Aieee2012 Paper

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394,50 - Rajeev Gandhi Nagar Kota, Ph. No. : 93141-87482, 0744-2209671

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AIEEE EXAMINATION 2012

QUESTIONS WITH SOLUTIONS

PAPER CODE - B


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AIEEE Examination(2012) (Code - B)(Page # 2)



PART - I [CHEMISTRY]

SECTION ASingle Correct

1. The pH of a 0.1 molar solution of the acid HQ is 3.

The value of the ionization constant, Ka of this

acid is :

(1) 1 10-5 (2) 1 10-7

` (3) 3 10-1 (4) 1 10-3

Sol. (1)

pH =2

1(pKa logc) 3 =

2

1(pKa + 1 )

6 = pKa + 1pKa = 5Ka = 105

2. Which among the following will be named as

dibromidobis (ethylene diamine) chromium (III) bro-

mide ?

(1) [Cr (en) Br4]- (2) [Cr (en) Br

2]Br

(3) [Cr (en3)] Br

3(4) [Cr (en)

2Br

2]Br

Sol. (4)

3. Which method of purification is represented by the

following equation :

Ti(s)+2I2(g) K523 TiI4(g)

K1700

Ti(s)+2I2(g)

(1) poling (2) Van Arkel(3) Zone refining (4) Cupellation

Sol. (2)

4. The compressibility factor for a real gas at highpressure is :(1) 1 + pb/RT (2) 1 - pb/RT(3) 1 + RT/pb (4) 1

Sol. (1)P(V - nb) = nRTPV = nRT + Pnb

Z = 1 +RT

Pb

5. The increasing order of the ionic radii of the givenisoelectronic species is:(1) Ca2+, K+, Cl-, S2- (2) K+, S2-, Ca2+, Cl-

(3) Cl-, Ca2+, K+, S2- (4) S2-, Cl-, Ca2+, K+

Sol. (1)For isoelectronic system

z

er

6. The species which can best serve as an initiatorfor the cationic polymerization is :

(1) AlCl3 (2) BuLi (3) LiAlH4 (4) HNO3Sol. (1)

AlCl3Lewisacid

Cationicpolymerisation

CH=CH2 CHCH AlCl2 3 CH=CH2

7. The molecule having smallest bond angle is :(1) SbCl

3(2) PCl

3(3) NCl

3(4) AsCl

3

Sol. (1)Al we move down the group size of central atom

increases & hence bond angle decreases.

8. The equilibrium constant (Kc) for the reaction

N2(g)+O

2(g) 2NO(g) at temperature T is 4 104.

The value of Kcfor the reaction, NO(g) N

2(g) +

O2(g) at the same temperature is:

(1) 4 10-4 (2) 50.0(3) 0.02 (4) 2.5 102

Sol. (2)

[N2+ O

2 2NO] multiply by ( -

2

1) K

eq.= K

c

NO 2

1N

2+

2

1O

2K

eq.= (K

c)1/2

= (4 104) 1/2 = 41021

=

2100 = 50

9. Iron exhibits +2 and +3 oxidation states. Which ofthe following statements about iron is incorrect ?(1) Ferrous compounds are less volatile than thecorresponding ferric compounds.(2) Ferrous compounds are more easily hydrolysedthan the corresponding ferric compounds.(3) Ferrous oxide is more basic in nature than theferric oxide.(4) Ferrous compounds are relatively more ionicthan the corresponding ferric compounds.

Sol. (2)

Fe3+ compound are more easily hydrolysed then Fe2+due to more dectrophilic nature which facilitatesthe nucleophilic attack of H

2O and more over as per

fajan's rule Fe3+ compound are more covalent.

10. The electrons identified by quantum numbers 'n'and :(a) n = 4, = 1 (b) n = 4, = 0(c) n = 3, = 2 (d) n = 3, = 1can be placed in order of increasing energy as :(1) (b) < (d) < (a) < (c)(2) (a) < (c) < (b) < (d)(3) (c) < (d) < (b) < (a)(4) (d) < (b) < (c) < (a)


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AIEEE Examination(2012) (Code - B) (Page # 3)

Sol. (4)n + = 4 + 1 = 5n + = 4 + 0 = 5n + = 3 + 2 = 5n + = 3 + 1 = 4*Higher n + higher energy

*With same n + higher n higher energy

11. Which branched chain isomer of the hydrocarbonwith molecular mass 72u gives only one isomer ofmono substituted alkyl halide ?(1) Isohexane(2) Neohexane(3) Tertiary butyl chloride.(4) Neopentane

Sol. (4)

CH3 CH3CH3 CH3

CH3 CH3

CH3 CH Cl2

C CCl2 ,hv

Mono

chlorination

(All hydrogensare same type)

12. Which one of the following statements is correct ?(1) All amino acids except glycine are opticallyactive(2) All amino acids except glutamic acid are opti-cally active.(3) All amino acids except lysine are optically ac-tive.(4) All amino acids are optically active

