resonance dpp

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INSTRUCTIONS

A. General :

A. General : 1.

1. ThThis Qis Quesuestiotion Pn Papaper er cocontantaininss 5454 questions. questions. 2.

2. The queThe question papstion paper COer CODE is prDE is printed on inted on the rigthe right hand toht hand top corner p corner on this son this sheet of theet of this booklehis booklet.t. 3.

3. No adNo additditionaional sheel sheets wts will be pill be provrovided ided for rfor rougough worh work.k. 4.

4. Blank paBlank paperper, clipboa, clipboard, log tard, log tables, slidbles, slide rules, cale rules, calculatorsculators, cellular , cellular phones, pphones, pagers and agers and electroelectronic gadgetnic gadgetss in any form are

in any form are notnot allowed. allowed. 5.

5. The The ansanswer wer sheesheet, t, a ma machiachine-ne-gragradabldablee Objective Response Sheet (ORS)Objective Response Sheet (ORS), is provided separately., is provided separately. 6.

6. Do Do nonot Tt Tamamper per / mu/ mutitilatlate the thee ORSORS or this booklet. or this booklet. 7.

7. Do not bDo not break the sreak the seals of theals of the questie question-papeon-paper booklet r booklet before ibefore instructenstructed to do so bd to do so by the iny the invigilatovigilators.rs. 8

8.. W rW riitte e yyoouurr Name, Roll No.Name, Roll No. in the space provide on this page of booklet.in the space provide on this page of booklet. B. Filling the bottom-half of the ORS :

B. Filling the bottom-half of the ORS :

Use only Black ball point pen only for filling the ORS. Do not use Gel

Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen / Ink / Felt pen as it might smudge theas it might smudge the ORS.

ORS. 9.

9. Write your RWrite your Roll no. in the boxoll no. in the boxes given at thes given at the top left coe top left corner of yourner of your ORS wr ORS with black balith black ball point pen. l point pen. Also, darAlso, darkenken the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS in the space provided (if the ORS is both side printed).

in the space provided (if the ORS is both side printed). 10.

10. Fill your Paper CFill your Paper Code as mentioned on the Tode as mentioned on the Test Paper and darkest Paper and darken the corresponden the corresponding bubble witing bubble with Black ballh Black ball point pen.

point pen. 1

11.1. If If student doestudent does not fill his/her rols not fill his/her roll no. and paper code corrl no. and paper code correctly and propectly and properlyerly, then his/her mar, then his/her marks will not beks will not be displayed and 5 marks will be deducted (paper wise) from the total.

displayed and 5 marks will be deducted (paper wise) from the total. 12.

12. Since it is not possible to erase and correct pen filled bubbSince it is not possible to erase and correct pen filled bubble, you are advised to be extrele, you are advised to be extremely carefumely careful whilel while darken the bubble corresponding to your answer.

darken the bubble corresponding to your answer. 13.

13. Neither tNeither try to erase / rub / scrary to erase / rub / scratch the option notch the option nor make the Cross (Xr make the Cross (X) mark on the opti) mark on the option once filled. Don once filled. Do noto not scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the ORS.

ORS. 14.

14. If there is any discrepanIf there is any discrepancy betwecy between the written daten the written data and the bubbled data in your ORSa and the bubbled data in your ORS, the bubbled data will, the bubbled data will be taken as final.

be taken as final.

C. Question paper format and Marking scheme : C. Question paper format and Marking scheme :

15.

15. The queThe question pastion paper consper consists of 3 ists of 3 parts (parts (Chemistry, Physics Chemistry, Physics & Mathematic& Mathematics). Each pas). Each part consisrt consists ofts of FourFour Sections.

Sections. 16.

16. For For each each quesquestion tion inin SectionSection – –II, you will be, you will be awarded 4 marksawarded 4 marks if you darken the bubble(s) correspondingif you darken the bubble(s) corresponding to the correct choice(s) for the answer and

to the correct choice(s) for the answer and zero markzero mark if no bubbled is darkened. In case of bubbling ofif no bubbled is darkened. In case of bubbling of incorrect ans

incorrect answerwer,, minus one (minus one ( – –1)1)mark will be awarded.markwill be awarded. 17.

