Ai Aieee Modeltest 03

MODEL TEST TEST CODE - FEE

AIEEE PAGE 180 QUESTIONS TIME ALLOWED : 180 MINUTES

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STUDENT’S NAME :

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Read the instructions on the ANSWER SHEET. Fill in your NAME, TEST CODE and AIEEE Application form Number. Use the information provided to choose the BEST answer from the four possible options. On your ANSWER SHEET fill in the oval that matches your answer. Mark only ONE answer for each question. Q. 1 to 8, 61 to 68 & 121 to 130 carries1 12 marks each, Q. 9 to 52, 69 to 112 & 131 to 170 carries 3 marks each and Q. 53 to 60,113 to 120 & 171 to 180 carries 412 marks each. For each incorrect response,one-third of the total marks alloted to the question would be deducted from the total score.

PAGEPAGE You are NOT allowed to use a calculator

TM

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1

Questions - 180 1.

PHYSICS

Time - 180 Min

Two pendulum bobs of unequal mass are suspended from the same fixed point by strings of equal length. The lighter bob is drawn aside and then released so that it collides with the other bob on reaching the vertical position. The collision is elastic. What quantities are conserved in the collision ? a) Both kinetic energy and angular momentum of the system b) Only kinetic energy c) Only angular momentum d) None of the above

2.

3.

4.

Gravitational force is required for : a) Stirring of liquid

b) Convection

c) Conduction

d) Diffraction and dispersion

PAGE

A photon is a) A quantum of light energy

b) A quantum of matter

c) A positively charged particle

d) An instrument for measuring light intensity.

Acceptor atoms introduced into a pure semiconductor at room temperature : a) increase the number of electrons in the conduction band

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b) increase the number of holes in the valence band c) lower the Fermi level d) increase the electrical resistivity 5.

Biological importance of ozone layer is : a) It stops ultraviolet rays b) Ozone layer reflects green house effect c) Ozone layer reflects radio waves d) Ozone layer controls the ratio of O2/H2 present in the atmosphere

6.

Two beams of electrons travelling in the same direction a) attract each other b) repel each other c) spin in same direction

7.

A current loop placed in a magnetic field behaves like a a) magnetic dipole b) magnetic substance c) magnetic pole

8.

d) either ‘a’ or ‘c’

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d) all are ture.

If a diamagnetic substance is brought towards the north and south pole of a bar magnet, then the substance : a) Would be attracted by the poles b) Would be repelled by the poles

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c) At north pole it would be repelled and at sough pole it would be attracted d) At north pole it would be attracted and at south pole it would be repelled

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9.

The driver of an express train moving with a velocity v1 and that a goods train is moving with a velocity v2 in the same direction on the same track. He applies the brakes and produces a retardasition a. The minimum time required to avoid collision is a)

10.

v1 a

b)

c)

v2 a

d)

v1 + v 2 a

The escape velocity for a plane is ve . A particle is projeced from its surface with a speed v. For this particle to move as a satellite around the planet. a)

11.

v1 - v 2 a

ve . < V < Ve 2

ve .

b)

2

< V < Ve

c)

Ve < V > 2 ve

d)

ve 2


ve 2

A small ball suspended from a string is set in to oscillation. When the ball passes through the lowest point of the motion, the string is cut. If the ball is then moving with the velocity 0.8ms−1 at a height of

PAGE

5 m above the ground, the horizontal distance travelled by the ball is ( Given : g = 10ms −2 ) a) 0.2 m 12.

b) 0.4 m

c)

0.6 m

d) 0.8 m

A tube 1 cm2 in cross - section is attached to the top of a vessel 1 cm high and of cross section 100 cm2 . Water is poured into the system filling it to a depth of 100 cm above the bottom of the vessel as shown in figure. Take g = 10 ms−2 . Now

www.aieeepage.com 1 cm 2

99 cm

1 cm

a) The force exerted by the water against the bottom of the vessel is 100 N b) The weight of water in the system is 1.99 N c) Both (a) and (b) are correct d) Neither (a) nor (b) is correct 13.

A spherical body of mass m, radius r and moment of inertia 1 about its centre moves along the x-axis. V

Its centre of mass moves with velocity = 9 and it rotates about its centre of mass with angular velocity = ωo . Let L = Iωo + mvo r. The angular momentum of the body about the origin O is

PAGE ωo

r

O

a) L, only if vo = ωor

m

vo

x

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b) greater than Lo,if vo > ωor

c) less that Lo, if vo > ωor

d) L, for all values of ωo and vo

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14.

A parallel - plate air capacitor is connected to a battery. While connected to the battery a dielectric whose dielectric constant is 2 is inserted, filling th space between the plates. The energy stored in the capacitor before the dielectric is inserted is Eo . The energy stored in the capacitor after the dielectric has been inserted is E k . the ratio E k /Eo is a) 1/4

b) 1/2

c)

1

d) 2

15.

A car has a fresh battery of e.m.f 12v and internal resistance of 0.05Ω . If the starter motor draws a current of 90 A, the terminal voltage when the starter is on will be a) 12 V b) 10.5 V c) 8.5 V d) 7.5 V

16.

A charged particle moves with a speed v in a circular path of radius r around a long uniformly charged conductor b) v ∝

a) v ∝ r c) v ∝ 17.

PAGE

1 r

d) v is independent of r

(60ˆi + 15ˆj − 3kˆ ) N force produces velocity (2ˆi − 4ˆj + 5kˆ ) in a particle. The value of power at that time

will be : a) 45 W

b) 95 W www.aieeepage.com

c) 75 W 18.

d) 100 W

The K.E. of a person is just half of the K.E. of a boy whose mass is just half of that person. If person increases his speed by 1 m/s then its K.E. equals to that of boy, then initial speed of person was : 2 2 +2 a)  2 m / s

 2 +2 b)  2 m / s





19.

c)





2( 2 + 2)m / s

d) none

The young’s modulus of elasticity of a wire is Y and stress is F. The elastic potential energy per unit volume in wire will be : a) F2Y

20.

