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Page | 1 Assignment – 3 28-04-2020

SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

SR MPC JEE MAINS Date: 28-04-2020 Time: Max. Marks:

MATHS

Syllabus: CO-OORDINATE GEOMETRY:– 1. STRAIGHT LINES , 2. PAIR OF STRAIGHT LINES, 3.CIRCLES, 4.SYSTEM OF CIRCLES, 5. PARABOLA, 6. ELLIPSE, 7. HYPERBOLA

1. The set of real values of k for which the equation 2 2k 1 x 2 k 1 xy y x 2y 3 0

represents an ellipse is

(A) (0, 3) (B) ,0 (C) 3, (D) ,

2. The latus rectum of the conic section2 2

2 2

x y1

a b whose eccentricity = e, is

(A) 22a

b (B)

2

2b

a (C) 22a 1 e (D) 22b 1 e

3. In the ellipse x2 + 3y

2 = 9 the distance between the foci is

(A) 6 (B) 3 (C) 2

36 (D) 2 6

4. If in an ellipse the minor axis = the distance between the foci and its latus rectum = 10 then the

equation of the ellipse in the standard form is

(A)

2 2

2 2

x y1

10 5 2

(B)

2 2

2 2

x y1

105 2

(C)

2 2

2

x y1

25 5 2

(D) 2 2x y

25 10 = 1

5. If in an ellipse, a focus is (6, 7), the corresponding directrix is x + y + 2 = 0 and the eccentricity

= 1/2 then the equation of the ellipse is

(A) 2 27x 2xy 7y 44x 108y 684 0 (B) 2 27x 2xy 7y 52x 116y 676 0

(C) 2 29x 2xy 9y 44x 108y 684 0 (D) 2 29x 5xy 4y 12x 89y 676 0

6. A point P on the ellipse2 2x y

125 9

has the eccentric angle8

. The sum of the distance of P from

the two foci is

(A) 5 (B) 6 (C) 10 (D) 3

7. The equation of the tangent to the ellipse 4x2 + 3y

2 = 12 at the point whose eccentric angle is

4

is

(A) 3x 2y 2 6 (B) 2x 3y 2 6

(C) 2x 3y 2 6 (D) x – 7 y = 3 2

8. The number of values of m for which the line y = mx + 2m 4 touches the hyperbola

2 24 x 1 y is

(A) 2 (B) 0 (C) None (D) Infinite

9. The length of the common chord of the parabola 2y2 = 3(x + 1) and the circle

2 2x y 2x 0 is

(A) 1.732 (B) 3.464 (C) 0.866 (D) 9.898

UNIT – III

ASSIGNMENT – 3



10. The eccentricity of the ellipse2 2x y

14 9 is

(A) 1.128 (B) 0.666 (C) 0.719 (D) 0.444

11. The ellipse2 2

2 2

x y1

a b passes through the point (– 3, 1) and has the eccentricity

2

5. Then the

major axis of the ellipse has the length b

ac

such that a + b – c =

(A) 6 (B) 7 (C) 8 (D) 9

12. The major axis of the ellipse 9x2 + 5y

2 = 30y is

(A) 6.000 (B) 4.472 (C) 2.449 (D) 2.236

13. An ellipse having foci at (3, 1) and (1, 1) passes through the point (1, 3). Its eccentricity is

(A) 0.414 (B) 0.732 (C) 0.207 (D) 0.369

14. If two foci of an ellipse be (– 2, 0) and (2, 0) and its eccentricity is 2/3 then the ellipse has the

equation

(A) 5x2 + 9y

2 = 45 (B) 9x

2 + 5y

2 = 45 (C) 5x

2 + 9y

2 = 90 (D) 9x

2 + 5y

2 = 90

15. If for a conic section a focus is (– 1, 1), eccentricity = 3 and the equation of the corresponding

directrix is x – y + 3 = 0 then the equation of the conic section is

(A) 7x2 – 18xy + 7y

2 + 50 x – 50y + 77 = 0 (B) 7x

2 + 18xy + 7y

2 = 1

(C) 7x2 + 18xy + 7y

2 – 50 x + 50y + 77 = 0 (D) None of these

16. A point on the ellipse2 2

16 2

x y at a distance 2 from the centre of the ellipse has the eccentric

angle

(A)4

(B)

3

(C)

6

(D)

2

17. 'PP is a diameter of the ellipse 2 2 2 2 2 2b x a y a b such that 2

'PP is the AM of the squares of

the major and minor axes. Then the slope of 'PP is

(A)b

a (B)

a

b (C)

4

(D)

3

18. The line 3x + 5y = k is a tangent to the ellipse 2 216 25 400x y if k is

(A) 5 (B) 15 (C) 25 (D) 10

19. The line px + qy = r touches the hyperbola 2 2 2 2 2 2b x a y a b if

(A) 2 2 2 2 2a p b q r (B) 2 2 2 2 2a p b q r

(C) 2 2 2 2 2a q b p r (D) 2 2 2 2 2a q b p r

20. If the tangents from the point , 3 to the ellipse2 2

9 4

x y = 1 are at right angles then is

(A) 1 (B) 3 (C) 2 (D) None of these

21. A point on the ellipse x2 + 3y

2 = 9, where the tangent is parallel to the line y – x = 0 is

(A) 3, 2 (B)3 3 3

,2 2

(C)3 3 3

,2 2

(D) 3, 2

22. If the tangent to the ellipse x2 + 4y

2 = 16 at the point ‘ ’ is a normal to the circle

2 2 8 4 0x y x y then is equal to

(A)2

(B)

4

(C)

3

(D)

4

23. Find a so that distance between (– 2, 1, – 3) and (a, 3, – 6) be 7 units.

(A) – 4 (B) – 8 (C) 8 (D) 5



24. Determine the point in XY-plane which is equidistant from the points A(1, – 1, 0), B(2, 1, 2) and

C(3, 2, – 1).

(A) (3/2, 1, 0) (B) (– 4, 0, 0) (C) (3, – 2, 5) (D) (– 2/5, 1, – 3/7)

25. Find the equation of the common tangent in first quadrant to the circle 2 2 16x y and the ellipse2 2

125 4

x y .

(A) 12 7 7

43

x y (B) 1

7 3

x y (C) 1

3 5 7 11

x y (D) 3x + 5y = 7

26. Let P be a point on the ellipse2 2

2 21,0

x yb a

a b . Let the line parallel to y-axis passing through

P meet the circle x2 + y

2 = a

2 at the point Q such that P and Q are on the same side of x-axis. For

two positive real numbers r and s, find the locus of the point R on PQ such that PR : RQ = r : s as

P varies over the ellipse.

(A)

222

221

2

y r sx

a a b

(B)

222

21

y rsbx

a ar bs

(C)

2 2

21

1

bx y a

br s

(D)

222

221

y r sx

a ar bs

27. Find the equation of the hyperbola whose one directrix is 2x + y = 1 and the corresponding focus

is (1, 2) and eccentricity is 3 .

(A) 2 29 16 72 96 144 0x y x y (B) 2 27 2 12 2 14 22 0x y xy x y

(C) 2 23 5 89 29 17 0x y x y (D) 2 25 9 17 15 21 0x y xy x y

28. If sec , tana b and sec , tana b are the end points of a focal chord of the hyperbola

2 2

2 21

x y

a b , then evaluate

1tan tan

2 2 1

e

e

(A) – 1 (B) 0 (C) 2 (D) 9

29. Let P sec , b tana and Q sec , b tana where2

, be two points on the hyperbola

2 2

2 21

x y

a b . If (h, k) is the point of intersection of the normals at P and Q, then k is equal to

(A)2 2a b

a

(B)

2 2a b

a

(C)

2 2a b

b

(D)

2 2a b

b

30. If x = 9 is the chord of contact of the hyperbola x2 – y

2 = 9, then the equation of the

corresponding pair of tangents is

(A) 2 29 8 18 9 0x y x (B) 2 29 8 18 9 0x y x

(C) 2 29 8 18 9 0x y x (D) 2 29 8 18 9 0x y x

31. A hyperbola, having transverse axis of length 2sin , is confocal with the ellipse 3x2 + 4y

2 = 12.

Then its equation is

(A)2 2 2 2cos sec 1x ec y (B)

2 2 2 2cosec 1x sec y

(C)2 2 2 2sin cos 1x y (D)

2 2 2 2cos sin 1x y



32. Consider a branch of the hyperbola 2 22 2 2 4 2 6 0x y x y with vertex at the point A. Let

B be one of the end points of the latus rectum. If C is the focus of the hyperbola nearest to the

point A, then the area of the triangle ABC is

(A)2

13

(B)3

12 (C)

21

3 (D)

31

2

33. Let a and b be non-zero real numbers. Then the equation 2 2 2 25 6 0ax by c x xy y

represents

(A) Four straight lines when c = 0 and a, b are of same sign

(B) Two straight lines and a circle when a = b and c is of sign opposite to that of a

(C) Two straight lines and a hyperbola when a and b are the same sign and c is of sign opposite

to that of a

(D) A circle and an ellipse when a and b are of same sign and c is of sign opposite to that of a.