Sol. (1)

H N2 C OH

(It is not chiral carbon.optically inactive)

Glycene

H

H

C

O

13. 2 - Hexyne gives trans - 2 - Hexene on treatmentwith :(1) Pd/BaSO

4

(2) Li AlH4

(3) Pt/H2

(4) Li/NH3Sol. (4)

CH3 CH

2 CH

2 C C CH

3 Li/NH3

2-hexene

CH CH CH3 2 2 H

CH32-hexene

HC C

14. Iodoform can be prepared from all except :(1) 3 - Methyl - 2 - butanone(2) Isobutyl alcohol(3) Ethyl methyl ketone(4) Isopropyl alcohol

Sol. (2)

CH CH CH3 2 OH

CH3OH/I2 No Iodo form

testIsobutyl alcohol

15. The incorrect expression among the following is :

(1)RT

STHKln

=

(2) K = e-G/RT

(3) TS

G

total

system=

(4) In isothermal process,

wreversible

= -nRT lni

f

V

V

Sol. (1)G = RTlnK = H TS

lnK =

RT

STH 00

16. The standard reduction potentials for Zn2+/Zn,Ni2+/Ni, and Fe2+/Fe are 0.76, 0.23 and 0.44 Vrespectively. The reaction X + Y2+ X2+ + Y will

be spontaneous when:(1) X = Fe, Y = Zn(2) X = Zn, Y = Ni(3) X = Ni, Y = Fe(4) X = Ni, Y = Zn

Sol. (2)Zn + Ni2+ Zn+2 + Ni

E = 2 20 0Zn/Zn Ni /Ni

E E+ ++

= 0.76 + (0.23)= + 0.53 (spontaneous)

17. Lithium forms body centred cubic structure. Thelength of the side of its unit cell is 351 pm. Atomicradius of the lithium will be:(1) 240 pm (2) 152 pm(3) 75 pm (4) 300 pm

Sol. (2)

3 a = 4r r =4

a3

= 3514

73.1 = 151.99 pm


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18. How many chiral compounds are possible onmonochlorination of 2methyl butane?(1) 4 (2) 6 (3) 8 (4) 2

Sol. (1)

H HH H

CH3 CH3H H

CH3 CH2 Cl

CH3 CH3

Cl , h2 v

Mono

chlorination

+

H

H

CH Cl2H

CH3

CH3

+

H

H

CH3Cl

CH3

CH3

+

H

Cl

CH3H

CH3

CH3

All above 4 products are optically active.

19. Kffor water is 1.86 K kg mol1. If your automobile

radiator holds 1.0 kg of water, how many grams of

ethylene glycol (C2H6O2) must you add to get thefreezing point of the solution lowered to 2.8C?(1) 39 g (2) 27 g (3) 72 g (4) 93 g

Sol. (4)

Tf= K

f.m

2.8 = 1.86 1

62/w

w = 93.333 gm 93 gm

20. In which of the following pairs the two species arenot isostructural?

(1) PF5 and BrF5 (2) AlF63 and SF6

(3) CO32 and NO3 (4) PCl4+ and SiCl4Sol. (1)

PF5

P is sp3d TBP.

BrF5Br is sp3d2 square pyrimidal.

AlF63 and SF6 sp

3d2 octahedral

CO32 and NO3

sp

2 Trigonal planer

PCl4+ and SiCl4 sp

3 Tetrahedral

21. For a first order (A) Products, the concentrationof A changes from 0.1 M to 0.025 M in 40 minutes.The rate of reaction when the concentration of A is0.01 M, is :

(1) 3.47 105 M/min (2) 1.73 104 M/min

(3) 1.73 105 M/min (4) 3.47 104 M/min

Sol. (4)

t75%

= 2 t1/2

40 = 2 t1/2t1/2 = 20 min

Rate =2/1t

693.0[A] =

20

693.0 0.01

= 3.47 104 M/min

22. Ortho-nitrophenol is less solution water than p-andm-nitrophenols because

(1) o-Nitrophenol shows Intermolecular Hbonding

(2) Melting point of o-Nitrophenol is lower than thoseof m- and p-isomers.

(3) o-Nitrophenol is more volatile in steam thanthose of m-and p-isomers.

(4) o-Nitrophenol shows Intramolecular Hbonding

Sol. (4)

NO

OOH

Intra molecularH-bonding

Inter molecular Hbonding with H2O in

p-nitrophenol is more, therefore p-nitrophenol ismore soluble in H

2O.

23. In the given trasformation, which the following isthe most appropriate reagent?

CH=CHCOCH3

HO

reagent

CH=CHCH CH2 3

HO

(1) Na, Liq. NH3 (2) NaBH4(3) NH2NH2, OH (4) Zn-Hg/HCl

Sol. (3)

CH=CHCCH3

HO

O

NH -NH2 2/

Wolff kishner

reduction

OH

CH=CHCH CH2 3

HO

24. According to Freundlich adsorption isotherm, which

the following is correct?

