AIEEE Part Test-3

8/13/2019 AIEEE Part Test-3

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Endeavour classes 4th

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INSTRUQuestion Paper forma

1. The test is of 3 hours duration.

2. The Test Booklet consists of 90 q

3.

There are THREE parts in thequestion.

Part A-Physics (144 marks)- Q

correct response.

Part B- Chemistry (144 marks)-

correct response.

Part C- Mathematics (144 mar

correct response.

4. Candidates will awarded marks a

be deducted for indicating incor

indicated for an item in the answe

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Booklet/Answer Sheet.

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consisting of MATHS of 30 ques

For each incorrect response, one

deduction from the total score, ho

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done on the space provided for thi

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[email protected] Help line – 09708037020 /21 /

E

TION

R A N C H I

t :

estions. The maximum marks are 432.

uestion paper, consisting of , Physics Chemistry and Mathema

uestion No. 1 to 24 consist 4 marks each and Que. No 25 to 30

Que. No 31 to 54 and consist 4 marks each and Que. No 55 to 6

s)-Que. No 61 to 84 consist 4 marks each and Que. No 85 to 90

stated above in instructions No.3 for correct response of each que

ect response of each question. No deduction from the total score

r sheet.

nly for writing particulars/ marking responses on Side-1 and Side-2

ROHIBITED.

any textual material-printed or written, bits of papers, pager, mobithe examination hall/room.

pace provided for this purpose in the Test Booklet only.

arks on the Answer Sheet.

tion on the Back Cover of this Test Booklet.

quired particulars on the Test Booklet and Answer Sheet (Side-1)

ROHIBITED.

on Side-2 of the Answer Sheet, use Blue/Black Ball Point

te their Registration Numbers anywhere else (except in the

uestion paper, Part A consisting of PHYSICS, Part B consistin

tion each.

-third of the total marks allotted to the question would be ded

wever, will be made if no response is indicated for an item in the A

er Sheet with care, - as under no circumstances.

do any rough work or writing work on the Answer Sheet. All cal

s purpose in the Test Booklet itself, marked ‘Space for Rough Wor

didates must hand over the Answer Sheet to the Invigilator on du

e away this Test Booklet with them.

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ission of the Superintendent or Invigilator, should leave his/her se

he Examination Hall without handing over their Answer Sheet to

where a candidate has not signed the Attendance Sheet a second t

d dealt with as an unfair means case. The candidates are also r

provided in the Attendance Sheet.

tor and any Electronic item like mobile phone etc. is prohibited.

ll Rules and Regulations of the Institute with regard to their condu

t with as per Rules and Regulations of the Institution

y any textual material, printed or written, bits of papers, pager, mo

it Card inside the examination hall/room.

1- 2563739 / 40

1

2

S/PT-03, AIEEE -2010

tics. In each part, there are 30

consist 8 marks each for each



stion.1/4(one fourth) marks will

will be made if no response is

of the Answer Sheet.

le phone, any electronic device,

with Blue/Black Ball Point Pen.

en only. Use of PENCIL is

specified space) on the Test

of CHEMISTRY and Part C

cted from the total score. No

swer Sheet.

ulations/writing work are to be

k’.

ty in the Room/Hall. However,

at.

the Invigilator on duty and sign

ime will be deemed not to have

quired to put their left hand

ct in the Examination Hall. All

bile phone, electronic device or




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1. On a glass plate a light w

angle of 60o. If the reflect

waves are mutually

refractive index of materia

(A)2

3 (B) 3

(C)2

3 (D)

3

1

2. if iµ j represents refractive

ray goes from medium i t

product 2µ1 × 3µ2 × 4µ3 is e

(A) 3µ1 (B) 3µ2

(C)41µ

1 (D) 4µ2

3. if ε0 and µ0 are respe

permittivity and the magn

free space, ε and µ

quantities in a medium, th

the medium is

(A)

00εµ

µε (B)

0εµ

µε

(C)µε

εµ 00 (D)εε

µµ

4. A double convex lens h

equal radii R and refractThen we have,

(A) f = R/2 (B) f = R

(C) f = –R (D) f = 2

5. A symmetric double conv

equal parts by a plane

principal axis. If the powewas 4 D, the power of a cu

(A) 2 D (B) 3 D

(C) 4 D (D) 5 D

6. A ray of light incident on

parallel to the second is

second mirror parallel t

angle between two mirrors(A) 30

o (B) 60

o

(C) 75o (D) 90

o

7. In a concave mirror, an

distance x1, from focus, ana distance x2 form focus.

