Ai Aieee Modeltest 09

Questions - 180

1.

2.

Time - 180 Min

What will be the ratio of temperatures of sun and moon if the wavelengths of their maximum emission radiations are 140Å and 4200Å respectively : a) 1 : 30 b) 30 : 1 c) 42 : 14 d) 14 : 4235. A charge Q is situated at the corner of a cube, the electric flux passed through all the six faces of the cube is : a)

3.

PHYSICS

Q 6ε 0

Q

b) 8ε 0

c)

Q ε0

Q

d) 2ε 0

A Carnot heat engine and an irreversible heat engine both operate between the same high temperature and low temperature reservoirs. They absorb the same energy from the high temperature reservoir as heat. The irreversible engine. a) does mote work

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b) rejects more energy to the low temperature reservoir as heat c) has the same efficiency

d) has the same efficient as the reversible engine 4.

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If radius of earth shrinks by 1%, then for acceleration due to gravity : 1) No change at poles 2) No change at equator 3) Max. change at equator a) 3, 4

5.

4) Equal change at all locations

b) 2, 4

c)

d) 1, 2

A galvanometer based on the action of two uniform mutually perpendicular fields on a magnet, is called : a) sine galvanometer b) tangent galvanometer c) ballistic galvanometer

6.

1, 4

d) moving coil galvanometer

Due to earth’s magnetic field, the charged cosmic rays particles : a) Require greater kinetic energy to reach the equator than pole b) Require less kinetic energy to reach the equator than pole c) Can never reach the pole d) Can never reach the equator.

7.

If yellow light emitted by sodium lamp in Young’s double slit experiment is replaced by monochromatic blue light of same intensity : a) The fringe width will remain unchanged

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b) Fringes will become less intense c) Fringe width will decrease d) Fringe width will increase 8.

Nuclear fission is best explained by : a) Liquid droplet model

b) yukawa p = meson theory www.aieeepage.com

c) Independent particle model of nucleus

d) Proton - proton cycle

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21.

The effective capacity of the network between terminal A and B is : (All capacity in µF)

a) 6 b) 20 c) 3 d) 10

22.

A potentiometer has 4 meter long wire of 10 Ω resistance, connected to it. This wire is also connected with a cell of 2 volt e.m.f. The potential difference of unit length of the wire will be: a) 0.5 volt/meter b) 2 volt/meter c) 5 volt/meter d) 10 volt/meter

23.

If two bulbs, whose resistance are in the ratio of 1 : 2 are connected in series, the power dissipated in them has the ratio of : a) 1 :1 b) 1 : 2 c) 2 : 1 d) 1 : 4

24.

In a coil of 0.1 m radius and 1000 rounds. 0.1 amp current is passed. What will be the magnetic field at the centre of coil : a) 2 x 10-1 T b) 4.31 x 10-2 T c) 6.28 x 10-4 T d) 9.81 x 10 - 4 T

25.

A bar magnet of magnetic moment M is cut into two parts of equal length. The magnetic moment of each part will be : a) Zero b) 0.5 M c) M d) 2 M

26.

Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to 100 π radian/sec. The maximum value of emf in the second coil is : (maximum of current is 10 AMP) a) 2 π b) 5 π c) 6 π d) 12 π

27.

A convex lens is made of the substance of refractive index 1.6. Radius of curvature of spherical surface is 60 cm. the focal length of the lens is : a) 50 cm b) 100 cm c) 200 cm d) 400 cm

28.

The ratio of maximum and minimum intensities obtained in the interference of waves emitted by two coherent sources is 121 : 81. The ratio of amplitudes of two coherent sources will be : a) 1 : 10 b) 10 : 1 c) 81 : 121 d) 121 : 81

29.

When an electron is accelerated through 100 volt, then its kinetic energy becomes : a) 1.602 x 10-17 joule b) 418.6 calorie

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c) 1.16 x 104 °K 30.

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d) 6.626 x 10 - 34 watt - sec

When an electron do transition from n = 4 to n = 2, then emitted line in spectrum will be : a) First line of Lyman series b) Second line of Balmer series c) First line of Paschen series

31.

d) Second line of Paschen series

The S.I. unit of magnetic permeability is : a) Weber m-2 amp-1 c) Weber m-1 amp

b) Weber m amp www.aieeepage.com d) Weber m amp -1

-1

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43.