(1)n/1p

m

x

(2)m

x p0

(3)m

x p1

(4) All the above are correct for different rangesof pressure.


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Sol. (4)

n/1pm

x If pressure is moderate

m

x p0 If pressure is very high

m

x p1 If pressure is very low

25. The density of a solution prepared by dissolving120 g of urea (mol. mass = 60 u) in 1000 g of wateris 1.15 g/mL. The molarity of this solution is :(1) 1.02 M (2) 2.05 M(3) 0.50 M (4) 1.78 M

Sol. (2)

M =v

n=

31015.1

1120

2

= 15.11120

2000 = 2.05 M

26. Which of the following on thermal decomposition

yields a basic as well as an acidic oxide?(1) CaCO3 (2) NH4NO3(3) NaNO3 (4) KClO3

Sol. (1)CaCO

3 CaO + CO

2

(basic oxide) (Acidic oxide)NH4NO3 N2O + H2ONaNO3 NaNO2 + O2KClO

3 ICCI + O

2

27. Aspirin is known as(1) Acetyl salicylate (2) Methyl salicylic acid(3) Acetyl salicylic acid (4) Phenyl salicylate

Sol. (3)

O C CH3

O

COOHAcetyl salicylic acid

28. Which of the following compounds can be detected

by Molisch's test?

(1) Amines (2) Primary alcohols

(3) Nitro compounds (4) Sugars

Sol. (4)

Molish's test is for carbohydrates. i.e.,

sugar(carbohydrate)molish reagent

conc. H SO2 4Purple rings in test

tube

29. What is DDT among the following

(1) Biodegradable pollutant

(2) Non-biodegradable possutant

(3) Greenhouse gas

(4) A fertilizer

Sol. (2)

Cl Cl

C HCCl3

DDT(Di chloro Di phenyl Trichloro ethane)

It is non-biodeqradable pollutant.

30. Very pure hydrogen (99.9%) can be made by which

of the following processes?

(1) Electrolysis of water

(2) Reaction of salt like hydrides with water(3) Reaction of methane with steam

(4) Mixing natural hydrocarbons of high molecular

weight

Sol. (2)


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PART - II [MATHEMATICS]

31. Let a and b be two unit vectors. If the vectors

c a 2b= + and d 5a 4b= are perpendicular to

each other, then the angle between a

and b

is:

(1)3

(2)

4

(3)

6

(4)

2

Sol. (1)

c.d 0=

5 4(a.b) 10(a.b) 8 0 + =

( )6 a.b 3= 1a.b2

=3

=

32. If the integral

5tanx

dx x a ln| sinx 2cosx| ktanx 2

= + +

then a is equal to :

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

Sol. (2)

5sinxdx

sin x 2 cos xLet 5 sin x = A(sin x 2 cos x) + B(cos x + 2 sin x)

5 = A + 2B

0 = 2A + B B = 2A

5 = 5A A = 1, B = 2(sinx 2cosx) 2(cosx 2sinx)

sin x 2 cos x

+ +

= x + 2 ln|sin x 2cos x| + c

33. Consider the function,

f(x) = |x 2| +|x 5|,x R

Statement 1 : f'(4) = 0Statement2: f is continous in [2, 5],

differentiable in (2, 5) and f(2) = f(5)

(1) Statement 1 is true, Statement 2 is true,

Statement 2 is not a correct explanation forstatement 1.

(2) Statement 1 is true, Statement 2 is false.

(3) Statement 1 is false, Statement 2 is true.


Statement 2 is a correct explanation forstatement 1.

Sol. (1)

f(x) is constant in [2, 5]

34. If the line 2x + y = k passes through the point

which divides the line segment joining the points(1, 1) and (2, 4) in the ratio 3 : 2, then k equal:

(1) 6 (2) 11/5 (3) 29/5 (4) 5Sol. (1)

2 6 2 12P ,

5 5

+ +

8 14

P ,5 5

P point will satisfy the given straight line k = 6

35. Statement1 : An equation of a common tangent

to the parabola 2y 16 3x= and the ellipse

2 2

2x y 4+ = is y 2x 2 3= +

Statement 2: If the line4 3

y mx ,(m 0)m

= +

is a common tangent to the parabola

2y 16 3x= and the ellipse 2 22x y 4,+ =

then m satisfies 4 2m 2m 24+ =(1) Statement 1 is true, Statement 2 is true,

Statement 2 is not a correct explanation for

statement 1.(2) Statement 1 is true, Statement 2 is false.