34. If any point on a hyperbola has the coordinates 5tan ,4sec then the eccentricity of the

hyperbola is

(A) 1.222 (B) 1.280 (C) 1.562 (D) 1.600

35. The foci of the ellipse2 2

21

16

x y

b and the hyperbola

2 2 1

144 81 25

x y coincide. Then the value of 2b

is

(A) 5 (B) 7 (C) 9 (D) 1

36. The area (in sq. units) of the quadrilateral formed by tangents at the end points of latus recta of

the ellipse2 2

19 5

x y is

(A) 6.75 (B) 9.00 (C) 13.5 (D) 27

37. If y = x and 3y + 2x = 0 are the equations of a pair of conjugate diameters of the ellipse2 2

2 21

x y

a b then its eccentricity is

(A) 0.5 (B) 0.333 (C) 0.577 (D) 0.866

38. Find the distance between the points P(– 3, 7, 2) and Q(2, 4, – 1).

(A) 6.855 (B) 6.557 (C) 6.403 (D) 6.244

39. If the eccentricity of a hyperbola2 2

21

9

x y

b , which passes through (k, 2), is

13

3, then the value

of k2 is

(A) 18 (B) 8 (C) 1 (D) 2

40. The equation of the hyperbola whose foci are (– 2, 0) and (2, 0) and eccentricity is 2 is given by

(A)2 23 3x y (B)

2 23 3x y (C)2 23 3x y (D)

2 23 3x y

41. For the hyperbola2 2

2 21

cos

x y

sin , which of the following remains constant when varies =

(A) Abscissae of vertices (B) Abscissae of foci

(C) Eccentricity (D) Directrix

42. The locus of a point ,P moving under the condition that the line y = x is a tangent to

the hyperbola2 2

2 21

x y

a b is

(A) An ellipse (B) A circle (C) A parabola (D) A hyperbola



43. Find eccentricity of a hyperbola passing through (3, 0) and 3 2, 2

(A) 4 (B)13

5 (C) 1.5 (D)

13

3

44. A common tangent to the conics2 6x y and

2 22 4 9x y is

(A) x – y = 3/2 (B) x + y = 1 (C) x + y = 9/2 (D) x – y = 1

45. A tangent to the hyperbola2 2

14 2

x y meets x-axis at P and y-axis at Q. Lines PR and QR are

drawn such that OPRQ is a rectangle (Where O is the origin). Then R lies on

(A)2 2

4 21

x y (B)

2 2

2 41

x y (C)

2 2

2 41

x y (D)

2 2

4 21

x y

46. P, Q and R are three points on the hyperbola xy = c2. If PQ is parallel to the normal at R, then

the angle subtended by PQ at R is

(A) / 2 (B) / 6 (C) 1cos 2 / 3c (D) 1tan 2 / 3c

47. A hyperbola whose transverse axis is along the major axis of the conic,2 2

43 4

x y and has

vertices at the foci of this conic. If the eccentricity of the hyperbola is 3/2, then which of the

following points does NOT lie on it?

(A) 5, 2 2 (B) (0, 2) (C) 5,2 3 (D) 10,2 3

48. If P, Q, R and S are the points of intersection of a circle and a rectangular hyperbola and if PQ

passes through the centre of hyperbola, then RS passes through the

(A) Centre of hyperbola (B) centre of circle

(C) Circumference of circle (D) None of these

49. A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. Then the locus of

the point which divides the line segment between these two points in the ratio 1 : 2, is

(A)2 216 10 2 0x y xy (B)

2 216 2 10 0x y xy

(C)2 216 8 19 0x y xy (D)

2 216 10 2 0x y xy

50. A hyperbola passes through the point 2, 3P and has foci at 2,0 . Then the tangent to this

hyperbola at P also passes through the point

(A) 2, 3 (B) 3 2,2 3 (C) 2 2,3 3 (D) 3, 2

51. The locus of the point of intersection of the straight lines, tx – 2y – 3t = 0,

x – 2ty + 3 = 0 t is:

(A) An ellipse with eccentricity2

5

(B) An ellipse with the length of major axis 6

(C) A hyperbola with eccentricity 5

(D) A hyperbola with the length of conjugate axis 3

52. The perpendicular focal chords of a rectangular hyperbola are

(A) In the ratio 1 : 2 (B) In the ratio 2 : 1 (C) Equal (D) None of these

53. PQ is the ordinate of any point on the hyperbola2 2

2 21

x y

a b , if QR is perpendicular to 'A P ,

where 'AA is transverse axis, then AR/RP =

(A) /a b (B) a/b (C) 2 2/a b (D) None of these



54. If a tangent to the hyperbola2 2

2 21

x y

a b cuts the ellipse

2 2

2 21

x y

a b at P and Q, then the locus of

mid-point of PQ is

(A)2 2 2 2

2 2 2 2

x y x y

a b a b

(B)

22 2 2 2

2 2 2 2

x y x y

a b a b

(C)2 2 2 2

4 4 2 2

x y x y

a b a b

(D)

22 2 2 2

4 4 2 2

x y x y

a b a b

55. For a hyperbola, if the focal distance of any point and the perpendicular from centre upon the

tangent at it meet on a circle whose centre is focus, then its radius is equal to

(A) Semi-conjugate axis (B) Conjugate axis

(C) Semi-transverse axis (D) Transverse axis

56. An ellipse passes through the foci of the hyperbola, 2 29 4 36x y and its major and minor axes

lie along the transverse and conjugate axes of the hyperbola respectively. If the product of

eccentricities of the two conics is ½, then which of the following points does not lie on the

ellipse?

(A)13

, 62

(B)39

, 32

(C)1 3

13,2 2

(D) 13,0

57. An ellipse intersects the hyperbola2 22 2 1x y orthogonally. The eccentricity of the ellipse is

reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinates, then

(A) Equation of the ellipse is2 22 2x y (B) The foci of ellipse are

(C) Equation of the ellipse is2 22 4x y (D) The foci of ellipse are 2,0

58. If be the angle between the asymptotes of hyperbola2 2

2 21

x y

a b then cos / 2

(A) e (B) 1/e (C) e + 1

e– 1 (D) e/2

59. If 1e and 2e be the eccentricities of hyperbola and its conjugate. then 2 2

1 21 / 1 /e e

(A) 0.176 (B) 0.25 (C) 1.00 (D) 4.00

60. The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of

its conjugate axis is equal to half to the distance between its foci, is

(A) 1.154 (B) 1.732 (C) 1.333 (D) 2.309

61. Let a and b respectively be the semi-transverse and semi-conjugate axes of a hyperbola whose

eccentricity satisfies the equation29 18 5 0e e . If S(5, 0) is a focus and 5x = 9 is the

corresponding directrix of this hyperbola, then2 2a b is equal to

(A) – 7 (B) – 5 (C) 5 (D) 7

62. The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola2 2

14 5

x y ,

meet x-axis and y-axis at A and B respectively. Then 2 2

OA OB , where O is the origin,

equals:

(A) – 2.222 (B) 1.777 (C) 4.00 (D) – 1.333

63. If the foci of the ellipse2 2

21

16

x y

b coincide with the foci of the hyperbola

2 2 1

144 81 25

x y , then b

2

is equal to

(A) 8 (B) 10 (C) 7 (D) 9

2,0



64. The normal to the rectangular hyperbola xy = c2 at the point 1' 't meets the curve again at the point

2' 't . The value of 3

1 2.t t is

(A) 1 (B) c (C) – c (D) – 1

65. Number of circles drawn through two points is

(A) One (B) Two (C) Three (D) Infinite

66. Find the equation of the circle passing through (– 2, 14) and concentric with the circle 2 2x y 6x 4y 12 0 .

(A) 2 2x y 6x 4y 156 0 (B) 2 2x y 6x 4y 156 0

(C) 2 2x y 6x 4y 156 0 (D) 2 2x y 6x 4y 156 0

67. For the circle 2 2ax y bx dy 2 0 centre is (1, 2) then 2b + 3d + 4a =

(A) – 12 (B) 16 (C) 8 (D) – 8

68. If the two circles 2 2x y 2gx c 0 and 2 2x y 2fx c 0 have equal radius then locus of (g, f) is

(A) 2 2 2x y c (B) 2 2x y 2c (C) 2 2x y c (D) 2 2 2x y 2c

69. The diameters of a circle are along 2x + y – 7 = 0 and x + 3y – 11 = 0. Then the equation of this

circle which also passes through (5, 7) is

(A) 2 2x y 4x 6y 16 0 (B) 2 2x y 4x 6y 20 0

(C) 2 2x y 4x 6y 12 0 (D) 2 2x y 4x 6y 12 0

70. The shortest distance from (– 2, 14) to the circle 2 2x y 6x 4y 12 0 is

(A) 4 (B) 6 (C) 8 (D) 10

71. The least distance of the line 8x – 4y + 73 = 0 from the circle 2 216x 16y 48x 8y 43 0 is

(A) 5 / 2 (B) 2 5 (C) 3 5 (D) 4 5

72. The equation of the tangents to the circle 2 2x y 25 with slope 2 is

(A) y 2x 5 (B) y 2x 2 5 (D) y 2x 3 5 (D) y 2x 5 5

73. If the line x y touch the circle 2 2x y 1 then 2 is

(A) 1 (B) 2 (C) 1/2 (D) 3/2

74. The normal at (1, 1) to the circle 2 2x y 4x 6y 4 0 is

(A) 4x + 3y = 7 (B) 4x + y = 5 (C) x + y = 2 (D) 4x – y = 5

75. The length of the tangent from (1, 1) to the circle 2 22x 2y 5x 3y 1 0 is

(A) 13 / 2 (B) 3 (C) 2 (D) 1

76. A chord of length 24 units is at a distance of 5 units from the centre of a circle then its radius is

(A) 5 (B) 12 (C) 13 (D) 10

77. The equation of the circle with centre at (4, 3) and touching the line 5x – 12y – 10 = 0 is

(A) 2 2x y 4x 6y 4 0 (B) 2 2x y 6x 8y 16 0

(C) 2 2x y 8x 6y 21 0 (D) 2 2x y 24x 10y 144 0

78. The equation of the image of the circle 2 2x y 6x 4y 12 0 by the mirror x + y – 1 = 0 is

(A) 2 2x y 2x 4y 4 0 (B) 2 2x y 2x 4y 4 0

(C) 2 2x y 2x 4y 4 0 (D) 2 2x y 2x 4y 4 0

79. Equation of tangent to circle 2 2x y 6x 2y 90 0 drawn from centre of the circle 2 2x y 6x 14y 23 0 is

(A) 3x + 4y = 37 (B) 4x – 3y = 73 (C) 4x + 3y = 37 (D) 3x – 4y = 37

80. If the tangent at the point P on the circle 2 2x y 6x 6y 2 meets the straight line 5x – 2y + 6 = 0

at a point Q on the y-axis then the length of PQ is

(A) 4 (B) 2 5 (C) 5 (D) 3 5



81. Area of circle touching both the lines 3x + 4y = 3 and 3x + 4y = 18 is

(A)4

9

(B)

