PAPER - I - eenadupratibha.neteenadupratibha.net/pratibha/OnlineDesk/jee_key/documents/jee_mains... · 06 April 2014 JEE MAINS 2014 :: PAPER 1 - (CODE-E) 2 PAPER ... having 30 questions

06 April 2014 JEE MAINS 2014 :: PAPER 1 - (CODE-E)

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PAPER - I

INTERNET

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INTERNET

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PAPER - 1 : PHYSICS ; CHEMISTRY & MATHEMATICS

Do not open this Test Booklet until you are asked to do so.Read carefully the Instructions on the Back Cover of this Test Booklet.

Important Instructions :1. Immediately fill in 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 Mathematicshaving 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for eachcorrect response.

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

7. There is only one correct response for each question. Filling up more than one response in eachquestion will be treated as wrong response will be deducted accordingly as per instruction 6 above.

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12. Tthe CODE for this Booklet is E. Make sure that the CODE printed on Side-2 of the Answer Sheetis the same as that on this booklet. In case of discrepancy, the candidate should immediately reportthe matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet.


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PHYSICS

1. The current voltage relation of diode is given by 1000 / 1 ,V TI e mA where the applied voltageV is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring

0.01V while measuring the current of 5 mA at 300 K, what will be the error in the value ofcurrent in mA?1) 0.2 mA 2) 0.02 mA 3) 0.5 mA 4) 0.05 mAAns : 1

Sol. : 1000 / 1 5V TI e mA

1000 1000

VI e VT T

1000 6 0.011300

0.2mA

2. From a tower of height H, a particle is thrown vertically upwards with a speed u. The time takenby the particle, to hit the ground, is n times that taken by it to reach the highest point of its path.

1) 2 22gH = n u 2) 2 2gH = (n-2) u 3) 22gH = nu ( 2)n 4) 2gH = ( 2)unAns : 3Sol. : 0 u gt

212

H u nt nt

2 2 2

2

12

nu gn uHg g

2 22

2n uHg nu

2 12nHg nu

22 2Hg nu n

3. A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass mand radius R. If the stirng does not slip on the cylinder, with what acceleartion will the mass fallon release?

1) 23g

2) 2g

3) 56g

4) g


4

Ans : 2

Sol. : 2

mg ga

m m

4. A block of mass m is placed on a surface with a vertical cross section given by 3

.6

xy If the

coefficient of friction is 0.5, the maximum height above the ground at which the block can beplaced without slipping is:

1) 16

m 2) 23

m 3) 13

m 4) 12

m

Ans : 1

Sol. : 23tan

6dy xdx

12 2 12

x

16

y

5. When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude2F ax bx where a and b are constants. The work done in stretching the unstretched rubber--

band L is:

1) 2 3aL bL 2) 2 312

aL bL 3) 2 3

2 3aL bL

4) 2 31

2 2 3aL bL

Ans : 3

Sol. : 2F ax bx

2dw ax bx dx 2 3

02 3

Lax bxw

2 3

2 3aL bLw

6. A bob of mass m attached to an inextensible string of length l is suspended from a verticalsupport. The bob rotates in a horizontal circle with an angular speed /rad s about the vertical.About the point of suspension:1) angular momentum is conserved2) angular momentum changes in magnitude but not in direction3) angular momentum changes in direction but not in magnitude4) angular momentum changes both in direction and magnitudeAns : 3Sol. : Conceptual


5

7. Four particles, each of mass M and equidistant from each other, move along a circle of radius Runder the action of their mutual gravitational attraction. The speed of each particle is:

1) GM

R2) 2 2 GM

R3) 1 2 2GM

R 4) 1 1 2 2

2GM

R

Ans : 4

Sol. :

Net force on each M

2 2

2 2222

GM GMFRR

CF F (centrifugal force)2 2 2

2 24 2GM GM MV

R RR

4 2GM GMV

R R

1 1 2 22

GMVR

8. The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its lengthconstant when its temperature is raised by 1000C is:(For steel Young's modulus is 11 22 10 Nm and coefficient of thermal expansion is 5 11.1 10 K )

1) 82.2 10 Pa 2) 92.2 10 Pa 3) 72.2 10 Pa 4) 62.2 10 Pa

Ans : 1

Sol. : 82.2 10F y t PaA

9. There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 andd2 are filled in the tube. Each liquid subtends 900 angle at centre. Radius joining their interface

makes angle with vertical. Ratio 1

2

dd is:

1) 1 sin1 sin

2) 1 cos1 cos

3) 1 tan1 tan

4) 1 sin1 cos


6

Ans : 3

Sol. : 1

2

1 tan1 tan

dd

10. On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take thebubbles to be spheres of radius R and making a circular contact of radius r with the bottom ofthe vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatchis:

1) 2

3wgRT

2) 2

6wgRT

3) 2 wgR

T

4) 2 3 wgRT

Ans : 1

Sol: 3 24 4TR .g . r3 R

2 .gr R3T

11. Three rods of copper, Brass and Steel are welded together to form a Y - shapped structure. Areaof cross - section of each rod = 4 cm2. End of copper rod is maintained at 1000C where as endsof brass and steel are kept at 00C. Lengths of the copper, brass and steel rods are 46, 13 and 12cms respectively. The rods are thermally insulted from surroundings except at ends. Thermalconductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate ofheat flow through copper rod is:1) 1.2 cal/s 2) 2.4 cal/s 3) 4.8 cal/s 4) 6.0 cal/sAns : 3

Sol. :

0.92 4 10046

0.26 4 0 0.12 4 00

13 12

0.92 100 0.26 0.1246 13 12

2 0.02 0.03

02 200 400.05 5

C

0.92 4 604.8 /

46cal s


7

12. One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The processBC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively.Choose the correct statement:

1) The change in internal energy in whole cyclic process is 250 R2) The change in internal energy in the process CA is 700 R3) The change in internal energy in the process AB is -350 R4) The change in internal energy in the process BC is -500 RAns : 4Sol. : Conceptual

13. An open glass tube is immersed in mercury in such a way that a length of 8 cm extends abovethe mercury level. The open end of the tube is then closed and sealed and the tube is raisedvertically up by additional 46 cm. What will be length of the air column above mercury in thetube now?(Atmospheric pressure = 76 cm of Hg)1) 16 cm 2) 22 cm 3) 38 cm 4) 6 cmAns : 1

Sol. : 1 1 2 2PV PV

276 8A P A x

276 8 P x ----(1)

2 054 P x P

2 54 76P x

2 76 54P x

2 22P x -----(2)

76 8 22 x x

276 8 22x x 2 22 608 0x x

16x cm14. A particle moves with simple harmonic motion in a straight line. In first s , after starting from

rest it travels a distance a, and in next s it travels 2a, in same direction, then:1) amplitude of motion is 3a 2) time period of oscillations is 83) amplitude of motion is 4a 4) time period of oscillations is 6Ans : 4

Sol. : 1 cosa A


8

3 1 cos 2a A

22sina A

2 22 4sin cosa A

28 . cos2aa AA

21 cos4

1cos2

3

23T

6T 15. A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of

air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is340m/s.1) 12 2) 8 3) 6 4) 4Ans : 3

Sol. : 4 4V Vn l

l n

340 0.068 6.84 1250

l m cm

Max. length possible 11 6.8 74.8cm Number of possible oscillations = 6

16. Assume that an electric field 2ˆ30E x i exists in space. Then the potential difference 0 ,AV V

where 0V is the potential at the origin and AV the potential at x = 2 m is:1) 120 J 2) -120 J 3) -80 J 4) 80 JAns : 3Sol. : 2ˆ30E x i

2

20

0

ˆ ˆ30 .AV V x i dx i 23

00

303AxV V

0 80AV V J 17. A parallel plate capacitor is made of two circular plates separated by a distance of 5mm and with

a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is3×104 V/m, the charge density of the positive plate will be close to:1) 7 26 10 /C m 2) 7 23 10 /C m 3) 4 23 10 /C m 4) 4 26 10 /C m


9

Ans : 1

Sol. : 120 2.2 8.85 10

EK

4123 10

2.2 8.85 10

4 12 23 10 8.85 10 /c m 8 258.41 10 /c m

7 26 10 /c m 18. In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of

kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of thebuliding will be:1) 8 A 2) 10 A 3) 12 A 4) 14 AAns : 3Sol. : 15 bulbs of 40 W5 bulbs of 100 W5 fans of 80W1 heater of 1 KW

40 100 80 100015 5 5 1220 220 220 220

1 600 500 400 1000220

1 2502500 11.3220 22

12A

19. A conductor lies along the z-axis at 1.5 1.5z m and carries a fixed current of 10.0 A in ˆza

direction (see figure). For a field 4 0.2 ˆ3.0 10 ,xyB e a T

find the power required to move the

conductor at constant speed to x = 2.0 m, y = 0 m in 35 10 s . Assume parallel motion along thex-axis.