Statement 2 is a correct explanation for

statement 1.Sol. (4)

36. Three numbers are chosen at random without

replacement from {1, 2, 3, ....8}. The probability

that their minimum is 3, given that their maximumis 6, is :

(1)1

4(2)

2

5(3)

3

8(4)

1

5

Sol. (4)

( )P(min.3 max.6)

P min.is3 / max.is6P(max.6)

=

21

52

C

C=

1

5=


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37. Let ABCD be a para llelogram such that

AB q, AD p= =

and BAD be an acute angle. If

r

is the vector that coincides with the altitude

directed from the vertex B to the side AD, then

r is given by :

(1)p.q

r q pp.p

=

(2)( )

( )

3 p.qr 3q p

p.p= +

(3)( )

( )

3 p.qr 3q p

p.p=

(4)p.q

r q pp.p

= +

Sol. (4)

BR.AD 0=

( p q).b 0 =

p.q

p.p =

r p q= p.q

q pp.p

= +

C

BA

D

R)p(

)p(

)q()0(

38. An equation of a plane parallel to the plane

x 2y +2z 5 = 0 and at a unit distance from

the origin is :

(1) x 2y + 2z 1 = 0 (2) x 2y +2z + 5 = 0

(3) x 2y + 2z 3 = 0 (4) x 2y + 2z + 1= 0Sol. (3)

x 2y + 2z + k = 00 0 0 k

13

+ + += k = 3

x 2y + 2z 3 = 0

39. In a PQR if 3 sin P + 4 cos Q = 6 and4 sin Q + 3 cos P = 1, then the angle R is equal

to :

(1)4

(2)

3

4

(3)

5

6

(4)

6

Sol. (4)

square and add

40. If f : R R is a function defined by

f(x) = [x] cos2x 1

2

, where [x] denotes the

greates integer function, then f is:

(1) discontinuous only at non-zero integral values

of x.

(2) continuous only at x = 0.(3) continuous for every real x.

(4) discontinuous only at x = 0

Sol. (3)

41. Statement 1 : The sum of the series

1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) +.....+(361 + 380 + 400) is 8000.

Statement 2:

n3 3 3

k 1

(k (k 1) ) n ,

=

= for any

natural number n.






Statement 2 is a correct explanation forstatement 1.

Sol. (4)

1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) +

... +(361 + 380 + 400)k2 + k 1 + k(k 1)

{ }20

3 3

k 1

k (k 1)

=

2 2 2 2n (n 1) (n 1) n

4 4

+

{ }2n

4n4

= n3 = 203 = 8000

42. The length of the diameter of the circle which

touches the x-axis at the pint (1, 0) and passes

through the point (2, 3)

(1) 6/5 (2) 5/3 (3) 10/3 (4) 3/5Sol. (3)

2k 1 (k 3)= +

k 5 / 3 =

diameter = 10/3

(2,3)

(1,0)

(1,k)

43. Let

1 0 0

A 2 1 0

3 2 1

=

. If u1 and u2 are column

matrices such that 1

1

Au 0

0

=

and 2

0

Au 1

0

=

then u1 + u2 is equal to

(1)

1

1

0

(2)

1

1

1

(3)

1

1

0

(4)

1

1

1


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Sol. (2)

1 0 0 a 1

2 1 0 b 0

3 2 1 c 0

=

for U1

a 1=

2a + b = 0 b = 2 1

1

U 2

1

= 3a + 2b + c = 0 c = 1

for U2a = 0

2a + b = 1 b = 1

3a + 2b + c = 0 c = 2 2

0

U 1

2

=

44. I f n is an posi ti ve in teger, then

( ) ( )2n 2n

3 1 3 1+ is :

(1) an even positive integer

(2) A rational number other than positive integers

(3) an irrational number

(4) An odd positive integer

Sol. (3)

( ) ( )2n 2n

3 1 3 1+

n n(4 2 3) (4 2 3)= +

( )n n n2 (2 3) (2 3)= +

( )n n n 1 1 n n 3 31 32 .2 C 2 ( 3) C 2 ( 3) ...... = + +45. Assuming the balls to be indentical except for

difference in colours, the number of ways in which

one or more balls can be selected from 10 white,

9 green and 7 black balls is:

(1) 630 (2) 879 (3) 880 (4) 629

Sol. (2)

10 white, 9 green, 7 black

Total ways = 11.10.81 = 880 1 = 879

46. An ellipse is drawn by taking a diameter of thecircle (x 1)2 + y2 = 1, as its semi-minor axis

and a diameter of the circle x2 + (y 2)2 = 4 as

its semi-major axis. If the centre of the ellipse is

at the origin and its axes are the coordinate

axes, then the equation of the ellipse is :(1) 4x2+ y2 = 8 (2) x2 + 4y2 = 16

(3) 4x2 + y2 = 4 (4) x2 + 4y2 = 8

Sol. (2)

2 2

2 2

x y1

a b+ = b = 2, a = 4 2 2x 4y 16+ =

47. If the linesx 1 y 1 z 1

2 3 4

+ = = and

x 3 y k z

1 2 1

= = intersect, then k is equal to :

(1) 9/2 (2) 0 (3) 1 (4) 2/9Sol. (1)

3 1 k 1 1

2 3 4 0

1 2 1

+

= 9

2

48. Let a, b R be such that the function f given

by f(x) = ln |x| + bx2 + ax, x 0 has extremevalues at x = 1 and x = 2.