9

(C)

9

4

(D)

25

4

82. If origin be shifted to point (1, 2) by parallel translation of axis. Then new equation of circle 2 2x y 2x 4y 20 0 is

(A) 2 2

x 1 y 2 5 (B) 2 2x y 5

(C) 2 2x y 25 (D) 2 2

x 1 y 2 2 x 1 4 y 2 20 0

83. If y = 2x is a chord of circle 2 2x y 10x 0 . Then the equation of the circle with this chord as a

diameter is

(A) 2 2x y 2x 4y 0 (B) 2 2x y 2x 4y 0

(C) 2 2x y 2x 4y 0 (D) 2 2x y 2x 4y 0

PHYSICS

Syllabus: HEAT, HYDROSTATICS AND UNITS & MEASUREMENTS:– 1. THERMAL PROPERTIES, 2. THERMODYNAMICS, 3. KINETICTHEORY OF GASES, 4. ELASTICITY, HYDROSTATICS AND DYNAMICS (Including surface tension and viscosity) 5. UNITS,MEASUREMENTS AND ERRORS.

1. When temperature of a black body increases, it is observed that the wavelength corresponding

to maximum energy changes from 0.26 m to 0.13 m . The ratio of the emissive powers of the

body at the respective temperature is

(A) 16/1 (B) 4/1 (C) 1/4 (D) 1/16

2. A copper block of mass 4 kg is heated in a furnace to a temperature 425°C and then placed on a

large ice block. The mass of ice that will melt in this process will be 0.5 x, where x is (specific

heat copper = 500 J/kg°C– 1

and heat of fusion of ice = 336 kJ/kg)

(A) 1 (B) 2 (C) 3 (D) 5

3. If temperature of the sun were to increase from T and 2T and its radius from R to 2R, then how

many times the radiant energy will be received on the earth in form of 2n. Where n is?

(A) 2 (B) 4 (C) 5 (D) 6

4. Total energy emitted by a perfectly black body is directly proportional to Tn (T is temperature),

where n is

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

5. An object is cooled from 75°C to 65°C in two minutes in a room temperature at 30°C. Then

time taken to cool the same object from 55°C to 45°C in the same room (in minute) is

(A) 7 (B) 6 (C) 5 (D) 4

6. The temperature at which centigrade and Fahrenheit scales give same reading is – 10 x, where x

is

(A) 4 (B) 5 (C) 3 (D) 2

7. Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total

radiant power, incident on Earth, at a distance r from the Sun. (earth radius = r0)

(A)2 4

2

R T

r

(B)

2 2 4

0

2

4 r R T

r

(C)

2 2 4

0

2

r R T

r

(D)

2 2 4

0

2

r R T

4 r



8. A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The

variation of temperature along the length x of the bar from its hot end is best described by

which of the following figures

(A) (B) (C) (D)

9. If a piece of metal is heated to temperature and then allowed to cool in a room which is at

temperature 0 , the graph between the temperature T of the metal and time t will be closest to

(A) (B) (C) (D)

10. Two rectangular blocks, having identical dimensions, can be arranged either in configuration I

or in configuration II as shown in the figure, On of the blocks has thermal conductivity k and

the other 2k. The temperature difference between the ends along the x-axis is the same in both

the configurations. It takes 9s to transport a certain amount of heat from the hot end to the cold

end in the configuration I. The time to transport the same amount of heat in the configuration II

is :

(A) 2.0 s (B) 3.0 s (C) 4.5 s (D) 6.0 s

11. The temperature of a body is increased from 27°C to 127°C. The radiation emitted by it

increased by a factor of

(A) 256/81 (B) 15/9 (C) 4/5 (D) 12/27

12. On investigation of light from three different stars A , B and C , it was found that in the

spectrum of A the intensity of red colour is maximum, in B the intensity of blue colour is

maximum and in C the intensity of yellow colour is maximum. From these observations it can

be concluded that

(A) The temperature of A is maximum, B is minimum and C is intermediate

(B) The temperature of A is maximum, C is minimum and B is intermediate

(C) The temperature of B is maximum, A is minimum and C is intermediate

(D) The temperature of C is maximum, B is minimum and A is intermediate

13. Certain substances emit only the wavelength 1 2 3 4, , , when it is a high temperature. When

this substance is at a cold temperature it will absorb only the following wavelength

(A) 1 (B) 2 (C) 1 & 2 (D) 1 2 3, , & 4

14. Ice starts forming in a lake with water at 0°C when the atmospheric temperature is – 10°C. If

the time taken for the first 1 cm of ice to be formed is 7 hrs, then the time taken for the

thickness of ice to change from 1 cm to 2 cm is

(A) 7 hours (B) 14 hours (C) 21 hours (D) 3.5 hours

SECTION-II

(Numerical Value Answer Type)



15. A metal rod AB of length 10 x has its one end A in ice at 0ºC and the other end B in water at

100ºC. If a point P on the rod is maintained at 400ºC, then it is found that equal amounts of

water and ice evaporate and melt per unit time. The latent heat of evaporation of water is 540

cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of x from the

ice end A, find the value of .

[Neglect any heat loss to the surrounding]

(A) 9 (B) 8 (C) 7 (D) 6

16. Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperature T1 and T2

respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of

B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total

energy radiated by A to that of B ?

(A) 8 (B) 5 (C) 9 (D) 6

17. Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B

and A emits 104 times the power emitted from B. The ratio A

B

for their wavelengths A and

B at which the peaks occur in their respective radiation curves is:

(A) 4 (B) 2 (C) 3 (D) 6

18. A rod of length L is fixed between two rigid supports and supplied heat to raise its temperature

T. If is the coefficient of volume expansion of the wire and y is young’s modulus of the wire

then the elastic potential energy density stored in the wire is

(A) 2 2

2

T y (B)

2 2 3

3

T y (C)

2 2

18

T

y

(D)

2 2

18

T y

19. The limbs of a manometer consist of uniform capillary tubes of radii 1.4x 10-3

m and

7.2 x10-4

m. The liquid in the tubes have density 1000 kg/ m3 and surface tension 0.072 N/m.

The level of liquid in the narrower tube stands 0.2 m above that in the broader tube. If the angle

of contact is zero, the pressure difference between them is (g = 9.8 m/s2)

(A) 1.1 x 103 Pa (B)1.863 x10

3 Pa (C) 1.96x 10

3Pa (D) 9.8 x 10

3 Pa

20. Two different liquid films of surface tensions T1 and T2 are held between three concentric

wires of radii a, b and c as shown in the figure. The outermost and the innermost wires are

fixed. Neglecting gravity, the tension in the middle wire is

a

T1

b

c

T2

(A) (T1 – T2)b (B) 1 2

aT c T b

b c

(C) 2(T1 – T2)b (D) (T1c – T2b)

21. A soap bubble has a thickness of 100nm and a refractive index of 1.35. What is the wavelength

of the colour does the bubble appear to be at the point by reflection on its surface closest to an

observer when it is illuminated by the white light?

22. A uniform rope is rotated about an axis perpendicular to length and passing through one of its

end. The ratio of stresses at end near the axis of rotation and middle point is (neglect gravity)

(A) 2:1 (B) 3:2 (C) 4:3 (D) 5:4



23. Consider the following diagram in which a capillary tube of radius 1mm is

dipped into a fluid whose density 3800 /kg m and surface tension

0.1 /N m .The gauge pressure required in the tube to blow a hemisphere

bubble at the dipped end is

(A) 2800 /N m (B) 21000 /N m

(C) 21200 /N m (D) 21600 /N m

24. In a capillary tube of radius ‘r’, neglecting the meniscus weight, the maximum height up to

which a liquid can be filled without any dripping is [density of liquid is , surface tension of

fluid is T and contact angle is 090 ]

(A) 4T

gr (B)

2T

gr (C)

T

gr (D)

2

T

gr

25. A ball of mass ‘m’ and density is being released inside a fluid of density 2

and coefficient

of viscosity .Find the net force on the ball when speed achieved by ball is 60% of the terminal

speed.

(A) 0.6 mg (2) mg (C) 0.4 mg (D) 0.2 mg

26. A cylindrical container of cross sectional area 2100cm is containing water upto a height of 2m.

Now a cork ball of 5 kg is put into the container and it floats in equilibrium. If a tiny hole is

made on vertical walls very close to base then the velocity of efflux will be (in m/s).

(A) 2 10 (B) 5 (C) 5 2 (D) 10

27. A body is rotated in a circular path by means of a wire, which fails at angular velocity 0. If the

wire is cut into two equal pieces and the same body is rotated by means of the two pieces

together, then the failure takes place at angular velocity . The ratio 0

is (neglect gravity)

(A) 1 (B) 2 (C) 2 (D) 2 2

28. A uniform rope of mass m and length L is hanged freely from stationary ceiling. If the cross

sectional area of rope is A and Young’s modulus Y, then net elongation in the rope due to its

own weight

(A) mgL

AY (B)

2

mgL

AY (C)

3

mgL

AY (D)

4

mgL

AY

29. Two square plates of side length ‘ a ’ are stick together by putting a thin layer of liquid between

them having thickness t. If liquid wets the plates completely and surface tension is S then the

force required to pull them apart is

(A) 2

4

Sa

t (B)

2

2

Sa

t (C)

2Sa

t (D)

22Sa

t

30. Two wires of the same material and same mass are stretched by same force. Their lengths are in

the ratio 2: 3. Then their elongations are in the ratio

(A) 3 : 2 (B) 2 : 3 (C) 4 : 9 (D) 9 : 4

31. The work done in stretching a wire by 0.1 mm is 4 J. The work done in stretching another wire

of same material, but with double the radius and half the length by 0.1mm is

(A) 16 J (B) 32 J (C) 64 J (D) 128 J

32. The rubber cord catapult has cross-sectional are 6 210 m and total un stretched length 0.1m. It is

stretched to 0.12 m and then released to project a stone of mass 35 10 kg . If young’s modular

of rubber is 0.5 Gpa, the velocity projection of the stone is

(A) 0.5 m/s (B) 0.1 m/s (C) 2 m/s (D) 20 m/s



33. How much work will be done in increasing the diameter of a soap bubble from 2 cm to 5cm?

Surface tension of soap solution is 23 10 N/m.