mirror is

(A)21 x x (B)

2

1 x −

(C)2

+21 x x

(D)

2

1

x

x

PHYSICS



E

ave is incident at an

ed and the refracted

perpendicular, the

is

index when a light

medium j, then the

qual to

tively the electric

etic permeability of

the corresponding

refractive index of

0

0

as two surfaces of

ive index µ = 1.5.

R.

x lens is cut in two

erpendicular to the

r of the original lenst lens will be

the first mirror and

reflected from the

first mirror. The

is

bject is placed at a

d image is formed athen focal length of

2 x

8. A point object is pl

sphere of radius 6 c

The distance of th

surface of the spher

(A) 2 cm (

(C) 6 cm (

9. Two waves originat

having zero phase

wavelength λ will

interference at a poi

(A) 5 λ (

(C)2

4λ (

10. The ratio of

intensities in the i

sources is 4:1. The

(A) 1:3 ((C) 1:9 (

11. In YDSE, two slits

the screen is place

fringe separation

500 nm is used ?

(A) 0.002 mm (

(C) 0.2 mm (

12. Which one of the fo

(A) Both, light and

vacuum

(B) Both, light an

transverse

(C) The sound wa

while the light

(D) both, light an

longitudinal

13. The wave front of a

shape is approximat

(A) spherical (

(C) elliptical (

14. The focal lengths

lenses of a telesco

and 5 cm. The maxi

the telescope will b

(A) –40 (

(C) –60 (

15. Light takes 4.5 × 1

transparent mediu

covered by it :

(A) 11.5 cm (

(C) 15. 5 cm (

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2

2


ced at the centre of a glass

m and refractive index 1.5.

e virtual image from the

is

) 4 cm

) 12 cm

ing from sources S1 and S2

difference and common

show complete destructive

nt P if (S1 P – S2 P) =

)4

3λ

)2

11λ

aximum and minimum

terference pattern of two

atio of their amplitudes is

) 3:1) 1:16

are made 5 mm apart and

d 2 m away. What is the

hen light of wavelength

) 0.02 mm

) 2 mm

llowing statements is true?

sound waves can travel in

sound waves in air are

es in air are longitudinal

waves are transverse

sound waves in air are

distant source of unknown

ely

) cylindrical

) plane

of the objective and eye

e pre respectively 200 cm

mum magnifying power of

) –48

) –100

0–10

s to travel 10 cm in a

. The optical path length

) 13.5 cm

) 17.5 cm




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16. A particle is moving at

from a large distance towa

of radius R along the prispeed of image formed by

of the distance x of the par

will be

(A)( )2

2

2 R x

V R

− (B)

(2 x

X

(C)( )2

2

R x

V R

− (D)

( x

X

−

17. A far sighted person cann

closed to 50 cm. then the

to see the objects at 20 cm

(A) 3D (B) 2D

(C) 0.5D (D) 0.3D

18. The thickness of the plate

a change in optical path e

length λ of the light

normally (the refractive in

will be

(A)( )12 − µ

λ (B)

µ

λ

2

(C)( )12 + µ

λ (D)

µ

λ

19. A slab of glass of thicknes

index2

3 is placed with it

to the principle axis of th

the radius of mirror is 10

which an object must b

mirror so that the image

object is

(A) 9 cm

(C) 11cm

20. In young’s double sli

intensity at the bright friidentical slits are used on

covered. The new intensit

screen will be

(A)2

0 I

(C)22

0 I

21. A real image I is formed

L on its optic axis. An

rectangular glass slab o

refractive index µ betwee

the image displaced by



E

a constant speed ν

rds a concave mirror

nciple axis then themirror as a function

ticle from the mirror

)2

2

R

V

)2 R

V

t see objects placed

ower of lens needed

will be

which will produce

ual to half the wave

passing through it

ex of the plate is µ)

s 3cm and refractive

s face perpendicular

concave mirror. If

cm, the distance at

e placed from the

coincides with the

(B) 10 cm

(D) 12 cm

t experiment, the

ge is I0, when twoe of the slit is now

at any point on the

(B)20 I

(D)40 I

y a converging lens

introduction of a

f thickness d and

the image and lens

(A) d (µ–1) away fr

(B) d (µ–1) towards

(C)

− µ

11d awa

(D)

− µ

11d tow

22. The ratio of the

(600nm) to that

scattered by earth’s

(A) 4 : 9 (

(C) 1 :16

23. Statement 1: In op

the core is kept smaStatement 2: The s

ensures that the fi

angle more than th

total

internal reflection.

