jee adv practice paper 1 part 1

8/12/2019 Jee Adv Practice Paper 1 Part 1

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TIME : 3 HRS DATE: 18/05/2013PT TEST - 1IIT-JEE 2013 PAPER - I MAX.MARKS : 210

I N S T R U C TI O N S T O C A N D I D A TE

1. Thisbooklet is yourQuestion paper.

2. Blank spaces and blank pages are provided in this booklet for your rough work. No

additionalsheets will be provided forrough work.

3. Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular,

phones, pagers and electronic gadgets are NOT allowed inside the examination

hall.

4. Using ball point pen,darkenthe bubbleson the ORS Shee

The question paper consists of (Physics, Chemistry and Mathematics). Each partconsistsof three sections.

1. contains Each question has four choice

(A),(B),(C)and(D)outofwhich

2. contains Each questions has four choices (A),

(B),(C)and(D)outofwhich

3. contains The answer to each question is a

ranging from 0 to 9 (both inclusive).

t.

Question paper format

Markingscheme:

3 sections

Part I 10multiple choice questions.

ONLY ONE is correct.

Part II 5 multiple choice questions.

t.

Part III 5 questions. single digit

integer,

ONE orMOREare correc

Part I, 3 marksONLY zero (0) marks iminus one (-1)mark

Part II, 4 marks if ALL

ONLY. zero (0)

marks No negative marks

Part III, 4 marks

ONLY zero (0)

No negative marks

1. For each question in you will be awarded if you darken thebubble corresponding to the correct answer and f nobubbles are darkened. In all other cases, will be awarded inthispart.

2. For each question in you will be awarded you darken the

bubble(s) corresponding to the correct answer(s) In all other cases

will be awarded. will be awarded for incorrect answers

in this part.

3. For each question in you will be awarded if you darken the bubble

corresponding to thecorrect answer . In all other cases marks will be

awarded. will b e awarded f or incorrect a nswer i n this p art.

Name :_____________________________________________________

Batch : ________________________ _____________________________

Centre : _______________________Test ID :50945

MUMBAI / AKOLA / DELHI / KOLKATA / LUCKNOW / NASHIK / GOA/ KOTA / FARIDABAD

EDUCATION PVT LTD

IIT- ians JEEADVANCED -2013


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CENTERS : MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA

SECTION - I PHYSICS

PART I: Single Correct Answer Type

This section contains 10 multiple choice questions.Each question has four choices (A), (B), (C)

and (D) out of which ONLY ONE is correct.

1. A parallel beam of light falls axially on a thin converging lens of focal length 20 cm. the emergentlight falls or a screen placed 30 cm beyond the lens. An opaque plate with a triangular aperture, side1 cm, is in contact with the lens.

Aperture side

1.0 cm

f=20 cm

Screen

Opaque plate

30 cm

Triangularaperture

Which of the following diagrams best shows to appearance of the patch of light seen on the screen?

(a) (b) (c) (d)

2. When an electron accelerated by potential difference U is

bombarded on a specific metal, the emitted X-ray

spectrum obtained is shown in Fig. If the potentialdifference is reduced to U/3, the correct spectrum is

(a) (b)

(c) (d)

SPACE FOR ROUGH WORK


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3. The distance between plates of a parallel-plate capacitor is 5d. The positively charged plate is at x =

0 and negatively charged plate is at x = 5d.

Two slabs, one of conductor and the other of a dielectric of same thickness d, are inserted between

the plates as shown in Fig. Potential V versus distance x graph will be

(a) (b)

(c) (d) None of these

4. There is an infinite wire grid with cells in the form of

equilateral triangles. The resistance of each wire between

neighboring joint connections is 0R , The net resistance of

the whole grid between the points A and B as shown in Fig.

is

(a) 0R (b)0R

2

(c) 0R

3 (d) 0

R

4



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5. CV is the ideal voltmeter in the figure. Resistance of the resistor shown is R. Initially the switch is in

position 2 when charging of the capacitor starts. Initially the capacitor was uncharged. The switch in

circuit shifts automatically from 2 to 1 when CV 2V/3 and goes back to 2 from 1 when cV V 3 . The ideal voltmeter reads voltage across capacitor as plotted. What is the period T of the wave form

in terms of R and C?

