In all the form

2

3

3

2

Select the correct statement(s) about cubic structure of diamond: 1. Effective number of atoms present in a diamond cubic cell is 8. 2. Each carbon is surrounded by four more carbon atoms. 3. Atomic radius of carbon is

5.

2

Sodium carbonate exists as: (A) Na CO .10H O(s) (C) Na C0 2

4.

2

3

a

. Where a is edge length of cube.

4. Approximate packing fraction of unit cell is

—

(A) 1,2 and 4 are correct (C) 2 and 3 are correct

(B) 2, 3 and 4 are correct (D) 1,2,3 and 4 are correct

Iodine can be decolorised by: (A) AICI (C) SnCI

(B) HgCI (D) ZnCI

3

2

.

2

2

Space for rough work

«TJ€£ Ltd., FIITJEE

House,

29-A, Kalu

Saral,

Sarvapriga Vlhar, New Delhi website: wurw.fUtjee.com

110016,

Ph 46106000,

26569493,

Fax

26513942

11 AITS-PT-III (Paper-1)-PCM-JEE(Advanced)/14 +2

6.

+2

Which ion can be separated from the mixture of Be , Ca , Mg (A) Be * (B)-Ga (C) Mg (D) Al 2

, 7.

+2

and A l

+3

by using EDTA?

2+

2+

3+

What is the value of pK (CH COO~), if T = 390 and X = 7.8 for 0.04 M of a CH COOH solution at 25°C? (A) 9.3 (B) 9.2 (C) 4.7 (D) 4.8 b

m

3

m

3

Multiple Correct Answer(s) Type This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 8.

Which of thefollowing reactions can not give CO~as a gaseous product? (A) ( C 0 0 ) B a ^ - > (B) ( C O O ) M g - ^ - > 2

2

(C) ( C O O A g ) ^ - >

(D) ( C O O H ) ^ - >

2

9.

2

Which metal oxide(s) can decompose on heating? (A) MgO (B) A l 0 (C) Ag 0 (D) Cu 0 2

2

10.

3

2

Which of the followingxquations is/are correct? 2

(A) Sn+NaOH(conc.)—^->[Sn(OH) ] " 6

(B) P b 0 + S 0 ^ - ^ P b S 0 2

2

(C) 5CS +12NaOH 2

(D) SiCI +NaOH(aq) 4

11.

4

>Na S + +3Na CS +2Na C0 +6H 0 2

2

3

2

3

2

>Na„Si0 +4HCI 4

When NaN0 is heated in absence of air, the products is/are? (A) NaN0 (B) Na 0 (C) N (D) 0 2

3

2

2

2

Space for rough work

FHTJCC Ltd., FIITJEE

House,

29-A, Kalu

Saral,

Sarvaprhja Vihar, New Delhi -110016, website; www.flltjee.com

Ph 46106000,

26569493,

Fax

26513942

12 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

Comprehension Type This section contains 2 paragraphs. Based upon the paragraph 2 multiple choice questions and base upon the paragraph 3 multiple choice questions have to be answered. Each of these questions has • choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Question Nos. 12 to 13

Adiabatic walls

Container (A)

12.

H

2 °

0.1 M aq. solution of urea Container (B)

H0 2

If we create vacuum in container A at 25°C then: (A) Water will be completely vaporised in the container. (B) There will be no vaporisation in the container. (C) The equilibrium will establish in between water vapour and liq. H 0 and vapour pressure of water will remain same as it would be in presence of atmospheric pressure. (D) The equilibrium in between H 0 (v) and H 0 ( / ) w i l l establish but vapour pressure of H 0(v) 2

2

2

2

will be more than as it would be in presence of atmospheric pressure. 13.

Which of the following statement is conect regarding container B? (A) water will migrate from Glass (i) to Glass-riband no equilibrium will establish. (B) water will migrate from Glass (i) to Glass (ii) and equilibrium will establish after some time. (C) water will not migrate to any side. (D) water will migrate from Glass (ii) to Glass (i) and equilibrium will establish after some time. Space for rough work

FOTJCC Ltd., FIITJEE

House,

29-A, Kalu

Sarai,

Sarvapriya Vihar, New Delhi -110016, website: www.fiitjee.com

Ph 46106000,

26569493,

Fax

26513942

13 AITS-PT-III (Paper-1)-PCM-JEE(Advanced)/14

Paragraph for Question Nos. 14 to 16 The accompanying diagram represents a reversible carnot cycle for an ideal gas: A Isotherm: T = 1000 K Heat absorbed = 150 KJ

Isotherm: T = 200 K

V 14.

How much heat is rejected at the lower temperature, 200 K, during the isothennal compression? (A) 150 kJ (B) 30 kJ (C) 120 kJ (D) data are not sufficient to calculate exact value

15.