A sound is produced between two vertical parallel walls. The echo from one walls is heard after 2s while from the other 2s after the first echo. The speed of sound in air is 340 m/s. a) The distance between two walls is 680 m b) The distance between two walls is 1020 m c) The next echo will be heard after 8s from the instant original sound was produced d) The next echo will be heard after 9s from the instant original sound was produced.

44.

45.

A ray of light when incident upon a prism in the minimum deviation position suffers a deviation of 39°. If the shaded half portion of the prism is removed, the same ray will

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a) suffer a deviation of 19.5°

b) suffer a deviation of 39°

c) not suffer any deviation.

d) be totally internally reflected

A particel free to move along the x-axis has potential energy given by U( x) = k[1 − exp(− x 2 )] for

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−∞ ≤ x ≤ +∞ , where k is a positive constant of appropriate dimensions, Then

a) at points away from the origin, the particle is in unstable equilibrium b) for any finite non-zero value of x, there is a force directed away from the origin c) It its total mechanical energy is k/2 it has its minimum kinetic energy at the origin. d) for small displacements from x = 0, the motion is simple harmonic. 46.

Which one of the following is not true in case of Rutherford’s α -particle scattering experiment ? a) The majority of any atom is an empty space b) The atom’s positive charge is present in a small, dense nucleus c) The scattering of α -particle by the nucleus is not in accordance to Coulomb’s law d) The magnitude of positive charge in the nuclei of different metals is different.

47.

A hollow ball completely filled with water rolls without sliding on a horizontal floor. If the water freezes, which of the parameter given below will remain unchanged ? a) Angular speed and kinetic momentum b) Linear momentum and angular momentum c) Angular momentum and knetic energy

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d) Angular momentum and total energy 48.

Three containers of the same volume contain three different gases. The masses of the moelcules are M1 , M 2 and M 3 and the number of molecules in their respective containers is N1 , N 2 and N 3 . The gas pressure in the containers are P1 , P2 and P3 respectively. All the gases are now mixed and put in one of these containers. The pressure P of the mixture will be a) P < (P1 + P2 + P3 )

www.aieeepage.com c) P = P + P + P

b) P = P1 + P2 + P3

1

3

2

3

d) P > (P1 + P2 + P3 )

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54.

The value of current in the given circuit is :

a) 8.31 A 55.

b) 2.00 A

d) 1.33 A

d) 125 W

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A bubble in glass slab (µ = 1.5) when viewed from one side appears at 5 cm and 2 cm from other side, then thickness of slab is : a) 3.75 cm b) 3.0 cm c) 10.5 cm

57.

4.92 A

( 100 W, 200 V) bulb is connected to a 160 volts supply. The power consumption would be : a) 64 W b) 80 W c) 100 W

56.

c)

d) 2.5 cm

Light of wavelength 5000Å falls on a sensitive plate with photoelectric work function of 1.9 eV. The kinetic energy of the photoelectron emitted will be a) 0.58 eV b) 2.48 eV

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c) 1.24 eV 58.

For a prism, its refractive index is cot A/2, then minimum angle of deviation : a) 180 - A

59.

d) 1.16 eV

b) 180 - 2A

c)

d)

A 2

In an experiment to demonstrate Coulomb’s Law in electrostatics, the force F between two small charged spheres is measured for various distances r between their centres. A graph is plotted of In F (y-axis) against In r (x-axis). What is the slope of this graph ? a) -2 b) 1/2 c) -1/2

60.

90 - A

d) 2

In the shown figure minimum value of F to be applied on wedge A and B to lift up the sphere of mass M is

A

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F a) Mg

b)

B

60°

60°

Mg 2

c)

3 Mg 2

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F d)

2 3

Mg

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74.

Which of the following is the true structure of H2O2? H

a) H - O - O - H

O

b)

O

c)

H

75.

