Jee Main2013key

8/13/2019 Jee Main2013key

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Sri Chaitanya IIT Academy., India

2013

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2013 JEE-Main QPaper with Solutions

Sri Chaitanya IIT Academy., India#Corporate Office : Plot No 304, Kasetty Heights, Ayyappa Society Madhapur, Hyderabad

E-Mail - [email protected], Web - www.srichaitanya.net 2/ 34

IMPORTANTINSTRUCTIONS: CODE:P1. Immediately f ill the particulars on this page of the Test Booklet with Blue/ Black ball point pen.

Use of pencil is strictly prohibited.

2. The answer sheet is kept inside this test booklet. When you are directed to open the test booklet, take

out the answer sheet and fill in the particulars carefully.

3. The test is of 3 hours duration

4. The test booklet consists of 90 questions. The maximum marks are 360

5. There are three parts in the question paper A,B,C consisting of physics, chemistry and mathematics having

30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct re-

sponse.

6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each

question. 1/ 4 (one fourth) marks will be deducted for indicating incorrect response of each question. No

deduction from the total score will be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in any question

will be treated as wrong response and marks for wrong response will be deducted accordingly as per

instruction 6 above.

8. Use Blue/ Black Ball Pen only for writting partulars/ marking responses on side-1 and side-2 of the An-swer sheet. Use of pencil is strictly prohibited.

9. No candidate is allowed to carry any textual material, printed or written, bits of papers, paper, mobile

phone, any electronic device, etc. except the admit card inside the examination hall/ room.

10. Rough work is to be done on the space provided for this purpose in the test booklet only. This space is

given at the bottom of each page and in 3 pages (pages 21-23) at the end of the booklet.

11. On completion of the test, the candidate must hand over the answer sheet to the invigilator on duty in the

room/ hall. However, the candidates are allowed to take away this test booklet with them.

12. The CODEfor this booklet is P. Make sure that the CODEprinted on side-2 of the answer sheet is the

same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter

to the invigilagor for replacement of both the test booklet and the answer sheet.

13. Do not fold or make any stray marks on the answer sheet.


3/35




PART-A_PHYSICS1. A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with

its length vertical, from a fixed point by massless spring, such that it is half submerged in a

liquid of density at equilibrium position. The extension 0x of the spring when it is in

equilibrium is

1)Mg

k2) 1

Mg LA

k M

3) 12

Mg LA

k M

4) 1Mg LA

k M

(Here k is spring constant)Ans : 3

Sol :

0

LA gkx Mg

2

0

LA gkx Mg

2

0kxL

B A g2

Mg0Mg LA

x 1k 2M

2. A metallic rod of length 1 is tied to a string of length 21and made to rotate with angularspeed on a horizontal table with one end of the string fixed. If there is a vertical magneticfield B in the region, the e.m.f. induced across the ends of the rod is:

1)22

2

B l2)

23

2

B l3)

24

2

B l4)

25

2

B l

Ans : 4

Sol :

3l

x 2l

E B x dx

25Bl

2


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3. This question has Statement 1 and Statement II. Of the four choices given after the State-ments, choose the one that best describes the two Statements.

Statement-I: A point particle of mass m moving with speed collides with stationary pointparticle of mass M. If the maximum energy loss possible is given as

21

2f m

then

.m

f

M m

Statement -II: Maximum energy loss occurs when the particles get stuck together as a resultof the collision.

1) Statement -I is true, Statement - II is true, Statement - II is a correct explanation of Statement -I

2) Statement -I is true, Statement - II is true, Statement -II is not a corect explanation of Statement -I

3) Statement -I is true, Statement - II is false

4) Statement -I is false, Statement - II is true.

Ans : 4

Sol :

Conceptual

4. Let 0 denote the dimensional formula of the permittivity of vacuum. If M=mass,

L = length, T=time and A=electric current, then :

1) 1 3 20 M L T A 2)

1 3 4 20 M L T A

3) 1 2 1 20 M L T A 4)

1 2 10 M L T A

Ans : 2

Sol :

1 20 2

q q

r F

1 3 4 2M L T I

5. A projectile is given an initial velocity of 2 / ,i j m s where i is along the ground and j isalong the vertical. If 210 / ,g m s the equation of its trajeclory is

1) 25y x x 2) 22 5y x x 3) 24 2 5y x x 4) 24 2 25y x x

Ans : 2

Sol :

2y ax bx = 22x 5x

a tan 2 , 2 2g

b 52u cos


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6. The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. Inanother 10s it will decrease to times its original magnitude, where equals

1) 0.7 2) 0.81 3) 0.729 4) 0.6

Ans : 3

Sol :

kt

0A e

5k

0 00.9A A e ...... (1)

15 k

0 0A A e ......... (2)