(A) If Statement I i

Statement II is

Statement I.

(B) If Statement I i

Statement II isfor Statement

(C) If Statement I is(D) If Statement I is

24. Statement 1: Thin

a thin layer of oil

colours where illum

Statement 2: It

interference of ligh

lower face of the thi


Statement II is

Statement I.


Statement II is

for Statement I.(C) If Statement

false.

(D) If Statement

true.

25. The speeds of light

2.2 × 108 m/s an

critical angle for limedium will be

(A) sin–1

11

12 (

(C) sin–1

24

21 (

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3

2


m L

L

from L

rds L

intensity of visible red

f blue (400 nm) light

atmosphere will be

) 1 : 5

(D) 16 :1

tical fibre, the diameter of

ll.maller diameter of the core

bre should have incident

critical angle required for

true, Statement II is true,

a correct explanation for


not a correct explanationI.

true, Statement II is false.false, Statement II is true.

ilm such as soap bubble or

on water show beautiful

inated by white light.

happens due to the

t reflected from upper and

n film.




not a correct explanation

I is true, Statement II is

I is false, Statement II is

in two media I and II are

2.4 × 108 m/s resp. The

ght refracting from I to II

) sin–1

12

11

) sin–1

21

24




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26. A light ray is incident nor

of a right – angle prism

shown in the fig, then thewhich the light ray is tot

surface AC will be

(A)3

2cos 1−

(B) cos

(C)3

1cos 1−

(D)−sin

27.

In the situation as showposition of image formed

be

(a) 100 cm

(c) 75 cm

28. A thin lens made of a

index µ2 has a medium o

on one side and a mediu

µ3 on the other side. The l

the two radii of cur

magnitude R. A beam

parallel to the principle ax

lens. Than the position of t

when the light incident

having refractive index µ1

(A)

312

3

2 µ µ µ

µ

−−

R

(C)

213

2

2 µ µ µ

µ

++

R

29.

Two plane mirror A andeach other as shown in th

is incident at an angle ofinside one end at A. th

coincides with the pla

maximum number of time

reflection before the emer

(A) 28 (B) 30

(C) 32 (D) 34

φ

µ=1

s

25 cmk

m320.2 m



E

ally on the face AB

ABC (µ = 1.5) as

value of angle φ forally reflected at the

2

11

3

21

n in the figure theafter refraction will

(b) 50 cm

(d) 25 cm

aterial of refractive

refractive index µ1

of refractive index

ens is biconvex and

ature have equal

of light travelling

is is incident on the

he image formed

from the medium

ill be

(B)

312

3

2 µ µ µ

µ

++

R

(D)

213

2

2 µ µ µ

µ

−−

R

we kept parallel tofigure. A light ray

30° at a point justplane of incident

e of figure. The

s the ray under goes

es out

30. A narrow slit S t

length λ is placed

plane mirror as sho

The light coming di

coming after the ref

placed at distance

distance from O do

(A)

d

D

4

λ

(C)d

Dλ

31. Addition of HBr to

type of mechanism(A) Electrophilic ad

(B) Electrophilic su

(C) Nucleophilic ad

(D) Free radical add

32. (CH3)3CMgCl on re

(A) (CH3)3CD (

(C) (CD3)3CD (

33. Cottrell precipitator

(A) precipitate mud

(B) precipitate carb

(C) purify the ordin

(D) precipitate salts

34. Rhombic sulphur is

at room temp

temperature, the foll

S(r) → S(m).

∆H=276.14 J and

temperature, both

equilibrium ?