(A) 48.96 10 J (B) 43.96 10 J (C) 40.96 10 J (D) 410 J

34. The following 4 wires are made of the same material subjected to same force. Arrange them

with their elongations in ascending order

(1) l = 50 cm and r = 0.5 mm (2) l = 100 cm and r = 1 mm

(3) l= 200 cm and r = 2 mm (4) l = 300 cm and r = 3 mm

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

35. Liquid is filled in a vessel of square base (2m x 2m) up to a height of 2 m and the vessel is tilted

from the horizontal at 030 as shown.

Find the velocity of efflux if liquid does not spills out?

(A) 3.2 m/s (B) 4.96 m/s (C) 5.6 m/s (D) 2.68 m/s

36. A tank is filled with a liquid up to a height H. a small hole is made at the bottom of this tank.

Let 1t be the time taken to empty first half of the tank and 2t the time taken to empty the rest

half of the tank. Then find 1

2

t

t.

(A) 0.414 (B) 0.82 (C) 0.2 (D) 1.6

37. In a tank, having a large base area a liquid of density 1200 3/kg m is filled up to a height 5m is

placed on a platform. The platform is moving up with an acceleration 5 2/m s . A very small

hole is made in the tank at a height of 2 m from the bottom. Find the distance of the point

where the liquid falls on the platform w.r.to the edge of the tank. (g = 10 2/m s )

(A) 4.9 m (B) 9.8 m (C) 19.6 m (4) 29.4 m

38. A wire of length L and cross-section A is made of material of Young’s modulus Y. It is

stretched by an amount x, the work done is

(A) 2

YxA

L (B)

2

2

Yx A

L (C)

2Yx A

L (D)

22Yx A

L

39. A uniform bar of square cross-section is lying along a

frictionless horizontal surface. A horizontal force is

applied to pull it from one of its ends then

(A) The bar is under same stress throughout its length

(B) The bar is not under any stress because force has been applied only at one end

(C) The bar simply moves without any stress in it

(D) The stress developed reduces to zero at the end of the bar where no force is

Applied

40. A steel wire with cross section 3 cm2 has elastic limit 82.4 10 Pa . The maximum upward

acceleration that can be given to a 1200 kg elevator suppoted by this cable if the stress is not to

exceed 1/ 3rd of the elastic limit is 210 /g m s

(A) 29ms (B) 210ms (C) 211ms (D) 212ms

F



41. The length of a metal wire is 1l when the tension in it is 1 2&T l when the tension is 2T . The

natural length of the wire is

(A) 1 2 2 1

2 1

l T l T

T T

(B) 1 2 2 1

1 2

l T l T

T T

(C) 1 2 2 1

1 2

l T l T

T T

(D) 1 1 2 2

1 2

l T l T

T T

42. A cube with a mass m = 20 g wettable by water floats on the surface of water. Each side of the

cube has length l = 3 cm. The angle of contact between water and glass is zero degree and the

surface tension of the water is 7.5 × 10–2

N/m. The distance between the lower face of the cube

and the surface of the water is

(A) 20/22 cm (B)2.222 cm (C) 2.322 cm (D)2.434 cm

43. Two soap bubbles of same soap solution touch each other and are in equilibrium. One soap

bubble has radius twice that of the other. Neglecting the effect of gravity, the angle of contact

between them is

(A) 060 (B) 090 (C) 0120 (D) can’t be determined.

44. In the Searle’s experiment of determination of Young’s modulus of a wire, the quantity which

should be measured with greater precision is

(A) Diameter of the wire (B) length of the wire

(C) Deflection of loaded wire (D) Loading weights

45. A 2m long light metal rod AB is suspended from the ceiling horizontally by means of two

vertical wires of equal length tied to its ends. One wire is of brass and has cross section of 4 20.2 10 m and the other is of steel with 4 20.1 10 m cross section. In order to have equal stress

in the two wires, a weight is hang from the rod. The position of the weight along the rod from

end A should be.

(A) 66.6 cm (B) 133 cm (C) 44.4 cm (D)155.6 cm

46. External forces acting on a rod of length L, cross - sectional area A and Young’s modulus Y are

as shown in the figure. Choose the correct alternative.

(A) There will be no change in length of rod.

(B) The net change in length of rod is 2FL

AY

(C) The net change in length of rod is 2

FL

AY

(D) The net change in length of rod is FL

AY

47. A liquid drop is sandwiched between two plates as shown. Consider the contact angle to be

180 . The separation between the plates is H (<<R). What is excess pressure in the drop?

(Neglect the effect of gravity. the shape of the drop is like a circular tablet. Take surface tension

as S.

(A) 2S/H + S/R (B) 2S/R (C) S/H (D) S/H + S/R



48. A uniform metal wire of cross sectional radius r and Young’s modulus Y is in the form of a ring

of radius R and it is rotated about a vertical axis through its center at an angular speed of .

The change in radius R of the ring due to ratation would be ?

(A) 2 2

2 2

M R

r Y

(B)

2 2

2 22

M R

r Y

(C)

2 2

2 2

M r

r Y

(D)

2 2

2 22

M r

r Y

49. The change in volume of a cylinder of length 65cm when subjected to a compressive force of

1000N over the end face would be? The Young’s modulus and Poisson’s ratio of the material of

the cylinder are 130x109Pa and 0.34 respectively.

(A) 1.0mm3 (B) 1.6mm3 (C) 2.5mm3 (D) 3.2mm3

50. The shearing stress on the area PQ is.

(A) cosA

F

(B) sin

F

A

(C)

cosF

A

(D) A

F

where A = given area of the plane PQ of the wire.

51. Two parallel glass plates separated by a small gap x are dipped in a liquid of surface tension T,

density p. if the angle of contact is then the height upto which the liquid rises is.

(A) h=0 (B) 2 cosT

x g

(C)

2 cosTh

x

(D)

cos

xTh

gh

52. A smooth spherical ball of radius 1 cm and density 4x103 kg/m

3 is dropped gently in a large

container containing viscous liquid of density 2x103 kg/m

3,n=0.1 N-s/m

2. The distance moved

by the ball in 1-0.1 sec after it attains terminal velocity is.

(A) 4

5 m up (B)

4

9m up (C)

2

3m down (D)

4

9m down

53. A steel wire of length 4 m and diameter 5 mm is stretched by 5 kg-wt. Find the increase in its

length, if the Young’s modulus of steel of wire is 2.4 × 1012

dyne/cm2.

(A) 1.0041 cm. (B) 0.0041 cm. (C) 4.1 cm. (D) 1.2 cm.

54. A uniform elastic rod of cross section are A, natural length L and Youngs modulus Y is placed

on a smooth horizontal surface. Now two horizontal forces (of magnitude F and 3F) directed

along the length of rod and in opposite direction act at two of its ends as shown. After the rod

has acquired steady state, the extension of the rod will be

F 3F

Elastic rod

(A)2F

LYA

(B) 4F

LYA

(C) F

LYA

(D) 3F

L2YA

55. A composite wire (uniform cross section of 5 25.5 10 m ) is made of a steel wire of length 1.5

m and a copper wire of length 2.0 m. The extension produced in this composite wire, when it is

loaded with a mass of 200 kg is 11 2

SteelY = 2×10 N / m ,

11 2 2Copper

Y =1×10 N / m ,g =10m / s (Weight of the composite wire is negligible)

(A) 0.5 mm (B)1mm (C)2 mm (D) 4 mm



56. The work done in stretching a wire by 0.1 mm is 4 J. The work done in stretching another wire

of same material, but with double the radius and half the length by 0.1mm is

(A) 16 J (B) 32 J (C) 64 J (D) None

57. A water drop is divided into 8 equal droplets. The pressure difference between the inner and

outer side of the big drop will be:

(A) Same as for smaller droplet (B) 1/2 of that for smaller droplet

(C) ¼ of that for smaller droplet (D) Twice that for smaller droplet

58. If the excess pressure inside a soap bubble is balanced by an oil column of height 2 mm, then the

surface tension of soap solution will be (r = 1 cm and density of oil = 0.8 gm/cc) (g = 9.8 m/s2)

(A) 3.9 N/m (B) 3.9 x 10-1

N/m (C) 3.9 x 10-3

N/m (D) 3.9 d/m

59. In a surface tension experiment with a capillary tube water rises 0.1m. If the same experiment is

repeated in an artificial satellite, which is revolving around the earth, water will rise in the

capillary tube up to a height of :

(A) 0.1 m (B) 0.2 m (C) 0.98 m (D) full length of tube

60. Two glass plates are separated by water. If surface tension of water is 75 dynes per cm and area

of each plate wetted by water is 8 cm2 and the distance between the plates is 0.12 mm, then the

force required to separate the two plates is

(A) 102 dynes (B) 10

4 dynes (C) 10

5 dynes (D) 10

6 dynes

61. There is a small hole in a hollow sphere. The water enters in it when it is taken to a depth of

40cm under water. The surface tension of water is 0.07 N/m. The diameter of hole is:

(A) 7mm (B) 0.07 mm (C) 0.0007mm (D) 0.7 m

62. A sphere of solid material of relative density 9 has a concentric spherical cavity, just sinks in

water. If the radius of the sphere be R, then the radius of the cavity (r) will be related to R as :

(A) 3 38

9r R (B) 3 32

3r R (C) 3 38

3r R (D) 3 32

3r R

63. If S and V are the change is surface area and volume when two soap babbles coalesce, then (

is surface tension PO is atmospheric pressure).