210ke 0.9

0.9

Solving 0.729 7. Two capacitors 1C and 2C are charged to 120 V and 200 V respectively. It is found that by

connecting them together the potential on each one can be made zero. Then:

1) 1 25 3C C 2) 1 23 5C C 3) 1 23 5 0C C 4) 1 29 4C C

Ans : 2

Sol :

1 1 2 2

1 2

C V C V

V C C

V 0

1 2120C 200C 0

1 23C 5C

8. A sonometer wire of length 1.5m is made of steel. The tension in it produces an elastic strainof 1%. What is the fundamental frequency of steel if density and elasticity of steel are

3 3

7.7 10 /kg m and11 2

2.2 10 /N m respectively?1) 188.5 Hz 2) 178.2 Hz 3) 200.5 Hz 4) 770 Hz

Ans : 2

Sol :

0

strain1 T 1 stress 1n

2l 2l 2l

= 178.17 Hz.


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9. Acircular loop of radius 0.3cm lies parallel to a much bigger circular loop of radius 20cm.The centre of the small loop is on the axis fo the bigger loop. The distance between theircentres is 15cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with

bigger loop is:

1) 119.1 10 weber 2) 116 10 weber 3) 113.3 10 weber 4) 96.6 10 weber

Ans : 1

Sol :

According to reciprocity theorem,

220

3/22 2

irR

2 r x

= 119.1 10 Wb.

10. Diameter of a plano - convex lens is 6cm and thickness at the centre is 3 mm. If speed of light

in material of lens is 82 10 / ,m s the focal length of the lens is :

1) 15 cm 2) 20 cm 3) 30 cm 4) 10 cm

Ans :3

Sol :

22 2R 3 R 0.3

R = 15 cm

a

m

V 3

V 2 ,

1 1

f R

, f = 30 cm

11. Whata is the minimum energy required to launch a satellite of mass m from the surface of aplanet of mass M and radius R in a circular orbit at an altitude of 2R?

1)5

6

GmM

R2)

2

3

GmM

R3)

2

GmM

R4)

3

GmM

R

Ans : 1

Sol :

i

GMmE

R f

GMmE

2 3R

f i

5GMmW E E

6R


7/35




12. A diode detector is used to detect an amplitude modulated wave of 60% modulation by usinga condenser of capacity 250 pico farad in parallel with a load resistance 100

kilo ohm. Find the maximum modulated frequency which could be detected by it.

1) 10.62 MHz 2) 10.62 kHz 3) 5.31 MHz 4) 5.31 kHz

Ans : 4(approximate)

Sol :

Question is ambiguity

13. A beam of unpolarised light of intensity 0I is passed through a polaroid A and then through

another polaroid B which is oriented so that its principal plane makes an angle of 045 relative

to that of A. The intensity of the emergent light is:

1) 0I 2) 0 / 2I 3) 0 / 4I 4) 0 / 8I

Ans : 3

Sol :

Polarised light intensity =0I

2

when passed through the second one =2 00 0I Icos 45

2 4

14. The supply voltage to a room is 120V. The resistance of the lead wires is 6 . A 60 W bulb isalready switched on. What is the decrease of voltage across the bulb, when a 240 W heater isswitched on in parallel to the bulb?

1) zero Volt 2) 2.9 Volt 3) 13.3 Volt 4) 10.04 Volt

Ans : 4(approximate)

Sol :

Question is ambiguity

Assuming 120 V rating,120 120

R 24060

Case I :

> > > >

120 V

60 W6

1R R

1

RV 120

R 6

Case II :


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> > > >

120 V

6R

2

R240W, R

4

2

RR

4R

RV R4

V ' 6 30

2

RV 120

R 30

15.

02V0V

V

02p

0p p

The above p-v diagram represents the thermodynamic cycle of an engine, operating with anideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is

1) 0 0p v 2) 0 013

2p v

3) 0 0

11

2p v

4) 0 04p v

Ans : 2

Sol :

Heat is extracted from the source from A to B and from B to C

0 0AB v

3p vnRdTQ nC dT

1 2

BC p 0 0

n RdTQ nC dT 5p v

1

0 0AB BC

13p vQ Q Q

2


9/35




16. A hoop of radius r and mass m rotatin with an angular velocity 0 is placed on a rough hori-

zontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocityof the centre of the hoop when it ceases to slip?