1) 1.57 W 2) 2.97 W 3) 14.85 W 4) 29.7 WAns : 2


10

Sol : Work done2

0

Bil dx

2

4 0.2

0

3 10 10 3xW e dx

39 1.67 10W J

Power 3

3

9 1.67 105 10

W Wt

Power is slightly less than 3 wattsAnswer is 2.97 W

20. The coercivity of a small magnet where the ferromagnet gets demagnetized is 3 13 10 .Am Thecurrent required to be passed in a solenoid of length 10 cm and number of turns 100, so that themagnet gets demagnetized when inside the soleniod is:1) 30 mA 2) 60 mA 3) 3 A 4) 6 AAns : 3Sol. : 0 0 B H niH = ni

3 1003 100.1

i

i = 3 A21. In the circuit shown here, the point 'C' is kept connected to point 'A' till the current flowing

through the circuit becomes constant. Afterward, suddenly, point 'C' is disconnected from point'A' and connected to point 'B' at time t = 0. Ratio of the voltage across resistance and theinductor at t = L/R will be equal to:

1) 1e

e 2) 1 3) -1 4) 1 e

e

Ans : 3

Sol. : /0

ti i e

/0

/0

1

tR

tL

i e RV iRdiV L L i edt

1 R

L

V RV L


11

22. During the propagation of electromagnetic waves in a medium:1) Electric energy density is double of the magnetic energy density2) Electric energy density is half of the magnetic energy density3) Electric energy density is equal to the magnetic energy density4) Both electric energy magnetic energy densities are zero.Ans : 3Sol. : Conceptual

23. A thin convex lens from crown glass 32

has focal length f. When it is measured in two

different liquids having refractive indices 43 and

53 it has the focal lengths f1 and f2 respectively..

The correct relation between the focal length is:

1) 1 2f f f 2) 1 2f f and f becomes negative

3) 2 1f f and f becomes negative 4) 1 2f and f both become negativeAns : 3

Sol. : 1 2

1 1 1 1k, kf 2 R R

1

1 3 1 k4f 23

9 11 k k8 8

2

1 3 9 11 k 1 k k5f 10 1023

1 2f f and f 0

24. A green light is incident from the water to the air - water interface at the critical angle ().Select the correct statement.1) The entire spectrum of visible light will come out of the water at an angle of 900 to the normal2) The spectrum of visible light whose frequency is less than that of green light will come out to the airmedium3) The spectrum of visible light whose frequency is more than that of green light will come out to the airmedium4) The entire spectrum of visible light will come out of the water at various angles to the normal.Ans : 2

Sol. :

m

CC R V

1 1sinsin

CC


12

C value is less for voiletAll colours also having frequency less than green.Have critical angle greater than green.Y, O, R have frequency less than green. Yellow, Organce, Red will not comes out of water..Where as Blue, Indigo, Violet has total internal reflection.

25. Two beams, A and B, of plane polrized light with mutually perpendicular planes of polarizationare seen through a polaroid. From the position when the beam A has maximum intensity (andbeam B has zero intensity), a r otat ion of polaroid through 300 makes the two beams appear

equally bright. If the initial intensities of the two beams are IA and IB respectively, then A

B

II

equals :1) 3 2) 3/2 3) 1 4) 1/3Ans : 4

Sol. : 2 0 2 0cos 30 cos 60A BI I

21

1233

2

A

B

II

26. The radiation corresponding to 32 transition of hydrogen atom falls on a metal surface toproduce photoelectrons. These electrons are made to enter a magnetic field of 310–4T. If theradius of the largest circular path followed by these electrons is 10.0 mm, the work function ofthe metal is close to1) 1.8 eV 2) 1.1 eV 3) 0.8 eV 4) 1.6 eVAns : 2

Sol. : 2mV mEr

Bq Bq

313

4 19

2 9 10 1.910 10

3 10 1.6 10W

3112

19

2 9 10 1.99 10

1.6 10W

0.8 1.9 W

1.9 0.8 1.1W eV 27. Hydrogen (1H

1), Deuterium (1H2), singly ionised Helium (2He4)+ and doubly ionised lithium

(3Li6)++ all have one electron around the nucleus. Consider an electron around the nucleus.Consider an electron transition from n = 2 to n = 1. If the wave lengths of emitted radiation are1, 2, 3 and 4 respectively then approximately which one of the following is correct ?1) 41 = 22 = 23 = 4 2) 1 = 22 = 23 = 4