H H

d)

O=O

H H

O

O

The IUPAC name for the compound, CH 3 − CH − C − CH 2CH 3 is CH3 CH2

76.

a) 2-Ethyl-3-methybut - 1- ene

b) 2 - Isopropylbut -1-ene

c) 2 - Methyl - 3- ethyl - 3 butene

d) 2-(Methylehl) but -1 ene

A mixture of ethane, ethyne, and accetylene gases is passed through a Woulfe’s bottle containing ammoniacal silver nitrate solutions. The gas coming out is a) Both ethane and ethyne b) Original mixture c) Acetylene

O - Na +

Cl NO 2

77.

NO 2

Dil.NaOH  →

The above transformation proceeds through

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NO 2

78.

PAGE d) Ethane

NO 2

a) Electrophilic-addition

b) Benzyne intermediate

c) Activated nucleophilic substitution

d) Oxirane

For the reaction A( g ) + B ( g )

c(g) the equilibrium partial pressures are PA = 0.15 atm, PB = 0.10

atm and Pc = 0.30 atm . The value of the pressure was so reduced that after attainment of equilibrium again, the partial pressure of A and B were doubled. The partial pressure of C would be a) 0.30 atm b) 0.60 atm c) 1.20 atm 79.

d) 1.80 atm

Using the standard electrode potential values given below, decide which of the statements I, II, III, IV are correct, Choose the right answer from (a), (b), (c) and (d) Fe 2+ + 2e − → Fe; E o = − 0.44V Cu 2+ + 2e− → Cu; E o = +0.34V

Ag+ + e− →Ag;Eo = +0.80V

II. Fe can displace Cu from CuSO4 solution

III. Ag can displace Cu from CuSO4 solution

IV. Fe can disple Ag from AgNO3 solution

a) I and II 80.

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I. Cu can displace Fe from FeSO4 solution b) II and III

c)

II and IV

d) I and IV

Which of the following contains maximum number of atoms ?

b) 22.4 L of CO www.aieeepage.com

a) 6.023× 10 21 molecules of CO 2 c) 0.44 gm of CO 2

2

at S.T.P.

d) None of these

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87.

88.

For a reaction, 2A + B R C + D the active mass of B is kept constant and that of A is tripled. It is observed that the rate of reaction : a) Decreases nine times

b) Increases nine times

c) Decreases three times

d) Increases six times

 an 2  P +  (V − nb) = nRT . The ratio a/b has the The vander Waal’s equation of state is given by  V2   dimension of : b) lit. atm mol-1

a) atm lit -1 89.

d) lit. mol

What is the co-ordination number of sodium in Na 2O ?

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a) 6 90.

lit. atm mol-2

c)

b) 4

c)

8

d) 2

The following kinetic data are provided for a reaction between A and B : Conc. of A

Conc. of B

Rate of reaction

(mol L-1 )

(mol L-1 )

0.50

0.022

0.50

0.04

0.01

1.00

2.3 × 10 −6

0.02

1.00

0.92 ×10−5

1.15 × 10 −4

www.aieeepage.com 2.30 × 10 −4

Pick up the false statement about this reaction : a) The reaction is of 2nd order in A and 1st order in B b) The rate law of the reaction is,

dx = k[ A] [ B]2 dt

c) The value of the rate constant k is 0.025 dm 6 mol-2 min -1 c) None of these 91.

92.

Which has the highest freesing point at 1 atmosphere : a) 0.1 M NaCl solution

b) 0.05 M KCl solution

c) 0.1 M BaCl2 solutions

d) 0.1 < FeCl3 solution

For the reaction, 2-

PAGE

+ S2O3 +2H 3O(aq) R S(s) +H 2SO3(aq) +H 2O

2-

Rate = k[S2 O3 ] [H 3O + ].

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This reaction proceeds at a faster rate in : a) 0.1 M acetic acid

b) 0.1 M NH 4OH ]

c) 0.1 M NaOH

d) 0.1 M Hydrochloric acid

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105. Equilvalent weight of organic acid is determined by : a) Silver salt method

b) Platinichloride method

c) Victor meyer method

d) Carius method

106. Which is Z-Isomer : a) Maleic aicd CH 2

107.

b) Fumaric acid CH 3

Cl 2 , hv

c)

Succinic acid

d) Malonic acid

(A) + HCl

a) (A) is

CH 2 CH 2 substituti on

b) (A) is

CH

Cl and is free radical substitution

PAGE CH 3 and is free radical

Cl substitution

www.aieeepage.com CH(Cl) CH 3

c) (A) is

and in electrophilic

substituti on d) None of these K + Cl 2 800  →(X); (X) is :

108.