17. For For each each quesquestion tion inin SectionSection – –IIII, you will be, you will be awarded 4 marksawarded 4 marks if you darken the bubble corresponding toif you darken the bubble corresponding to the correct answer, and

the correct answer, and zero markzero mark if no bubble is darkened. In cif no bubble is darkened. In case of bubbling of incorrect answer,ase of bubbling of incorrect answer, minusminus one (

one ( – –1)1) markmark will be awarded.will be awarded. 18.

18. For For each each quesquestion tion inin SectionSection – –IIIIII, you will be, you will be awarded 2 marksawarded 2 marks for each row in which you have darkened thefor each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 10 marks

10 marks. There is. There is no negative markingno negative marking for incorrect answer(s) for this this section.for incorrect answer(s) for this this section. 19.

19. For For each each quequestiostion inn in SectionSection – –IVIV, you will be awarded 3 marks, you will beawarded 3 marks if you darken the bubble(s) correspondingif you darken the bubble(s) corresponding to the correct choice(s) for the answer and

to the correct choice(s) for the answer and zero markzero mark if no bubbled is darkened. There isif no bubbled is darkened. There is no negativeno negative marking

marking for incorrect answer(s) for this this section.for incorrect answer(s) for this this section.

D D O O N N O O T T B B R R E E A A K K T T H H E E S S E E A A L L S S W W I I T T H H O O U U T T B B E E I I N N G G I I N N S S T T R R U U C C T T E E D D T T O O D D O O S S O O B B Y Y T T H H E E I I N N V V I I G G I I L L A A T T O O R R

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

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MAJOR TEST (MT)

(JEE ADVANCED PATTERN)

Target : JEE(Main+Advanced) 2016

Course Name : JR,JP,JF

Resonance Eduventures Ltd.

CORPORATE OFFICE :

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Name of the Candidate

Roll Number

O E O E

APER

2

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PART-I

Atomic masses : Atomic masses : [H = 1, D = 2, [H = 1, D = 2, Li = 7, C = 12, Li = 7, C = 12, N = 14, O = N = 14, O = 16, F = 19, 16, F = 19, Na = 23, Mg = 24, Al = 27, Si = 28,Na = 23, Mg = 24, Al = 27, Si = 28, P = 31, P = 31, S = 32, S = 32, Cl = 35.5, Cl = 35.5, K = 39, K = 39, Ca = 40, Ca = 40, Cr = 52, Cr = 52, Mn = 55, Fe Mn = 55, Fe = 56, Cu = = 56, Cu = 63.5, 63.5, Zn = 65, Zn = 65, As = 75,As = 75, Br = 80, A Br = 80, Ag = 108, I = 127, g = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]Ba = 137, Hg = 200, Pb = 207]

SECTION - I

Straight Objective Type

This section contains 8 questions. Each question has 5 choices (A), (B), (C), (D) and

This section contains 8 questions. Each question has 5 choices (A), (B), (C), (D) and (E) for its answer, out(E) for its answer, out of which

of which ONLY ONE ONLY ONE is correct.is correct.

1.

1. Calculate Calculate value value of of ''!!_{n K}_{n K}

eq

eq' ' for the for the reaction reaction at at 250 250 K.K.

N

N₂₂OO₄₄(g) (g) 2NO2NO₂₂ (g) (g) Given :

Given : !!_H_H_ºº ƒ

ƒ (NO (NO22))gg = + 40.407 kJ / mol = + 40.407 kJ / mol ! !_H_H_ºº ƒ ƒ (N (N22OO44))gg = + 70 kJ / mol = + 70 kJ / mol ! !_S_S_ºº rr = 10 JK = 10 JK – –11

((AA) ) 44 ((BB)) – – 4 4 ((CC) ) 11..22 ((DD)) – – 1.2 1.2 (E) 10(E) 1044

2.