3) 1 = 2 = 43 = 94 4) 1 = 22 = 33 = 44


13

Ans : 3

Sol. : 21 1 11 4

RZ

21 34

RZ

1

1 34R

2

1 34R

3

1 3R

4

1 274R

28. The forward biased diode connection is

1) 2)

3) 4)

Ans : 1Sol. : Conceptual

29. Match List-I (Electromagnetic wave type) with List-II (Its association / application) and selectthe correct option from the choices given below the lists :List - I List - IIa) Infrared waves i) To treat muscularb) Radio waves ii) For broadcastingc) X-rays iii) To detect fracture of bonesd) Ultra violet rays iv) Absorbed by the ozone layer of the atmosphere.

a b c d a b c d1) iv iii ii i 2) i ii iv iii3) iii ii i iv 4) i ii iii ivAns : 4Sol. : Conceptual

30. A student measured the length of a rod and wrote it as 3.50cm. Which instrument did he use tomeasure it ?1) A meter scale2) A vernier calliper where the 10 divisions in vernier scale matches with 9 division in main scale and mainscale has 10 divisions in 1 cm.3) A screw gauge having 100 divisions in the circular scale and pitch as 1mm.4) A screw gauge having 50 divisions in the circular scale and pitch as 1mm.Ans : 2Sol. : Conceptual


14

CHEMISTRY31. The correct set of four quantum numbers for the valence electronsof rubidium atom (Z=37) is

1)15,0,0,2

2) 15,1,0,2

3) 15,1,1,2

4)15,0,1,2

Ans: 1Sol.: z 37 5s

n = 5, l = 0, m = 0, 1s2

32. If Z is a compressibility factor, van der walls equation at low pressure can be written as:

1)RTZ 1Pb

2)aZ 1

VRT 3)

PbZ 1RT

4)PbZ 1RT

Ans: 2

Sol.: 2

ap v b RTv

at low pressure

v b v 2

ap v RTv

apv RTv

pv a 1RT vRT

pv a1RT vRT

33. CsCl crystallises in body centred cubic lattice.If 'a' is its edge length then which of the followingexpressions is correct ?

1)sC cl

r r 3a 2) sC cl

3ar r2 3)

sC cl

3r r a2 4)

sC clr r 3a

Ans: 3

Sol.: Cs Cl3a 2 r r

Cs Cl

ar r 32

34. For the estimation of nitrogen,1.4g of an organic compound was digested by Kjeldahl method

and the evolved ammonia was absorbed in 60 mL of M10 sulphuric acid. Theunreacted acid

required 20mL of M10 sodium hydroxide for complete neutralization. The percentage of nitrogen

in the compound is :1) 6% 2)10% 3) 3% 4)5%Ans: 2

Sol.: 2 41.4 no.of mil.eq.of H SO used%of N

wt of org.compound

no.of mil.eq. of 2 4H SO used = 1 160 2 20 10%

10 10


15

35. Resistance of 0.2 M solution of an electrolyte is 50 . The specific conductance of the solutionis 11.4 S m . The resistance of 0.5Msolution of the sameelectrolyte is 280 . The

molarconductivity of 0.5M solution of the electrolyte in 2 1S m mol is:

1) 45 10 2) 35 10 3) 35 10 4) 25 10Ans: 1

Sol : 2 1 1

2 11 2 2

k R Rk kk R R

150 1.4Sm280

13

2m 1

1 Smk 1 104C 0.50molL 4 0.50

4 2 15 10 Sm mol

36. For complete combustion of ethanol, 2 5 2l 2 g 2 g lC H OH 3O 2CO 3H O , the amount of heatproduced as measured in bomb calorimeter, is 1364.47 kJ 1mol at 025 C . Assuming ideality the

Enthalpy of combustion, cH , for the reaction will be: 1R 8.314 kJ mol

1) 11366.95 kJ mol 2) 11361.95 kJ mol 3) 11460.50 kJ mol 4) 11350.50 kJ molAns: 1

Sol : C gH U n RT

1364.47kJ 1 8.314 298J 1364.47 2.48 kJ 1366.95kJ

37. The equivalent conductance of NaClat concentration C and at infinite dilution are C and ,respectively. The correct relationship between C and is given as : (where the constant B ispositive)

1) C B C 2) C B C 3) C B C 4) C B C Ans: 3Sol : conceptual

38. Consider separate solutions of 0.500 M 2 5 3 4aq 2 aqC H OH ,0.100 M Mg PO aq0.250 M KBr

and 3 4 aq0.125 M Na PO at 025 C .Which statement is true about these solutions, assuming allsalts to be strong electrolytes ?1)They all have the same osmotic pressure