Statement 1 : f has local maximum at x = 1

and at x = 2

Statement 2:1 1

a and b2 4

= =




(3) Statement 1 ix false, Statement 2 is true.


Statement 2 si a correct explanation forstatement 1.

Sol. (4)

1f '(x) 2bx a 0

x= + + =

1 2b + a = 0 ;1

4b a 02 + + =

a 2b = 1 ;1

b4

=

1a

2=

49. If2z

z 1 andz 1

is real, then the point

represented by the complex number z lies:

(1) either on the real axis or on a circle not

passing through the origin.

(2) On the imaginary axis.

(3) either on the real axis or on a circle passingthrough the origin.

(4) on a circle with centre at the origin.

Sol. (3)

2 2 2z x y 2xyi

z 1 (x 1) iy

+=

+

{ }{ }2 22 2

x y 2ixy (x 1) iy

(x 1) y

= +

+

Img. Part = 2xy(x 1) (x2 y2)y = 0

y = 0 or x2 + y2 2x = 0


9/16




50. The negation of te statement

"If I become a teacher, then I will open a school",is :

(1) Neither I will become a teacher nor I will

open a school.

(2) I will not become a teacher or I will open aschool.(3) I will become a teacher and I will not open a

school.

(4) Either I will not become a teacher or I will

not open a school

Sol. (3)

51. If x

0g(x) cos4t dt, then g(x )= + equals :

(1) g(x) g() (2) g(x).g ()

(3)g(x)

g( )(4) g(x) + g()

Sol. (1, 4)

x

0

g(x) cos 4t dt= x

0

sin4t sin4x

4 4

= =

sin(4(x ))g(x )

4

+ + =

sin4x

4= = g(x)

sin4g( ) 0

4

= = so ans. (1 & 4)

52. A spherical balloon is filled with 4500 cubic

meters of helium gas. If a leak in the ballooncauses the gas to escape at the rate of 72

cubic meters per minute, then the rate (in meters

per minute) at which the radius of the balloon

decreases 49 minutes after the leakage began is

:(1) 2/9 (2) 9/2 (3) 9/7 (4) 7/9

Sol. (1)

V = 4500 =34 r

3

dv72

dt

= ; 2dr 72

dt 4 r

=

4500 72 49 = 972 =34 r

3 r = 9

dr

dt=

2

9

53. The equation esin x esin x 4 = 0 has :

(1) exactly one real root

(2) exactly four real roots.

(3) infinite number of real roots.

(4) no real roots.

Sol. (4)

sinxsinx

1e 4

e =

1t 4

t =

4 16 4

t 2

+

= t

4 2 5

2

= t 2 5=

so no solution

54. Let X = {1, 2, 3, 4, 5} The number of different

ordered pairs (Y, Z) that can be formed such

that Y X,Z X and Y Z is empty, is:

(1) 25 (2) 53 (3) 52 (4) 35

Sol. (4)

1 can be placed in Y or Z or empty setso 1 has three options

similarly 2, 3, 4, 5 also have three options

55. The area bounded between the parabola

2 2yx and x 9y4

= = and the straight line y = 2

is:

(1)20 2

3(2) 10 2 (3) 20 2 (4)

10 2

3

Sol. (1)

)2,23(

2,21

y = 2

2 2

0 0

1area 2 3 ydy ydx

2

=

20 23

=

56. Let P and Q be 3 3 matrices with P Q. If

P3

= Q3

and P2

Q = Q2

P, then determinant of(P2 + Q2) is iqual to :

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

Sol. (1)

P3 = Q3

P2Q = Q2PP3 P2Q = Q3 Q2P(Q P)

P2 (P Q) Q2 (Q P) = 0

|P2 +Q2| |PQ| = 0 P2+ Q2 = 0


10/16




57. Let x2, x2 ......xn be n observatyions, and let xbe their arithmetic mean and 2 be their variance.

Statement 1 : Variance of 2x1 , 2x2 ....., 2xn is

4 2 .

Statement 2: Arithmetic mean of

1 2 n2x ,2x ....,2x is4x.

(1) Statement 1 is true, Statement 2 is true,Statement 2 is not a correct explanation for

statement 1.



(4) Statement 1 is true, Statement 2 is true,Statement 2 is a correct explanation for

statement 1.