(a) 3 RC In 3 (b) 2 RC In 2 (c) (RC/2) In 2 (d) none of these

6. The wire loop PQRSP formed by joining two semicircular wires to radii 1R and 2R carries a current

I as shown in fig. The magnitude of the magnetic field at center C is

(a) 0

1 2

I 1 1

4 R R

(b) 0

1 2

I 1 1

4 R R

(c) 0

1 2

I 1 1

2 R R

(d) 0

1 2

I 1 1

2 R R

7. Calculate the inductance of a unit length of a double tape line as shown in Fig., if the tapes areseparated by a distance h which is considerably less than their width b.

(a) 0h

b

(b) 0

h

2b

(c) 02 h

b

(d) 0

2 h

b



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8. Which voltmeter will give zero reading at resonance?

(a) 1V (b) 2V (c) 3V (d) None

9. The relation between internal energy U, pressure P and volume V of a gas in an adiabatic process is

U a bPV where a and b constants. What is the effective value of adiabatic constant ?

(a)a

b (b)

b 1

b

(c)

a 1

a

(d)

b

a

10. A thin-walled tube of mass m and radius R has a rod of mass m and very small cross section soldered

on its inner surface. The side-view of the arrangement is as shown in the following figure.

R

O

m

The entire arrangement is placed on a rough horizontal surface. The system is given a small angular

displacement from its equilibrium position, as a result, the system performs oscillations. The time

period of resulting oscillations if the tube rolls without slipping is

(a)4R

2g

(b)2R

2g

(c)R

2g

(d) None of these



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PART II: Multiple Correct Answer(s) Type

This section contains 5 multiple choice questions.Each question has four choices (A),(B), (C) or (D) out of which ONE or MORE are correct.

11. A small sphere of mass m is connected by a string to a nail at o and moves in a circle of radius r on

the smooth plane inclined at an angle with the horizontal. If the sphere has a velocity u at the top

position A. Mark the correct options.

(a) Minimum velocity at A so that the string does not get slack instantaneously is3

gr.5

(b) Tension at B is 9mg/5 if the sphere has the required velocity as in option (a)

(c) Tension at C is 18 mg/5 in situation of option (b)

(d) None of these

12. In Fig., a massive rod AB is held in horizontal position by two massless strings. If the string at B

breaks and if the horizontal acceleration of centre of mass, vertical acceleration and angular

acceleration of rod about the centre of mass are x ya ,a and , respectively, then

O30 O30

A B

(a) y x2 3a 3 2a l + (b) y x3a 3 2a l +

(c) y xa 3 2a l + (d) y x2a 2 3a l +



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13. A transparent slab of thickness t and refractive index is inserted in front of upper slit of YDSE

apparatus. The wavelength of light used is . Assume that there is no absorption of light by the slab.Mark the correct statement(s).

(a) The intensity of dark fringes will be 0, if slits are identical.

(b) The change in optical path due to insertion of plate is t .

(c) The change in optical path due to insertion of plate is 1 t .

(d) For making intensity zero at centre of screen, the thickness can be 5

2 1

.

14. Plane harmonic waves of frequency 500 Hz are produced in air with displacement amplitude of 10

m. Given that density of air is 1.29 kg/3m and speed of sound in air is 340 m/s. Then

(a) the pressure amplitude is 13.8 2N/m

(b) the energy density is 4 36.4 10 J/m

(c) the energy flux is 0.22 2J/ m s (d) only (a) and (c) are correct

15. A plane wave y = sin (kx + ct) is incident on a surface. Equation of the reflected wave is :

y = a sin (ct - bx). Then which of the following statements are correct?