2)0.100 M 3 4 2 aqMg PO has the highest osmotic pressure

3) 0.125 M 3 4 aqNa PO has the highest osmotic pressure

4) 0.500 M 2 5 aqC H OH has the highest osmotic pressureAns: 1Sol : conceptual


16

39. For the reaction 2 g 2 g 3 g1SO O SO2

, if xP CK K RT where the symbols have usual

meaning then the value of x is: (assuming ideality)

1) 1 2) 12

3) 12 4) 1

Ans: 2Sol : conceptual

40. For the non- stoichiometre reaction 2A B C D , the following Kinetic data were obtainedin three separate experiments, all at 298 K.

Initial Concentration (A) Initial Concentration (B) Initial rate of formation of C mol L S

0.1 M 0.1 M 31.2 100.1 M 0.2 M 31.2 100.2 M 0.1 M 32.4 10The rate low for the formation of C is:

1) dc k A Bdt

2) 2dc k A Bdt

3) 2dc k A Bdt

4) dc k Adt


41. Among the following oxoacids, the correct decreasing order of acid strength is:1) 2 3 4HOCl HClO HClO HClO 2) 4 2 3HClO HOCl HClO HClO

3) 4 3 2HClO HClO HClO HOCl 4) 2 4 3HClO HClO HClO HOCl Ans: 3Sol : conceptual

42. The metal that cannot be obtained by electrolysis of an aqueous solution of its salts is:1) Ag 2) Ca 3) Cu 4) CrAns: 2Sol : conceptual

43. The octahedral complex of a metal ion 3M with four monodentate ligands 1 2 3L ,L ,L and 4Labsorb wavelengths in the region of red, green, yellow and blue, respectively. The increasingorder of ligand strength of the four ligands is:1) 4 3 2 1L L L L 2) 1 3 2 4L L L L 3) 3 2 4 1L L L L 4) 1 2 4 3L L L L Ans: 2Sol : conceptual

44. Which one of the following properties is not shown by NO ?1) It is diamagnetic in gaseous state 2) It is neutral oxide3) It combines with oxygen to form nitrogen dioxide 4) It's bond order is 2.5Ans: 1Sol : conceptual

45. In which of the following reactins 2 2H O acts as a reducing agent ?

a) 2 2 2H O 2H 2e 2H O b) 2 2 2H O 2e O 2H

c) 2 2H O 2e 2OH d) 2 2 2 2H O 2OH 2e O 2H O 1) a, b 2) c, d 3) a, c 4) b, dAns: 4Sol : conceptual


17

46. The correct statement for the molecule 3Csl , is:

1) It is a covalent molecule 2) It contains Cs and 3I ions.

3) It contains 3Cs and I ions 4) It contains Cs , I and lattice 2I moleculeAns: 2Sol : conceptual

47. The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1:4. The ratioof number of their molecule is:1) 1:4 2) 7:32 3) 1:8 4) 3:16Ans: 2

Sol : 2

2

O

N

1N 732

4N 3214

48. Given below are the half- cell reactions:2 0Mn 2e Mn;E 1.18V

3 2 02 Mn e Mn ;E 1.51V

The 0E for 2 33Mn Mn 2Mn will be:1) 2.69 V; the reaction will not occur 2) 2.69 V; the reaction will occur3) 0.33 V; the reaction will not occur 4) 0.33 V; the reaction will occurAns: 1

Sol:

2Mn 2e Mn,E 1.18v 2 32Mn 2Mn 2e ,E 1.51v 2 33Mn Mn 2Mn ,E ?

