class: sz2 jee-adv(2014-p2) model date: 26-12-2020 time: … · 2020. 12. 27. · class: sz2...

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Class: SZ2 JEE-ADV(2014-P2) MODEL Date: 26-12-2020

Time: 3hrs WAT-14 Max. Marks: 180

IMPORTANT INSTRUCTIONS

PHYSICS Section Question Type

+Ve Marks

- Ve Marks

No.of Qs

Total marks

Sec – I(Q.N : 1 – 10) Questions with Single Correct Choice 3 -1 10 30

Sec – II(Q.N : 11 – 16) Questions with Comprehension Type

(3 Comprehensions – 2 +2+2 = 6Q) 3 -1 6 18

Sec – III(Q.N : 17 – 20) Matrix Matching Type 3 -1 4 12

Total 20 60

CHEMISTRY Section Question Type

+Ve Marks

- Ve Marks

No.of Qs

Total marks





Total 20 60

MATHEMATICS Section Question Type

+Ve Marks

- Ve Marks

No.of Qs

Total marks





Total 20 60

mailto:[email protected]://www.narayanagroup.com/

SZ2_JEE-ADV(2014-P2)_WAT-14_QP_Exam.Dt.26-12-2020

Narayana CO Schools

2

SECTION –I (01 TO 10) (ONLY ONE OPTION CORRECT TYPE)

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which only one option is correct. Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.

01. Gravitational potential energy of a point mass m0 and a thin

uniform rod of mass m0 and length l , if they are located along a

straight line at a distance d measured from the Centre of the rod is

A) 2

0 logeGm d r

l d r

+ −

− B)

2 2log

2e

Gm d l

l d l

+ −

−

C) 2

0 2log2

e

Gm d l

l d l

+ −

− D) All of these

02. A straight smooth tunnel is dug through a spherical planet whose

mass density 0 is constant. The tunnel passes through the centre

of the planet and is perpendicular to the planet’s axis of rotation,

which is fixed in space. The planet rotates with the angular velocity

so that objects in the tunnel have no acceleration relative to the

tunnel, the value of is

A) 04

3G B) 0

2

3G C) 0

1

3G D) 2 0

2

3G

03. Gravitational field intensity at the centre of the semi-circle formed

by a thin wire AB of mass m and length L is

A) 2

2( )

Gmi

L B) ( )

2

2

Gmj

L C)

2

2( )

Gmi

L

D)

2

2( )

Gmj

L


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04. There is a concentric hole of radius R in a solid sphere of radius

2R. Mass of remaining portion is M, then gravitational potential at

centre is

A)3

7

GM

R

−

B)

3

14

GM

R− C)

9

14

GM

R− D)

15

14

GM

R−

05. The density of the core of a planet is 1 and that of the outer shell

is 2 . The Radii of the core and that of the planet are R and 2R,

respectively. If the acceleration due to gravity at the surface is same

as at a depth R, then ratio 1

2

is

A) 5

3 B)

7

3 C)

7

5 D) 3

06. From a solid sphere of mass M and radius R, a spherical portion of

radius R/2 is removed, as shown in the figure. Taking gravitational

potential V=0 at r = , the potential at the Centre of the cavity thus

formed is (G = gravitational constant)

A) 2

GM

R

− B)

GM

R

− C)

2

3

GM

R

− D)

2GM

R

−


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07. A spherically symmetric gravitational system of particles has a

mass density0 for r R

0 for r >R

=

where0 is a constant. A test mass can

undergo circular motion under the influence of the gravitational

field of particles. Its speed V as a function of distance r(0


Narayana CO Schools

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09. Consider a spherical gaseous cloud of mass density ( )r in a free

space where r is the radical distance from its center. The gaseous

cloud is made of particles of equal mass m moving in circular orbits

about their common centre with the same kinetic energy K. The

force acting on the particles is their mutual gravitational force. If

( )r is constant in time. The particle number density is ( ) ( ) /n r r m=

[ G is universal gravitational constant]

A)2 2

3K

r m G B)

2 22

K

r m G C)

2 2

K

r m G D)

2 26

K

r m G

10. Consider two solid spheres of radii1 21 , 2R m R m= = and masses 1M

and 2M respectively. The gravitational field due to sphere (1) and (2)

are shown. The value of 1

2

M

Mis

A)1

3 B)

1

2 C)

1

6 D)

2

3

SECTION – II (11 TO 16) (COMPREHENSION TYPE)

This section contains 3 paragraphs each describing theory, experiments, data etc. Six questions relate to the three paragraphs with two questions on each paragraph. Each question has only one correct answer among the four given options (A), (B), (C) and (D). Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.