1 r

b)

F2 2Y

c)

2Y F2

d)

Y2 2F

The threshold wavelength for lithium is 5250 Ao .For photo emission to take place, the wavelength of the incident light must be o

a) more than 5250 A

o

b) exactly equals to 5250 A

PAGE o

c) equal to or more than 5250 A

o

d) equal to or less than 5250 A

21.

For an inductor coil L = 0.04, then work done by source to establish a current of 5A in it is : a) 0.5J b) 1.00J c) 100J d) 20 J

22.

The interplaner distance in a crystal is 2.8 x 10-8 cm. The value of maximum wavelength which can be driffracted : a) 2.8 × 108m b) 5.6 × 10-8 m

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c) 1.4 × 10-8 m

d) 7.6 × 10-8 m

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23.

Two block of masses 1 kg. and 4 kg. are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is 3.18 x 1010 N/m2, then the radius of the wire is :

↑ 1Kg

a) 1 × 10-5 m 24.

b) 2 × 10-5 m

26.

c)

3 × 10-5 m

d) 4 × 10-5 m

A 5o C rise in temperature is observed in a conductor by passing the current. When the current is doubled the rise in temperature will be approximately : a) 5o C b) 10o C

PAGE

c) 20o C 25.

↓ 4Kg

d) 40o C

The relation between l and T1/2 as : (T1/2 → half life) a) T1/ 2 =

ln2 λ

c) T1 / 2 =

1 λ

b) T ln2 = 1 www.aieeepage.com 1/ 2

d) (λ + T1/ 2 ) = ln2

If earth describes an orbit round the sun of double its present radius, the year on the earth will be of a) 182 days b) 730 days c) 1032 days

d) None of the above

27.

Young’s modulus of the material of a wire of length L and radius r is Y N/m 2 . If the length is reduced to L/2 and radius to r/2, the Young’s modulus will be a) Y b) 2Y c) Y/2 d) Y/4

28.

In diagrams (1. to (4., variation of volume with changing pressure is shown. A gas is taken along the path ABCD. The change in internal energy of the gal will be V D

C

A

B (1)

V

P

D

D

C

C

PAGE A

V A

B

(2)

B

(3)

P

P

V D

C

A

B (4)

P

a) Positive in all the cases (1. to (4

b) Positive in cases (1., (2., (3. but zero in case (4.

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c) Negative in cases (1., (2., (3., but zero in case (4. d) Zero in all the cases

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29.

Three progressive waves A, B and C are shown in the figure below. With respect to the wave A, the wave C B

A

C

a) leads in phase by π and B lags behind by π b) lags behind in phase by π/2 and B leads by π/2 c) lags behind in phase by π and B leads by π

PAGE

d) leads in phase by π/2 and B lags behind by π/2 30.

A compound microscope has an objective and eye-piece s thin lenses of focal lengths 1 cm and 5 cm respectively. The distance between the objective and the eye-piece is 20 cm. The distance at which the object must be placed in front of the objective if the final image is located at 25 cm from the eye-piece, is numerically a)

b)

95 5 cm cm www.aieeepage.com c) 89 6

a) 100 32.

25 cm 6

R

b) 200 / 2

c)

200

d) 280

A moving coil galvonometer of resistance 50 ohm gives a full scale deflection, when a current of 0.5 mA is passed through it. To correct it into a voltmeter of range 10 volts, the resistance required to be placed in series is a) 2000 Ω c) 1995 Ω

33.

d)

A sinusoidal voltage of peak value 200 volts is connected to diode and resistor R in the circuit shown so that half-wave rectification occurs. If the forward resistance of the diode is negligible compared to R, the r.m.s voltage across R is approximately

Peak voltage = 200V

31.

95 cm 6

PAGE b) 20000 Ω d) 19950 Ω

If a bar magnet of magnetic moment 80 units be cut into two halves of equal lengths, the magnetic moment of each half will be a) 80 units b) 40 units c) 160 units

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34.

A convex lens forms a real image on a screen placed at a distance 60 cm from the object. When the lens is shifted towards the screen by 20cm., another image of the object is formed on the screen. The focal length of the lens is : a) 45 cm b) 40/3 cm c) 30 cm d) 12 cm

35.

Which bulb will fuse, when two bulbs rated as (25 W and 220 V) and (100 W and 220 V) are connected in series to 40 V ? a) 20 W b) 25 W c) 30 W d) 15 W

36.

If t a certain instant, the magnetic induction of the electromagnetic wave in vaccum is 6.7 × 10-12 T, then the magnitude of electric field intensity will be b) 3 × 10-3 N/C

a) 2 × 10-3 N/C 37.

c) 4 × 10-3 N/C

In which of the indicator diagrams AB, BC, and CA represents isothermal, adiabatic and isochoric changes respectively A

P

a)

C

P B

c)

PAGE P A

B

b)

V

V

www.aieeepage.com P A

A

d)

C

B

C

V

If the angular speed of rotation of an armature of alternating current generator is doubled, then the induced electromotive force will be a) twice b) four times c) no change

d) half

The variation of electric potential with distance from a fixed point is shown in figure. What is the value of electric field at x = 2m. y 6 v(volt)

39.

B

C

V

38.

d) 1 × 10-3 N/C

4

PAGE 2

0

a) Zero

1

b) 6/2

2

c)

3

6/1

4

X(m)

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d) 6/3

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40.

A vechicle to carry astronatuts on the surface of the moon has spring suspension and has a natural up and down frequency of 0.40 Hz when fully loaded on the earth. What will be its natural frequency on the moon where it and everything in it will weight only one -sixth what it weighs on earth b) 0.40 Hz

a) 0.40/ 6 Hz 41.

c)

0.80 Hz

d) 0.40 6 Hz

In the circuit shown in figure potential difference between X and Y will be

40Ω X Y

120V

PAGE 20Ω

a) Zero 42.

b) 20 V

60 v

d) 120 V

A quantity X is defined by the equation X = 3 C B 2 , where C is capacitance in farad and B represents magnetic field in tesla. The dimansions of X are ___

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a) [ML−2 ] 43.

c)

b) [ML−2T -2 A]

c)

[ML−2T 2 A 2 ]

d) [L−1A -1 ]

Radius of a conductor increases uniformly from left end to right end as shown in fig. Material of the conductor is isotropic and its curved surface is thermally isolated from surrounding. Its ends are maintained at temperatures. T1 and T2 (T1 > T2 ) : If, in steady state, heat flow rate is equal to H, then which of the following graphs is correct ?

a)

O

H

H

H

x

b)

O

x

c)

O

H

x

d)

O

x

44.