(A) 412.15 K (

(C) 406 K (

35. Cow milk is an ex

stabilized by

(A) Fat (

(C) Casein (

CHEc

=1.5

0 cm

30°

d

S

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4

2


ransmitting light of wave

a distance d above a large

n in figure.

rectly from the slit and that

lection interfere at a screen

D from the slit. At what

s the first maximum occur

(B)

d

D

2

λ

(D)d

Dλ 2

propene proceeds by which

dition

stitution

dition

ition

action with D2O produces

) (CH3)3OD

) (CD3)3OD

is used to

from muddy water

n particles from smoke

ary drinking water

in qualitative analysis.

the stable allotropic form

erature. Above room

owing reaction occurs:

t 298K and 1atm, if

G = 75.31 J , then at what

the allotropes are in

) 298 K

) 273 K

ample of natural emulsion

) Water

) Mg+2

ions

ISTRY

P




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36. Which of the followin

responds to Beayer’s reagcarbon tetrachloride test ?

(A)

(B)

(C)

(D)

37. Which shape selective

convert alcohol to gasoline

(A) Trypsin (B) Calg

(C) ZSM-5 (D) Zeig

38. The enthalpy of hydrogen

is –119.5 kJ mol–1

. If r

benzene is –150.4kJ mohydrogenation would be(A) –358.5kJ mol –1

(C) –208.1kJ mol–1

39. A heat engine absorbs hea

temperature T1 and heat

temperature T2. Work don

J (q1 + q2). This is in accor

(A) first law of thermodyn

(B) second law of thermod

(C) Joule’s equivalent law

(D) none of the above

40. Select the properties whic

colloidal sols :

(i) Surface tension same as

(ii) Viscosity higher than t

(iii) irreversible nature

(iv) particles can b

ultramicroscope

(A) 1, 2, 3

(C) 2, 3, 4

41. Which of the following i

reaction equal to heat of fo

(A)

(B)

(C)

(D)

42. Identify the correct senzymes

(A) Enzymes are specific

that cannot be poisone

(B) Enzymes are norm

catalysts that are ve

action

(C) Enzymes are specific

that can normally fu

temperature (T ∼ 1000

(D) Enzymes are specific

that possess well-defi

CH3 CH = CH

(CH3)2C = C(CH3)2

C6H6 CH = CH2

CH3 CH = CH2

C(graphite) + O2(1 atm)

C(diamond) + O2(1 atm)C(graphite) + O2(1 atm)

C(diamond) + O2(1 atm)



E

alkenes do not

nt test or Bromine–

atalyst is used to

?

n

er-Natta catalyst

tion of cyclohexene

sonance energy of

l

–1

, its enthalpy of

(B) –508.9kJ mol–1

(D) –269.9kJ mol–1

q1 from a source at

2 from a source at

is found to be

ance with

mics

ynamics

h are for lyophobic

that of the medium

at of the medium

detected under

(B) 1, 3, 4

(D) 2, 4

ndicates the heat of

rmation ?

atement regarding

biological catalysts

d

ally heterogeneous

ry specific in their


nction at very high

K)


ed active sites.

43.

Hydrogen is not owith

(A) Cold water

(C) Dil HCl

44. The structure of H2

(A)

(C)

45. Which one of the

produce hard water

(A) Saturation of w

(B) Saturation of w

(C) Addition of Na2

(D) Saturation of w

46. Which of the follo

mode of hybridizati

right ?

(A)

(B)

(C)

(D)

47. Which of the follow

(A) CCl3CH(OH)2

(C) CH3C.Cl(OH)2

48. In the following co

The order of basicit

(A) IV > I > III > II

(C) II > I > III > IV

49. The two compound

are

(A) diastereomers

(C) epimers

H3

CO2 (1 atm)

CO2 (2 atm)CO2 (2 atm)

CO2 (1 atm)

HO O

H O O

H2C CHHC C

H2C C

H2C

(I)

N

H

(II)

N

O

or

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5

2


btained when Zn reached

(B) Dil H2 SO4

(D) 20% NaOH

2 is :

(B)

(D)

following processes will

?

ter with MgCO3

ter with CaSO4

SO4to water

ter with CaCO3

wing represents the given

on sp2 –sp

2–sp–sp from to

ing is most stable

(B) (CH3)2.C.(OH)2

(D) CH3CH(OH)2

pounds

is :

(B) III > I > IV > II

(D) I > III > II > IV

shown in the figure below

(B) enantiomers

(D) regiomers

H

O OH

HH

O OH

C CH

CH

C CH2

CH2

O

N

H

(III) (IV

N

H

O




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50. In the following structureare staggered conformatio

(A) 1 and 4(C) 1 and 2

51. Which pair does not show

(A) ortho and para hydrog

(B) protium and deuterium

(C) deuterium and tritium

(D) tritium and protium

52. Among CaH2, NH3, NaH

covalent hydrides ?