(a) The wave is incident normally on the surface

(b) Reflecting surface is y z plane

(c) Medium, in which incident wave is travelling, is denser than the other medium

(d) a cannot be greater than a



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PART III: Integer Answer Type

This section contains 5 questions. The answer to each question is a single digitinteger, ranging from 0 to 9 (both inclusive)

16. A vessel with a symmetrical hole in its bottom is fastened

on a cart. The mass of the vessel and the cart is 1.5 kg.

With what force 2F in 10 N should the cart be pulledso that the maximum amount of water remains in the

vessel. The dimensions of the vessels are as shown in the

figure. Given that b = 50 cm, c = 10 cm, area of base A =

40 2cm , L = 20 cm,2g m/s .

17. A thin wire AC shaped as a semi-circle of diameter d rotates

with a constant angular frequency in a uniform magnetic

field of induction B

. The vector

is parallel to B

and therotation axis XY passes through the end A of the wire and is

perpendicular to the diameter AC (see Fig.) B

is directed left

to right in the plane of the paper. The value of the line integral

I E.dr

taken along the wire from the point A to the point

C will be2Bd

?

. What integer should be inserted in place of question mark.


C

F

L

b

X Y

0

C

A

B


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18. An ac ammeter is used to measure current in a circuit. When a given direct current passes through

the circuit, the ac ammeter reads 3 A. When another alternating current passes through the circuit,

the ac ammeter reads 4 A. Then find the reading of this ammeter (in A), if dc and ac flow through the

circuit simultaneously.

19. In two experiments with a continuous flow calorimeter to determine the specific heat capacity of a

liquid, an input power of 16 W produced a rise of 10 K in the liquid. When the power was doubled,

the same temperature rise was achieved by making the rate of flow of liquid three times faster. Find

the power lost (in W) to the surrounding in each case.

20. A point source of sound is located somewhere along the x-axis. experiments show that the same

wavefront simultaneously reaches listeners at x = - 8 m and x = + 2. 0 m. A third listener is

positioned along the positive y-axis. What is his y-coordinate (in m) if the same wave front reaches

him at the same instant as it does the first two listeners?



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CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA

SECTION II : CHEMISTRY

PART I : Single Correct Answer Type

This section contains 10 multiple choice questions.Each question has four choices (A), (B), (C)and (D) out of which ONLY ONE is correct.

21. The ratio between time periods taken by electron in Bohrs 2nd and 3rd orbits for each revolution is

A) 9 : 4 B) 4 : 9 C) 8 : 27 D) 27 : 8

22. At what23

Br

CO

does the following cell have its reaction at equilibrium?

Ag(s) |Ag2CO

3(s)| Na

2CO

3(aq)| |KBr(aq)| AgBr(s)| Ag(s)

Ksp

= 8 1012for Ag2CO

3and K

sp= 4 1013 for AgBr

A) 71 10 B) 72 10 C) 73 10 D) 74 10

23. Which of the following will give blood-red colour in Lassaignes test for nitrogen

A) PhNH2 B) PhNO

2 C) D) PhSO

3H


O2N SO3H


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27. The ZnS zinc blende structure is cubic. The unit cell may be described as a face-centred sulfide ionlattice with zinc ions in the tetrahdral voids. Choose the correct statement(s)

Among the following which are correct:

1) The nearest neighbours of Zn2+are four

2) The angle made by the lines connecting any Zn+2to any two of its neighbours is 109028.3) The nearest neighbours of S2are four4) The nearest neighbours of S2are eight

A) 1,2,3 B) 1,2,4 C) 1,3 D) none

28.

The compound is B

a) b) c) d)

29.a) NH

2-NH

2/OH b) con.HNO

3c) HI/P d) CrO

3/Py/CH

2Cl

2

30. Which of the following orders are/is correct .

1) F > N > C > Si >Ca - Non-metallic character

2) F >Cl> O > N - oxidising nature

3) C > Si > P > N - electron affinity

4) O > N > F > C - second ionisation potential

A) 1,2,3 B) 1,2,4 C) 1,3 D) none


H2CNH2 C H

O

COOH CH2OH

CH2OH

?