2. Select the INCORRECT statement for the phase Select the INCORRECT statement for the phase change equilibriuchange equilibrium,m, H

H₂₂O(s) O(s) HH₂₂O(l)O(l)

(A) Melting point of ice is decreased if pressure

(A) Melting point of ice is decreased if pressure of system at equilibrium in increased.of system at equilibrium in increased. (B) Conversion of ice into liquid water is an endotherm

(B) Conversion of ice into liquid water is an endothermic process.ic process. (C) Melting point of ice is decreased if pr

(C) Melting point of ice is decreased if pressure of the system at equilibrium is decreased.essure of the system at equilibrium is decreased. (D) Boiling point of water is lesser than that of hydrogen peroxide.

(D) Boiling point of water is lesser than that of hydrogen peroxide. (E) Melting of ice is favourable at high

(E) Melting of ice is favourable at high temperature and high pressure.temperature and high pressure. 3.

3. When lead acid accumulator (When lead acid accumulator (battery) is discharged, following reactiobattery) is discharged, following reaction takes place.n takes place. Pb(s) + PbO

Pb(s) + PbO₂₂(s) (s) + + 2H2H₂₂SOSO₄₄(aq.)(aq.) " " "#"#_2PbSO_2PbSO

4

4(s) + 2H(s) + 2H22OO

If 1.25 ampere current is drawn for a period of 1930 minutes, mass

If 1.25 ampere current is drawn for a period of 1930 minutes, mass of Hof H₂₂SOSO₄₄ consumed is : consumed is : ((AA) ) 11996 6 gg ((BB) ) 449 9 gg ((CC) ) 998 8 gg ((DD) ) 11447 7 gg ((EE) ) 112222..5 5 gg

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(3)

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4. A freshly prepared saturated solution of a potassium salt produces a yellow precipitate with a highly concentrated solution of cobalt(II) chloride, when acetic acid is added to it. The potassium salt may be :

(A) KNO₂ (B) K₂SO₃ (C) KNO₃ (D) KBr

(E) CH₃COOK

5. The INCORRECT statement is :

(A) In metallurgy, flux is a substance used to convert infusible impurities to fusible m ass. (B) Cryolite is Na₃AlF₆ and is used in the electrolysis of alumina.

(C) Extraction of iron metal from iron oxide ore is carried out by heating with coke and lime stone. (D) Lead can be extracted by self reduction of galena.

(E) Haematite, Cassiterite and argentite are oxide ores.

6. Write order of electron density in aromatic ring of following compounds.

I II III IV

(A) IV_> III_> II_> I _(B) I_> II_> III_> IV _(C) IV_> II_> I_> III _(D) III_> IV_> II_> I

(E) II_> IV_> III_> I

7. Which will be the least stable resonating structure of nitrobenzene.

(A) (B) (C) (D)

(E) None of these

(4)

8. For the following species.

The correct order of acidity is :

(A) IV > III > II > I (B) III > IV > I > II (C) III > I > IV > II (D) IV > II > III < I (E) None of these

SECTION - II

Reasoning Type

This section contains 2 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

9. STATEMENT -1 : Negatively charged As₂S₃ colloidal sol is obtained when As₂O₃ solution is saturated with H₂S.

STATEMENT -2 : Selective adsorption of As3+ does take place on As₂S₃ when As₂O₃ solution is saturated with H₂S.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

(5)

10. Statement 1 : Major product of the reaction " " CF " 3COOOH " " " # is

Statement 2 : Migratory aptitude of (CH₃)₃C – is better than CH₃ – in Baeyer-Villiger reactions.

SECTION - III

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, D and E, while the statements in Column-II are labelled p, q, r, s. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The appropriate bubbles corresponding to the answers to these questions have to be drakened as illustrated in the following example.

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

(6)

11. Column-I Column-II

(A) XeF₄(s) + H₂O(!₎ "# _(p) _{Show disproportionation reaction.}

(B) P₄(white) (s) + OH – (aq) + H₂O (!₎# _(q) _{One of the products is a monobasic Lewis acid.}

(C) B₂H₆(g) + H₂O(!₎ "# _(r) _{One of the products is a gas at 25}_ºC.

(D) Br₂(g) + Na₂CO₃(aq) "# _(s) _{One of the products has a pyramidal molecular}

structure. (E) CaCN₂(s) + H₂O (!₎ "#

12. Match the reactions (Column-I) with the mechanistic path (Column-II) of first step leading to major reaction product.