2 2 32Mn Mn Mn 2Mn

2

2

49. Which series of reactions correctly represents chemical relations related to iron and itscompound?

1) 2SO 2 4 24dil H H SO .O heat4 2 4 3

Fe FeSO Fe SO Fe

2) 2 2 4O ,heat dil H SO heat4Fe FeO FeSO Fe

3) 2Cl ,heat heat ,air Zn3 2Fe FeCl FeCl Fe

4) 0 02O ,heat CO,600 C CO,700 C

3 4Fe Fe O FeO Fe

Ans: 4Sol :conceptual


18

50. The equation which is balanced and represents the correct product(s) is:

1) 2 2Li O 2KCl 2LiCl K O

2) 23 45

CoCl NH 5H Co 5NH Cl

3) 2 24 excess NaOH

2 26Mg H O EDTA Mg EDTA 6H O

4) 4 2 2 44CuSO 4KCN K Cu CN K SO

Ans: 2Sol :conceptual

51. In NS 2 reactions, the correct order of reactivity for the following compounds:

3 3 2 3 2CH Cl,CH CH Cl, CH CHCl and 3 3CH CCl is

1) 3 3 3 2 32 3CH Cl CH CHCl CH CH Cl CH CCl

2) 3 3 2 3 32 3CH Cl CH CH Cl CH CHCl CH CCl

3) 3 2 3 3 32 3CH CH Cl CH Cl CH CHCl CH CCl

4) 3 3 2 3 32 3CH CHCl CH CH Cl CH Cl CH CCl


52. On heating an aliphatic primary amine with chloroform and ehtanolic potassium hydroxide, theorganic compound formed is :1) an alkanol 2) an alkanediol3) an alkyl cyanide 4) an alkyl isocyanideAns: 4Sol : conceptual

53. The most suitable reagent for the conversion of 2R CH OH R CHO is:

1) 4KMnO 2) 2 2 7K Cr O

3) 3CrO 4) PCC(Pyridinium Chlorochromate)Ans: 4Sol : conceptual

54. The major organic compound formed by the reaction of 1, 1, 1- trichloroethane with silver powderis:1) Acetylene 2) Ethene3) 2 -Butyne 4) 2 - ButeneAns: 3Sol : conceptual


19

55. Sodium phenoxide when heated with 2CO under pressure at 0125 C yields a product which onacetylation produces C.

ONa0

2

125 H2 5 Atm Ac OCO B C

The major product C would be :

1) 2) 3) 4)


56. Considering the basic strength of amines in aqueous solution, which one has the smallest

bpK value?

1) 3 2CH NH 2) 3 2CH NH 3) 3 3CH N 4) 6 5 2C H NH


57. For which of the following molecule significant 0 ?

a) b) c) d)

1) Only a 2) a and b 3) Only c 4) c and dAns: 4Sol : conceptual

58. Which one is classified as a condensation polymer ?1) Dacron 2) Neoprene 3) Teflon 4) AcrylonitrileAns: 1Sol : conceptual

59. Which one of the following bases is not present in DNA?1) Quinoline 2) Adenine 3) Cytosine 4) ThymineAns: 1Sol : conceptual

60. In the reaction, 4 5LiAlH PCl Alc.KOH3CH COOH A B C , the product C is :

1) Acetaldehyde 2) Acetylene 3) Ethylene 4) Acetyl chlorideAns: 3Sol : conceptual


20

MATHEMATICS

61. If nX 4 3n 1: n N and Y 9 n 1 : n N , where N is the set of natural numbers,then X Y is equal to:1) X 2) Y 3) N 4) Y-XAns : 2Sol. : x yx y y

62. If z is the complex number such that z 2, then the minimum value of 1z :2

1) is strictly greater than 52 2) is strictly greater than

32 but less than

52

3) is equal to 52 4) lies in the interval (1, 2)

Ans :4Sol. :

2z 2z

1 1 12 2 2z z z 1 1

2 22z

1 12 2z z 31

2 2z

63. If a R and the equation 2 23 x x 2 x x a 0 (where [x] denotes the greatestinteger x ) has no integral solution, then all possible values of a lie in the interval:

1) (-2, -1) 2) , 2 2,

3) 1,0 0,1 4) (1,2)

Ans : 3

Sol. : 2 23 2 0x x x x a

x x y , 0 1y

2 23 2 0y y a

2 23 2 3 2a y y y y

230,y y


21

20 1a

1,0 0,1

64. Let and be the roots of equation 2px qx t 0, p 0 . If p,q,r are in A.P. and1 1 4 , then the value of is

1) 349

2) 2 13

93)

619

4) 2 17

9Ans: 2

Sol. : 2 0px qx r 1 1 4

2 4q prp

2q p r 4 2 216 369

r rr

8r p r 4q rp p

2 13

99p r 4q r

65. If , 0 and n nf n and

2 2 23 1 f 1 1 f 2

1 f 1 1 f 2 1 f 3 K 1 11 f 2 1 f 3 1 f 4

,

then K is equal to

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

Ans : 1

Sol. :