Narayana CO Schools

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Comprehension – I:

A non-homogeneous sphere of radius R has the following density

variation

0 = for /3r R

0

2

= for

3

3 4

R Rr and

0

8

= for

3

4

Rr R

11. The gravitational field due to the sphere at r=2

Ris

A) 043

50

GR B) 0

23

100

GR

C) 035

81

GR D) None of these

12. The gravitational field due to the sphere at r= 5

6

Ris

A)0.98 0GR B) 0.48 0GR

C) 0.23 0GR D) 0.68 0GR

Comprehension – II:

Infinite numbers of masses, each of mass m, are placed along a straight

line at a distance of r, 2r, 4r, 8r etc. From a reference point O. Then

13. The gravitational field intensity at point 0 is

A) 2

4

3

Gm

r B)

2

3

4

Gm

r C)

2

5

8

Gm

r D)

2

8Gm

r

14. The magnitude of the gravitation potential at point 0 is

A) Gm

r B)

2Gm

r C)

4Gm

r D)

6Gm

r


Narayana CO Schools

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Comprehension – III:

A solid sphere of uniform density and radius 4 m is located with its centre

at the origin O of coordinates. Two spheres of equal radius 1m with their

cavities at A (-2, 0, 0) m and B (2, 0, 0) m, respectively are taken out

leaving behind spherical cavities. The mass of each sphere taken out is

M.

15. The gravitational potential at any point on the circle 2 2 36Y Z+ = is

A) 10 32

10 3GM

−

B)

5 32

100 3GM

−

C) 10 32

50 3GM

−

D) None of these

16. The gravitation potential at any points on the circle 2 2 4Y Z+ = is

A) 2

222

GM

−

B) 2

112

GM

−

C) 2

222

GM

+

D) 6

222

GM

−

SECTION – III (17 TO 20) (MATCHING LIST TYPE)

This section contains four questions, each having two matching lists. Choices for the correct combination of elements from Column-I and Column-II are given as options (A), (B), (C) and (D), out of which one is correct. Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.


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17. Match the following.

Column-I Column-II

A)

The gravitational field at some point in

space is ˆ ˆ3 4 /E i jN kg= + .The force

exerted on a 2kg mass placed at that

point is

P) 3

3Gm

a

B) Three particles each of mass ‘m’ are

located at the three vertices of an

equilateral triangle of side ‘a’. If the

system is revolving in a uniform circle

due to their mutual force of attraction,

then the angular velocity of each

particle is

Q)

10N, 53 with x-

axis

C)

A uniform spherical shell gradually

shrinks maintaining its shape. The

gravitational potential at the Centre

R)

Reduced 1

4th

D)

If the distance between the earth and

moon were doubled, The gravitation

force between them will be

S)

Decreases

A) , , ,A Q B P C S D RS→ → → →

B) , , ,A P B Q C R D PS→ → → →

C) , , ,A S B R C P D QS→ → → →

D) , , ,A R B Q C S D QR→ → → →


Narayana CO Schools

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18. Match the following

Column-I Column-II

A) The unit of the quantity g/G in SI

system will be

P) X = 2h

B)

If the change in the value of ‘g’ at a

height ‘h’ above the surface of the

earth is the same as at a depth x

below it, and when both x and h are

much smaller than the radius of the

earth

Q)

Kg 2m−

C)

If the mass of a planet is 10% less

than that of the earth and the radius

is 20% greater than that of the earth,

the acceleration due to gravity on the

planet will be

R)

2

23

4

Gm

r

D)

If three uniform spheres, each having

mass m and radius r, are kept in such

a way that each touches that other

two. The magnitude of the

gravitational force on any sphere due

to the other two is

S)

5/8 times that on

the surface of the

earth

A) , , ,A P B Q C R D S→ → → →

B) , , ,A Q B P C S D R→ → → →

C) , , ,A S B R C P D Q→ → → →

D) , , ,A R B S C Q D P→ → → →


Narayana CO Schools

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19. Density of a planet is two times the density of earth and radius of

this planet is half the radius of earth. Match, the following (as

compared to earth)