CHO

CN 23

/SnCl HCl

H O B


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31. A + B C + D is a stoichiometric ally balanced reaction. The initial rate of the reaction is doubled ifthe initial concentration of A is doubled, but is quadrupled if the initial concentration of B is doubled.

Select the correct statement(s)A) The reaction is first order in B and second order in A

B) The reaction is first order in A and second order in B

C) The reaction can not be a single-step reactionD) The overall order of the reaction is 3

32. Choose the correct option(s)

A) KClO4and KMnO

4are isomorphous in nature

B) Equivalent weight of Fe0.9

O when it is converted to FeO is 332. (At wt. of Fe = 56)

C) Molar volume of water at STP is 22.4 litre

D) When w gm Na2SO

4. 10 H

2O is added in x gm of water, molality of is

33. By which of the following reactions can MIC (methyl isocyanate) be obtained?

A) B)

C) D)


2

4SO

1000

332

w

x

3CH N C HgO 3 3CH N C O

3CH N C S 3CH N C DMSO


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34. Which of the following statement is correct?

A) In the coagulation of positively charged solution the flocculating power is in the order [Fe(CN)6]4>

PO4

3> SO42

B) Physiosorption decreases with increase of temperature

C) The formation of micelles takes place only below a particular temperature called Kraft temperatureD) The minium concentration at which micelles forms is called CMC

35 . In which of the following cases will a violet colouration be observed

A) An alkaline solution of sodium nitroprusside is treated with a solution of Na2S

B) A solution of sodium coballinitrite is treated with KCl

C) A solution of Mn(NO3)

2is treated with sodium bismuthate or red lead in the presence of

concentrated HNO3

D) A solution of sodium nitroprusside in aqueous, NaOH is heated ith Na2SO

3



15/30




36. How many of the following reactions are addition-elimination reactions of carbonyl compounds?

I) Cyanohydrin formation II) Acetal formation III) Semicarbazone formation

IV) Aldol formation V) Hemiacetal formation VI)OximeformationVII) Ketal formation VIII) Imine formation IX)2,4-DNPderivative formation

37. No. of atoms present in the same plane in dimer of ICl3i.e. I

2Cl

6

38. The number of possible isomers for the complex ion 2

3 32CrCl OH NH

is

39. The solubility product constant (Ksp) of M(OH)2is at 250C. pH of a saturated aqueous solution of M(OH)2

when large excess of base is dissolved at 25

0

C would be40. How many of the following compounds undergo both self aldol condensation and crossed aldol

condensation?

I) Methanal II) 2-Methylpentanal III) Benzaldehyde IV) Benzophenone

V) Cyclohexanone VI) 1-Phenylpropanone VII) PhenylacetaldehydeVIII) Butan-1-ol IX) 2, 2-Dimethylbutanal



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SECTION III : MATHEMATICS

PART I : Single Correct Answer Type

This section contains 10 multiple choice questions.Each question has four choices (A), (B), (C)and (D) out of which ONLY ONE is correct.

41. The value of 500 5 400 5 300 5 200 5 1004 1 4 2 4 3 4 4 4C C C C C C C C C is

(a) 1010 (b) 105 (c) 5 102 (d) None of these

42. Let a 5i 3j 4k

, b 4i 2j 5k

such that r a a b

and r b b a

then the unit vector in

the direction of r

is

(a) i j 9k

83

(b)

i j 9k

83

(c)

i j 9k

83

(d) None of these

43. Let a, b

and c

be three vectors having magnitude 1, 5 and 3 respectively such that the angle between

a

and b

is and a b a c 0

then tan

(a) 0 (b) 2/3 (c) 3/5 (d) 3/4

44. The value oftn r 1

n r

r t nnr 1 t 0

3lim C C

5

(a) -1 (b) 0 (c)1 (d) 2

45. If r 2r 2r a cos i sin9 9

, then 1 2 3

4 5 6

7 8 9

a a a

a a a where i 1

a a a

(a) 1 (b) 0 (c) 1 (d) 1 i 3 2



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46. If ABCD is a convex quadrilateral in which 2 2 2 2AB CD BC AD . Then the angle between AC

and BD is

(a)2

(b)