Column-I Column-II

(A) (p) Acid Base reaction

(B) (q) Elimination reaction

(C) (r) Carbanion as intermediate

(D) (s) Nucleophilic addition reaction.

(E)

(7)

SECTION - IV

Integer Answer Type

This section contains 6 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubble below the respective question number in the ORS have to be darkened.

13. A 200 ml aqueous solution of KCl was electrolysed for 16 min and 5 sec. If the pH of the final solution was 13 and volume of solution remains practically unchanged, then the average current used in ampere is ... (Assume negligible evolution of O₂ gas)

14. Reaction of hydrated ferric chloride (FeCl₃.6H₂O) with thionyl chloride gives anhydrous ferric chloride with evolution of hydrochloric acid (HCl) and sulphur dioxide (SO₂) gases. The number of sulphur dioxide (SO₂) molecules involved in the balanced chemical equation is.

15. A complex compound is represented as CoCl₃.xNH₃. Its 0.1 M solution in water shows depression in freezing point equal to 0.0558K. Assuming 100% ionisation of complex and coordination number of Co to be six,

calculate the value of x. K_f for H₂O is 1.86 K kgmol –1.

16. How many stereoisomers of Pt(gly)₂Cl₂ are possible ?

(8)

17. Identify the compounds in given set which can form enol.

1. 2. 3.

4. 5. 6.

7. 8. 9. 10.

18. Along how many planes, a benzene molecule has plane of symmetry.

(9)

(SPACE FOR ROUGH WORK)

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PART- II

SECTION - I

Straight Objective Type

This section contains 8 multiple choice questions. Each question has choices (A), (B), (C), (D) and (E), out of which ONLY ONE_{is correct.}

19. _{Equal volumes of two immiscible liquids of densities}

!

_{and 3}

!

_{are filled in a vessel. Two small holes are}

punced at depth h/3 and 4h/3 from upper surface of lighter liquid. If v₁ and v₂ are velocities of efflux at these two holes, then v₁ /v₂ is :

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

20. _{Two identical drops are falling through air with steady speed v. If the two drops coalesce, what would be the}

terminal speed.

(A)v (B)2v (C)3v

(D) 4v (E) none of these

21. _{In case of a liquid :}

(A) only bulk modulus is defined

(B) only bulk and Young's modulus are defined (C) only bulk and shear modulus are defined

(D) all the three modullii (bulk, Young's and shear are defined) (E) Young's modulus is defined but shear modulus is not defined

(10)

22. _{Rod AB is placed against a block which is moving towards right with a speed of 1m/s. If at an instant when}

the rod makes an angle 600_{with the horizontal and end A is sliding left with constant speed of 1m/s. Then the}

speed of the point of contact 'B' of the rod is :

(A) 1m/s (B) 3m / s 2 (C) 1 m / s 2 (D) _{2 3 m / s} (E) 3 7 m/s

23. _{System shown in figure is released from rest. Then the acceleration of 2kg block is : (g = 10 m/s}2₎

(A)

25 m / s

2

9

(B) 2

25 2

m / s

9

(C) 2 25 m / s 3 (D) 3 2 25

(11)

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24. _{A and B are massless supports attached to two springs, both the springs are identical and light. Friction}

coefficient between block C and horizontal surface is 0.5. When both the springs are in their natural length block C was given a velocity of 2m/s towards right. Then the distance travelled by block before coming to rest for the first time is : (g = 10 m/s2₎

(A) 10cm (B) 20cm (C) 15cm

(D) 25 cm (E) none of these

25. _{A car is travelling on a straight road running along a field. A person standing at a distance of 'd' from the road.}

If the speed of car is 'u' and the actual frequency of its horn is 'f₀' then the frequency heard by the observer when the car is closest to him is : (the velocity of sound in air is v) :

(A) f _o (B) o v f c (C) 2 o 2 2 v f v u

"

#

$

_&

%

'

(

(D) 2 2 o 2 v u f v

"

&

#

$

%

'

(

(E)

%

(

#

$

'

"

)

2 2 2 0 u v v f

26. _{A simple pendulum has a time period of T}

0 on the surface of the earth. On another planet whose density is

same that of earth but radius is 4 times then time period of this simple pendulum would be :

(A) T₀ (B) T0 4 (C) 0 T 2 (D) 4T₀ (E) 2T₀

(12)

SECTION - II

Reasoning Type

This section contains 2 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE_{is correct.}

27. STATEMENT-1: _{A man is standing at the centre on a horizontal rotating turn table (rotating on a smooth}

horizontal surface) has two dumbells in his hands. If he brings them closer to himself then the kinetic energy of the whole system increases.