Column-I Column-II

A) Gravitational strength at the surface

of this planet

P) Half

B) Gravitational potential on the surface Q) Same

C) Gravitational potential at centre R) Two times

D) Gravitational strength at centre S) Four times

A) , , ,A P B Q C R D S→ → → → B) , , ,A R B P C S D Q→ → → →

C) , , ,A Q B P C P D Q→ → → → D) , , ,A S B R C Q D R→ → → →


Column-I Column-II

A)

The gravitational field due to a uniform rod

of length(L) and mass(M) at a point on its

perpendicular bisector at a distance (d) from

the centre is

P)

2( 2) 1

4

GM

R

+

B)

Four particles of equal masses (M) move

along a circle of radius(R) under the action of

their mutual gravitational attraction. Then

the speed of each particle is

Q)

2 2

2

4

GM

d L d+

C)

The value of acceleration due to gravity at a

point 5km below the earth’s surface is (The

radius of the earth is 6400km, acceleration

due to gravity at the surface of the earth is

9.8m/ 2s

R)

h=R

D)

The height at which the gravitational field of

the earth becomes one fourth(1

4th ) the field

at the surface is

S)

9.79m/ 2s

A) , , ,A Q B P C S D R→ → → →

B) , , ,A P B Q C R D S→ → → →

C) , , ,A S B R C Q D P→ → → →

D) , , ,A R B S C P D Q→ → → →


Narayana CO Schools

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21. The colloidal system of a solid dispersed in liquid medium is called:

A) aerosol B) sol C) gel D) foam

22. Sulphur sol contains:

A) discrete sulphur atoms B) discrete sulphur molecules

C) water dispersed in solid sulphur

D) large aggregates of sulphur molecules

23. Which of the following statements is correct

A) Metal sulphides are examples of negatively charged sols

B) Emulsion can be broken into constituent liquids by heating,

freezing and centrifugation

C) Milk of magnesia, an emulsion is used for stomach disorders

D) All the above

24. The movement of colloidal particles under an applied electric

potential is called:

A) electro-osmosis B) peptization

C) electrophoresis D) electro-dispersion

25. An emulsifier is a substance which:

A) helps in the dispersion of liquid in liquid

B) stabilizes the emulsion

C) coagulates the emulsion

D) purifies the emulsion

26. Froth floatation process is based on:

A) specific gravity of the ore particles

B) magnetic properties of the ore particles

C) wetting properties of the ore particles

D) electrical properties of the ore particles


Narayana CO Schools

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27. Heating of pyrites in presence of air to remove sulphur is called as:

A) roasting B) calcination

C) smelting D) leaching

28. Which one of the following ores is best concentrated by froth-

flotation method?

A) Sulphide ores B) Oxide ores

C) Carbonate ores D) All

29. ( ) 2 2 2Ag S NaCN H O O Air A OH−+ + + → +

A Zn B+ →

[B] is a metal, Hence, [A] and [B] are:

A) ( )2 4 ,Na Zn CN Zn B) ( )2 ,Na Ag CN Ag

C) ( )2 4 ,Na Ag CN Ag D) ( )3 4 ,Na Ag CN Ag

30. Oxidation states of the metal in the minerals haematite and

magnetite, respectively are:

A) II, III in haematite and III in magnetite

B) II, III in haematite and II in magnetite

C) II in haematite and II, III in magnetite

D) III in haematite and II, III in magnetite

SECTION – II (31 TO 36)

(COMPREHENSION TYPE)

This section contains 3 paragraphs each describing theory, experiments,

data etc. Six questions relate to the three paragraphs with two

questions on each paragraph. Each question has only one correct

answer among the four given options (A), (B), (C) and (D). Marking

scheme: +3 for correct answer, 0 if not attempted and -1 in all other

cases.


Narayana CO Schools

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There are certain substances which behave as normal, strong electrolytes

at low concentration but at higher concentration they behave as colloidal

solutions due to the formation of aggregated particles. Such colloids are

called associated colloids and the aggregated particles are called micelles.

Soaps and detergents are the examples of associated colloids. Teh

formation of micelles takes place above certain concentration called

critical micellization concentration (CMC) and a characteristic

temperature.

31. Micelles are:

A) Emulsion B) associated colloids

C) adsorbed catalysts D) ideal solutions

32 Micelles are formed only:

A) below the CMC and the Kraft temperature

B) above the CMC and below the Kraft temperature

C) above the CMC and above the Kraft temperature

D) below the CMC and above the Kraft temperature


Emulsions are also the colloidal solutions in which dispersed phase as

well as dispersion medium are liquids. It may be oil in water or water in

oil type. Bancroft proposed that the phase in which is the emulsifier is

more soluble becomes the outer phase of the solution. Emulsifiers can be

used to stabilize the emulsion. Soaps, detergents, proteins and gum, etc.,

are used as emulsifiers.