Cl

Cl Cl

a)

109.

b)

Cl

c)

Cl

d)

H

NaBH4 CH 3CHO OH →(A)   →( B); (B) is :

a) Crotoyl alcohol

b) Butan-1-ol

c) Isobutyl alcohol

d) 2-Methyl propanol

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110. Methyl cyanide is converted to methyl amine by : a) LiAlH 4

b) NaBH 4

c)

Na/alcohol

d) None

c)

Thyroxine

d) None

111. Which harmone contains iodine ? a) Insulin

b) Progesterone

112. Which polymer contains nitrogen : a) P. V. C

c) Nylon www.aieeepage.com

b) Terylene

d) Teflon

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MATHEMATICS 121. The line y = mx + 1 is a tangent to the parabola y 2 = 4 x, is : a) m = 1 122.

b) m = 2

c)

m=4

x2 | x | 3

c)

x2 | x | 2

d) m = 3

∫ x | x | dx =

a)

x3 3

b)

d) None of these

123. The value of the expression ( 3 sin 75° − cos 75°) is : a) 2 sin 15°

c)

b) 1 + 3

2 sin 105°

d)

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2

124. If n arithmetic means are inserted between 2 and 38, then the sum of the resulting series is obtained as 200, then the value of n is a) 6 b) 8 c) 9 d) 10 0, x is irrational

125. The function f (x) =  1, x is rational is 

a) continuous at x = 1

b) discontinuous ony at 0 www.aieeepage.com

c) discontinuous only at 0, 1

d) discontinuous everywhere

1 f ( x) = 126. If f(x) = x sin  , x ≠ 0 then xlim →0 x

a) 1

b) 0

c)

-1

d) does not exist

dy

2 2 127. Solution of the differential equation dx + y sec x = tan x sec x is

a)

y = tan x − 1 + ce − tan x

b) y 2 = tan x − 1 + ce tan x

c)

ye tan x = tan x − 1 + C

d) ye − tan x = tan x − 1 + C

128. If

f :R→ R

and

g:R→ R

are one to one, real valued function, then the value of the integral

π

∫ [ f ( x) + f( − x)] [g(x) - g(-x)]dx is

-π

a) 0

b)

c)

π

1

d) none of these

129. Ten different letters of an alphabet are given. words with five letters are formed from these given letters. Then the numbers of words which have at least one letter repeated is a) 69760 b) 30240 c) 99784 d) none of these G G G 130. Let a, b and cG be vectors with magnitudes 3, 4, and 5 respectively and aG + b + cG = 0 then the value of GG GG GG a .b + b .c + c .a is a) 47 b) 25 c) 50 d) -25

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131. The function y = 3 x − | x − 1 | is continuous at a) x < 0

b) x ≥ 1

c)

0 ≤ x ≤1

d) x ≥ 0

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142. The dimensions of the rectangle of greatest area that can be inscribed in a semi-circle of radius a is a)

143. If ∫

b) a × 2a

a×a

c)

a 2

×a 2

d) a × a 2

3x 3 + 2x 2 + x + 1 dx = Ax 2 + Bx − log | x + 1 | +17log | x + 2 | +c. Then (x + 1)(x + 2)

a) A = 1, B = -17

b) A = 3, B = 0

c)

A = 3, B = -7

3 2

d) A = , B = −7

144. If there exists a geometric progression containing 27, 8 and 12 as three of its terms (not necessarily consecutive) then how many progressions are possible ? a) 1 b) 2 c) infinite d) none of these