1) 04

r2) 0

3

r3) 0

2

r4) 0r

Ans : 3

Sol :

i fL L

f

0

r r

2 2

0Mr M r r Mr 0

2

0rv2

17. An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston ofmass M. The piston and the cylinder have equal cross sectional area A. When the piston is in

equilibrium, the volume of the gas is 0V and its pressure is 0.P The piston is slightly displaced

from the equilibrium position and released. Assuming that the system is completely isolatedfrom its surrounding, the piston executes a simple harmonic motion with frequency:

1)0

0

1

2

A P

V M

2)

0 02

1

2

V MP

A 3)

20

0

1

2

A P

MV

4)

0

0

1

2

MV

A P

Ans : 3

Sol :

In adiabatic process

0

0

pp v

v

00

A pF Ax

v

,

2

0

0

pk

v

frequency,2

0

0

p1n

2 Mv


10/35




18. If a piece of metal is heated to temperature and then allowed to cool in a room which is at

temperature 0 , the graph between the temperature T or the metal and time t will be closest

to:

1)

tO

T2)

tO

T0 3)

tO

T

0 4)

tO

T

0

Ans : 3

Sol :

0d

kdt

0

t

here decreases exponentially and reaches 0 at infinite time

19. This question has Statement I and Statement II. Of the four choices given after the State-ments, choose the one that best describes the two Statements.

Statement - I : Higher the range, greater is the resistance of ammeter.

Statement - II : To increase the range of ammeter, additional shunt needs to be used across it.

1) Statement - I is true, Statement - II is treue, Statement - II is the correct explanation of Statement - I

2) Statement - I is true, Statement - II is true, Statement - II is not the correct explanation of Statement - I

3) Statement - I is true, Statement - II is false

4) Statement - I is false, Statement - II is true

Ans: 4

Sol :

When range is increased shunt will be lesser so net resistance decreases. Statement I isfalse when additional shunt is connected across ammeter net resistance decreases hencerange increases. Statement II is true


11/35




20. In an LCR circuit as shown below both switches are open initially. Now switch 1S is closed,

2S kept open. (q is charge on the capacitor and RC is Capacitive time constant). Which of

the following statement is correct?

C

L

2S

1S

V

R

1) Work done by the battery is half of the energy dissipated in the resistor

2) At , / 2t q CV

3) 22 , 1t q CV e

4) 1, 12

t q CV e

Ans : 3

Sol :

S1R

C

V

When S1is closed, capacitor change becomes

tTmax maxq q 1 e ,q CV

t = 2T

q = CV (1 e2)


12/35




21. Two coherent point sources 1S and 2S are separated by a small distance d as shown. The

fringes obtained on the screen will be :

D

d

1S 2S

S c r e e n

1) points 2) straight lines 3) semi - circles 4) concentric circles

Ans : 4

Sol :

1S 2S

For a given , path difference and hence resultant intensity will be constant.

In 3D, it gives circle on the screen.

Fringes will be concentric circles.

22. The magnetic field in a travelling electromagnetic wave has a peak value of 20nT. The peakvalue of electric field strength is :

1) 3 V/m 2) 6 V/m 3) 9 V/m 4) 12 V/m

Ans : 2

Sol :

o

8 9

1

CB

3 10 20 10

6Vm


13/35




23. The anode voltage of a photocell is kept fixes. The wavelength of the light falling on thecathode is gradually changed. The plate current I of the photocell varies as follows:

1)O

I

2)

O

I

3)O

I

4)

O

I

Ans : 4

Sol :

At any partof wave length, current never increases

24. The I - V characteristic of an LED is :

1)

B G Y RR

ed

yellow

Green

Blu

e

VO

I

2)VO

IRYGB

3)VO

I

4)

V O

I

RYGB

Ans : 1

Sol :

LED just like silicon diodes but threshold voltages increases from red to violet.

25. Assume that a drop of liquid evaporates by decrease in its surface energy, so that its tempera-ture remain unchanged. What should be the minimum radius of the drop for this to be pos-sible? The surface tension is T, density of liquid is and L is its latent heat of vaporization

1) /L T 2) /T L 3) /T L 4) 2 /T L

Ans : 4 Given answer ambiguity

Sol :

Decreases in surface energy = energy spent in evaporation

2 34

d T 4 r d r p L 3

2T 8 rdr 4 r dr L2T

rL

Given answer is equilibrium condition


14/35




26. In a hydrogen like like atom electron makes transition from an energy level with quantumnumber n to another with quantum number (n - 1). If n>>1, the frequency of radiation emittedis proportional to:

1)1

n2) 2

1

n3) 3

2

1

n4) 3

1

n

Ans : 4

Sol :

If is frequency of radiation

2 2

1 1h

nn 1

22

2n 1

n n 1

if n > > 1

3

1

n

27. The graph between angle of deviation and angle of incidence (i) for a triangular prism isrepresented by:

1)

iO

2)

iO

3)

iO

4)

iO

Ans : 3No other answer is nearer

Sol :

i d curve is

d

i


15/35




28. Two charges, each equal to q, are kept at x a and x a on the .x axis A particle of mass

m and charge 02

qq is placed at the origin. If charge 0q is given a small displacement

y a along the y axis, the net force acting on the particle is proportional to:

1) y 2) -y 3)1

y4)

1

y

Ans : 1

Sol :

a+q

r

f 'F

y

+qa

F 2F ' cos

2 2 2 20q q /21 y2.