33. Which of the following examples is oil in water type emulsion?

A) Butter B) Detergent C) Soap D) Milk

34. Milk is an emulsion in which:

A) liquid fat is dispersed in water

B) oil is dispersed in oil

C) a gas is dispersed in water

D) water dispersed in oil


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To extract metal from concentration ore, it must be converted to a form

which is suitable for reduction to metal usually sulphide ores are

converted to oxide before reduction because oxides are easier to reduce .

Thus isolation of metals from concentrated ore involves two major steps

viz.

a) conversion of oxide and b) reduction of the oxide to metal.

35. Which of the following is/are belongs to Calcination

A) ( ) ( ) ( )2 3 2 2 23s s gFe O xH O Fe O xH O⎯⎯→ +

B) ( ) ( ) ( )3 2s s gZnCO ZnO CO⎯⎯→ +

C) ( ) ( ) ( ) ( )3 3 2. 2S S gSCaCO MgCO CaO MgO CO⎯⎯→ + +

D) All the above

36. Which of the following is/are reducing agents in the reduction of

oxide to the metal

A) C B) CO

C) Both (A) and (B) D) 2N

SECTION – III (37 TO 40) (MATCHING LIST TYPE)

This section contains four questions, each having two matching lists. Choices for the correct combination of elements from Column-I and Column-II are given as options (A), (B), (C) and (D), out of which one is correct. Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.

37.

Column-I Column-II

I. Coagulation p. Scattering of light

II. Negatively charged sols q. Purification of colloidal solution

III. Tyndall effect r. Electrophoresis

IV. Dialysis s. 2 3As S

A) I-p; II-q; III-r; IV-s B) I-r; II-s; III-p; IV-q

C) I-p; II-q; III-s; IV-r D) I-r; II-s; III-q, IV-p


Narayana CO Schools

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38.

Column-I Column-II

I. Malachite p. Aluminium

II. Siderite q. Copper

III. Sphalerite r. Zinc

IV. Bauxite s. Iron

A) I-q; II-s; III-r; IV-p

B) I-q; II-s; III-p; IV-r

C) I-p; II-q; III-r; IV-s

D) I-p; II-q; III-s; IV-r

39.

Column-I Column-II

I. Calcination P. 2 2 2 22 3 2 2Cu S O Cu O SO+ ⎯⎯→ +

II. Roasting Q. ( ) ( ) ( )2 3 2 2 23. s s gFe O nH O Fe O nH O⎯⎯→ +

III. Flux R. x yM O yc xM yco+ ⎯⎯→ +

IV. Reduction of oxide to the metal S. 2 3SiO Feo FeSiO+ ⎯⎯→

A) I-p; II-q; III-r; IV-s

B) I-p; II-q; III-s; IV-r

C) I-q; II-p; III-s; IV-r

D) I-q; II-p; III-r; IV-s

40

Column-I Column-II

I. ( ) ( )3 2 33 3FeCl H O Fe OH sol HCl+ ⎯⎯→ + P. Oxidation

II. ( )2 2 22 3 2SO H S S Sol H O+ ⎯⎯→ + Q. Reduction

III. ( )3 22 3 3 2 3 6AuCl HCHO H O Au sol HCOOH HCl+ + ⎯⎯→ + + R. Hydrolysis

IV. ( )2 3 2 2 3 23 3AS O H S AS S sol H O+ ⎯⎯→ + S. Double

decomposition

A) I-r; II-p; III-q; IV-s

B) I-p; II-q; III-r; IV-s

C) I-p; II-q; III-s; IV-r

D) I-q; II-p; III-r; IV-s


Narayana CO Schools

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41. A circle of constant radius a passes through the origin O and cuts

the axes of coordinates at point P and Q. Then the equation of the

locus of the foot of perpendicular from O to PQ is

A) ( )2 2 22 21 1

4x y ax y

+ + =

B) ( )