Sol. (2)

58. The population p(t) at time t of a certain mouse

species satisfies the differential equation

dp(t)

dt=0.5 p(t) 450. If p(0) = 850, then the

time at which the population becomes zero is:

(1) ln 182

1(2) ln 18 (3) 2 ln 18 (4) ln 9

Sol. (3)

dp P450

dt 2=

dp dt

P 900 2

=

tln(P 900) c

2 = +

P 900 = k.et/2

P(0) = 850

50 = k k = 50

If p = 0

900 = 50 et/2 t = 2 ln 18.

59. A line is drawn through the point (1, 2) to meet

the coordinate axes at P and Q such that it

forms a triangle OPQ, where O is the origin. If

the area of the triangle OPQ is least, then the

slope of the line PQ is :

(1) 2 (2) 1/2 (3) 1/4 (4) 4

Sol. (1 )

1 m 2area (2 m)

2 m

=

2

1 (m 2)2 m

=

dA0 m 2

dm= =

60. If 100 times the 100th term of an AP with non

zero common difference equals the 50 times its

50th term, then the 150th term of this AP is :

(1) 150 (2) zero

(3) 150 (4) 150 times its 50th term

Sol. (2)

100(a + 99d) = 50(a + 49d)

50a + (149 50)d = 0

a + 149 d = 0


11/16




PART - III [PHYSICS]

61. This question has Statement 1 and Statement2. Of the four choices given after the State-

ments, choose the one that best describes thetwo statements.If two springs S

1and S

2of force constants k

1

and k2, respectively, are stretched by the

same force, it is found that more work is doneon spring S

1than on spring S

2.

Statement 1: If stretched by the sameamount, work done on S

1, will be more than

that on S2.

Statement 2: k1< k

2

(1) Statement 1 is true, statement 2 is true,statement 2 is the correct explanation ofStatement 1.

(2) Statement 1 is true, Statement 2 is true,Statement 2 is not the correct explanation ofstatement 1.(3) Statement 1 is false, Statement 2 is true.(4) Statement 1 is true, Statement 2 is false.

Sol. 3

W = 1/2kx2

if F is constantW 1/kIf x is fixed w k


ments, choose the one that best describes the

two Statements.

An insulating solid sphere of radius R has a uni-

formly positive charge density . As a result ofthis uniform charge distribution there is a finite

value of electric potential at the centre of the

sphere, at the surface of the sphere and also at

a point out side the sphere. The electric poten-

tial at infinity is zero.Statement 1: When a charge 'q' is taken from

the centre to the surface of the sphere, its po-

tential energy changes byo3

q

Statement 2: The electric field at a distance

r(r


12/16




66. A radar has a power of 1 kW and is operating ata frequency of 10 GHz. It is located on a moun-tain top of height 500m. The maximum distanceupto which it can detect object located on thes u r f a c e o f t h e e a r t h ( R a d i u s o f e a r t h = 6 . 4 106

m) is :

(1) 40 km (2) 64 km(3) 80 km (4) 16 km

Sol. 3

Distance = Rh2 500104.62 6 = = 80 km

67. Truth tabel for system of four NAND gates asshown in figure is.

A

B

Y

(1)

(2)

(3)

(4)

Sol. 3

A

B

YC

D

E

A B C D E Y

0 0 1 1 1 0

0 1 1 1 0 1

1 0 1 0 1 1

1 1 0 1 1 0

68. A spectrometer gives the following readingwhen used to measure the angle of a prism.Main scale reading: 58.5 degreeVernier scale reading : 09 divisionsGiven that 1 division on main scale correspondsto 0.5 degree. Total divisions on the vernierscale is 30 and match with 29 divisions of themain scale. The angle of the prism from theabove data(1) 58.65 degree (2)59 degree(3) 58.59 degree (4) 58.77 degree

Sol. 1Reading by vernier scale

= 0.529

130

= 0.15

Reading = 58.65


ments, choose the one that best describes thetwo statements.Statement 1: Davisson-Germer experimentestablished the wave nature of electrons.Statement 2: If electrons have wave nature,they can interfere and show diffraction.

(1) Statement 1 is true, statement 2 istrue, statement 2 is the correct explanation ofStatement 1.(2) Statement 1 is true, Statement 2 is true,Statement 2 is not the correct explanation ofstatement 1.(3) Statement 1 is false, Statement 2 is true.(4) Statement 1 is true, Statement 2 is false.