STATEMENT-2: _{In asbsence of external torque kinetic energy of system remains conserved.}

28. STATEMENT-1 :_{A uniformly distributed direct current flows through a solid long metallic cylinder along its}

length. It produces magnetic field only outside the cylinder .

STATEMENT- 2 :_{A thin long hollow cylindrical tube carrying uniformly distributed direct current along its}

length does not produce a magnetic field inside it. Moreover, a solid cylinder can be supposed to be made up of many thin cylindrical tubes.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False

(13)

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SECTION - III

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, D and E, while the statements in Column-II_{are labelled p, q, r, s. Any}

given statement inColumn-I_{can have correct matching with}ONE OR MORE

statement(s) inColumn-II_{. The appropriate bubbles corresponding to the answers}

to these questions have to be darkened as 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 E- q; then the correct darkening of bubbles will look like the following :

29. _{Figure in column}_–_{I shows some fixed charge systems. (+Q /}_–_{Q) and movable point charge (q /}_–_{q), match}

the options in column –II for equilibrium of (q / –q) in the given direction.

Column_–_I Column_–_II (A) (p)unstable Equilibrium in y –direction (B) (q) accelerating (non-equilibrium) Equilibrium in x –direction (C) (r)stable equilibrium in x –direction

(system consist of a uniformly charged fixed non –conducting spherical shell and neglect effect of induction)

(D) (s)neutral

(E)

(A uniformly charged fixed ring)

(14)

30. _{Column-I has some statements about the system shown in column-II, Match approprtate column.}

Column-I Column-II

(A) kinetic energy of system continiously decreases. (p)

[Neglect other gravitational forces, system consists of ring and point mass]

(B) kinetic energy of system continiously increases. (q)

d GM 2 v

*

[Neglect other gravitational force, system consists of two point massage M and m.]

(C) Potential energy of system continiously increases. (r)

+

_ball >

+

_liquid

‘liquid’ is viscous and filled in a very long tube.

(D) Total mec hanical energy of system remains (s)

conserved both the charges are free to move

(E) Total mechanical energy of system continiously decreases.

(15)

SECTION - IV

Integer Answer Type

31. _{The difference between (n + 2)th Bohr radius and n}th_{Bohr radius is equal to the (n}

– 2)th Bohr radius. The value of n is ?

32. _{The figure shows an RC circuit with a parallel plate capacitor. Before switching on the ci rcuit, plate A of the}

capacitor has a charge –Q ₀ while plate B has no net charge. Now, at t = 0, the circuit is switched on. How much time (in second) will elapse before the net charge on plate A becomes zero. (Given C = 1

,

F, Q ₀ = 1mC,

-

= 1000 V and

0 /

.

3 ln 10 2 6 R ) R A B – Q0

-S

(16)

33. _{A thin non conducting disc of mass M = 2kg, charge Q = 2 x 10}-2_{C and radius} 1

6

R

0

m is placed on a

frictionless horizontal plane with its centre at the origin of the coordinate system. A non uniform, radial magnetic field B

0

B r ₀

!"

#_{exists in space, where B}

0 = 10T and r # is a unit vector in the radially outward

direction. The disc is set in motion with an angular velocity

1

= x × 102_{rad/sec, about an axis passing}

through its centre and perpendicular to its plane, as shown in the figure. At what value of x, the disc will lift off from the surface.

(17)

34. _{All springs, string and pulley shown in figure are light. Initially when both the springs were in their}

natural state, the system was releas ed from rest. The maximum displacement of block m is x 5mg k

2

3 / 4

₆

5 ₇

. Calculate x.