The ratio of the pressure exerted by electromagnetic waves on reflecting surface and the absorbing surface will be a) 2 : 1 b) 1 : 2 c) 3 : 1 d) 1 : 3

45.

A man’s near point is 0.5m and far point is 3m. Power of spectacle lenses required for (i) reading purposes, (ii) seeing distant objects, respectively are a) -2 D and +3d b) +2D and -3D c) +2 D and -0.33 D

46.

PAGE

d) -2 D and + 0.33 D

Interference fringes are obtained due to interference of waves from two coherent sources of light with amplitudes a1 and a2 (a1 = 2a2). What is the ratio of the maximum and minimum intensities of light in the interference pattern : a) 2 b) 4 c) 9 d) ∝ (infinite)

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47.

The (W/Q) of a carnot engine is

1 , now the temp. of sink is reduced by 62°C, then this ratio becomes 6

twice, therefore the initial temp. of the sink and source and respectively : a) 33°C, 67°C b) 37°C, 99°C c) 67°C, 33°C 48.

If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved, then its fundamental frequency will become : a) n/4

49.

c)

2n

1 V2 ε0 2 d2

b)

1 V2 2ε 0 d 2

c)

3 λ 2 m

b)

c)

d)

Q2 2C

16 λ 81 m

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d)

81 λ 16 m

d) no relation can be

If the specific resistance of a potentiometer wire is 10-7 W m and current flow through it is 0.1 amp.Cross-sectional area of wire is 10-6 m2, then potential gradient will be : a) 10- 2 volt/meter b) 10- 4 volt/meter d) 10 - 8 volt/meter

The position x of a particle varies with time (t) = as x = at2 - bt3. The time t, when the acceleration is zero is equal to : a)

54.

1 CV 2 2

Two bulbs of (40 W, 200 V) and (100 W, 200 V). Then correct relation for their resistances : a) R40 < R100 b) R40 > R100

c) 10- 6 volt/meter 53.

d) n / 2

PAGE 2 λ 3 m

c) R40 = R100 52.

n

A black body has maximum wave length lm at 2000°K. Its corresponding wavelength at 3000°K will be a)

51.

b)

Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by : a)

50.

d) 9°K, 37°K

2a 3b

b)

a b

c)

a 3b

d) zero

Two particles A & B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown. The velocity of A to the left is 10 m/s. What is the velocity of B, when angle α = 60o ↑ B

PAGE ←A

0

a) 9.8 ms-1

c) 5.8 ms www.aieeepage.com

b) 10 ms-1

-1

d) 17.3 ms-1

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55.

The moment of inertia of a disc of mass M and radius R about the axis which is parallel to the diameter and passing through the tangential direction of the circumference : a) 3/2 MR2 b) 2/3 MR2 c) 5/4 MR2

56.

The K.E. of electron and photon is each of 10-32J, then relation between their De-Broglie wavelength : a) λ p < λ e

57.

d) 4/5 MR2

b) λ p = λ e

c)

λp > λe

d) λ p = 2λ e

The equations of two waves given are X = a cos (ωt + δ) and y = a cos (ωt + a ) , where δ = α + π / 2 , then resultant wave represents : a) A circle (c . w) b) A circle (a . c . w .) c) An ellipse (c . w) d) An ellipse (a . c . w .)

58.

PAGE

A spring elongated by length ‘l’ when a mass ‘M’ is suspended to it. Now a tiny mass ‘m’ is attached and then released, its time period of motion is : a) 2π

(M + m)l mg

b) 2π

ml mg

2π

l g

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d) 2π

Ml (m + M)g

59.

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms-1. To give an initial upward acceleration of 20 ms-2, the amount of gas ejected per second to supply the needed thrust will be : a) 127.5 kg - s-1 b) 137.5 kg - s-1 c) 185.5 kg - s-1 d) 187.5 kg - s-1

60.

From the top of building a ball is dropped while another is thrown horizontally at the same time. The ratio of velocities attained and the ratio of time taken by the bodies while hitting the ground are respectively a) equal to 1, greater than 1 b) less than 1, equal to 1 c) equal to 1, equal to 1

d) less than 1, greater than 1

PAGE

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CHEMISTRY 61.

In the anion HCOO− the two carbon-oxygen bonds are found to be equal length. What is the reason for it ? a) electronic orbitals of carbon atom are hybridised b) the C = O bond is weaker than the C-C bond c) The anion HCOO− has two reasonating structures d) the anion is obtained by removal of a proton from the acid molecule

62.

For preparing an alkane, a concentrated aqueous solution of sodium or potassium salt of a saturated acid is subjected to a) hydrolysis b) oxidation c) hydrogenation d) electrolysis

63.

Pure chloroform is prepared by a) distilling chloral hydrate with aqueous sodium hydroxide

PAGE

b) heating ethanol with bleaching powder

c) heating acetone with bleaching powder d) reducing carbon tetrachloride 64.

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Phenol on reaction with Br2 in non-polar aprotric solvent furnishes a) 2, 4, 6-Tribromophenol b) p-Bromophenol c) o-and p-Bromphenol d) m-Bromophenol

65.

The one which is least basic is a) NH3

66. 67. 68.

b) C6H5 NH2

c) (C6H5 )3 N

Terylene is a condensation polymer of ethylene glycol and a) Benzoic acid b) Phthalic acid c) Salicyclic acid DNA has deoxyribose a base and the third component which is a) Phosphoric acid b) Ribose c) Adenine Which of the following is an antidiabetic drug ? a) insulin

b) penicillin

c) chloroquine

d) aspirin

d) (C6H5 )2 NH d) Terephthalic acid d) Thymine

69.