3 1 1 1 21 1 1 2 1 11 2 1 3 1 4

f ff f ff f f

2 2

2 2 3 3

2 2 3 3 4 4

3 1 11 1 1

1 1 1

2

2 2 2

1 1 1 1 1 11 11 1

1 1

1k


22

66. If A is an 3 3 non-singular matrix such that AA ' A 'A and 1B A A', then BB' equals

1) 1B 2) 1B ' 3) I+B 4) IAns : 4Sol. : T TAA A A

1 1B A A

1 1T T TT T TB A A A A 1TA A

11 . .T T TBB A A A A 11 .T TA A A A

.I I I

67. If the coefficients of x3 and x4 in the expansion of 1821 ax bx 1 2x in powers of x areboth zero, then (a,b) is equal to

1) 27214,

3

2) 27216,

3

3) 25116,3

4) 25114,3

Ans : 2

Sol. : Coefficient of 3 23 18 18 183 2 12 . 2 2 0x C a C b C

Coefficient of 4 3 24 18 18 184 3 22 . 2 2 0x C a C b C

18 18 184 3 216 8 4 0C C a C b

18 18 183 2 116 8 4 0C C a C b

18 18 18 18 18 183 4 2 3 1 216 8 4 0C C a C C b C C

19 19 194 3 216 8 4 0C a C b C

Equation satisfies when 25116,3

a b

68. If 9 1 8 2 7 9 910 2 11 10 3 11 10 .... 10 11 k 10 , then k is equal to

1) 100 2) 110 3) 12110 4)

441100

Ans : 1

Sol. : 9 1 8 2 7 910 2 11 10 3 11 10 .... 10 11S

8 2 7 9 1011 11 10 2 11 10 .... 9 11 1110

S

8 7 109 1 2 91 10 11 10 11 10 .... 11 1110

S

10 10

1010 11 111

1110S


23

69. Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, thenew numbers are in A.P. Then the common ratio of the G.P. is

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

Sol. : 2, ,a ar ar where 1r 24ar a ar

2 4 1 0r r

2 3r

70. 2

2x 0

sin cos xlim

x

is equal to

1) 2) 3) 2

4) 1

Ans : 2

Sol. : 2

20

sin sinx

xLt

x

2 2

2 20

sin sin sinsinx

x xLtx x

2

20

sin.x

xLtx

71. If g is the inverse of a function f and 5

1f ' x1 x

, then g ' x is equal to

1) 51

1 g x 2) 51 g x 3) 51 x 4) 45x

Ans : 2

Sol. : fog x x

f g x x

' . ' 1f g x g x

1'

'g x

f g x

51 g x

72. If f and g are differentiable functions in [0,1] satisfying f 0 2 g 1 ,g 0 0 and

f 1 6 , then the for some c ]0,1[

1) f ' c g ' c 2) f ' c 2g ' c 3) 2f ' c g ' c 4) 2f ' c 3g ' c

Ans : 2


24

Sol. : 1 0' 4

1f f

f c

1 0' 2

1g g

g c

' 2 'f c g c

73. If x = -1 and x=2 are extreme points of 2f x log x x x then

1) 12,2

2) 12,2

3) 16,2

4) 16,2

Ans : 1

Sol. : ' 2 1f x xx

2 1 0

4 1 02

8 2 0

16 3 0,2

1 1 2

74. The integral 1xx11 x e dx

x is equal to

1) 1xxx 1 e c

2)

1xxx e c

3)

1xxx 1 e c

4)

1

.x

xx e c

Ans : 4

Sol. : 1 1

2

11x x

x xe dx xe dxx

1 1 1

1.x x x

x x xe dx xe e dx

75. The integral 2

0

x x1 4sin 4sin dx2 2

equals

1) 4 3 4 2) 4 3 43

4) 4 4) 2 4 4 33

Ans : 2

Sol. :0

1 2sin2x dx

3

03

1 sin sin 12 2x xdx dx

4 3 13


25

76. The area of the region described by 2 2A x, y : x y 1 and 2y 1 x is

1) 2

2 3 2)

22 3 3)

42 3 4)

42 3

Ans : 3

Sol. : 2 2 1x y 21x y

2 1y x 1

20

2 1R x dx

2 1 1x x 43

0, 1x x 1 2R

1 24

2 3R R

77. Let the population of rabbits surviving at a time t be governed by the differential equation

dp t 1 p t 200dt 2

. If p 0 100 , then p(t) equals:

1) t/2600 500 e 2) t/2400 300 e 3) t /2400 300 e 4) t/2300 200 e

Ans : 3

Sol. : 2.t

I F e

2 2 2200 400t t t

P t e e dt e C

0 100P

300C

2400 300t

P t e

78. Let PS be the median of the triangle P(2,2), Q(6,-1) and R(7,3). The equation of the linepassing through (1,-1) and parallel to PS is1) 4x+7y+3=0 2) 2x-9y-11=0 3) 4x-7y-11=0 4) 2x+9y+7=0Ans : 4Sol. :