(A) NH3 and B2H6

(C) NaH and NH3

53. What is the volume of

required to produce 500NTP ?

(A) 125 cm3

(C) 450 cm3

54. In evaporation of water ∆

(A) +, +

(C) –, –

55. An organic compoun

hydrogenation gives co

Compound A on ozonolysi

2–Ketopropanal. What is

(A)

(B)

(C)

(D)

H

H

HH

H

H(1)

H

H

H

H

H

H H

H

(3)

H

H

CH2= C C ≡ CH

CH3

CH2= C CH = C

CH3

CH3 C = C = CH2

CH3

CH3 CH CH2

CH3



E

s, which two formss of ethane ?

(B) 2 and 3(D) 1 and 3

hydrogen isotopes?

n

nd B2H6, which are

(B) NaH and CaH2

(D) CaH2 and B2H6

“20 volume H2O2”

cm3 of oxygen at

(B) 250 cm3

(D) 100cm3

and ∆S are :

(B) +, –

(D) –, +

A (C5H8) on

pound B (C5H12).

s give methanol and

?

56. Which statement is

(A) Ordinary hyd

mixture of ort

(B) In ortho hydro

same direction

(C) Ortho and para

their chemical

(D) In para hydrog

opposite direc

57. H2O2 is prepared in

(A) MnO2 is added

(B) BaO2 is added

cold water

(C) PbO2 is addedKMnO4

(D) Na2 O2 is added

58. The reaction

Is fastest when X is

(A) OCOR

(C) NH2

59. Identify the corre

spontaneous proces(A) Endothermic

spontaneous.

(B) Exothermic

spontaneous.

(C) Lowering of en

is the only crite

(D) For a spontane

system, the cha

60. Calculate the entha

at –25°C , if the s5950 cal/mol. Give

Cp(l)= 20.6 cal/mol

(A) 6119.5 cal/mol(C) 5950 cal/mol

H

H

(2)

H

H

H

(4)

2

CH3

R C

O

X

+ Nu

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6

2


wrong

rogen is an equilibrium

o and para hydrogen

en spin of two nuclei is in

forms do not resemble in

properties

n spin of two nuclei is in

ion

laboratory when

o dil cold H2SO4

to CO2 bubbling through

to an acidified solution of

to boiling water

(B) OC2H5

(D) Cl

t statement regarding a

:processes are never

processes are always

rgy in the reaction process

rion for spontaneity

ous process in an isolated

nge in entropy is positive.

py of vaporization of SO2

me at its b.pt. (–10°C) bethe molar heat capacities,

nd Cp(g) = 9.3 cal / mol

(B) 5780.5 cal/mol(D) None

C

Nu

O

+ XR




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61. If the line ax + by + c =

curve xy =4, then (A) a > 0, b > 0

(C) a < 0, b > 0

62. If the angle between the s

foci and the ends of mino

1=+ 2

2

2

2

b

y

a

xis 90°, then th

(A)2

1 (B)

2

3

(C)2

1 (D) none

63. The portion of a tangent to

cut off between the dire

subtends an angle θ at th

equal to

(A)3

π (B)

4

π

(C)2

π (D) none

64. A hyperbola, having the

length 2 sinθ, is conforcal3x2 + 4y2 = 12. Then, its e

(A) x2 cosec

2 θ − y

2 sec

2 θ

(B) x2 cos

2 θ − y

2 sin

2 θ =1

(C) x2 sec

2 θ − y

2 cosec

2 θ

(D) x2 sin

2 θ − y

2 cos

2 θ =1

65. If the tangent to the curve

(1, 1) is inclined at an aaxis, then

(A) a = 1, b =2

(C) a = −1, b =−2

66. The longest distance of t

the curve 2x2 + y

2 – 2x = 0

(A) 221 aa +− (B) 1+

(C) 221 aa −+ (D) 1−

67. Axis is of parabola is y

focus are at a dista

respectively from the origi

the parabola is

(A) (x − y)2 = 8(x + y − 2)