22 2 2

2 2

1 1x y a

x y

+ + =

C) ( )2

2 2 2

2 2

1 14x y a

x y

+ + =

D) ( )2 2 22 2

1 1x y a

x y

+ + =

42. The difference between the radii of the largest and the smallest

circles which have their center on the circumference of the circle

2 2 2 4 4 0y x yx + + + − = and pass through the point (a, b) lying outside

the given circle is

A) 6 B) ( ) ( )2 2

1 2a b+ + +

C) 3 D) ( ) ( )2 2

1 2 3a b+ + + −

43. An isosceles triangle ABC is inscribed in a circle 2 2 2y ax + = with

the vertex A at (a,0) and the base angle B and C each equal to 075

. Then the coordinates of an endpoint of the base are

A) 3

,2 2

a a −

B) 3

,2

aa

−

C) 3

,2 2

a a

D) 3

,2 2

a a −

44. A circle passing through origin O cuts two straight lines x-y=0 and

x+y=0 in points A and B respectively. If abscissae of A and B are

roots of the equation 2 0x ax b+ + = , then the equation of the given

circle is :

A) 2 2 0x y ax by+ + − = B) 2 2 24 0x y x b a yb+ − − + =

C) 2 2 2 4 0x y ax y a b+ + − = D) 2 2 2 4 0x y ax y a b+ − − =


Narayana CO Schools

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45. Let PQR be a right angled isosceles triangles, right angled at P(2,1).

If the equation of the line QR is 2x+y=3, then the equation

representing the pair of lines PQ and PR is :

A) 2 23 8 20 10 25 03 y xy x yx − + + + + =

B) 2 23 8 20 10 25 03 y xy x yx − + − − + =

C) 2 23 8 10 15 20 03 y xy x yx − + + + + =

D) 2 23 8 10 15 20 03 y xy x yx − − − − − =

46. There exists two ordered triplets ( )1 1 1, ,a b c and ( )2 2 2, ,a b c for (a,b,c)

for which the equation 2 24 1 04 xy ay bx cyx − + + + + = represents a pair

of identical straight lines in x-y plane. Find the value of

1 1 1 2 2 2b c a b ca + + + + + .

A) 3 B) 1 C) 2 D) 4

47. The lines 1L and 2L denoted by 2 23 10 8 14 22 15 0x xy y x y+ + + + + =

intersects at the point P and having slopes 1m and 2m respectively.

The acute angle between them is . Which of the following relations

hold good.

A) 1 25

4m m+ = B) 1 2

2

8m m = C) 1

1sin

5 5

− =

D) Sum of abscissa and ordinate of point P is 1−

48. Area of the triangle formed by the line x+y=3 and angle bisector of

the pair of straigh t lines 2 2 2 1 0x y y− + − = is :

A) 2 sq.units B) 4 sq. units

C) 6 sq.units D) 8 sq.units

49. The orthocentre of a triangle formed by the line 3x y+ = and pair of

lines 2 26 5 6 5 1 0x xy y x y− − + + − = is

A) 13 65

,169 169

B) 13 65

,169 169

−

C) 13 65

,169 169

− −

D) 13 65

,169 169

−


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50. If 1x y

a b+ = intersects 2 25 5 5 5 9 0x y bx ay ab+ + + − = at P and Q,

2POQ

= then the relation between a and b is

A) a b= B) 2 2a b or b a= =

C) 3 3a b or b a= = D) 5a b+ =

SECTION – II (51 TO 56)

(COMPREHENSION TYPE)

This section contains 3 paragraphs each describing theory, experiments, data etc. Six questions relate to the three paragraphs with two questions on each paragraph. Each question has only one correct answer among the four given options (A), (B), (C) and (D). Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.


Consider a Circle 2 2 2y ax + = . Let A(a,0) and ( ),D be the given interior

points of the circle. BC be an arbitrary chord of the circle through point

D inclined at an angle with the positive x-axis. Also, 1DB r= and

2DC r= .

51. The harmonic mean of BD and DC is

A) ( )

2 2 2

2 cos sin

a

+ −

+ B)

( )

2 2 2

cos sin

a

+ −−

+

C) 2 2 2

sin cos

a

+ −

+ D)

( )2 2 22cos sin

a

+ −

+

52. The locus of the centroid of ABC is

A) ( )2

2 1 2

3 3

a r rx y

− − + =

B) ( )

22 1 2

3 3

a r rx y

+ + + =

C) ( )2

2 1 2

3 3

a r ry x

+ − + =

D) ( )