Slope of 2

9PS

2 9 7 0x y


26

79. Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4ax 2ay c 0

and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes then:1) 3bc 2ad 0 2) 3bc 2ad 0 3) 2bc 3ad 0 4) 2bc 3ad 0 Ans :1Sol. : 4 2 0ax ay c

56 2 0x by d

12 2 5 4 2

x yad bc bc ad ab

2 2 5 4 02 2

ad bc bc adab ab

3 2 0bc ad

80. The locus of the foot of perpendicular drawn from the centre of the ellipse 2 2x 3y 6 onany tangent to it is

1) 22 2 2 2x y 6x 2y 2) 22 2 2 2x y 6x 2y

3) 22 2 2 2x y 6x 2y 4) 22 2 2 2x y 6x 2y

Ans : 1

Sol. : 1 10,0c p x y

Slope of cp

1

1

yx

slope of tangent 1

1

xy

2 2 2y mx a m b

2 21 1 1 16 2yy xx x y

22 2 2 26 2x y x y

81. Let C be the circle with the centre at (1,1) and radius = 1. If T is the circle centred at (0,y),passing through origin and touching the circle C externally, then the radius of T is equal to

1) 12 2)

14 3)

32

4) 3

2Ans : 2


27

Sol. : 2 21 1 1x y

2 2 2 0x y fy

0, f r f

21 1 1f f

21 1 1f f

2 1 2f f

4 1f

14

f

14

r

82. The slope of the line touching both the parabolas 2y 4x a nd 2x 32y is

1) 18 2)

23 3)

12 4)

32

Ans : 3

Sol. : 1y mxm

2 3232 0x mxm

0

12

m

83. The image of the line x 1 y 3 z 4

3 1 5

in the plane 2x y z 3 0 is the line

1) x 3 y 5 z 2

3 1 5

2) x 3 y 5 z 2

3 1 5

3) x 3 y 5 z 2

3 1 5

4) x 3 y 5 z 2

3 1 5

Ans : 3

Sol. : 2, 1, 13, 1, 5

1 3 4 22 1 1

x y z

, , 3,5, 2x y z 3 5 2

3 1 5x y z


28

84. The angle between the lines whose direction cosines satisfy the equation m n 0 and2 2 2m n is

1) 6

2) 2

3) 3

4) 4

Ans : 3

Sol. : 1 1 1, , 1,0,1a b c

2 2 2, , 1,1,0a b c

1cos2

3

85. If 2

a b b c c a abc

then is equal to

1) 0 2) 1 3) 2 4) 3Ans : 2

Sol. : .a b b c c a

.a b a b c c b c c a . 0a b a b c c

2.a b c a b c a b c

86. Let A and B be two events such that 1P A B6

, 1P A B4

and 1P A4

, where e Astands for the complement of the event A. Then the events A and B are1) independent but not equally likely 2) independent and equally likely3) mutally exclusive and independent 4) equally likely but not independentAns : 1

Sol. : 16

P A B

56

P A B

14

P A

34

P A

56

P A P B P A B

13

P B

P A B P A P B


29

87. The variance of first 50 even natural numbers is

1) 437 2) 437

4 3) 833

4 4) 833

Ans : 4Sol. : Variance of first 50 even natural numbers 2, 4,.....50....100

2 50 5151

2 50A

Variance 2 2 22 2 49 47 ....... 1

50 50xi A

22 21 3 ...... 4925

242

02 1

nn

24

2

04 4 1

nn n

833

88. Let k kk

1f x sin x cos xk

where x R and k 1 . Then 4 6f x f x equals

1) 14 2)

112 3)

16 4)

13

Ans : 2

Sol. : 4 4 6 64 6

1 1sin cos sin cos4 6

f x f x x x x x 1 14 6

89. A bird is sitting on the tope of a vertical pole 20m high and its elevation from a point O on theground is 450. It flies off horizontally straight away from the point O. After one second, theelevation of the bird from O is reduced to 300. Then the speed (in m/s) of the bird is

1) 20 2 2) 20 3 1 3) 40 2 1 4) 40 3 2

Ans : 2

Sol. :

0 20cot 3020

x

20 3 1x

90. The statement p q is1) a tautology 2) a fallacy 3) equivalent to p q 4) equivalent to p qAns : 3

Sol. : p q q p q p q p qT T F F T TT F T T F FF T F T F FF F T F T T

V

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