A metallic oxide contains 60% of the metal. The equivalent weight of metal is a) 12 b) 24 c) 40 d) 20

70.

At - 40°C, a sample of gas has a volume of 233 ml on heating the volume expands to 313 ml. Assuming constant pressure, what is new timperature ? a) 40°C b) 80°C c) 20°C d) none of these

71.

A half filled or completely filled set of p of d orbitals is symmetrical. Which of the following species has symmetrical electronic charge distribution ? a) Chlorine atom (Cl) b) carbon atom (C)

PAGE

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c) Chloride ion Cl-

d) Iron atom (Fe)

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72.

100 cc of 1.5% solutionof urea is found to have an osmotric pressure of 6.0 atm and 100 cc of 3.42% solution of canesugar is found to have an osmotic pressure of 2.4 atm. If the two solutions are mixed, the osmotic pressure of the resulting solution will be a) 8.4 atm

73.

b) 4.2 atm

c)

16.8 atm

d) 2.1 atm

At constant T and P which one of the following statement is correct for the reaction ? S8 (s) + 8O 2 → 8SO 2 (g)

a) ∆H < ∆E b) ∆H = ∆E c) ∆H > ∆E d) ∆H is independent of the physical state of the reactants. 74.

To Ag 2 CrO 4 solution over its own precipitate, CrO 4 2− ions are added. This results in

PAGE

a) increase in Ag + concentration

b) decrease in Ag + concentration c) increase in solubility product

d) shifting of Ag + ions from the precipitate into the solution. 75.

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KM n O 4 reacts with oxalic acid according to the equation : 2MnO-4 + 5C2O4− + 16H+ → 2Mn + + + 10CO2 + 8H 2O

Here 20 mL of 0.1 M KMno4 is equivalent to :

76.

a) 20 mL of 0.5 M H2C4O4

b) 50 mL of 0.5 M H2C2O4

c) 50 mL of 0.1 M H2C2O4

d) 20 mL of 0.1 M H2C2O4

For the reaction A + 2B → 2C + D the concentration of A is kept constant and that of B is tripled, the rate of reaction will become a) three times b) six times c) eight times

d) nine times

77.

The coagulation of 10 cm3 of gold sol. is completely prevented by addition of 0.025 g of startch to it. The GOLD NUMBER of starch is a) 0.025 b) 0.25 c) 2.5 d) 25

78.

The position of some metals in electrochemical series in decreasing order of electroposition character isMg>Al>Zn>Cu>Ag. What will happen if a copper spoon is used to stid a solution of aluminium nitrate. a) The spoon will get coated with aluminium

PAGE

b) An alloy of Cu and Al is formed c) The solution becomes blue d) There is no reaction

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79.

80.

In the reaction 2Ag + 2H 2SO 4 → Ag 2SO 4 + 2H 2 O + SO 2 , sulphuric acid acts as a) an oxidizing agent

b) a reducing agent

c) a catalyst

d) an acid as well as an oxidant

Under what conditions of temperature and pressure, the formation of atomic hydrogen from molecular hydrogen will be favoured most ? a) High temperature and high pressure b) Low temperature and low pressure c) High temperature and low pressure

81.

d) Low temperature and high pressure

Nitrogen form N2, but phosphorus is converted in P2, reason is : a) triple bond present between phosphorous atom b) pp - pp bond is weak c) pp - pp bond is strong

PAGE

d) multiple bond form easily 82.

When a substance A reacts with water it produces a combustible gas B and a solution of a substance C in water. When another substance D reacts with this solution of C, it also produces the same gas B even on smokeless flame of Bunsen burner. A, B, C and D respectively are a) Na, H 2 , NaOH and Zn

b) K, H 2 , KOH and Al

d) CaC , C H , Ca(OH) and Fe www.aieeepage.com Copper is extracted from copper pyrites ore by heating in a blast furnace. The method is based on the c) Ca, H 2 , Ca(OH) 2 and Sn

83.

2

2

2

2

principle that a) Copper has more affinity for oxygen than sulphur at high temperature b) Iron has less affinity for oxygen than sulphur at high temperature c) Sulphur has less affinity for oxygen at high temperature d) Copper has lee affinity for oxygen than sulphur at high temperature 84.

85.

A gas ‘X’ is passed through water to form a saturated solution. The aqueous solution on treatment with silver nitrate gives a white precipitate. The saturated aqueous solution also dissolves magnesium ribbon with evolution of a colourlesss gas ‘Y’ identify ‘X’ and ‘Y’. a) X = CO 2 , Y = Cl 2

b) X = Cl 2 , Y = CO 2

c) X = Cl 2 , Y = H 2

d) X = H 2 , Y = Cl 2

In the complexes [Fe(H2 O) 6 ]3+ , [Fe(CN)6 ]3- , [Fe(C2 O 4 ) 3 ]3- and [FeCl6 ]3- , more stability is shown by a) [Fe(H2 O)6 ]3+

86.

c)

[Fe(C2 O 4 ) 6 ]3-

PAGE

d) [FeCl6 ]3-

Which of the following will give maximum number of isomers : a) [CO(NH3)4 Cl2] b) [Ni (en) (NH3)4]2+ c) [Ni(C2O4)(en)2]2 -

87.

b) [Fe(CN)6 ]3-

d) [Cr (SCN)2(NH3)4]+

A certain nuclide has a half life of 30 minutes if the sample containing 6 × 1010 atoms is allowed to decay for 90 minutes below. How many atoms will remain ? a) 2 × 10 atoms 10

c) 7.5 ×10 atoms www.aieeepage.com

b) 4.5 × 10 9 atoms

9

d) 1.5 × 109 atoms

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13

88.

89.