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145. If x = 9950 + 10050 and y = (101)50 then a) x = y

b) x < y

c)

x>y

d) None of these

G 146. If the vectors αG = aˆi + ˆj + kˆ, β = ˆi + bˆj + kˆ, γG = ˆi + ˆj + ckˆ are coplanar, where a ≠ 1, b ≠ 1, c ≠ 1, then the value 1 1 1 + + is 1− a 1− b 1− c

a) 1

c) 2 www.aieeepage.com

b) -1

1+

147. Sum of the n terms of the series a) infinite rational number c) irrational number

d) None of these

1 1.4 1.4.7 + + .... is a 6 6.12 6.12.18

b) infinite d) none of the above

148. The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of 100m from its base 45°. If the angle of elevation of the top of the pillar after completion at the same point is 60°,then the height to be increased for the completion of the pillar in meters is : a) 50 3

b) 100 2

c)

d) 100( 3 − 1)

100 3

149. A point moves so that the sum of squares of its distances from the four sides of a square is constant. This point always lies on a) straight line b) circle c) Parabola d) Ellipse 150. Mean deviation of the data a, a+d, a+2d, ......a,+ 2nd from the mean is equal to a)

n(n + 1) | d | 2n + 1

n(n + 1)d 2n + 1

b)

c)

(n + 1) | d | 2n

d) None of these

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151. The range of values of m for which the line y = mx + 2 cuts the circle x 2 + y 2 = 1 at distinct or coincident points is a) (−∞ − 3 ] ∪ [ 3 + ∞) c) [ 3 + ∞ ]

b)

[− 3

3]

d) None of these

1

−1

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 2−x  dx is  2+x 

152. The value of ∫ log a) 0

b) 2

c)

log e 2

d) π log e 2

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164. The equation of hyperbola referred to its axes as axes of coordinate whose distance between the foci is 20 and eccentricity equals

2 is

a) x 2 − y 2 = 25

b) x 2 − y 2 = 50

c) x 2 − y 2 = 125

d) x 2 + y 2 = 25

165. If the origin is shifted to 4, 5, -3 without changing the direction of the axes then the new co-ordinates of the point (0, 8, 5) with respect to new frame is a) (-4, 3, 8) b) (4, -3, -8) c) (4, 13, 2) d) None of these G G 166. A vector r has length 21 and its DR’s are 2, -3, 6 the component of vectro r are a) 2, -3, 9 b) 6, -9, 18 c) -2, -3, 9 d) -2, -3, -9

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167. The vector equation of the symmetrical form of equation of straight line

x−5 y + 4 z −6 = = is 3 7 2

G a) r = (3iˆ + 7 ˆj + 2kˆ ) + µ(5 ˆi + 4ˆj - 6kˆ)

b)

G r = (5iˆ + 4 ˆj − 6kˆ ) + µ(3ˆi + 7ˆj + 2kˆ)

G c) r = (5iˆ − 4 ˆj − 6 kˆ ) + µ(3ˆi - 7 ˆj − 2kˆ)

d)

G r = (5iˆ − 4 ˆj + 6kˆ ) + µ(3ˆi + 7ˆj + 2kˆ)

168. Let numbers 1, 2, 3,.....4n be pasted on 4n blocks the probability of drawing a number is proportional to r, then probability of drawing an even number in one draw is (n ∈ N )

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a)

n +1 2n + 1

b)

2n + 1 4n + 1

c)

n+2 n+3

d)

2n + 3 4n + 1

169. If cos −1 (4 x 3 − 3x) = 2π - 3cos -1 x, then x satisfies in interval

1  a) − 1, −  2 

b) | x |<

1 2

c)

1   2 , 1  

d) none of these

9 2

d)

170. If r1 = 3, r2 = 10 r3 = 15 then the value of R equals a)

171

15 2

b)

11 2

c)

13 2

A B C If sides a, b, c are in the ratio 19 : 16 : 5 then cot 2 : cot 2 : cot 2 equal a) 1 : 15 : 4

b) 15 : 1 : 4

c)

4 : 1 : 15

d) 1 : 4 : 15

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1 − 3 x, ∀x < 0  f ( x) =  3, x = 0, 172. Let then at x = 0  x 2 + 3, x > 0  a)

f (x) is continuous from left

c)

f (x) is right continuous

b)

f (x) is continuous

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f (x) has removable discontinuity

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