3

(c)

4

(d)

6

47. In a group there are 5 men and a certain number of women. From this group, 6 persons including atleast 4 men are being sent to a tour every week. Different group is being sent for each week. During

the trip, each women is presented with a bouquet of flowers each costing Rs. 252. If the total moneyspent in buying the bouquets is Rs. 39,312.00 only, the number of women is group are(A) 4 (B) 5 (C) 6 (D) 12

48. Let f(x) be a continuous and differentiable function and f y f x y f x x, y R . If f(5)=3 andf(3)=7, then the value of f(8) is(A) 0 (B) 1/7 (C) 7/3 (D) 7

49. The expression2 2x 4px q 0 x R and also 2 2r p qr, then range of 2 2

x rf x

x qx p

is

(A)p q

,2r 2r

(B) R (C) R (D) R

50. The coefficient of1

x 1when

f x

O xis expressed as partial fractions; where, f(x) is a cubic

polynomial and f (- 1) = 1 also O x x 1 x 2 x 3 x 4 is(A) 1/2 (B) 1/3 (C) 1/6 (D) -1/6



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51. If a b c 2

and a.b b.c c.a 2

andp

, q

and r

is reciprocal system of a

, b

and c

, then

(whereb c c a a b

p ,q , ra b c a b c a b c

)

(a) a b c 4 2

(b) a b c 8

(c) 2p 2q 2r 2

(d) 32 p q r 4 2

52. If

5 3

1/211 4

f x f x f xx 1 x dx c

5m 3n 2

, then

(a) 1

4 2f x 1 x (b) 1

4 2f (x) 1 x (c) m + 3n =1 (d) m + 2n =1

53. If m

nx 0

1 cos xlimsin

x

exists ; where, m, n N, then

(A) m N, n 1 (B) m 2, n 2 (C) m 1,5,9,... ;n 2 (D) m N, n N

54. If the equation2 2ax 6xy y 0 represents a pair of lines having gradients m and 2m , then the

value of a is/ are(A) - 8 (B) 8 (C) - 27 (D) 27

55. If 1 2 3r , r and r are radii of escribed circles of a ABC and r is the radius of incircle then the roots of

the equation 2 1 2 2 3 3 1 1 2 3x r r r r r r r x r r r 1 are

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



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56. If

n n n

1 2 n

n n n

1 2 n

2 4 2C sin C sin .... C sin

3n 3n 3p2 4 2

1 C cos C cos ... C cos3n 3n 3

, then find the value of p2 1.

57. The thousands digit in the coefficient of4

8 4 9a b c d in (abc + abd + acd + bcd)10is

58. If A, B, C and D are four points in space forming a linearly dependent system then

AB CD BC AD CA AB p

. Also, if the area of ABC is m, then find the value of p m.

59. The value of 1007

2

n 1

1 4n 2n 1 2n 1 ! 2013 k !

then minimum possible value of k = _____

60. If1 1 1 1

....0 1.2 1.2 2.3 1.2 2.3 3.4

(n terms) then2

2n

S n n 13lim _______

4 n n 1

where [.]

represents greatest integer function.



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ANSWER KEY

1. D 2. D 3. (d) 4. (c) 5. (b) 6. (a) 7. C

8. C 9. 10. C 11. A,C,D 12. A, C 13. (A, B, C)

14. B, C 15. (A, D) 17. 5 18. 4 19. 1 20. 1


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PAPER I (SOLUITON)

1.