An organic compound containing carbon, hydrogen and oxygen contains 52.2% carbon and 13.04% hydrogen. Vapour density of the compound is 23. Its molecular formula will be a) C 2 H 6 O

b) C3 H 8 O

c) C 4 H 8 O

d) C5 H10 O

Which of the following statement is / are correct for D(+) - glyceraldehyde ? a) The symbol D indicates that the compound is dextrorotatory b) The sign (+) indicates that the compounds is dextrorotatory c) The symbol D indicates that hydrogen atom lies left to the chiral centre in the Fischer projection formula d) The symbol D indicates that hydrogen atom lies right to the chiral centre in the Fischer projection formula

90.

PAGE

The method that would provide the highest yield of pure ethylbenzene involves the reaction of benzene with a) ethanol and sulphiric acid b) ethyl chloride in the presence of aluminium chloride

c) acetyl chloride in the presence of aluminium chloride followed by reduction with ZnHg/HCl

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d) ethanoyl chloride in presence of aluminium chloride 91.

Identify the set of reagent/reaction conditions ‘X’ and ‘Y’ in the following set of transformations : x y → → CH 3 − CH 2 − CH 2 Br  Product  CH 3 − CH − CH 3

Br

a) X = dilute aqueous NaOH, 20°C; Y = HBr/acetic acid, 20°C b) X = concentrated alcoholic NaOH, 80°C; Y = HBr/acetic acid, 20°C c) X = dilute aqueous NaOH, 20°C; Y = Br2 /CHCl 3 , 0°C d) X = concentrated alcoholic NaOH, 80°C; Y = Br2 /CHCl 3 , 0°C 92.

Consider the following reactions 1. Knoevenagel condensation 3. Benzoin condensation

2.Cannizzaro reaction 4. Perikin reaction

The reactions which can be used for the preparation of α, β - unsaturated acids are a) 1 and 4 93.

b) 2 and 3

c)

1, 2 and 3

d) 2, 3, and 4

The oxidation of m-dinitrobenzene with alkaline potassium ferricyanide gives

OH

a)

PAGE NO 2

NO 2

NO 2

b)

NO 2

OH

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NO 2

c)

d) There is no reaction

OH

NO 2

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14

94. 95.

Terylene is a condensation polymer of ethylene glycol and a) Benzoic acid b) Phthalic acid c) Salicyclic

d) Terephthalic acid

Most favourable conditions for ionic bonding are a) low charge on ions, large cation, large anion b) low charge on ions, large cation, small anion c) high charge on ions, large cation, small anion d) high charge on ions, small cation, large anion.

96. 97.

Which of the following is basic dye a) Alizarine b) Aniline yellow

c)

Orange - I

d) Maritus yellow

The ideal gas obeying kinetic theory of gases can be liquefied if : a) it cannot be liquefied at any temperature and pressure b) its pressure is greater than PC at temperature less than TC c) its temperature is greater than critical temperature TC

PAGE

d) its pressure is greater than critical pressure PC 98.

The vapour pressure of CCl4 is 143 mm at 25°C. What will be the vapour pressure of 100 ml CCl4 solution dissolving 0.5 gm of a non-volatile substance (molecular weight = 65) a) 141.57 mm b) 94.39 mm c) 199.34 mm d) 419.39 mm

99.

The compound which is most acidic among the following is a) p-Chlorophenol b) p-Nitrophenol c) p-Aminophenol

100.

d) p-Cresol www.aieeepage.com Which is the strongest oxidising agent from the following. The standard reduction potential at 25°C

are given (in volts): Li+/Li = -3.05V, Ba2+/Ba = - 2.73 V, Na+/Na = - 2.71 V, Mg2+/Mg = -2.37 V a) Na+ b) Li c) Ba2+

d) Mg2+

101. 0.246g of an organic compound contains oxygen, carbon, hydrogen gave 22.4 cm3 or nitrogen at STP. What is the % of oxygen in the compound. Given % of carbon - 58.53%, hydrogen - 4.06% a) 52.06% b) 26.03% c) 13.2% d) 62.59% 102. The product formed by the reaction of H 2C − −CH 2 with RMgX is :

O a)

R R

b) R --O--CH2--CH3

CH - -CH 2 − −OH

PAGE

c) CH 3 − −CH − CH 3

d) R --CH2 --CH2--OH

OH

103. Which of the following given electrophilic substitution reaction readily :

www.aieeepage.com a)

b)

c)

d)

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15

104. A solution containing ammonium chloride and sodium nitrate on boiling produces : a) ammonia b) nitrous oxide c) nitrogen peroxide d) nitrogen 105. The number of geometrical isomers of the complex [Co (NO2)3 (NH3)3 is : a) 4 b) 3 c) 2 106.

d) 0

In graphite, electrons are : a) localized on each carbon atom

b) localized on every third carbon atom

c) spread out between the sheets

d) present in anti-bonding orbitals

107. The work of enzyme in living system is : a) to catalyse bio-chemical reaction

b) oxygen transfer

c) to provide immunity

d) to provide energy.

108. The most reactive compound for electrophilic nitration will be : a) benzene b) toluene c) benzoic acid

PAGE

d) nitro benzene

109. 8 gms of a radioactive substance is reduced to 0.5 g after 1 hour. The t1/2 of the radioactive substance is a) 15 min b) 30 min c) 45 min d) 10 min 110. An alloy of copper, silver and gold is found to have copper constituting the ccp lattice. If silver atoms occupy the edge centres and gold is present at body centre the alloy has a formula. a) Cu 4 Ag 2 Au

www.aieeepage.com c) Cu Ag Au

b) Cu 4 Ag 4 Au

4

3

d) CuAgAu

111. Thermal stability of alkaline earth metal carbonates decreases in the order

112.

a) BaCO 3 > SrCO 3 > CaCO 3 > MgCO 3

b) BaCO 3 > SrCO 3 > MgCO 3 > CaCO 3

c) CaCO 3 > SrCO 3 > MgCO 3 > BaCO3

d) MgCO 3 > CaCO 3 > SrCO 3 > BaCO3

N 2(g) + 3H 2(g)