(18)

35. _{In Young's Double slit experiment, a thin glass mica strip of thickness (t = 8}

₈

_{) is placed infront of slit S}

1. If

the same strip is now shifted in front of other slit S₂. If the number of fringes which will cross the central point on the screen is N. Find N ? (d >> D,

8

<< d and n_mica = 1.5)

36. _{A ray of light from a liquid}

9

, 0

3

:

_{is incident on a system of two right angled prism of refractive indices} 3 and ₂ as shown in the figure. The light suffers zero net deviation when it emerges into air from surface CD. If the angle of incidence (in degrees) is 5n. Find n ?

(19)

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PART- III

SECTION - I

Straight Objective Type

This section contains 8 questions. Each question has 5 choices (A), (B), (C), (D) and (E) for its answer, out of which ONLY ONE_{is correct.}

37. _{If f(x) is differentiable function such that}

!

x 0 dt ) t ( f = 2 )) x ( f ( 2

for all x and f(2)" 0, then value of f(2) is

(A)3 (B)1 (C)2 (D) –1 (E) – 2

38. _{A rigid body rotates about an axis through the origin with angular velocity}

_{10 3}

_{radian/sec. If}

#

_{points in the}

direction $

_{i j k}

_{% %}

$ $ then the equation to the locus of the points having tangential speed 20m/sec. is (A)

_{x y z xy yz 1 0}

2

% % & & & '

2 2 (B)

_x

2

% % & & & & '

_{y z 2xy 2yz 2zx 1 0}

2 2 (C)

x y z xy yz zx 2 0

2

% % & & & & '

2 2 (D)

x

2

% % & & & & '

y z 2xy 2yz 2zx 2 0

2 2

(E) none of these

39. _{If arg (x) =}

_#

%

_"

%

_!

_{, x is not equal to}

_#

_,

_"

_,

_!

_and

! " # x x x x x x = 0, then

!

"

#

%

&

%

&

x x x

1

is equal to (A)1 (B) x

1

(C) -1 (D) 0 (E) may not exist

40. _Let 1 1 1

P r.r d

(

'

! "! 2 2 2

P r.r d

(

'

! "! 3 3 3

P r.r d

(

'

! "!

be three planes where

r , r , r

_{1 2 3}

"! "! "!

are three non-coplanar vectors.Then the lines P₁ = 0 = P₂ ; P₂ = 0 = P₃; & P₃ = 0= P₁ are

(A) Parallel lines (B) coplanar lines (C) co-incident lines (D) concurrent lines (E) none these

(20)

(SPACE FOR ROUGH WORK) 41. _If 4 2 2

dx

I

x

a

x

'

%

!

, then _I equals (A) 4 2 2 3 2 2

1 1

1 a

x

a

x

c

a

x

3x

)

_%

_&

_%

*

+

,

-

.

(B)

/

0

3 2 2 2 2 2 4 3

1 1

1 a

x

a

x

c

a

x

3x

)

_%

_&

_%

*

_%

+

,

-

.

(C)

/

0

3 2 2 2 2 2 4

1 1

1 a

x

a

x

c

a

x

2 x

)

*

%

&

%

+

,

-

.

(D) 2 2 2 2 4 3

1 1

1 a

x

a

x

c

a

x

3x

)

_%

*

+

,

-

.

(E) None of these

42. _{For any integer n the integral}

!

1 % 0 3 x cos _cos ₍₍₂_n ₁₎_x₎_dx

e 2 has the value

(A) 1 (B) 1 (C)0 (D)

2

1

(E) none of these

43. _If

/ 0

/ 0 / 0

/

0

t x 2 t x

e f x e f t

lim

2 t x f x

2

&

'

&

and f(0) = 2 1

, then find the value of f3(0).