Ans. (d)

Sol.

The image on the screen is real and inverted.

The size of the image on the screen has aperture size given by

10Size 1.0 0.5 cm

20

Hence, the path of light on the screen is best represented by

Diagram (d).

2.

Ans. (b)Sol. m will increase to m3 due to decrease in the energy of bombarding electrons. Hence, no

characteristic X-rays will be visible, only continuous X-ray will be produced.

3.

Ans. (b)

Sol. Electric field is the ve slope of V - x graph. Inside the conductor, electric field is zero, so slope of

V x graph is zero. Inside dielectric, field decreases, so slope also decreases.

4.

Ans. (c)

Sol. We will solve this problem by the superposition principle. Let current Ienters at A, then current I/6 will flow through AB. Now, in the

second case, let the current is extracted from B, again current I/6 willflow through AB. Now, if simultaneously current enters at A and

leaves at B, then the current I/6+I/6=I/3 should flow through AB and

current I-I/3=2I/3 will flow, through the remaining part. Let the

resistance of the remaining part be 1R .

Now 0 01 1R I RR 2I

R3 3 2

0 01 0 0

eq1 0 0 0

R / 2 RR R R

R R R R /2 R 3 5.

Ans. (b)

Sol. 1t is the time of capacitor to discharge from 2 V / 3 t o V / 3 .

For this, 1t / 1V 2V

e t ln 2 RC ln 23 3

2t is time for charging of capacitor from V/3 to 2V/3.

So22VC/3 t

2VC/3 0

dq dtt RC ln 2

VC q RC

1 2T t t 2RC ln 2


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6.

Ans. (a)

7.

Ans. (a)

Sol. 0 0B.d I V2b I

l

0IB

2b

due to one tape

Net field = 2 B

Magnetic flux passing through this double tape

0I

2BA 2B hb

l h l

0 0h hLLI b b

l

l

8.

Ans. (b)

Sol. At resonance, the series combination of L and C gives zero impedance.

At resonance, the voltages across L and C are equal but opposite in phase.

9.

Ans. (b)

Sol. For an adiabatic process,

0 dU PdV Or d a bPV PdV 0 Or bP dV bV dP p dV 0

Or dV dP

b 1 b 0V P

Or b 1 log V b log P constantb 1 bV p constant

Orb 1

bPV

constantb 1

b

10.

Ans. (a)

Sol. Rolling can be considered as pure

rotation about point of contact. We can

consider this system as a compound

pendulum oscillating about P.

Time period PI

t 2mgd

PI moment of inertia about rotation axis =2

0I mR

= 2 2 2mR mR 2mR The centre of mass of tube and rod will be at a height R/2 from P, hence d = R/2

22mR 4RT 2 2

mgR /2 g

2m CM

P

0


23/30


11.

Ans. a, b, c

Sol. Minimum velocity at A should be

o

A

3v g sin 37 r gr

5

Velocity at B : 2 2 oB Av v 2g r sin 37

2B B3 6 9grv gr gr v

5 5 5

2

BB

mv 9mgT

r 5

Velocity at C: 2 2 oC Cc v 2g2r sin 37

2

C C

3 12v gr gr V 3gr

5 5

2o C

C

mvT mg sin37

r

C C3 18T mg 3mg T mg5 5

12.

Ans. (d)Sol. Acceleration of point A along the string is zero. Therefore,

o o o

x y

ala cos 30 a cos 60 cos 60 0

2

13.

Ans. (a, c, d)

Sol. x at P after insertion of slab

1 medium 2 airairS P t t S P 1 t

Earlier, 1 2x at P s P S P 0

So, change in optical path due to insertion of slab is 1 t .For intensity to be zero at P, we have

2n 1x n 1,2,...

2

3 5

1 t , , ,...2 2 2

14.