2NH3(g) At 2270C, heat enthalpy for the above reaction is -22.40 kcal. If gas

constant is 1.98 x 10-3 kcal k-1 mol-1, find enthalpy at constant volume a) 21.40 b) -20.42 c) -21.40

d) 20.42

113. When a substance A reacts with water it produces a combustible gas B and a soluton of substance C in water. When another substance D reacts with thesolution C, it also produces the same gas B on warning but D can produces b on reaction with dilute H 2SO 4 at room temperature. A impart a deep golden yellow colour to a smokeless flame of busen burner. A,B,CD and arew respectively. a) K, H 2 KOH, Al

b) Na, H 2 , NaOH, Zn

c) CaC 2 , CaH 2 , Ca(OH) 2 Fe

d) Ca, H 2 , Ca(OH) 2 , Sn

114. Given the following data (i) H 2 (g) → 2H(g) (ii) Br2 (g) → 2Br (g)

PAGE ∆H° = 436.0 KJ

∆H° = 192.0KJ

(iii) H 2 (g) + Br2 (g) → 2HBr(g)

∆H° = 104.0 KJ

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∆H 0 for the reaction H(g) + Br(g) → HBr(g) is

a) − 376 KJ mol−1

b) + 366 KJ mol−1

c)

− 366 KJ mol−1

d) − 327 KJ mol−1

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115. Calculate the Volume of hydrogen at NTP obtained by passing a current of0.4 ampere through acidified water for 30 minutes. a) 0.0836 litre b) 0.1672 litre c) 0.0432 litre

d) 0.836 litre

116. What will be the k b value of a weak base (BOH) of which a 0.1 M solution has a pH of 8, when it is half neutralized with 0.1 M HNO 3 a) 10-8

b) 10-4

c)

d) 10-7

10-6

117. the coeefficient of expansion for anidealgas isgiven by α =

1  dV    Using theideal gas equation V  dT 

pV= nRT, we get a) α =

1 V

PAGE

1  dV  b) α = V  dp  T 

c)

α=

1 p

d) α =

1 T

118. Bulbs A and b contain an aquous solution and pure water respectively. The bulbs are connected, and dryair is passed through them forsome time. The air passes first through bulbA and then throughbulb B. If the vapour pressure of water is P1 and that the solution is P1 , theweight losses of the bulbs containing the solution and the solvent are directly proportional to a) P1 and p10

www.aieeepage.com b) P and P - p 1

1

0 1

d) p10 + P and p10 − P

c) P1 and p10 - P1

119. A galvanic cell is set up according to the following specifications.

Zn(s)|Zn 2+ (aq),1M)|KCl(sat'd)|Cu 2+ (aq1 M) |Cu(s) Choose the correct option. a) Druing the overall redox reaction, electrons flow externally from the anode (Zn electrode) through the wire and voltmeter to the cathode (Cu electrode) b) Inthe solution, the cations (Zn 2+ .Cu 2+ and k + ) move towards the anode, while the anions (SO 24− , Cl − ) move towards the cathode.

c) k + and Cl− do not move the either electrode d) The conductance of the saturated KCl solution is very low. So a KCl salt bridge is used. 120. In [Fe(CN)6 ]3− the d electrons occupy the

PAGE

a) dxy dyz dzx anddx2 orbitals b) d xy d yz and d zx orbitals c) d x 2 -y2 and d x 2 orbitals d)

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d xy d yz d zx d 2 2 and d 2 orbitals x -y x

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17

MATHEMATICS 121. If (1 + i) n = (1 − i) n , then the least value of n is a) 3

b) 4

c)

2

d) 1

c)

e10

d) e x

122. The inverse of the function f ( x) = log10 x is b) x10

a) 10x

123. If m, n, are any two odd positive integer with n < m, then the largest positive integers whcih divides all the numbers of the type m 2 − n 2 is a) 4

b) 6

c)

8

d) 9

124. The mean of a set of observation is x . If each observation is divided by a, a ≠ 0 and then is increased by 10, then mean of the new set is a)

x a

b)

PAGE x + 10 a

c)

x + 10a a

d) ax + b

125. The ecentricity of the hyperbola x 2 − y 2 = 4, is a)

b)

2

GG G

www.aieeepage.com G G G G G c)

3

2 2

d) 2 3

126. Let the vectors a, b, c and d be such that (a × b) × (c × d) = 0 . Let P1 and P2 be planes determined by the G G

G G

pairs of vectors a, b and c, d respectively. Then the angle between P1 and P2 is : a) 0

b)

π 4

c)

π 3

d)

π 2

127. If each element of a third order determinant of value ∆ is multiplied by 5, then the value of the new determinant is : b) 5 ∆

a) ∆

c)

25 ∆

d) 125 ∆

128. A survey of 200 Indians shows that 140 like apples whereas 120 like cheese. Let n be the number of persons who like both apple and cheese. Then the value of n is a) 60 b) 120 c) 20 d) none 129. If the rate of change in the circumference of a circle is 0.3 cm/sec, then the rate of change in the area of the circle when the radius is 5 cm is: a) 1.5 sq. cm/sec b) 0.5 sq. cm/sec c) 0.045 sq.cm/sec d) 3 sq.cm/sec 130. Diagonals of a parallelogram lie along the vectors 3 ˆi + ˆj − 2 kˆ and ˆi + 3 ˆj + 4 kˆ . The area of the parallelogram in (square units) is a) 5 13

PAGE

b) 6 10

c)

3 10

d) 8

131. The number of combinations of atleast one fruit out of 3 mangoes, 4 oranges and 5 bananas is a) 59 b) 60 c) 119 d) none of these

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132. In how many ways 4 different coloured balls can be placed in 4 boxes (one ball in each box) of same colours as of the balls, so that no ball is placed in a box of same colour, is a) 16 b) 9 c) 10 d) none of these for IIT - JEE & AIEEE at the National PAGE- A Premier Institution www.iitjeepage.com www.bitsatpage.com