(A)4 (B)2 (C)0 (D) 1 (E) 3

44. _{If A is the area of figure bounded by the straight line x = 0 and x = 2 and the curves y = 2}x_{and y = 2x - x}2_{, then}

the value of

6

3 A

n2

4 _&

5

6

7

8

#

9

is (A)4 (B)8 (C)9 (D) 12 (E) 15

(21)

SECTION - II

Reasoning Type

This section contains 2 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE_{is correct.}

45. _{Let A be a square matrix of order 3 so that sum of elements of each row is 1} Statement-1: _{Sum of elements of each row of A}2 _{is 1}

Statement-2: _{Sum of elements of each row of a square matrix A is 1 implies that sum of elements of}

An_{is n-1.}

(A) Statement -1 is True, Statement -2 is True ; Statement -2 is a correct explanation for Statement -1 (B) Statement-1 is True, Statement-2 is True ; Statement-2is NOT_{a correct explanation for Statement-1}

(C) Statement -1 is True, Statement -2 is False (D) Statement -1 is False, Statement -2 is True

46. Statement-1: _{The common chord of the circles x}2_{+ y}2_{- 10x + 16 = 0 and x}2 _{+ y}2_{= r}2_{is of maximum length}

if r2_{= 34}

Statement-2: _{The common chord of two circles is of maximum length if it passes through the centre of the}

circle with smaller radius.

(A) Statement -1 is True, Statement -2 is True ; Statement -2 is a correct explanation for Statement -1 (B) Statement-1 is True, Statement-2 is True ; Statement-2is NOT_{a correct explanation for Statement-1}

(C) Statement -1 is True, Statement -2 is False (D) Statement -1 is False, Statement -2 is True

(22)

SECTION - III

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, D and E, while the statements in Column-II_{are labelled p, q, r, s. Any}

given statement inColumn-I_{can have correct matching with}ONE OR MORE

statement(s) inColumn-II_{. The appropriate bubbles corresponding to the answers}

to these questions have to be darkened as 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 E- q; then the correct darkening of bubbles will look like the following :

47. Column-I Column-II

(A) Numbers of ways in which all the letters of word"RESONANCE" _(p) ₇₂₀

can be arranged such that vowels & consonants occurs alternately is

(B) If probability of scoring a total of 20 in 4 throws of a die is (q) 210 p then 65_{p is}

(C) If probability that product of four whole numbers ends in '5' is (r) 370 q then 104_{q is less than}

(D) The variance of a binomial random variable is 180. The minimum (s) 360 numbers of trials possible for the experiment are

(E) If sum of roots of equation 12x4_{- 56x}3_{+ 89x}2_{- 56x + 12 = 0 be A,}

then value of A ! 7 9 7 9 5 6 8 4 is

(23)

48. _Let

A

cos

2k

i sin

2k

; k 0,1, 2,...., n 1

n

1

1 :

;

'

_<

%

'

&

₌

>

?

&

2k

B

cos

i sin

; k 0,1, 2,...., m 1

m

1

1 :

;

'

_<

%

'

&

₌

>

?

for m , n

@

N - {1}.Also let w, w2 be the imaginary cube roots of 1.

Column -I Column-II

(A) If n = 6, m = 8, then number of elements in (p) 2

A

B is

(B) If n = 12, m = 18, then number of elements in (q) 4

A

B

is

(C) If z is such that

arg

z 1

2 &

1

4

5 _'

6 _%

7

8

9

and z@ B for (r) 24

m = 48, then number of possible values of z are (D) If i, -i, w, w2_{are elements of}

A

Bthen least value of m + n is (s) 23

(24)

SECTION - IV

Integer Answer Type

49. _{Let a}

i denote the number of non-negative integral solutions of the equation

1 2 11 i

x x

% % %

... x

&

'

i

If‘i’ varies from 1 to 9 and

a a

₁

%

₂

%

a ....a

₃

%

₉= S, then find the probability that sum of digits of S is 1022.

50. _{If points (0,0,9), (1,1,8), (1,0,7) and (2,2,}C_{) are coplanar, then}C₌

51. _{The summation of series}

2 2 2 2 2 2

3

5

7 ...

1 1 2 1 2 3

%

upto infinite terms is equal to length of

latus rectum of standard hyperbola with e = 2. If r is radius of director circle of its conjugate hyperbola, then r2₌

(25)

52. _Let

1

3 A 5 2 6

2

1

3 )

*

+

,

' +

,

+

&

,

-

.

. Find tr( AA2012₎

53. _{Let P,Q be points of the ellipse 16x}2_{+ 25y}2_{= 400 so that PQ = 96/25 and P,Q lie above major axis.Circle}

drawn with PQ as diameter touch major axis at positive focus.If m is slope of PQ then find the value of 1/|m|.