4 a y a y

,

3

2 2 2

yF

a y

,if y < < a

F y

29. Two short bar magnets of length 1cm each have magnetic moments 21.20Am and 21.00Am re-

spectively. They are placed on a horizontal table parallel to each other with their N poles

pointing towards the South. They have a common magnetic equator and separated by a dis-tance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid - pointO. of the line joining their centres is close to(Horizontal component of earths magnetic induction is 5 23.6 10 /Wb m )

1) 5 23.6 10 /Wb m 2) 4 22.56 10 /Wb m 3) 4 23.50 10 /Wb m 4) 4 25.80 10 /Wb mAns : 2

Sol :

0.2m

S

NN

SHB

1B

2B

2

1M 1.2Am 22M 1.0Am

H 1 2B B B B

4 20 11 3

1

MB 1.2 10 wb/m

4 d

5 4 2

HB 3.6 10 0.36 10 wb/m

4 2B 2.56 10 wb/m


16/35




30. A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. Theelectric potential at the poitn o lying at a distance L from the end A is :

LAO B

L

1)08

Q

L 2) 0

3

4

Q

L 3) 04 2

Q

L ln 4) 0

ln 2

4

Q

L

Ans : 4

Sol :

O

dxx

At O, dv =0

Qdx

1 L

4 x

2L

x L0

Q dxv

4 L x

0

Qln 2

4 L


17/35




PART-B_CHEMISTRY31. Which of the following complex species is not expected to exhibit optical isomerism?

1) 3

3Co en

2) 22Co en Cl

3) 3 33Co NH Cl 4) 3 22Co en NH Cl

Ans : 3

Sol :

[Co(NH3)3Cl3] do not exhibit optical isomers but other exhibit.

32. Which one of the following molecules is expected to exhibit diamagnetic behaviour?

1) 2C 2) 2N 3) 2O 4) 2S

Ans : 1 and 2

Sol :

According to MO theory in N2and C

2all electron s are paired. So dia magnetic.

33. A solution of ()1chloro1phenylethane in toluene racemises slowly in the presence of

a small amount of 5SbCl , due to the formation of :

1) carbanion 2) carbene 3) carbocation 4) free radicalAns : 3

Sol :

5SbCl

3 3 6Ph CH CH Ph CH CH SbCl

Cl

6SbCl

|

3

Cl

Ph C H CH

Recimization due to formation of carbocation.

34. Given 3 24

0 0

/ /0.74 ; 1.51

Cr Cr MnO MnE V E V

2 32 7

0

/1.33

Cr O Cr E V 0

/; 1.36

Cl ClE V

Based on the data given above, strongest oxidising agent will be:

1) Cl 2) 3Cr 3) 2Mn 4) 4MnO

Ans : 4

Sol :

It RP value is high easily reduces powerful oxidizes agent.


18/35




35. A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a

constant temperature of 37.0 C . As it does so, it absorbs 208J of heat. The values of q and wfor the process will be:

( 8.314 /R J molK ) ( ln 7.5 2.01 )

1) 208 , 208q J w J 2) 208 , 208q J w J

3) 208 , 208q J w J 3) 208 , 208q J w J Ans : 1

Sol :

Work done by system is Ve

36. The molarity of a solution obtained by mixing 750 mL of 0.5(M) HCl with 250 mL of 2(M)HCl will be:1) 0.875M 2) 1.00 M 3) 1.75 M 4) 0.975 M

Ans : 1

Sol :

1 1 2 2

1 2

M V M V

V V

37. Arrange the following compounds in order of decreasing acidity:

OH

Cl

OH

CH 3

OH

NO2

OH

OCH3

(I ) (II) (III) (IV)

; ; ;

1) II > IV > I > III 2) I > II > III > IV 3) III > I > II > IV 4) IV > III > I > IIAns : 3

Sol :

O H

C l C H 3 NO 2 O C H 3

O H O H O H

-I-effect Hyperconjugat iveinfluence

-R effect +R-effect

Electron donating groups decrease acidityElectron withdrawing groups increase acidity.