(A) 3P0V + 4 S = 0 (B) 4 P0V + 3 S = 0

(C) P0V + 4 S = 0 (D) 4 P0V + S = 0

64. Stress – Strain curve for the wire A and B are shown in figure. AY and BY are the young’s

modulii of wire A and B respectively, then

(A) A BY Y (B) A BY Y (C) A BY Y (D) A B2Y Y 65. A bar is subjected to equal and opposite forces as shown in the figure, PQ is plane making angle with the cross-section of the bar. If the area of cross section be ‘a’, then what is the tensile

stress on PQ?

(A) F/a (B) F cos /a (C) 2Fcos

a

(D) F/a cos

Q

P

FF



CHEMISTRY

Syllabus: FIRST YEAR PHYSICAL CHEMISTRY:– 1.ATOMIC STRUCTURE, 2. STATES OF MATTER, 3. STOICHIOMETERY, 4. THERMODYNAMICS, 5. CHEMICAL EQUILIBRIUM, 6. IONIC EQUILIBRIUM

1. Assuming that the system is at equilibrium, which of the following reactions goes most nearly

to 100% completion

(A) C(s) + H2O(g)

CO(g) + H2(g); Kc= 6.5× 10–23

(B) CO(g) + 3H2 (g)

CH4(g) + H2O(g); Kc= 0.176

(C) 2C(s) + O2(g)

2CO(g); Kc= 1 × 1016

(D) H2 (g)+ I2(g)

2HI(g); Kc= 54.5

2. An equilibrium system for the reaction between hydrogen and iodine to give hydrogen iodide at

765K in a 5 litre volume contains 0.4 mole of hydrogen, 0.4 mole of iodine and 2.4 moles of

hydrogen iodide. The equilibrium constant for the reaction is H2 + I2

2HI, is

(A) 36.0 (B) 15.0 (C) 0.067 (D) 0.028

3. The equilibrium constant of the reaction

SO2(g) + 2

1O2(g) SO3(g) is 4 × 10

–3 atm

–1/2. The equilibrium constant of the reaction

2SO3(g) 2SO2(g) + O2(g) would be

(A) 250 atm (B) 4 × 103 atm (C) 0.25 × 10

4 atm (D) 6.25 × 10

4 atm

4. The value of KP for the reaction.

2H2O(g) + 2Cl2(g) 4HCl (g) + O2(g)

is 0.03 atm at 427ºC, when the partial pressure are expressed in atmosphere, then the value of

KC for the same reaction is -

(A) 5.23 × 10–4

(B) 7.34 × 10–4

(C) 3.2 × 10–3

(D) 5.43 × 10–5

5. For the equilibrium 2NOBr(g) 2NO(g) + Br2(g), calculate the ratio P

KP , where P is the total

pressure and 2BrP =

9

P at a certain temperature -

(A) 9

1 (B)

81

1 (C)

27

1 (D)

3

1

6. 28g of N2 and 6g of H2 were mixed. At equilibrium 17g NH3 was produced. The weight of N2

and H2 at equilibrium are respectively -

(A) 11g , 0g (B) 1g , 3g (C) 14g , 3g (D) 11g , 3g

7. For the gas phase reaction

C2H4 + H2 C2H6, H = –32.7 kcal carried out in a vessel, the equilibrium concentration

of C2H4 can be increased by

(A) increasing the temperature (B) Increasing concentration of H2

(C) Decreasing temperature (D) Increasing pressure

8. In the system AB (s) A(g) + B(g) doubling the quantity of AB (s) would

(A) increase the amount of A to double its value

(B) increase the amount B to double its value

(C) increase the amount of both A & B to double their values

(D) cause no change in the amounts of A and B



9. Consider the heterogeneous equilibrium in a closed container

NH4HS (s) NH3 (g) + H2S(g)

If more NH4HS is added to the equilibrium

(A) Partial pressure of NH3 increases (B) Partial pressure of H2S increases

(C) Total pressure in the container increases (D) No effect on partial pressure of NH3 and H2S

10. For the reaction H2(g) + I2(g) 2HI(g)

KC = 66.9 at 350ºC and KC = 50.0 at 448ºC. The reaction has

(A) H = + ve (B) H = – ve

(C) H = zero (D) H = Not found the signs

11. N2 + 3H2

2NH3

1 mole N2 and 3 mole H2 are present at start in 1L flask. At equilibrium NH3 formed required

100mL of 5M HCl for neutralisation hence KC is -

(A) 3

2

)25.2()75.0(

)5.0( (B)

3

2

)5.2)(5.0(

)5.0( (C)

3)5.2()75.0(

L)5.0(

(D) none of these

12. The decomposition of N2O4 to NO2 was carried out in chloroform at 2800C. At equilibrium,

0.2 mol of N2O4 and 2 x 10-3 mole of NO2 were present in 2L of solution. The equilibrium

constant for the reaction N2O4

2NO2 is

(A) 0.01 × 10-3 (B) 2.0 x× 10-3 (C) 2.0 × 10-5 (D) .01 × 10-5

13. N2 + O2 2NO,K1

22 O2

1N

2

1

NO, K2

2NO N2 + O2, K3

NO 422 K,O2

1N

2

1

Correct relation between K1, K2 and K4 is :

(A) K1 × K3 = 1 (B) 1KK 41 (C) 1KK 23 (D) All of these

14. For the decomposition reaction

NH2COONH4 (s) 2NH3 (g) + CO2 (g) the KP = 2.9 × 10–5 atm3. The total pressure of

gases at equilibrium when 1 mol of NH2COONH4(s) was taken initially could be -

(A) 0.0194 atm (B) 0.0388 atm (C) 0.0582 atm (D) 0.0766 atm

15. A 1 litre container contains 2 moles of PCl5 initially. If at equilibrium , KC is found to be 1,

degree of dissociation of PCl5 is -

(A) 4 (B) 3 (C) 2

1 (D) 50

16. In a vessel containing SO3, SO2 and O2 at equilibrium, some helium gas is introduced so that

the total pressure increases while temperature and volume remains constant. According to Le-

chatelier principle, the dissociation of SO3

(A) Increase (C) decrease

(B) Remain unaltered (D) changes unpredictable



SECTION-II


17. Molar concentration of 96 g of O2 contained in a 2L vessel in mol/L is

18. At a certain temp. 2 22HI H I . Only 50% HI is dissociated at equilibrium. The equilibrium

constant is

19. The active mass of 64 g of HI in a two litre flask would be

20. On a given condition, the equilibrium concentration of H2, H2 and I2 are 0.80, 0.10 and 0.10

mole/litre. The equilibrium constant for the reaction H2 + I2 2HI will be

21. In a reaction A + B C + D, the concentrations of A, B, C and D (in moles/litre) are 0.5, 0.8,

0.4 and 1.0 respectively. The equilibrium constant is

22. Which of the following are Lewis acids?

(A) PH3 and BCl3 (B) AlCl3 and SiCl4

(C) PH3 and SiCl4 (D) BCl3 and AlCl3

23. 100 ml of 0.2 M H2SO4 is added to 100 ml of 0.2 M NaOH. The resulting solution will be

(A) Acidic (B) Basic (C) Neutral (D) Slightly basic

24. In the following reaction 3

2 4 4HC O aq PO aq

2 2

4 2 4HPO aq C O aq , which are the

two Bronsted bases?

(A) 2 4HC O and 3

4PO (B) 2

4HPO and 2

2 4C O

(C) 2 4HC O and 2

4HPO (D) 3

4PO and 2

2 4C O

25. The following equilibrium is established when 4HC O is dissolved in weak acid HF.

4HF HC O

4 2C O H F

Which of the following is correct set of conjugate acid base pair?

(A) HF and 4HC O (B) HF and 4C O (C) HF and

2H F (D) 4HC O and2H F

26. 10 ml of 1 M H2SO4 will completely neutralise

(A) 10 ml of 1 M NaOH solution (B) 10 ml of 2 M NaOH solution

(C) 5 ml of 2 M KOH solution (D) 5 ml of 1 M Na2CO3 solution

27. The hydrogen ion concentration in weak acid of dissociation constant Ka and concentration c is

nearly equal to

(A) aK / c (B) ac / K (C) aK c (D) aK c

28. The decomposition of 2 4N O is carried out at 280 K in chloroform. When equilibrium has been

established, 0.2 mol of 2 4N O and 2 × 10– 3

mol of 2NO are present in 2 litre solution. The

equilibrium constant for reaction 2 4N O 22NO is

(A) 1 × 10– 2

(B) 2 × 10– 3

(C) 1 × 10– 5

(D) 2 × 10– 5

29. Rate of reaction curve for equilibrium can be like: [rf = forward rate, rb = backward rate]

(A) (B) (C) (D)

t im e

ra

te



SECTION-II


30. In a chemical reaction, A + 2B 2C + D, the initial concentration of B was 1.5 times of the

concentration of A, but the equilibrium concentration of A and B were found to be equal. The

equilibrium constant (K) for the aforesaid chemical reaction is

(A) 1.4 (B) 16 (C) 1 (D) 4

31. If in the reaction 2 4N O 22NO , is that part of 2 4N O which dissociates and value of is

0.2, then the number of moles at equilibrium will be

(A) 3 (B) 1 (C) 1.2 (D) 1.4

32. Which of the following has a higher value for hK at 27°C?

(A) NaF (B) NaC (C) NaBr (D) NaI

33. A salt of weak acid and weak base undergoes

(A) Only cationic hydrolysis

(B) Only anionic hydrolysis

(C) Both cationic and anionic hydrolysis

(D) Neither cationic nor anionic hydrolysis

34. The solubility of calcium fluoride in saturated solution, if its solubility product is 3.2 × 10– 11

, is

(A) 42.0 10 M (B) 312.0 10 M (C) 40.2 10 M (D) 32.0 10 M

35. For the electrolyte of type, 2 spA B,K is given then its solubility is calculated by

(A) spK / 4 (B) sp

3K

4 (C) 3

spK (D)spK

4

36. The addition of KC to AgC decreases the solubility of AgC , because

(A) spK of AgC decreases (B) spK of AgC increases

(C) Solution becomes unsaturated (D) Ionic product exceeds the spK value

37. Calculate the hydrolysis constant of a salt of weak acid 6

aK 2 10 and of a weak base

7

bK 5 10 .