What is the entropy increase during isothermal expansion at 1000 K? (A) 0.15 JK" (B) 150 kJ K (C) 150 JK'' (D) 750 JK" 1

1

16.

What is the Gibbs free energy charge during the process A -> B? (A) 150 kJ (B) -150 kJ (C) 30 kJ (D) can not calculate as data are not sufficient Space for rough work

FirrjEC Ltd., FIITJEE .•

House,

29A, Kalu

Sa^xiL Sarvapriya Vihar, New Delhi -110016, website: www.fiitjee.com

Ph 46106000,

26569493,

Fax

26513942

14 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

SECTJON -C Integer Answer Type This section contains 7 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). ' 1.

In the cell reaction (i)

>Au ^+3e" +

(ii) Overall reaction

3

Au

3Au + 3e =

3Au

+

_

AG° = -n,FE°

> 3 Au

AG = -n FE° 2

3

>Au "+2Au

2

AG° = -nFE°

What should be the value of n here? 2.

How many of following elements will liberate H gas when treatedwith dil. HN0 ? Mg, Zn, Sn, Pb

3.

(A) Consider the following statements for blast furnace in the metallurgy of Fe from haematite. (1) In blast furnace carbon is oxidized by oxygen into carbon dioxide first and then C 0 is reduced by carbon. (2) Haematite^s reduced by CO. (3) In the blast furnace slag is FeSi0 . (4) tn the blast furnace Fe is obtained in trre^forrrrof pig iron.

2

3

2

3

(B) Also consider the following statements for roasting process during metallurgry of CuFeS . (1) As and Sb impurity evolve in the form of their oxides. (2) CuFeS will convert into FeS. (3) Some amount of S 0 is also evolved during the process of roasting. (4) Pyrite is converted into Cu S. How many of above statements from (A) and (B) are true? 2

2

2

2

4.

How many of following compounds will react with excess of KCN to form complex ions? AgN0 , PbN0 , CuS, CuCN, Cd(CN) , Fe(CN) , Fe(CN) , CoCI , NiCI , Ni(CN) 3

5.

3

2

2

3

2

2

2

How many coordination isomer are possible for the following compound? (excluding the given structure of molecule)

[C0(NH ) f[Cr(NO ) f 3

6.

6

2

6

7

If 10 g of AgCI is dissolved in 1 kg of H 0, relative lowering in vapour pressure is 3.6 » 10~ . Calculate the solubility product (K ) of AgCI. Give your answer by multiplying it by 10 . [density of H 0 can be assumed as = 1] 2

10

sp

2

7.

How many of following salt are first soluble in Na S 0 solution, followed by a white ppt. formation and finally ppt. turns dark black on standing? AgN0 , Pb(CH COO) Hg(N0 ) , BiCfe, CuS0 2

3

3

2l

3

2

2

3

4

Space for rough work

FinjCC Ltd., FIITJEE

House,

29-A, Kalu

Sarai,

Sarvapriya website:

Vihar, New Delhi www.fiitjee.com

-110016,

Ph 46106000,

26569493,

Fax

26513942

15 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

Mathematics

PART - in SECTION 4 A Single Correct Choice Type

This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1.

At a platform there are 3 gates numbered 1, 2 and 3. In how many ways can 100 people get inside the platform (Given that at a time only one person can get inside the platform through one gate) ^

~

_____

(B)

(O 1 2 " 4!

(D) '

x

f 1 0 2 0 !

5!

2.

In a country there are 25 states. Every state has 15 towns. Clearly there will be two kinds of pair of towns, one is intra-state and other is inter-state. For every intra-state pair there is a network of 2-highways between that pair of town. For inter-state there is network of 3-highways between that pair of town. Calculate the total number of highways in country (A) 197550 (B) 207750 (C) 217550 . (D) 227550

3.

If x > 0, then the minimum value of x

1 0 0 0

(A) 1000 (C) 1996 4.

+x

9 0 0

+x

90

6

+x +— x (B)2000 (D)3000

is

The perpendicular distance of the line r • a = 1, r • b = 1 from origin, is (B)

Ia-b| laxbf

(D) a x b|

|a x b| Space for rough work

FIITJCC Ltd., FIITJEE

House, 29-A, Kalu

Sarai,

Sarvapriya website:

Vihar, New Delhi www.filtjee.com

-110016,

Ph 46106000,

26569493,

Fax

26513942

16 AITS-PT-IU(Paper-1)-PCM-JEE(Advanced)/14

5.

In a plane there are 3 points A ( 1 , 2, 3), B(4, 5, 6) and C(7, 10, 12) from a point D(2, 6, 11), a perpendicular is dropped to this plane and foot is defined as F. Then the direction of A B x B C will be along DF (C) BD

FD (D) cannot be determined

(A)

6.

(B)

For each positive integer K, let S denotes the increasing arithmetic progression of positive integers whose first term is 1 and whose common difference is K. For example, S is the sequence 1, 4, 7, 10, For how many values of K, S contains the term 2005 (A) 12 (B)18 (C) 17 (D) 21 K

3

K

7.