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18

133. Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of sides. If Tn +1 − Tn = 21, then n equals a) 5

b) 7

c)

6

d) 4

134. In a ∆ABC, a, c, A are given and b1 , b 2 are two values of the third side b such that b 2 = 2b1 . Then sin A is equal to a)

9a 2 − c 2 8a

9a 2 − c 2

b)

2

8c 1 

9a 2 + c 2

c)

2

d) None of these

8a 2

4

−1 −1 135. If x = sin( 2 tan 2), y = sin  2 tan 3 , then

a) x > y and y 2 = 1 − x



b) x < y

c) x > y and y 2 = x

PAGE d) y 2 = 1 + x

136. If the line hx + ky = 1 touches x 2 + y 2 = a 2 , then the locus of the point (h, k) is a circle of radius a) a

b)

1 a

c)

d)

a

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1 a

137. The equation of the sphere concentric with the sphere x 2 + y 2 + z 2 − 2 x − 4 y − 6 z − 11 = 0 and double the radius is a) x 2 + y 2 + z 2 − 2 x − 4 y − 6 z − 22 = 0

b) x 2 + y 2 + z 2 − 2 x − 4 y − 6 z − 100 = 0

c) x 2 + y 2 + z 2 − 2 x − 4 y − 6 z + 11 = 0

d) x 2 + y 2 + z 2 − 2 x − 4 y − 6 z − 86 = 0

138. The expression

cos 6 x + 6 cos 4 x + 15 cos 2 x + 10 is equal to cos 5 x + 5 cos 3x + 10 cos x

a) cos 2x 139.

b) 2cos x

d) 1+ cos x

c)

cos 2 x

c)

greater than

  3 1   tan −1 cos 2 tan −1  + sin  2 cot −1   is 4 2    

a) not real

b) equal to

π 4

π 4

d) less than

π 4

140. The general value of θ that satisfies the equation 2 cot 2 θ + 2 3 cot θ + 4cosecθ + 8 = 0 is : (n ∈ z) a) nπ −

π 6

PAGE

b) nπ +

π 6

c)

2 nπ −

π 6

d) 2nπ +

π 6

141. If A, B, C are the angles of a triangle such that angle A is obtuse, then tan B tan C will be less than : a)

1 3

b)

3 2

c)

1

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d) none of these

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2 142. The solution to the differential equation ( x + y )

 y+c

a) x + y = a tan a  b) y = a tan −1 ( x + y) + c  

dy = a 2 is dx y  x y1 −  = tan + c a  4

c)

d) none of these

143. The general solution of the differential equation x 2 dy + y( x + y)dx = 0 is a) x 2 = cy( y + 2 x) 144

b) xy = c( y + 2 x)

x 2 y = c( y + 2 x)

c)

If φ( x) is a differentiable real valued function satisfying

d) none of these

d 1 φ( x) + 2φ( x) ≤ 1, then the function φ( x) - is dx 2

a) an increasing function

b) a non-increasing function

c) neither increasing nor decreasing function

d) a constant function

PAGE

2m Lim 145. If x is real number in [0, 1], then the value of the function f(x) = mLim (n!πx )} is given → ∞ n →∞ {1 + cos

by a) 2 or 1 according as x is rational or irrational

b) 2 or 1 according as x is irrational or rational

c) 1 for all x

d) 2 for all x

36 www.aieeepage.com as one directrix is 5

146. The equation of the ellipse with focus at (±5, 0) and x = a)

x2 y2 + =1 36 25

b)

x2 y2 + =1 36 11

c)

x2 y2 + =1 25 11

d) None of these

147. The equation of the hyperbola with vertices at (±5, 0) and foci at (±7, 0) is a)

x2 y2 − =1 25 24

b)

x2 y2 − =1 7 5

c)

x2 y2 − =1 49 25

d) None of these

148. The cirlce x 2 + y 2 − 6 x − 10 y + c = 0 neither touches nor intersects any of the coordinate axes and the point (1, 4) lies inside the circle. Then the range of possible values of c is given by a) 25 < c < 29 b) c < 25 c) c > 29 d) None of these 149. The condition that one of the straight lines given by the equation ax 2 + 2hxy + by 2 = 0 , may coincide with one of those given by the equation a' x 2 + 2h' xy + b' y 2 = 0 is a) (ab'−a' b) 2 = 4(ha'−h' a)(bh'− b' h)

b) (ab'−a' b) 2 = (ha'− h' a)(bh'− b' h)

c) (ha'− h' a) 2 = 4(ab'−a' b)(bh'− b' h)

d) (bh'−b' h) 2 = 4(ab'−a' b)(ha'−h' a)

PAGE

150. A and B are fixed points. The vertex C of ∆ABC moves such that cot A + cot B = constant. The Locus of C is a straight line a) perpendicular to AB b) parallel to AB d) none of these www.aieeepage.com

c) inclined at an angle A - B to AB

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20

151. A group of students decided to buy a tape-recorder from 170 to 195 rupees. But at the last moment, two students backed out of the decision so that the remaining students had to pay 1 rupee more than they had planned. If the students paid equal shares, the price of the tape-recorder was a) Rs 175 b) Rs 180 c) Rs 185 d) Rs 190 152. Three are 25 trees at equal distances of 5 meters in a line with a well, the distance of the well from the nearest tree being 100 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. The total distance the gardener will cover in order to water all the trees is a) 3550 m b) 3434 m c) 3370 m d) 3200 m 153. From the top of a tower of height 100 m, a ball is projected with a velocity of 10 m/sec. It takes 5 seconds to reach the ground. If g = 10 m/sec² then the angle of projection is : a) 30° b) 45° c) 60° d) 90°

PAGE

154. In a set of 10 coins one coin is counterfeit (i.e. heads on both sides ). One coin is chosen at random from the 10 coins and tossed 5 times. All the five times the result was head. The probability that it is the counterfeit coin is a)

32 41

b)

9 41

c)

5 41

d)

9 32

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155. If A, B, C are the vertices of ∆ABC having position vectors as the points (2, 1, 3), (4, 1, 3) and (0, 2, 1) respectively, then the magnitude of ∠BAC is a)