(B) (x + y)2 = 4(x + y − 2)

(C) (x − y)2 = 4(x − y − 2)

(D) (x − y)2 = 2(x − y + 2)

68. The value of 357.2 is

(A)

999

2355

MATHEMATI



E

is a tangent to the

(B) a > 0, b < 0

(D) None of these

traight lines joining

r axis of the ellipse

eccentricity is

of these

a parabola y2 = 4ax

trix and the curve

e focus, where θ is

of these

transverse axis of

with the ellipseuation is

=1

=1

xy + ax + by = 0 at

gle tan−1

2 with x-

(B) a = 1, b =−2

(D) a =−1, b =2

e point (a, 0) from

is given by

222 aa + 222 aa +

=x and vertex and

ce 2 and 22

n. Then equation of

(B)

1000

2355

(C)1111

2355

69. A parabola is drawn

vertex at the

y2 – 12x – 4y +

parabola is

(A) y2 – 8x – 6y + 2

(B) y2 – 6x + 8y − 2

(C) x2 – 6x − 8y + 2

(D) x2 + 6x − 8y −

70. If p, p' denote

perpendiculars fro

of an ellipse with s

respectively on a tdenotes the focal di

(A) a p' = rp + 1

(C) ap = r p' + 1

71. Locus of the poi

ordinate of the ellip

1:2 internally, is

(A)9

19x2

2

2

2

=−b

y

a

(C) 199x

2

2

2

2

=+

b

y

a

72. From any point on

, tangents are

2x

2

2

2

2

=−b

y

a. The

contact on the asym

(A)2

ab (

(C) 2ab (

73. The equation of t

coincident with the

touches the straigx+6y−20=0, is

(A) 185

22

=+ y x

(

(C) 11040

22

=+ y x

(

74. Let C be the

12

2

2

2

=−b

y

a

x. The

this hyperbola meet

=0 and bx + ay

respectively. Then,

S

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7

2


(D) none of these

with its focus at (3, 4) and

ocus of the parabola

=0. The equation of the

5=0

5=0

5=0

5=0

the lengths of the

the focus and the centre

emi major axis of length a

ngent to the ellipse and rtance of the point, then

(B) rp = a p'

(D) ap = r p'

nt which divides double

se 1x

2

2

2

2

=+b

y

a in the ratio

(B) 19x

2

2

2

2

=+b

y

a

(D) none of these

he hyperbola 1x

2

2

2

2

=−b

y

a rawn to the hyperbola

rea cut-off by the chord-of

ptotes is equal to

) ab

) 4ab

e ellipse whose axes are

coordinate axes and which

t lines 3x−2y−20=0 and

) 101040

22

=+ y x

) 14010

22

=+ y x

entre of the hyperbola

tangent at any point p on

s the straight lines bx – ay

0 at the points Q and R

Q.CR is equal to




Email: endea

(A) a2 − b2

(C)22

11

ba

+

75. A normal to the hyperbol

transverse and conjugate a

the lines MP and NP are

to the axes. The locus of P

(A) the parabola y2 =4a(x

(B) the circle x2 + y

2 =ab

(C) the ellipse b2x2 + a2y2

(D) the hyperbola a2x2 − b2

76. The eccentricity of the

changed at the rate of 0.1

at which it will touch the a(A) 2s (B) 3s

(C) 5s (D) 6s

77. The focal chord to y2 =

(x−6)2 + y

2 =2, then the p

slope of this chord are

(A) {−2, 2}

(C) {−1, 1}

78. Tangent is drawn to e

where)sin,cos3(3 ∈θ θ θ

value of θ such that the saxes made by this tangent i

(A)3

π (B)6

π

(C)8

π (D)4

π

79. The tangent at the poin

parabola

y2 = 4ax meets the parabo

Q and R, the coordinates

QR are(A) (x1 – a, y1 + b)

(C) (x1 + b, y1 + a)