19/35




38. For gaseous state, if most probable speed is denoted by *C , average speed by Cand mean

square speed by C, then for a large number of molecules the ratios of these speeds are:

1) *: : 1.225 :1.128 :1C C C 2) *: : 1.128 :1.225 :1C C C3) *: : 1:1.128 :1.225C C C 4) *: : 1:1.225 :1.128C C C

Ans : 3

Sol :

Conceptual

39. The rate of a reaction doubles when its temperature changes from 300K to 310 K. Activationenergy of such a reaction will be:

1 18.314 log 2 0.301R JK mol and

1) 153.6kJ mol 2) 148.6kJ mol 3) 158.5kJ mol 4) 160.5kJ mol

Ans : 1

Sol :

2

1 1 2

K Ea 1 12.303logK R T T

Ea 1 12.303 log 2

8.314 300 310

40. A compound with molecular mass 180 is acylated with 3CH COCl to get a compound with

molecular mass 390. The number of amino groups present per molecule of the formercompound is:1) 2 2) 5 3) 4 4) 6

Ans : 2Sol :

Mol mass difference = 390 180

= 210 = increased molar mass of||

3

O

CH C 43

No. of acetyl groups =210

43

= 5No.of Amino functions = 5

41. Which of the following arrangements does not represent the correct order of the propertystated against it?

1) 2 2 2 2V Cr Mn Fe : Paramagnetic behaviour

2) 2 2 2 2Ni Co Fe Mn : Ionic size

3) 3 3 3 3Co Fe Cr Sc : stability in aqueous solution

4) Sc Ti Cr Mn : number of oxidation statesAns : 1

Sol :

n n 2


20/35




42. The order of stability of the following carbocations:

CH2

2 2 3 2 2;CH CH CH CH CH CH ;

I II III

is:1) III > II> I 2) II > III > I 3) I > II > III 4) III > I > II

Ans : 4

Sol :

Conceptual

43. Consider the following reaction:

2 24 2 4 2 22

2

zxMnO yC O zH xMn yCO H O

The values of x, y and z in the reaction are, respectively:1) 5, 2 and 16 2) 2, 5 and 8 3) 2, 5 and 16 4) 5, 2 and 8

Ans : 3

Sol :

2 2

4 2 4 2 22MnO 5C O 16H 2Mn 10CO 8H O

44. Which of the following is the wrong statement?

1) ONCl and ONO are not isoelectronic

2) 3O molecule is bent

3) Ozone is violet black in solid state4) Ozone is diamagnetic gas

Ans : 1

Sol :

Conceptual

45. A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of 2CO . The

emperical formula of the hydrocarbon is:

1) 2 4C H 2) 3 4C H 3) 6 5C H 4) 7 8C H

Ans : 4

Sol :

2 2CO : H O

0.07 : 0.04, C : H = 7 : 8


21/35




46. In which of the following pairs of molecules/ions, both the species are not likely to exist?

1) 22 2,H He 2) 2

2 2,H He 3) 2

2 2,H He 4) 2

2 2,H He

Ans : 3

Sol :

In H22+and He

2Bond order is zero so do not exhist.

47. Which of the following exists as covalent crystals in the solid state?1) Iodine 2) Silicon 3) Sulphur 4) Phosphorus

Ans : 2

Sol :

2 4 8I , P , S are molecular crystals

Si is covert crystal

48. Synthesis of each molecule of glucose in photosynthesis involves:1) 18 molecules of ATP 2) 10 molecules at ATP3) 8 molecules of ATP 4) 6 molecules of ATP

Ans : 1

Sol :

Conceptual

49. The coagulating power of electrolytes having ions Na , 3Al and 2Ba for arsenic sulphidesol increases in the order:1) 3 2Al Ba Na 2) 2 3Na Ba Al 3) 2 3Ba Na Al 4) 3 2Al Na Ba

Ans : 2

Sol :

Conceptual

50. Which of the following represents the correct order of increasing first ionization enthalpyfor Ca, Ba, S, Se and Ar?1) Ca S Ba Se Ar 2) S Se Ca Ba Ar 3) Ba Ca Se S Ar 4) Ca Ba S Se Ar

Ans : 3

Sol :

Conceptual

51. Energy of an electron is given by

218

22.178 10 ZE J

n

. Wavelength of light required to

excite an electron in an hydrogen atom from level 1n to 2n will be:

34 8 16.62 10 3.0 10h Js and c ms 1) 71.214 10 m 2) 72.816 10 m 3) 76.500 10 m 4) 78.500 10 m

Ans : 1

Sol :hc

E


22/35




52. Compound (A), 8 9C H Br, gives a white precipitate when warmed with alcoholic 3AgNO . Oxi-

dation of (A) gives an acid (B) , 8 6 4C H O . (B) easily forms anhydride on heating. Identify the

compound (A).

1)

CH2Br

CH3

2)

C2H5

Br

3)

CH2Br

CH3

4)

CH2Br

CH3

Ans : 4

Sol :

3A g N O

8 9C H B r A g B r

A O

8 6 4B C H O A n h y d r i d e

" B " must be p hthaleic acid i.e.,COOH

COOH .. so

(ppt)

must be" A "2CH Br

3CH

53. Four successive members of the first row transition elements are listed below with atomic

numbers. Which one of them is expected to have the highest 3 20

/M ME value?