Ans. (a, b, c)

Sol. Pressure amplitude

2 aEP

Where E is the coefficient of elasticity. We have,

o30

xa

va

A

l

2

0

T

2S

1S t,

PS


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2 EE v v

2 2

0

2 av 2 avP

v

f

2

0P 2 avf 13.8N/m

Energy density is 2 2 2 4 32 a f 6.4 10 J/m

Energy flux is 2 2 2 22 a f v 0.22 J/ m /s 15.

Ans. (a, b, c, d)

Sol. A plane wave y = a sin (kx + ct) is incident on a surface.

Equation of the reflected wave is: y ' a 'sin ct bx .Then which of the following statements are correct?

a. The wave is incident normally on the surface

b. Reflecting surface is y z plane

c. Medium, in which incident wave is travelling, is denser than the other mediumd. a cannot be greater than a

16.

Ans. (1)

Sol. (i) As the cart is drawn by a force F, the water in the vessel takes up a slant position rising upward at

the black

(ii) wall of the vessel. To prevent water flowing out of the hole H, the acceleration of the vessel

should have such a value that it occupies a face area DBH and a width of vessel given by

(iii) a value that it occupies a face area DBH and a width of vessel given by A/L.

Area of1

DBH bc2

Volume of liquid retained 1 A

bc2 L

Mass of cart and waterbcA

M2L

matan

mg

ba g tan g

c

Required force bcAr gb

M 1.5 0.5 502L c

2.0 50 100 N 17.

Ans. (4)

Sol. It is clear that the diameter AC traces out a circle as the given wire rotates about axis XY. The emf

developed by induction between the ends A and C of the given semicircular wire is the same as if a

straight wire AC were rotating perpendicular to field B.

Hence flux linked 2

B

1B AC

2

Where is the angle traced in time t.

By Faradays law, the induced emf e E.d

l

But we also have, E.d

Bd

l = e = -dt

BF

L

b

mg

D

ma


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2d 1

E.dr d Bdt 2

2 21 d Bd B d2 dt 2

But we desire only theA

C

E.dr which will be1

or E.dr.2

HenceA 2

C

BE.dr d4

18.Ans. (5)

Sol. Net current : I 3 4 2 sin t

Now find

T

2

0v

3 4 2 sin t dt

I 5AT

19.

Ans. (8)Sol. Let power lost to surrounding is Q

dm

16 Q S 10dt

And dm

32 Q 3 S 10dt

32 Q3 Q 8 W

16 Q

20.Ans. (4)

Sol. Source should be located midway x = - 8 m and x = 2 m. that is at x = - 3 m. For the same wavefrontto reach at C, SC = SA = SB

2 25 3 y y 4m .

C

SB A

- 8 2- 3


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PAPER I ANSWER KEY

21. (c) 22. (b) 23. (c) 24. (a) 25. (c)

26. (a) 27. (a) 28. (b) 29. (d) 30. (a)

31. (b,c,d) 32. (a, b) 33. (a, b, d) 34. (a,b,d) 35. (a,c)

36. (4) 37. (8) 38. (3) 39. (8) 40. (3)


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PAPER I (SOLUTION)

41.Ans.: D

Sol: Coefficient of 4x in 500 4005 50 1C 1 x C 1 x ... 5100

1 x 1

Coefficient of 4x in

5

100 100 2 100 1001 2 100C x C x .... C x i.e Zero

42.Ans.: D

Sol: r a b 0

r a b

9i 5j k

r107

43.Ans. (d)

Sol. Since, a b a c 0

a b a c

1 1 5sin 3

44.

Ans. (c)

Sol.n r 1

n r t

r tnnr 1 t 0

1lim C C 3

5

n

n r r

rnnr 0

1lim C 4 3

5

n nn r n r

r rnxr 0 r 0

1lim C 4 C 3

5

n nnn1

lim 5 4 15

45.

Ans. (b)

r

ra a ; where,2 2

a cos isin9 9

1 2 3 2

4 5 6 4 7 2

7 8 9 2

a a a 1 a a

a a a a a a 1 a a 0

a a a 1 a a

46.