80. If an ellipse slides betweestraight lines, then the locu

(A) a parabola (B) an el

(C) a hyperbola (D) a cir

81. If P, Q,R are three points

4ax whose ordinates a

progression, then the tang

on

(A) The line through Q pa

(B) The line through Q par

(C) The line joining Q to t

(D) The line joining Q to t



E

(B) a2 + b2

(D)22

11

ba

−

12

2

2

2

=−b

y

a

xmeets

xes in M and N and

rawn at right angle

is

b)

a2 + b2

y2 =(a2 + b2)2

llipse 134

22

=+ y x is

er second. The time

xiliary circle is

16x is tangent to

ssible values of the

(B) {−2, 1/2}

(D) {2, −1/2}

llipse 127

22

=+ y x at

.2

0,

π Then, the

um of intercepts ons minimum, is

t P(x1, y1) to the

la y2 = 4a (x + b) at

of the mid-point of

(B) (x1, y1)

(D) (x1 – b, y1 – b)

n two perpendiculars of its centre is

lipse

le

on a parabola y2 =

re in geometrical

nts at P and R meet

allel to x-axis

allel to y-axis

e vertex

e focus.

82. The point of interse

parabola y2 = 4x at

(x – 3)2 + y

2 = 9 me

the origin, is

(A) (−2, 0)

(C) (0, 0)

83. If PQ is a focal cho

with focus at S, the

(A) a (

(C) 4a (84. If the tangent at P

11y2 = 256 touches

then θ =

(A) π /6 (

(C) 2π /3 (

85. The locus of the p

tangents at the extr

ellipse x2 + 2y

2 = 6

x2 + 4y2 = 4 is

(A) x2 + y

2 = 4 (

(C) x2 + y2 = 9 (

86. If P is a point on t

− y2 = a2 , C is its c

foci, then SP. S’ P

(A) 2 (

(C) (CS)2 (

87. Equation of a com

y2 = 8x and xy = −1

(A) 3y = 9x + 2 (

(C) 2y = x + 8 (

88. The tangent at a po

is not an extremit

directrix at T.

Statement – 1: Th

passes through tcorresponding to th

Statement – 1: PT

fcus of the ellip

direcrix on which T

(A) If Statement I is

Statement II is

Statement I.(B) If Statement I is

Statement II is n

Statement I.

(C) If Statement I is

(D) If Statement I is

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8

2


ction of the tangents to the

the points where the circle

ets the parabola, other than

(B) (1, 0)

(D) (−1, −1)

rd of the parabola y2 = 4ax

=+ SQSP

SQSP.2

) 2a

) a2

(θ) on the ellipse 16x2 +

the circle x2 + y

2+ 2x = 15,

) π /3

) 5π /6ints of intersection of the

mities of the chords of the

which touch the ellipse

) x2 + y

2 = 6

) None of these

e rectangular hyperbola x2

entre and S, S’ are the two

) (CP)2

) (SS’)2

on tangent to the curves

is

) y = 2x + 1

) y = x + 2

int P on the ellipse, which

y of major axis meets a

circle on PT as diameter

e focus of the ellipsedirectrix on which T lies.

subjects a right angle at the

se corresponding to the

lies.




ot a correct explanation for

true, Statement II is false.

false, Statement II is true.




Email: endea

89. Statement – 1: The tange

of a focal cord of the

intersect on the line x + a

Statement–2: The locu

intersection of perpendic

parabola is its directrix.

(A) If Statement I is true,

Statement II is a cor

Statement I.

(B) If Statement I is true,

Statement II is not afor Statement I.

(C) If Statement I is true, S

(D) If Statement I is false,



E

ts at the extremities

parabola y2 = 4ax

0.

of the point of

lar tangents to the

tatement II is true,

rect explanation for

tatement II is true,

correct explanation

tatement II is false.

Statement II is true.

90. y2 = 4x is the equati

Statement – 1: Thr

can be drown to the

Statement – 1: T

outside the parabola


Statement II is

Statement I.


Statement II is

for Statement I.

(C) If Statement I is

(D) If Statement I is

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9

2


on of a parabola.

ough (λ, λ + 1), 3 normals

parabola, if λ < 2

he point (λ, λ + 1) lies

for all λ ≠ − 1




not a correct explanation

true, Statement II is false.

false, Statement II is true.

AIEEE Part Test-3

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