1) 24Cr Z 2) 25Mn Z 3) 26Fe Z 4) 27Co Z

Ans : 4

Sol :

3 zFe / feE 0.77 , 3 2Ce /CoE 1.97

23Cr /CrE 0.41

, 3 2Mn / MnE 1.57

54. How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of1 to create an aqueous solution with pH of 2?1) 0.1 L 2) 0.9 L 3) 2.0 L 4) 9.0 L

Ans : 4

Sol :

1

1 1M 10 M, V 1 lit , 22 2M 10 M, V 10 lit


23/35




55. The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of Na will

be:1) 2.55 eV 2) 5.1 eV 3) 10.2 eV 4) +2.55 eV

Ans : 2

Sol :

Conceptual

56. An organic compound A upon reacting with 3NH gives B. On heating, B gives C. C in pres-

ence of KOH reacts with 2Br to give 3 2 2CH CH NH . A is:

1) 3CH COOH 2) 3 2 2CH CH CH COOH

3)3CH CH COOH

CH3

4) 3 2CH CH COOH

Ans : 4

Sol :

|| ||

3 2 3 3 2 4

O O

CH CH C OH NH CH CH C O NH

2H O

||

3 2 2 3 2 22

O

Br /kOHCH CH NH CH CH C NH

Hoffmann Bramamide rearrangement.

57. Stability of the species 2 2,Li Li and 2Li

increases in the order of:

1) 2 2 2Li Li Li 2) 2 2 2Li Li Li

3) 2 2 2Li Li Li 4) 2 2 2Li Li Li

Ans : 2

Sol :

Bond orders in Li2= 1

2Li 0.5

2Li 0.5 stability is proportional to bond order. Though

bond order in2 2Li and Li is same the electron in antibonding MO destabilize the

2Li so

order is2 2 2Li Li Li

58. An unknown alcohol is treated with the Lucas reagent to determine whether the alcohol isprimary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism:

1) secondary alcohol by 1NS 2) tertiary alcohol by 1NS

3) secondary alcohol by 2NS 4) tertiary alcohol by 2NS

Ans : 2


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Sol :

2ZnCl HClOH

2Cl H O

Mechanistic path is SN1

59. The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:

1) Methylisocyanate 2) Methylamine3) Ammonia 4) Phosgene\

Ans : 1

Sol :

Conceptual

60. Experimentally it was found that a metal oxide has formula 0.98 .M O Metal M, is present as

2M

and 3M in its oxide. Fraction of the metal which exists as 3M would be:

1) 7.01% 2) 4.08% 3) 6.05% 4) 5.08%

Ans : 2

Sol :

Percentage =4

100 4.08%98


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PART-C_MATHEMATICS

61. Distance between two parallel planes 2 2 8x y z and 4 2 4 5 0x y z is :

1)3

22)

5

23)

7

24)

9

2

Ans : 3

Sol :

Distance between the planes is16 5 21 7

6 216 4 16

62. At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of

production P w.r.t. additional number of workers x is given by 100 12 .dp

xdx

If the firm

employs 25 more workers, then the new level of production of items is:1) 2500 2) 3000 3) 3500 4) 4500

Ans : 3

Sol :

dp100 12 x p 100 x 8x x C

dx

At p 2000, x 0 c 2000

at x = 25, p 2000 100 25 8 25 5 3500

63. Let A and B be two sets contaning 2 elements and 4 elements respectively. The number ofsubsets of A B having 3 or more elements is:

1) 256 2) 220 3) 219 4) 211

Ans : 3

Sol :

n A B 2 4 8

8 8 8 8 8 8 8

3 4 3 0 1 2C C .... C 2 C C C

256 1 8 28 256 37 219

64. If the lines2 3 4

2 1

x y z

k

and

1 4 5

2 1

x y z

k

are coplanar, then k can have:

1) any value. 2) exactly one value.3) exactly two values. 4) exactly three values.

Ans : 3


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Sol :

1 1 k

k 2 1 0

1 1 1

1 k 1 k k 2 0

2k 3k 0 k = 0, - 3

65. If the vectors 3 4AB i k

and 5 2 4AC i j k

are the sides of a triangle ABC, then the

length of the median through A is:

1) 18 2) 72 3) 33 4) 45

Ans : 3

Sol :

B AC 2 AD

1 1 D AB AC 8i 2 j 8k2 2

= 4i j 4k

|AD| 16 1 16 33

66. The real number k for which the equation, 32 3 0x x k has two distinct real roots in

0,1

1) lies between 1 and 2. 2) lies between 2 and 3.

3) lies between -1 and 0. 4) does not exist.