2

2

2

Given that |Ax + Bx + C| > |ax + bx + c| for all x e R, where B > 4AC then which of the following options are correct (A)|A|>|a| _(B)4BUqb| (C) |C| = |c| (D) B + 4ac < b + 4AC 2

Multiple Correct Answer(s) Type This section contains 4 multiple choice questions. Each question has four choices (A), (B),(C) and(D) out of which ONE or MORE are correct. e

8.

2x _ x e

2 x

9.

+

1

Which of the following set of values y = — can attain? e +3e -7 (A) (-5,4) ^BH^-tL (C)[3,*>) (DM-1,3] x

Let - + - + - = 1 for x > 0, y > 0, z > 0. Which of the following sets could be the possible values x y z of(x-1)(y-1)(z-1) (A) 110, oo) (C)

10.

(B)[11,oo)

[7, oo)

(D) [6, oo)

Find the number of ways in which 1 0 apples can be distributed to 7 students such that 2 particular students get an odd number of apples each and every other gets an even number (> 0) of apples (A) 150 (C) 2 1 0

(B)1035

(D) 4 5 Space for rough work

FIITJCt Ltd., FHTJEE

House,

29-A, Kalu

Saral,

Sarvapriya Vihar, New Delhi website: Www.fiitjee.com

110016,

Ph 46106000,

26569493,

Fax

26513942

17 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

3

11.

2

x — 6x +11x — 6 a The values of a for which — + — = 0 does not have a real solution is x + x - 1 0 x + 8 30 (A) -10 (B) 12 (D)-30 (C)5 3

2

Comprehension Type This section contains 2 paragraphs. Based upon the paragraph 2 multiple choice questions and based upon the paragraph 3 multiple choice questions have to be answered. Each of these questions has 4 choices (A). (B). (C)and (D) out of which ONLY ONE is correct. Paragraph for Question Nos. 12 to 13 Read the following write up carefully and answer the following questions: +ve z-axis

+ve y - a x i S f , r _

->+ve x-axis A 4 B IrUhe above ^hown cuboid (AB = 4, AE = 3, AD = 5) an insect can only crawl along the wall and it cannot fly. 12.

Find out the length of the shortest path if an insect has to travels from A to G (A) 8 (B) V74 (C)10

13.

(D) V90

The direction ratios of a line followed by the insect during its journey from A to G along the shortest path, are (A) (3, 4, 5) (B) (0, 4, 5) (C) (7, 0, 5) (D) (0, 0, 1) Space for rough work

rllTJEE Ltd., FIITJEE

House, 29-A, Kalu

Sural,

Sarvaprtya website:

Vihar, New Delhi www.flltjee.com

-110016,

Ph 46106000,

26569493,

Fax

26513942

18 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

Paragraph for Question Nos. 14 to 16 Read the following write up carefully and answer the following questions: Let N = 2 x 3 x 7 ^ , 2

3

f

2

14.

How many factors of N which are less than N, are not the factors of N (A) 91 (B) 92 (C) 98 (D) 94

15.

How many factors of number N are in the form of 4k + 1, (k e N) (A) 9 (B)13 (C)11 (D)12

16.

How many factors of number N are multiple of 54 (A) 20 (B)18 (C) 12 (D) 10

SEGTION-C Integer Answer Type This section contains 7 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1.

Number of points having positive integral co-ordinate lying on the plane x + 2y + 3z = 15 is n, then ^ is equal to Space for rough work

FlrTJEC Ltd., FIITJEE

House,

29-A, Kalu

Saral, Sarvaprtya Vihar, New Delhi -110016, website: www.flltjee.com

Ph 46106000,

26569493,

Fax

26513942

19 AITS-PT-lll(Paper-1)-PCM-JEE(Advanced)/14

2.

3.

9 1 1 Let a, b, c be positive real numbers such that - + - + - = 1 and S is the minimum value of abc a b c then the value of the logarithm of S to the base 3 is —If n is number of ways of colouring a cube with the help of 4 distinct colour such that on exactly one face one colour goes and two faces remain empty then ^ is

4.

If n is the number of roots (real or imaginary) of the following complex equation z n is

100

= z then

17

If we write all multiples of 6 side by side then a large number N will be formed as follows N = 612182430 Then the 1000 digit of this number N from left is th

6.

ap a p If be + qr = ca + rp = ab + pq = - 1 then the value of bq b q , is cr c r

7.

The digit at thousand place in the expansion of 2 5 1

1000 1 u u u

is. j s

Space for rough work

FHTJtt

Ltd..

*

'

FUTJES

SoaM.

29-A, Kalu

Saral,

Sarvapriya website:

Vihar, New Delhi www.fUtjee.com

-110016,

Ph 46106000,

26569493,

Fax

26513942