2  

π 6

−1 b) cos  3 

c)

1 cos −1   3

d)

π 2

156. ABC is a triangle and P is any point on BC such that PQ is the resultant of the vectors AP, PB and PC and then . a) the position of Q depends on position of P b) Q is a fixed point c) Q lies on AB or Ac

d) None of these dy

157. If xy + x 2 y 2 = c; then the value of will be dx a)

x y

−y x

b)

c)

y x

d)

−x y

(1 − iz )

158. If z = x + iy and w = ( z − i ) , then |w|=1, shows that in complex plane

PAGE

a) z is situated on imaginary axis

b) z is situated on real axis

c) z is situated on unit circle

d) None of these

x

1

159. If f(x) = x − 1 = y , then f(y) =

c) 1-x www.aieeepage.com

a) x

b) x - 1

d) 1+x

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21

160.

xe x

∫ (1 + x)

2

dx =

ex +c (1 + x)

a)

b)

xe x +c (1 + x)

ex

c)

(1 + x)

3

+c

ex

d)

(1 + x) 2

+c

161. The area bounded by the curves y 2 − x = 0 and y − x 2 = 0 is a)

7 3

b)

1 3

c)

5 3

d) 1

c)

5

d) 0

162. Maximum value of x(1 − x) 2 when 0 ≤ x ≤ 2 is a) 2

b)

PAGE

π

163.

∫ log sin

2

xdx =

0

a)

1 2π loge    2

4 27

b) π log e 2 + c

π 1 log e   + c 2 2

c)

d) None of these

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164. If α, β are the roots of the equation Ax 2 + mx + n = 0 , then the equation whose roots are α 3β and αβ 3 is a) A 4 x 2 − nA(m 2 − 2nA) x + n 4 = 0

b) A 4 x 2 + nA(m 2 − 2nA) x + n 4 = 0

c) A 4 x 2 + nA(m 2 − 2nA) x − n 4 = 0

d) A 4 x 2 − nA(m 2 + 2nA) x + n 4 = 0

165. Let P (x) and Q(x) be two polynomials. Suppose that f ( x) = P( x 3 ) + xQ( x 3 ) is divisible by x 2 + x + 1, then

a) P(x) is divisible by (x-1) but Q(x) is not divisible by x - 1 b) Q(x) is divisible by (x-1) but P(x) is not divisible by x - 1 c) Both P(x) and Q(x) are divisible by x - 1 d) f(x) is divisible by x + 1 166. Let F(x) = x 3 + ax 2 + bx + 5 sin 2 x be an increasing function in the set of real number R. Then a and b satisfy the condition. a) a 2 + 3b − 15 > 0

b)

a 2 − 3b − 15 < 0

c)

a 2 − 3b + 15 > 0

d) a > 0 and b > 0

167. If z be a complex number such that | z + 5 | ≤ 7 , then the minimum and maximum values of | z + 2 |are a) 2 , 10

PAGE

b) 4 , 15

c)

168. The relation “congruence modulo m” is a) reflexive only c) symmetric only

0,∞

d) 0 , 10

b) transitive only

d) an equivalence relation



C





5

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2 169. The co-efficient of x in the expansion of  x + x  is

a) 20 C

b) 10 C

c)

10 C3

d) 20 C3

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22

170. Let Sp and Sq be the coefficent of x p and x q respectively in (1 + x) p+ q , then q

b) Sp = p Sq

a) Sp ≠ Sq

c)

Sp =

c)

3

p Sq q

d) Sp = Sq

α +β 2 = 171. If 3 sin α = 5 sin β, then α −β tan 2 tan

a) 1 172. If

b) 2

2r x n(n + 1) Sr = 6r 2 − 1 y n 2 (2n + 3) 4r 3 − 2nr z n 3 (n + 1)

d) 4

n

, then the value of

∑S

r

r =1

is independent of

a) x only b) y only c) x, y, z, n d) n only 173. If (a, b), (c, d), (e, f) are the vertices of a triangle such that a, c, e are in G.P with common ratio r and b, d, f are in G.P with common ratio s then the area of the triangle is a)

ab (r +1) (s + 2) (s + r) 2

c)

ab (r −1) (s + 1) (s - r) 2 → →

PAGE

ab (r −1) (s -1) (s - r) 2

b)

d) (r + 1) (s + 1) (s - r)

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→

→

→

→

→

→

→

→

174. If A, B and C are the non-coplanar vectors, then (A + B+ C) ⋅ {(A + B) × (A + C) equals : →

a) 0

→

→

b) [ A, B, C]

c)

→

→

→

2[ A, B, C]

→

→

→

d) − [ A, B, C]

175. A die is thrown n times. For the probability of a six appearing at least once to be more than c) n < 4 a) n = 2 b) n ≥ 4 176. The resultant of two unlike forces P and P at a distance of p is a : a) force P

b) couple of moment P

c)

a force 2P

1 is : 2

d) n = 3 d) a force

P 2

177. The acceleration of a particle at a distance x from O, moving in a straight line is inversely proportional to the square of the distance from O. If the particle starts from rest at a distance 2 p from O, the velocity of the particle at a distance 4 p from O is : a)

µ

µ

b)

2p

e cos x sin x, for | x | ≤ 2 . Then otherwise 2,

178. If f(x) = f (x) =  a) 0

µ 2p

c)

p

∫

3

2µ p

f (x) dx =

PAGE −2

d)

b) 1

c)

2

d) 3

179. Average rainfall of city from Monday to Saturday is 0.3 inch. Due to heavy rainfall on Sunday, the average rain fall increased to 0.5 inches. What was the rainfall on Sunday ? a) 1.7 inches b) 1.8 inches c) 0.8 inches d) 3.5 inches

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180. An equilateral triangle is inscribed in the parabola y 2 = 4ax whose vertex is at at the vertex of the parabola. The length of its side is a) 2a 3

b) 4a 3

c)

6a 3

d) 8a 3

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