(A) 10– 4

(B) 10– 2

(C) 10– 6

(D) 10– 8

38. The pH of an aqueous solution of a slat is 10, the salt is

(A) KC (B) 4 3NH NO

(C) NaCN (D) 4 42NH SO

39. The molar solubility of 2PbI in 0.2 M 3 2Pb NO solution in terms of solubility product, spK

(A) 1/2

spK / 0.2 (B) 1/3

spK / 0.8 (C) 1/2

spK / 0.4 (D) 1/2

spK / 0.8

40. At 25°C, the spK value of 3

Fe OH in aqueous solution is 3.8 × 10– 38

. The solubility of 3Fe ions

will increase when

(A) Hp is increased (B) Hp is 7 (C) Hp is decreased (D) Hp = 14

SECTION-II


41. Solubility product constant of a sparingly soluble salt MC is 4 × 10– 12

at 25°C. Also, at 25°C,

solubility of 2MC in an aqueous solution of 2CaC is 4 × 10–10

times less compared to its

solubility in pure water. Hence, concentration (molarity) of NaC solution is

(A) 0.01 (B) 3 (C) 4 (D) 5



42. Ksp of 2

M OH is 5 × 10– 16

at 25°C. The pH of its saturated solution at 25°C is

(A) 3 (B) 7 (C) 5 (D) 9

43. For the reaction,2 2H (g) I (g) 2HI(g), the equilibrium constant Kp changes with

(A) total pressure (B) catalyst

(B) the amounts of H2 and I2 present (D) temperature

44. The equilibrium constant, K for the reaction2 22HI(g) H (g) I (g) at room temperature is

2.85 and that at 698 K, it is 1.4 × 10–2

.

This implies that:

(A) HI is exothermic compound (B) HI is very stable at room temperature

(C) HI is relatively less stable than H2 and I2 (D) HI is resonance stabilised

45. A and B are gaseous substances which react reversibly to give two gaseous substances C and D,

accompanied by the liberation of heat. When the reaction reaches equilibrium, it is observed

that p cK K . The equilibrium cannot be disturbed by

(A) adding A (B) adding D

(C) raising the temperature (D) increasing the pressure

46. K1 and K2 are equilibrium constant for reactions (1) and (2)

2 2N (g) O (g) 2NO(g) ......(1)

2 2

1 1NO(g) N (g) O (g)

2 2 ......(2)

Then

(A)

2

1

2

1K

K

(B) 2

1 2K K (C) 1

2

1K

K (D) 0

1 2K (K )

47. For the gas phase reaction2 22NO N O , H 43.5 kcal mol

–1 which one of the

statement below is true for2 2N (g) O (g) 2NO(g)

(A) K is independent of T (B) K increases as T decreases

(C) K decreases as T decreases (D) K varies with the addition of NO

48. According to Le-Chatelier’s principle, adding heat to a solid and liquid in equilibrium will

cause the

(A) temperature to increase (B) temperature to decrease

(C) amount of liquid to decrease (D) amount of solid to decrease

49. The reaction, 2 2 2 2SO Cl SO Cl is exothermic and reversible. A mixture of SO2(g), Cl2 (g)

and 2 2SO Cl ( )l is at equilibrium in a closed container. Now a certain quantity of extra SO2 is

introduced into the container, the volume remaining the same. Which of the following is/are

true?

(A) the pressure inside the container will not change

(B) the temperature will not change

(C) the temperature will increase

(D) the temperature will decrease



50. The equilibrium constant for the reaction,2 2N (g) O (g) 2NO(g) is

44 10 at 2000 K. In

presence of a catalyst, equilibrium is attained ten times faster. Therefore, the equilibrium

constant, in presence of the catalyst, at 2000 K is:

(A) 440 10 (B)

44 10

(C)34 10 (D) difficult to compute without more data

51. Consider the reaction5 3 2PCl (g) PCl (g) Cl (g) in a closed container at equilibrium. At a

fixed temperature what will be the effect of addition of more PCl5 on the equilibrium

concentration of Cl2(g)?

(A) it decreases (B) it increases

(C) it remains unaffected (D) it cannot be predicted without the value of Kp

52. The standard state Gibb’s free energy change for the isomerisation reaction cis-2-pentene

trans-2-pentene is –3.67 kJ mol–1

at 400 K. If more trans-2-pentene is added to the reaction vessel

(A) more cis-2-pentene is formed (B) Equilibrium shifts in the forward direction

(C) equilibrium remains unaffected (D) more trans-2-pentene is produced

53. The following equilibria are given

2 2 3 1N 3H 2NH ,K

2 2 2N O 2NO,K

2 2 2 3

1H O H O,K

2

The equilibrium constant of the reaction

3 2 2

52NH O 2NO 3H O

2

in terms of K1, K2 and K3 is

(A) 1 2 3K K K (B) 1 2 3K K / K (C) 2

1 3 2K K / K (D) 3

2 3 1K K / K

54. At a given temperature, the equilibrium constant for the reaction,

5 3 2PCl (g) PCl (g) Cl (g) is 2.4 × 10–3

. At the same temperature the equilibrium constant

for the reaction, 3 2 5PCl (g) Cl (g) PCl (g) will be:

(A) 2.4 × 103 (B) 4.2 × 10

2 (C) – 2.4 × 10

–3 (D) 4.8 × 10

–2

55. XY2 dissociates as 2XY (g) XY(g) Y(g) When the initial pressure of XY2 is 600 mm Hg,

the total equilibrium pressure is 800 mm Hg. Calculate Kp for the reaction assuming that the

volume of the system remains unchanged.

(A) 50 (B) 100 (C) 166.6 (D) 400.0

56. A reaction is A + B C + D. Initially we start with equal concentrations of A and B. At

equilibrium we find that the moles of C is two times of A. What is the equilibrium constant of

the reaction?

(A) 1/4 (B) 1/2 (C) 4 (D) 2

57. If Kp for a reaction A(g) 2B(g) 3C(g) D(g) is 0.05 atm at 1000 K. Its Kc in terms of R

will be

(A) 20000 R (B) 0.02 R (C) 5 × 10–5

R (D) 55 10

R



58. On mixing equal volumes of two buffer solutions of pH value 3 and 4, the pH of the resultant

solution will be (approx)

(A) 3.3 (B) 3.5 (C) 4.7 (D) 5.3

59. 0.365g of HCl gas was passed through 100 cm3 of 0.2 M NaOH solution. The pH of the

resulting solution would be

(A) 13 (B) 6 (C) 8 (D) 9

60. 100 mL of a solution contains 0.1 M NH4OH and 0.1 M M NH4Cl. The pH of the solution will

not change on adding.

(A) 20 mL of 0.1 M NH4OH solution (B) 20 mL of 0.1 M NH4Cl solution

(C) 10 mL of 0.1 M NaOH solution (D) 10 mL of distilled water

61. Calculate the molar solubility of Ni(OH)2 in 0.10 M NaOH. The Ksp of Ni(OH)2 is 2.0 × 10–15

(A) 6.0 × 10–12

M (B) 8.0 × 10–13

M

(C) 2.0 × 10–13

M (D) 5.0 × 10–12

M

62. The change in pH near the end point will be maximum in the titration of

(A) strong acid and strong base (B) strong acid and weak base

(C) weak acid and weak base (D) weak acid and strong base

63. Given that Ka for acetic acid as 1.8 × 10–5

and Kb of NH4OH as 1.8 × 10–5

at 25oC, predict the

nature of aqueous solution of ammonium acetate

(A) Acidic (B) Basic

(C) Slightly acidic or basic (D) Neutral

64. The precipitate of CaF2 (Ksp = 1.7 × 10–10

) is obtained when equal volumes of the following are

mixed

(A) 4 2 410 M Ca 10 M F (B)

2 2 310 M Ca 10 M F

(C) 5 2 310 M Ca 10 M F (D)

3 2 510 M Ca 10 M F

65. The pH of the neutralization point of 0.1 M ammonium hydroxide with 0.1 M HCl is closest to

(A) 1 (B) 6 (C) 7 (D) 9

66. The compound whose 0.1 M solution is basic is

(A) Ammonium acetate (B) Ammonium chloride

(C) Ammonium sulphate (D) Sodium acetate

67. Which of the following salts undergoes anionic hydrolysis?

(A) CuSO4 (B) NH4Cl (C) FeCl3 (D) Na2CO3

68. At 90oC, pure water has [H3O

+] = 10

–6 mol L

–1. What is the value of Kw at 90

oC?

(A) 10–6

(B) 10–12

(C) 10–14

(D) 10–8

69. The solubility product of AgI at 25oC is 1.0 × 10

–16 mol

2 L

–2. The solubility of AgI in 10

–4 M

solution of KI at 25oC is approximately (in mol L

–1)

(A) 1.0 × 10–16

(B) 1.0 × 10–12

(C) 1.0 × 10–10

(D) 1.0 × 10–8

70. The pH of 0.1 M solution of a weak acid is 3. What is the value of the ionization constant for

the acid ?