Ans. (a)

Sol. Let A (origin), B b ,C c

and D d

are position vectors of points A, B, C and D


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22

2CD CD d c

2 2

d c 2d.c

22

2BC BC c b

2 2

c b 2c.b

By given arrangement

2 2 2 2

AB CD BC AD , we getd c c.b

or c. d b 0

AC BD

47.Ans. CSol. Total Bouquets purchased = 156

Let n be no. Of women in total

Men WomenCASE I 4 2CASE II 5 1

No. of possibilities 5 n 5 n4 2 5 1C C C C

5n n 1. n

2

Now, number of Bouquets 5n n 1

2 n.1 1562

25n 4n 156 0 n 6

48.Ans. CSol. If y = 5, then f(5).f(x + 5) = f(x)

Or 3f x 5 f x Differentiating wrt x, we get

3f ' x 5 f x

Now, at 7

x 3, f ' 8

3

49. Sol. Since, 2 2x 4px q 0 x R

0 a 0 2 24p q 0 (1)

Also given that z 2 2 rr p q (2)

Let2 2

x ry

x qx p

2 2yx yq 1 x yp r 0 Since, x is real 0

2 2yq 1 4y yp r 0

D d C c

A 0 B b


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2 2 2 2y q 2yq 1 4y p 4yr 0

2 2 2q 4p y 2 q 2r y 1 0

Now, 2 2 24 q 2r 4 q 4p 24 q 2 24qr 4r q 24p

2 216 r p qr 0 using (2) y R

50.Ans. C

51.Ans.: A,C,D

Sol:32

32 p q r a b c

4 2 2

a b c 2 4 2 4 2

2 2 4

52.Ans.: A, C

Sol: Substitute 4 2 41 x r x , then 241

1 rx

s

4dx 2rdr

x

Now,1 8

213

4

dx 1 2rdr I4 x

1x 1

x

5 3

221 1 r 2r I r 1 dr r c

2 2 5 3

5 3r r r

I c10 3 2

;4

1r 1

x

53.Ans. (A, B, C)

Sol. m m

n nx 0 x 0

1 cos x 1 cos xlimsin sin lim

x x

2

nx 0

sin x / 2sin lim 2 .m m N & n 1 or 2

x

54.Ans. B, C

Sol. m, 2m are roots of equation2

2

y ya 6 0x x

2 3m m 6 and m a Cubing both sides, we get


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3 2

2 3 3 2 3m m m m 3mm m m

2216 a a 3a 6 0 8, 27

55.Ans. (A, D)

Sol. Since,

3

1 2 2 3 3 1r r r r r r r s a s b s c

And

3

1 2 3r r rs a s b s c

2 1 2 2 3 3 1 1 2 3x r r r r r r r x r r r 1 0 is satisfied by x = 1 other root is

1 2 3r r r 1

57.Ans.: 5

Sol: coefficientof4

8 4 9a b c d in (abc + abd + acd + bcd)10orcoefficientof 2 6 1 6a b c d in

101 1 1 1

2520a b c d

.

58Ans.: 4

Sol: AB CD BC AD CA AB 2 a b b c c a

Where, a,b,c

and d

corresponds to pv. of points A, B, C and D respectively

59.Ans. 1

Sol. Let 2nt 4n 2n 1 ! 2n 2n 1 ! 2n 1 !

nt 2n 2n ! 2n ! 2n 1 ! nt 2n 1 ! 2n 1 !

Now, ns t 2n 1 ! 1

60.

Ans. 1

Sol. n

1 3 n 2 nt 1.2 2.3 ... n n 1 n n 1 n 2 2

n

3 1 1t

2 n n 1 n 1 n 2

1 4

S 3

Also,2

2n

n n 1lim 1

n n 1

2

2n n

S n n 1 4 1 1lim lim .1

4 n n 1 3 4 3

jee adv practice paper 1 part 1

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