Ans : 4

Sol :

Let 3f x 2x 3x k

2f ' x 6x 3 0 x R

f x is strictly increasing

67. The sum of first 20 terms of the sequence 0.7,0.77,0.777,..., is :

1) 207

179 1081

2) 207

99 109

3) 207

179 1081

4) 207

99 109


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Ans : 3

Sol :

7

0.9 0.99 0.999 .....20terms9

7 1 0.1 1 0.01 1 0.001 ....20 terms9

2 37 1 1 1

20 ....20 terms9 10 10 10

201

1107 1

2019 10

1 10

20207 179 10 7 179 10

9 9 81

68. A ray of light along 3 3x y gets reflected upon reaching x-axis, the equation of the

reflected ray is:

1) 3y x 2) 3 3y x 3) 3 3y x 4) 3 1y x

Ans : 2

Sol :

1y 0 x 33

3y x 3

69. The number of values of k, for which the system of equations:

1 8 4k x y k

3 3 1kx k y k

has no solution, is:

1) infinite 2) 1 3) 2 4) 3


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Ans : 2

Sol :

k 1 8 4k

k k 3 3k 1

k 3

70. If the equation 2 2 3 0x x and 2 0, , , ,ax bx c a b c R have a common root, then

a : b : c is

1) 1:2:3 2) 3:2:1 3) 1:3:2 4) 3:1:2Ans : 1

Sol :

2x 2x 3 0 4 12 8 0

both roots are common for the given equations

a b c1 2 3

a : b : c = 1 : 2 : 3

71. The circle passing through 1, 2 and touching the axis of x at 3,0 also passes through the

point:

1) 5,2 2) 2, 5 3) 5, 2 4) 2,5

Ans : 3

Sol :

Equation of the circle which touches x-axis at (3, 0) is in the form

2 2x 3 y y 0

It also passes through 1, 2 4

Equation of the circle is 2 2x 3 y 4y 0 and it also passes through

72. If , ,x y z are in A.P. and t 1 1tan , tanx y and 1tan z are also in A.P., then:

1) x y z 2) 2 3 6x y z 3) 6 3 2x y z 4) 6 4 3x y z

Ans : 1

Sol :

1 1 1 1tan y tan x tan z tan y

1 1y x z y y x z ytan tan

1 xy 1 2y 1 xy 1 2y

But x y y z

xy yz y 0 or x z , x y z


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73. Consider :

Statement-1: ~ ~p q p q is a fallacy

Statement-II: ~ ~p q q p is a tautology..

1) Statement-1 is true; Statement-II is true; Statement-II is a correct explanation for Statement-I.

2) Statement-1 is true; Statement-II is true; Statement-II is a not correct explanation for Statement-I.3) Statement-1 is true; Statement-II is false.

4) Statement-1 is false; Statement-II is true

Ans : 2

Sol :

S I : p ~ p q ~ q c c c

S II : p q ~ q ~ p

p q ~ q p is a tautology

74. If ,f x dx x then 5 3x f x dx is equal to:

1) 3 3 2 31

3x x x x dx C

2) 3 3 3 31

33

x x x x dx C

3) 3 3 2 313

x x x x dx C

4) 3 3 3 31

3x x x x dx C

Ans : 3

Sol :

Put 3x t, then 23x dx dt

1I t f t dt3

1

t t t dt3

3 3 3 21

x x 3 x x dx C3

3 3 2 31

x x x x dx C

3


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75.

0

1 cos 2 3 coslim

tan4x

x x

x x

is equal to:

1)1

4 2)

1

23) 1 4) 2

Ans : 4

Sol :

22

x 0 x 0

1 cos 2x 3 cos x 2sin x 3 cos xlt lt 2

x tan 4x 4x

76. Statement-I: The value of the integral

/3

/6 1 tan

dx

x

is equal to

6

Statement-II: b b

a a

f x dx f a b x dx 1) Statement -I is true; Statement-II is true; Statement-II is a correct explanation for Statement-I.2) Statement -I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I.3) Statement -I is true; Statement-II is false.4) Statement -I is false; Statement-II is true.

Ans : 4

Sol :

3

6

dx 3 6

dx 2 121 tan x

b b

a a

f x dx f a b x dx

77. The equation of the circle passing through the foci of the ellipse2 2

1,16 9

x y and having cen-

tre at 0,3 is:1) 2 2 6 7 0x y y 2) 2 2 6 7 0x y y

3) 2 2 6 5 0x y y 4) 2 2 6 5 0x y y

Ans : 1

Sol :Foci of the given ellipse are 7, 0

Equation of the circle is 22 2 2x y 3 7 9 x y 6y 7 0


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78. A multiple choice examination has 5 questions. Each question has three alternative answersof which exactly one is correct. The probability that a student will get 4 or more correctanswers just by guessing is :

1) 517

32) 5

13

33) 5

11

34) 5

10

3

Ans : 3

Sol :