(A) 0.1 (B) 10–3

(C) 10–5

(D) 10–7

71. The pH of 10–8

M aqueous solution of hydrochloric acid is

(A) 8.0 (B) more than 8.0 (C) 7 (D) less than 7.

72. The solubility of calcium phosphate in water is x mol L–1

at 25oC. Its solubility product is equal to

(A) 108 x2 (B) 36x

3 (C) 36 x

5 (D) 108 x

5

******



SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

SR MPC JEE MAINS Date: 28-04-2020 Time: Max. Marks:

MATHS

1) A 2) C 3) D 4) A 5) B 6) C 7) B 8) D 9) A 10) C

11) B 12) B 13) A 14) A 15) A 16) A 17) A 18) C 19) B 20) C

21) C 22) A 23) B 24) A 25) A 26) D 27) B 28) B 29) D 30) B

31) A 32) B 33) B 34) D 35) B 36) D 37) C 38) B 39) A 40) B

41) B 42) D 43) D 44) A 45) D 46) A 47) C 48) B 49) D 50) C

51) D 52) C 53) C 54) A 55) C 56) C 57) A 58) B 59) C 60) A

61) A 62) A 63) C 64) D 65) D 66) A 67) A 68) B 69) C 70) C

71) B 72) D 73) B 74) B 75) A 76) C 77) C 78) A 79) A 80) C

81) C 82) C 83) D

PHYSICS

1) D 2) D 3) D 4) D 5) D 6) A 7) C 8) A 9) C 10) A

11) A 12) C 13) D 14) C 15) A 16) C 17) B 18) D 19) B 20) C

21) D 22) C 23) C 24) B 25) D 26) C 27) C 28) B 29) D 30) C

31) B 32) D 33) B 34) D 35) B 36) A 37) A 38) B 39) D 40) B

41) A 42) C 43) C 44) A 45) A 46) C 47) A 48) B 49) B 50) C

51) B 52) D 53) B 54) A 55) B 56) B 57) B 58) A 59) D 60) C

61) A 62) A 63) A 64) A 65) C

CHEMISTRY

1) C 2) A 3) D 4) A 5) B 6) C 7) A 8) D 9) D 10) B

11) A 12) A 13) D 14) C 15) C 16) C 17) 1.5 18) 0.25 19) 0.25 20) 64.0

21) 0.10 22) D 23) A 24) D 25) C 26) B 27) D 28) C 29) A 30) D

31) C 32) A 33) C 34) A 35) B 36) D 37) B 38) C 39) D 40) C

41) A 42) D 43) D 44) C 45) D 46) A 47) C 48) D 49) C 50) B

51) B 52) A 53) D 54) B 55) B 56) C 57) D 58) A 59) A 60) D

61) C 62) A 63) D 64) B 65) B 66) D 67) D 68) B 69) B 70) C

71) D 72) D

UNIT – III

ASSIGNMENT – 3



HINTS & SOLUTIONS MATHS

1. (A) For ellipse, ab – h2 > 0

2k 1 .1 k 1 0 or k(k – 3) < 0

2. (C) Latus rectum = 2

2 22b 2.a 1 e

a a

3. (D) 2 2

2 2x y1 a 9,b 3

9 3

So, 2 2 2 2 2b a 1 e 3 9 1 e e

3

distance between foci = 2ae = 2 . 32

3

4. (A) 2

2 2 2 22b 12b 2ae, 10,b a 1 e e ,a 10,b 50

a 2

5. (B)

6. (C) The sum of distances of P from the foci = 2a = 2 × 5 = 10

7. (B)

8. (D) Here, 2 2x y

11 4 . Any tangent to the hyperbola is y = 2 2 2mx a m b i.e.,

y = 2mx m 4 in which m is any real number.

9. (A) Solving the equations, 2

3 x 1x 2x 0

2

or 2 7x 3

x 02 2

Or 2x2 + 7x + 3 = 0 or (2x + 1) (x + 3) = 0 or

1x , 3

2

But x = – 3 makes y imaginary because 2y2 = 3 (x + 1).

So, x = – 1/2 3

2

10. (C)

11. (B)

12. (B)

13. (A) The distance between foci = 2ae = 2 2

3 1 1 1 2 ae 1

The sum of the distance of foci from (1, 3) on the ellipse = 2a

2 2 2 2

3 1 1 3 1 1 1 3 2a 2a 2 2 2

1 2 1

e 2 1a 2 2 2 2 1

14. (A) Here, the situation is standard. The distance between foci = 2ae = 4 and e = 2/3

3a . So, b2 = a

2(1 – e

2) = 9

41 5

9

16. (A)Any point on the ellipse = 6 cos , 2 sin .

So, 2 2 1

6 cos 0 2 sin 0 4 cos2

20. (C) The equation of the pair of tangents is 2

1SS T

Or

22 2 2 9 31 1 1

9 4 9 4 9 4

x y x y



For right angle, a + b = 0 2 2 21 5 1 5 9

09 9 4 81 4 9 4 16

21. (C) The point is 1 1,x y if 1 13 9xx yy has the slope q, i.e., 1

1

13

x

y and 2 2

1 13 9x y . Solve the

two equations.

22. (A) The tangent at 4cos ,2sin is 4cos . 4. 2sin 16x y .

Being normal, it passes through the centre (4, 2)

So, 16cos 16sin 16 cos sin 1or . It is satisfied by2

23. (B) Let the points A, B be (– 2, 1, – 3), (a, 3, – 6) respectively, then

AB = 7 (given)

2 2 2

2 3 1 6 3 7a

2 24 4 4 9 49 4 32 0a a a a

4 8 0 4, 8a a a

26. (D) Given that R divides PQ in the ratio r : s.

Let R be (h, k), then

sin . sin .b s a r

kr s

sinar bs

r s

And h = cosa

Then

sin ,cosk r s h

ar bs a

222

221

k r sh

a ar bs

Hence the required locus of R is

222

221

y r sx

a ar bs

, which is an ellipse.

27. (B) Equation of directrix is 2x + y – 1 = 0

Let S be the focus, then 1,2S . Given e = 3

Let P(x, y) be any point on the required hyperbola. Let PM be the length of the perpendicular

from P to the directrix.

Then 3PS

ePM

2 23PS PM

Or 2

2 2 2 11 2 3

5

x yx y

Or 2 2 2

5 1 2 3 2 1x y x y

Or 2 2 2 25 2 4 5 3 4 1 4 4 2x y x y x y xy x y

Or 2 27 2 12 2 14 22 0x y xy x y

29. (D) Equation of normal to the given hyperbola at P is

2 2cos cotax by a b ………………….(A)



And equation of normal at Q is

2 2sin tan2

ax by a b

……………….(B)

Now, sin . 1 cos . 2

2 2cos sin sin cosby a b

2 2a b

yb

34. (D) 2 2

2 25tan , 4sec 1 16, 2516 25

y xx y a b

Also, b2 = a

2(e

2 – 1).

35. (B) For the ellipse, a2 = 16; b

2 = a

2(1 – e

2)

2

21616

4

be ae b

For the hyperbola, 2 2 2 2 2144 81 15, ; 1 3

25 25 12a b b a e e ae

216 3b

36. (D) Here, 2 29, 5a b . So, latus rectum = 22 2 5

3

b

a

5

,3

P

. It is on the ellipse. So,

2

2

5

31 2

9 5or

. So, 5

2,3

P

The tangent at P is

5

2 3 1 199 5 3

3

yx x y

or

area = 1 9

4 4 3 272 2

ar ROQ

37. (C) We know that two diameters 1 2,y m x y m x are conjugate diameters of2 2

2 21

x y

a b if

2

1 2 2

bm m

a

Hence, we have 2

2 2

2

2 21.

3 3

bor b a

a

2 2 2 2 2 2 22 21 1 1

3 3b a e a a e e

38. (B) The distance between the points P(– 3, 7, 2) and Q(2, 4, – 1) is given by

2 2 2

2 3 4 7 1 2PQ units

25 9 9 43units units

39. (A) Given hyperbola is2 2

21

9

x y

b

Since this passes through (K, 2), therefore



2

2

41

9

K

b …………….(A)

Also given 2

2

131

3

be

a

2

2

2

131 9 13

3

bb

a

2b

Now from equation (A), we have

2

241 18

9 4

KK

40. (B) ae = 2, e = 2

a = 1

2 2 2 2 21 1 4 1 3b a e b b

Equation of hyperbola, 2 2

2 21

x y

a b

2 2

11 3

x y

2 23 3x y

41. (B) 2 2 2sin cos 1 sece e

42. (D) Tangent to the hyperbola2 2

2 21

x y

a b is

2 2 2y mx a m b

Given that y = x is the tangent of hyperbola

m and2 2 2 2m b

2 2 2 2a b

Locus is2 2 2 2a x y b which is hyperbola.

43. (D) 2 2

2 21

x y

a b

2

91 3a

a

2

18 41 2

9n

b

24 9 1e

13

3e

44. (A) 2 6x y ………….(i)

2 22 4 9x y …….(ii)

Consider the line, 3

2x y ………….(iii)

On solving (i) and (iii), we get only

3

3,2

x y

Hence3

3,2

is the point of contact of conic (i), and line (iii)



On solving (ii) and (iii), we get only x = 3, y = 3/2

Hence (3, 3/2) is also point of contact of conic (ii) and line (iii).

Hence line (iii) is the common tangent to both the given conics.