22 1 2

3 3

a r rx y

+ − + =


Narayana CO Schools

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If 2 2 0g f c+ − , then the equation 2 2 2 2 0x y gx fy c+ + + + = represents a

circle with centre ( ),g f− − and radius 2 2g f c+ −

53. If 2 2 2 2 9 0x y gx fy+ + + + = represents a circle with centre ( )1, 3− , then

radius is

A) 1 B) 2 C) 3 D) –1

54. The length of the diameter of the circle 2 2 6 8 0x y x y+ − − = is

A) 5 B) 10 C) 15 D) 20


Consider a pair of perpendicular straight lines

2 23 2 5 5 0xy y x y cax + − − + + =

55. The value of c is

A) -3 B) 3 C) -1 D) 1

56. Distance between the orthocenter and the circumcenter of triangle

ABC is

A) 4 B) 9/2 C) 8/3 D) 7/4

SECTION – III (57 TO 60)

(MATCHING LIST TYPE)

This section contains four questions, each having two matching lists. Choices

for the correct combination of elements from Column-I and Column-II are given as options (A), (B), (C) and (D), out of which one is correct. Marking

scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.


Let 1C and 2C be two circles whose equations are 2 2 2 0y xx + − = and

2 2 2 0y xx + + = . ( ),P is a variable point. Then match the

following.

Column-I Column –II

P) P lies inside 1C but outside 2C . 1) ( ) ( ), 1 0, − −

Q) P lies inside 2C but outside 1C 2) ( ) ( ), 1 1, − −

R) P lies outside 1C but outside 2C . 3) ( )1,0 −

S) P does not lie inside 2C 4) ( )0,1

A) P-3; Q-1; R-2; S-4 B) P-4; Q-1; R-3; S-2

C) P-4; Q-3; R-2; S-1 D) P-1; Q-2; R-3; S-4


Narayana CO Schools

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58.


P) The pair of lines joining the origin to the

points of intersection of the curve

2 29 16 144x y+ = by the line 2 2 0x y+ + = are

coincident, then is divisible by

1) 2

Q) If the straight lines joining the origin to the

points of intersection of the straight line

4 3 24x y+ = and the curve

( ) ( )2 2 23 4 ,x y− + − = are at right angles,

then is divisible by

2) 3

R) The two line pairs 2 4 3 0y y− + = and

2 24 4 5 10 4 0x xy y x y+ + − − + = enclose a

4sided convex polygon, if area of polygon

is sq units, then is divisible by

3) 5

S) If the pairs of lines 2 23 2 3 0x pxy y− − = and

2 25 2 5 0x qxy y− − = are such that each pair

bisects the angle between the other pair. If

,pq = then is divisible by

4) 6

A) P-1,3; Q-3; R-1,2,4; S-2,3

B) P-2; Q-3,2; R-4;S-1

C) P-2,3;Q-2; R-3; S-1,3

D) P-1,2,4; Q-4;R-2; S-3


Narayana CO Schools

21

59. Let ( ) ( )1 1 2 2 3 3, , ( , ), ,A x y B x y C x y be 3 distinct points lying on circle

2 2 1: yS x + = , such that 1 2 1 2 2 3 2 3 3 1 3 13

2x y y x x y y x x y yx + + + + + = −


P) Let P be any arbitrary point lying on S, then

( ) ( ) ( )2 2 2

PA PB PC+ + =

1) 3

Q) Let the perpendicular dropped from point ‘A’

to BC meets S at Q and k

OBQ =

, where ‘O’

is origin, then k=

2) 4

C) Let R be the point lying on line x+y=2 at the

minimum distance from S and the square of

maximum distance of R from S is ba b+ ,

then a+b=

3) 5

D) Let I and G represent incenter and centroid of

ABC respectively, then

IA IB IC GA GB GC+ + + + + =

4) 6

A) P-1; Q-2; R-3;S-4 B) P-4; Q-1; R-3; S-2

C) P-2; Q-1; R-4; S-3 D) P-2; Q-3; R-1; S-4

60. Match the loci given in the column II with the equations given in

the column I


P) 3 3 0x y+ = 1) No real line

Q) 2 2 32 0x y xy y+ + = 2) One real line

R) ( ) ( )2 2

2 21 4 0x y− + − = 3) Two distinct real lines

S) ( )( ) ( ) ( )22 2 21 1 1 1 0x x x y y x− − + − + = 4) Four distinct real lines

T) 5) Four points

A) P-2; Q-3; R-1,5; S-2,5 B) P-1,2; Q-4,3; R-2,3; S-1,4

C) P-3; Q- 1,2; R-3,4; S -1,3 D) P-2; Q-3,4; R-4; S-1

class: sz2 jee-adv(2014-p2) model date: 26-12-2020 time: … · 2020. 12. 27. · class: sz2...

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