Probability =

4 5

5 5

4 5 5

1 2 1 11C C

3 3 3 3

79. The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its

sides as 0,1 1,1 and 1,0 is:

1) 2 2 2) 2 2 3) 1 2 4) 1 2

Ans : 2Sol :

From given data

Vertices of triangle are 0, 0 , B 2, 0 ,C 0,2

x-coordinate of1 2 3ax bx cxIa b c

=

42 2

4 2 2

0 4 02 2

4 2 2

80. The term independent of x in expansion of10

2/3 1/3 1/2

1 1

1

x x

x x x x

is :

1) 4 2) 120 3) 210 4) 310Ans : 3

Sol :

1010

1/3 1/31/2

x 1 x 11x 1 x

xx x 1

10np 3r 4

1 1p q

3 2

6 410

4C 1 1 210


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81. The area (in square units) bounded by the curves , 2 3 0,y x y x x-axis, and lying in the

first quadrant is :

1) 9 2) 36 3) 18 4)27

4

Ans : 1

Sol :

9 9

0 3

x 3x dx dx

2

(3, 0)x

y

(9, 0)

(9, 3)

(0, 0)

99 23/2

0 3

x 3x

3 / 2 4

= 18 9 = 9

82. LetnTbe the number of all possible triangles formed by joining vertices of an n-sided

regular polygon. If 1 10,n nT T then the value of n is

1) 7 2) 5 3) 10 4) 8

Ans : 2

Sol :

n 1 n

3 3C C 10

n 1 n n 1 n n 1 n 210

6

n n 1 20 5 4 n 5

83. If z is a complex number of unit modulus and argument , then1

arg1

z

z

equals:

1) 2) 2

3) 4)

Ans : 3


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Sol :

Given that |z| = 1

iz e

1 z 1 cos i sin

Arg Arg

1 z 1 cos i sin

rg cis

84. ABCD is a trapezium such that AB and CD are parallel and BC CD . If ,ADB BC p and

,CD q then AB is equal to :

1) 2 2 sin

cos sin

p q

p q

2)

2 2 cos

cos sin

p q

p q

3)2 2

2 2cos sin

p q

p q

4)

2 2

2

sin

cos sin

p q

p q

Ans : 1

Sol :

2 2 2 2

p qSin , cos

p q p q

A B

CD

p2 2p q

q

2 2

p qABsin sin

2 2p q sinAB

q sin p cos


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85. If

1 3

1 3 3

2 4 4

P

is the adjoint of a 3 3 matrix A and 4A ,then is equal t0:

1) 4 2) 11 3) 5 4) 0

Ans : 2Sol :

2|P| | A| 2 6 16 11

86. The intercepts on x-axis made by tangents to the cirve,0

, ,x

y t dt x R which are parallel to

the line 2 ,y x are equal to :

1) 1 2) 2 3) 3 4) 4

Ans : 1

Sol :

dy| x| 2 x 2

dx

If

2

1

x 2 y |t|dt 2 equation of tangent is 2x y 2 0

If2

1x 2 y |t |dt 2

equation of tangent is 2x y 2 0

87. Given: A circle 2 22 2 5x y and a parabola 2 4 5y x .

Statement-I: an equation of a common tangent to these curves is 5y x .

Statement - II : If the line, 5

0y mx mm

is their common tangent, then m staisfies

4 23 2 0m m .

1) Statement - I is true; Statment -II is true; Statement - II is correct explanation for Staement - I

2) Statement - I is true; Statment - II is true; Statement - II is not a correct explanation for Statement- I

3) Statement - I is true; Statment - II is false.

4) Statment - I is false; Statment - II is true.

Ans : 2


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SiCh it IITA d I di

Sol :

Equation of a tangent to the parabola y 4 5 x having slope m is

5y mx

m it also touches the circle

225 5 1 mm 2

2 2 2m 1 m 2 m 1 m 1

88. If 1y sec tan x , thendy

dxat 1x is equal to :

1)1

22)

1

23) 1 4) 2

Ans : 1

Sol :

1 1 2dy 1

sec tan x tan tan xdx 1 x

x 1

dy 1

dx 2

89. The expression1 1

tan A cot Acot A tan A

can be written as :

1) sinA cosA + 1 2) secA cosecA+1

3) tan A + cot A 4) secA +cosecA

Ans : 2

Sol :

2 3 2Tan A 1 1 tan A 1 tan A tan A

tan A 1 tan A 1 tan A tan A 1 tan A tan A

sec AcosecA 1

90. All the students of a class performed poorly in Mathematics. The teacher decided to givegrace marks of 10 to each of the students. Which of the following statistical measures willnot change even after the grace marks were given ?1) mean 2) median 3) mode 4) variance

Ans : 4

Sol :

Variance (x + a) = variance (x)

When a is constant

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