Sol. 1Davisson-Germer experiment supports Debroglieexperiment

70. In a uniformly charged sphere of total charge Qand radius R, the electric field E is plotted as afunction of distance from the centre. The graphwhich would correspond to the above will be :

(1)

R

E

r

(2)

R

E

r

(3)

R

E

r

(4)

R

E

r

Sol. 1E r. E 1/r2


13/16




71. A cylindrical tube, open at both ends, has a fun-damental frequency, f, in air. The tube is dippedvertically in water so that half of it is in water.The fundamental frequency of the air-column isnow:(1) 3f/4 (2) 2f

(3) f (4) f/2Sol. 3

=

=2

= = 2

2

vvf =

=

2

24

=

= 2= ; f2

v

f

'

==

72. If a simple pendulum has significant amplitude(up to a factor of 1/e of original) only in theperiod between t = 0s to t = s then may becalled the average life of the pendulum. Whenthe spherical bob of the pendulum suffers a re-tardation (due to viscous drag) proportional toits velocity, with 'b' as the constant of propor-tionality, the average life time of the pendulumis (assuming damping is small) in seconds.

(1)b

1(2)

b

2

(3)b

693.0(4) b

Sol. 2eqn of motion isF = -kx - mbvsolving we haveA = A.e - bt/2 = A

o/e

t = 2/b73. A coil is suspended in a uniform magnetic field,

with the plane of the coil parallel to the mag-netic lines of force. When a current is passedthrough the coil it starts oscillating; it is verydifficult to stop. But if an aluminium plate isplaced near to the coil, it stops. This is due to.

(1) shielding of magnetic lines of force asaluminium is paramagnetic material.(2) electromagnetic induction in the aluminiumplate giving rise to electromagnetic damping.(3) development of air current when the plateis placed.(4) induction of electrical charge on the plate

Sol. 2Due to oscillation of coil magnetic field changesin aluminium and eddy currents are made whichdamps coil.

74.

25

20

15

10

5

0 50 100 150 200 250 300

Time t in seconds

Pot

entialdi f

ference

V

in

volts

The figure shows an experimental plot fordischarging of a capacitor in an R-C circuit.The time constant of this circuit lies be-tween.(1) 50 sec and 100 sec(2) 100 sec and 150 sec(3) 150 sec and 200 sec(4) 0 and 50 sec

Sol. 2In one time constantVoltage becomes 0.37 times maximum voltageV = 0.37 25 = 9.25So time is between 100 sec to 150 sec.

75. A carnot engine, whose efficiency is 40% takesin heat from a source maintained at a tempera-ture of 500 K. It is desired to have an engineof efficiency 60%. Then, the intake tempera-ture for the same exhaust (sink) temperaturemust be.(1) 750 K(2) 600 K

(3) efficiency of Carnot engine cannot be madelarger than 50%(4) 1200 K

Sol. 1

=2

1

T1 100

T

.....(A)

0.4 =2

T1

500

.....(A)

0.6 = 1 2

1

T

T .....(B)

On solving T1

= 750 K

76. Two electric bulbs marked 25W - 220V and 100W- 220V are connected an series to a 440V sup-ply. Which of the bulbs will fuse ?(1) 25W (2) neither(3) both (4) 100W

Sol. 1

P

VR

2

= 25

220R

2

1 = ,100

220R

2

2 =

R1> R

2So R

1will fuse


14/16




77. An electromagnetic wave in vaccum has the elec-

tric and magnetic fields E

and B

, which are

always perpendicular to each other. The direc-

tion of polarization is given by X

and that of

wave propagation by k

. Then :

(1) BEkandBX

(2) EBkandEX

(3) EBkandBX

(4) BEkandEX

Sol. 4

Direction of wave velocity BE

direction of polarisation is parallel to E

78. The mass of a spaceship is 1000 kg. It is to belaunched from the earth's surface out into freespace. The value of 'g' and 'R' (radius of earth)

are 10 m/s2

and 6400 km respectively. The re-quired energy for this work will be :(1) 6.4 109 Joules (2) 6.4 1010 Joules(3) 6.4 1011 Joules (4) 6.4 108 Joules

Sol. 2

quiredRe

e

e ER

mGM= g

R

GM2

e

e =

E = (g Rem) = 6.4 1010 J

79. In Youngs double slit experiment one of the slitis wider than other so that the amplitude ofthe light from one slit is double of that fromother slit. If I

mbe the maximum intensity, the

resultant intensity I when they interfere atphase difference is given by.

(1)2m

I1 4cos

5 2

+

(2)

2mI

1 8cos9 2

+

(3) ( )mI

4 5cos9

+ (4)2m

I1 2cos

3 2

+

Sol. 2I A2

I1= I I

2= 4I

Inet

= I1+ I

2+ 1 22 I I cos

Inet = I + 4I + 2 I 4I cosI

net= 5I + 4I cos .....(1)

Imax

= Im

= ( )2

1 2I I+ = 9I

I =mI

9

from eq (i) Inet

= ( )mI

5 4cos9

+

=2mI 5 4 2 cos 1

9 2

+

2mI 1 8cos9 2

+

80. A boy can throw a stone up to a maximum heightof 10 m. The maximum horizontal distance thatthe boy can throw the same stone up to will be

(1) 10 2 m (2) 20 m

(3) 20 2 m (4) 10 m

Sol. 2

,10g2

u2= 210u =

Rmax

= m20g

u2=

81. Assume that a neutron breaks into a proton andan electron. The energy released during this pro-cess is :(Mass of neutron = 1.6725 10-27 kgMass of proton = 1.6725 10-27 kgMass of electron = 9 10-31kg)(1) 6.30 MeV (2) 5.4 MeV

(3) 0.73 MeV (4) 7.10 MeVSol. Bonus

Mass increases Reaction not Possible

82. An object 2.4 m in front of a lens forms a sharpimage on a film 12 cm behind the lens. A glassplate 1 cm thick, of refractive index 1.50 isinterposed between lens and film with its planefaces parallel to film. At what distance (fromlens) should object be shifted to be in sharpfocus on film?(1) 3.2 m (2) 5.6 m(3) 7.2 m (4) 2.4 m

Sol. 1

i f

1 1 1 1

v u v u

=

1 1 1 1

112 240 u12

3

+ = +

u = 3.2 m

83. A liquid in a beaker has temperature at time tand

0is temperature surroundings then ac-

cording to Newtons law of cooling the correctgraph between log

e(

0) and t is.

(1)

t

(2)

t

(3)

t0

(4)

t

Sol. 3

d

dt

= k (

0) n (

0) = kt + c


15/16




84. Helium gas goes through a cycle ABCDA (con-

sisting of two isochoric and two isobaric lines)

as shown in figure Efficiency of this cycle is nearly

(assume the gas to be close to ideal gas).

D

CB

V0 2V0

2P0

P0 A

(1) 10.5 % (2) 12.5 %

(3) 15.4% (4) 9.1 %

Sol. 3

QABC

= W +U = 2P0V

0+ n 3/2 R 3T

= 13/2 P0V

0

W = Area = P0V

0

= 2/13= 200/13% = 15.4%

85. Proton, Deuteron and alpha particle of the same

kinetic energy are moving in circular trajectories

in a constant magnetic field. The radii of proton,

deuteron and alpha particle are respectively rp,

rd

and r.Which one of the following relations is

correct?

(1) r> r

d> r

p(2) r

= r

d> r

p

(3) r= r

p= r

d(4) r

= r

p< r

d

Sol. 4

2mvqvB

r= r =

mv

qB=

2mk m

qB q

so r = rp < rd

86. Resistance of a given wire is obtained by

measuring the current flowing in it and the

voltage difference applied across it. If the

percentage errors in the measurement of the

current and the voltage difference are 3%

each, then error in the value of resistance of

the wire is:

(1) 1% (2) 3%

(3) 6% (4)zero

Sol 3

R =V

I

R V I

R V I

= + = 3% + 3% = 6%

Hence (2) is correct

87. A particle of mass m is at rest at the origin at

time t = 0. It is subjected to a force F(t) = Foe-

bt in the x direction. Its speed v(t) is depicted by

which of the following curves ?

(1)

mb

Fo

t

v (t)

(2)

mb

Fo

t

v (t)

(3)

mb

Fo

t

v (t)

(4)

m

Fob

t

v (t)

Sol. 1a = F

O/m e-ht

=

t

o

bto dte.m

Fv

( )bto e1mb

Fv =

88. A thin liquid film formedbetween a U-shaped wire anda light slider supports a weightof 1.5 102N (see figure). Thelength of the slider is 30 cmand its weight negligible. The

surface tension of the liquid filmis.

FILM

w

(1) 0.05 Nm1 (2) 0.025 Nm1

(3) 0.0125 Nm1 (4) 0.1 Nm1

Sol. 2

2T = mg

T = mg/2 =21.5 10

2 0.3

= 0.025


16/16




89. Two cars of masses m1

and m2

are moving incircles of radii r

1and r

2, respectively. Their speeds

are such that they make complete circles in thesame time t. The ratio of their centripetal accel-eration is :

(1) r1 : r2 (2) 1 : 1(3) m

1r

1: m

2r

2(4) m

1: m

2

Sol. 1a

1: a

2= 2r

1: 2r

2= r

1: r

2( is same)

90. A charge Q is uniformly distributed over the sur-

face of non- conducting disc of radius R. The

disc rotates about an axis perpendicular to its

plane and passing through its centre with an

angular velocity . As a result of this rotation a

magnetic field of induction B is obtained at the

centre of the disc. If we keep both the amount

of charge placed on the disc and its angularvelocity to be constant and vary the radius of

the disc then the variation of the magnetic in-

duction at the centre of the disc will be repre-

sented by the figure :

(1)

R

B(2)

R

B

(3)

R

B(4)

R

B

Sol. 3Q = constantBut r changes = Q/4r2

r dr

variabledq =2rdrdq =Q/4r2 2rdr

dB = ( )r22dq

r2

di 00

=

dB =( )

( )

r2r4

drr2Q

2 20

dB = 2r

Kdr

B 1/r

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