45. (D) Equation of the tangent at the point ' ' issec tan

1x y

a b

cos ,0P a and Q = 0, cotb

Let R be (h, k) cos , coth a k b

sinsin

k b bh

h a ak

and cos

h

a

By squaring and adding

2 2 2

2 2 21

b h h

a k a

2 2

2 21

b a

k h

2 2

2 21

a b

h k

Now, given equation of hyperbola is2 2

14 2

a y

2 24, 2a b

R lies on 2 2

2 21

a b

x y i.e.,

2 2

4 21

x y

47. (C) 2 2

112 16

x y

12 1

116 2

e

Foci (0, 2) & (0, – 2)

So, transverse axis of hyperbola = 2b = 4 b = 2 & a2 = 1

2 (e

2 – 1)

2 94 1

4a

2 5a

It’s equation is2 2

15 4

x y

The point 5, 2 3 does not satisfy the above equation.

50. (C) Equation of hyperbola is2 2

2 21

x y

a b

Foci is 2 22,0 2 4ae a e

since 2 2 2 1b a e

2 2 2 2b a e a

2 2 4a b ………(a)

Hyperbola passes through 2, 3

2 2

2 31

a b ……….(b)



2 2

2 31

4 b b

4 2 12 0b b

2 3b

2 4b (Not possible)

for2 3b

2 1a

2 2

11 3

x y

Equation of tangent is2 3

11 3

x y

Clearly 2 2,3 3 it.

51. (D) Here, tx – 2y – 3t = 0 & x – 2ty + 3 = 0

On solving, we get

2

2 2 2

6 3 3 3&

2 2 1 1

t t ty x

t t t

Put t = tan

3sec2 & 2 3 tan 2x y

2 2sec 2 tan 2 1

2 2

19 9 / 4

x y

Which represents a hyperbola

2 29 & 9 / 4a b

2 9 / 4 1 5. . 6; 1 1

9 4 2T A e e

56. (C) Equation of hyperbola is2 2

14 9

x y

Its foci = 13,0

13

2e

If e, be the eccentricity of the ellipse, then

1 1

13 1 1

2 2 13e e

Equation of ellipse is 2 2

2 21

x y

a b

Since ellipse passes through the foci 13,0 of the hyperbola, therefore a2 = 13

Now 2 2

1a b ae

213 1b

2 12b

Hence, equation of ellipse is



2 2

113 12

x y

Now putting the coordinate of the point13 3

,2 2

in the equation of the ellipse, we get

13 3

14 13 4 12

1 1

14 16

, which is not true.

Hence the point1 3

13,2 2

does not lie on the ellipse.

57. (A) 2e (hyperbola)

Therefore its foci = 1,0

1

2e (ellipse)

Therefore b = 1

60. (A) 22

8b

a and

12 2

2b ae

2 2 2 2 2 2 24 4 1b a e a e a e

2 2

3 43

e e

61. (A) S(5, 0) is focus 5ae (focus) ……….(a)

9

5 5

a ax

e (directrix) ……………(b)

(a) & (b)2 9a

(a) (e) = 5/3

2 2 2 21 16b a e b

2 2 9 16 7a b

62. (A) Given 2 2

14 5

x y

2 24, 5a b

2 2

2

4 5 3

4 2

a be

a

L = 3 5 5

2 , 3,2 2 2

Equation of tangent at 1 1,x y is

1 1

2 21

xx yy

a b

Here 1 1

53,

2x y

3

1 144 2 2

3

x y x y



x-intercept of the tangent, OA = 4/3

y-intercept of the tangent, OB = – 2

2 2 16 204

9 9OA OB

63. (C) Foci = 2

4 116

b (ellipse)

Foci = 3 (hyperbola)

64. (D) Normal: 3 4

1 1 1yt t x ct c

put 2 2

2

ct ct ,

t

66. (A) Let the required circle is 2 2x y 6x 4y k 0 and it is passing through (– 2, 14).

PHYSICS

1. (D)

T = doubled, 4P T

16 times increased.

2. (D)

4 × 500 × 425 = m × 336000

m = 2.53 kg

3. (D)

4u AT

2 4

2 2u R T

6

02u u

64 times.

4. (D)

K = 5 : 3

1

RK A

K

= 5 : 3

5. (D)

10

70 302

C

2

1050 30C

t

2 22

t

2t = 4 times

6. (A)

32

5 9

C F

32

5 9

x x

9x = 5x – 160

– 160 = 4x

x = – 40



7. (C)P = 4

2

02

ATr

4 r

2 4

0

2

Ar T

4r

2 4

0

2

4 Rr T

4r

2 4

0

2

Rr TP

r

8. (A) Temperature gradient graph.

9. (C) Newtons law of cooling.

10. (A) Td

dt R

I 1 2R R R

1 1

K A 2K A

I

3R

2KA

II 1 2

1 1 1

R R R

KA 2KA 3KA

I 1 II II

1 1I

R R

t t

II

3 1t

2 9 3

IIt 2s

11. (A)

4 3

f f

i i

u T 4 256

u T 3 81

12. (C)

Blue Yellow Red

B C AT T T

15. (A)

1 if

d dmL

dt dt

AP

400.80

R ….(i)

2H O2v

dmdL

dt dt

PB

300.540

R …..(ii)

PB

AP

4R 80

R 570



10x y 1

y 9

90x 9y y y 9x

9

16. (C)

A B3

A BT 3T

4u eAT

4

1 2 4

1 3u :u 9

9 1

17. (B)

r 400:1,p 104:1

42

PT

r

A A42 2

4BA

B

B

T P 100 10

T 20400rP

r

A

B

2

18. Strain = L

TL

Elastic potential energy = 1

2E stress strain

Per unit volume

2 2 2

2 2

y yE strain T

2

2 3

y rT

2 2

18

yr TE

19.

P1

P2

h

1 21 2 1 2

1 2 1 2

2 22

r rT TP P h g P P h g T

r r r r



21. Colour are seen because of the constructive interference between the light waves reflected from the two

surfaces of the thin film.

There is a phase change of at A and there is no phase change at B. So, for constructive interference,

For

= 540 nm

22. 2

2 2

2

T mL x

A LA

23. 2S

gauge pressure ghR

24. The diagram will be

2 2r h g rs

26.2

0 0

1

2

mgP gh P v

A

27. 2

0T M L

' 2

02

LT M

'

2

T T

A A

2

0

2 '

2 1

2

T

T

0 1 1

4 2

28.

mgx

T xL

Elongation in element

1T dx mg

x dxYA YA L

Net elongation



2

mgL

YA

29. 22 2S Sa

p Ft t

30. ,Fl l

e eAy A

as mass is same 1 1 2 2l A l A

2

1 1

2 2

4

9

e le l or

e l

Correct Option (c )

31. 1

2w Fx where x ix elongation =

Fl

Ay

Given x and y are constant

2

1 1 1 2 1 2

2

2 2 1 1 2 1

. .w F A l r l

w F A l r l

2 8 4 32w J

Correct option (b )

32. Elastic Potential energy = Kinetic energy of the stone

2

9 6 21 2 1 50.5 10 0.1 10

2 100 2 100v

2 /v m s

Correct option (d)

33. W T A

2 2

2 28 2.5 10 1.0 10A = 2 21.30 10 m

43.96 10W J

34. Conceptual

Correct Option (d)

35.

Volume of the liquid is constant

1 2

2 2 2 2 2 1.422 3

x x x m

H = x 0sin60 1.2 2 4.96 /m v gh m s

Correct option (b)

36. 1 /2

1/2

1

0

2

22 2

t H

H

A A Hdt y dy t H

a g a g

2 0

1/2

2

0 /22

t

H

A A Hdt y dy t

a ga g

1

2

2 1 0.414t

t



Correct option (a)

37.

22 ,

H hv g a h t

g a

22 . 2 2 2 3

H hx g a h h H h

g a

4.9 m

Correct option (a)

38. Work = average force x elongation

39. Maximum restoring force develops at the end where force is applied. This force decreases

linearly such that it becomes zero at the other end so stress also decreases linearly.

40. 8 4 21

1200 2.410 3 10 103

g a or a ms

41. 1 1 2 2&l L l l L l

1 1l L l

11l

T LL

ys

22l

T LL

ys

1 1

2 2

l L T

l L T

42. (c) Fupthrust = Fsurface tension + Weight

l2xg = 4lT + mg

(.03)2 × 10

3 × 10 = .009 + .2

9x = .209

x = .02322 m = 2.322 cm

43. Three equal magnitude forces Tdl keep a small element in equilibrium. So angle between them

is 0120 .

44. Relative error in diameter is multiplied by two so more accuracy in diameter

measurement.

45.

Let T1 and T2 be the tensions in brass and steel wire respectively. Let weight ‘w’ be hanged

from a point which is at a distance x from A.

Then 1 2 2 (1)T x T x

1 2 2T T w

As stresses in the wires are same

4

1` 11 24

2 2

0.2 102 2 (3)

0.1 10

T AT T

T A

From (2) and (3)

1 2

2

3 3

w wT and T



From (1) 2

2 3 2 0.666 66.63 3

w wx x x x m cm

46. (C)

Only part ‘1’ and ‘2’ will elongated. There will be no deformation in part ‘3’. net change in

length of ROD is = 24

F L

AY

2

FL

AY

47. Excess pressure in drop = ( / 2)

S S

H R

=

2S S

H R

53. Here, = 4 m = 400 cm,

2r = 5 mm or r = 2.5 mm = 0.25 cm

f = 5 kg-wt = 5000 g-wt = 5000 × 980 dyne

= ?, Y = 2.4 × 10–12 dyne/ cm2

As 2

FY

r

or

2

F

r y

= 2 12

(5000 980) 400

(22 / 7) (0.25) 2.4 10

= 0.0041 cm.

54. Tension in rod at a distance x from right edge is

net extension in rod

55. Stress S is same for both wires, so

. 1

2w Fx where x ix elongation

Fl

Ay

56 Given x and y are constant



57. 3 34 48

3 3R r

. .,2

Ri e r

If smaller drop 2 2 4

/ 2s

T T TP

r R R

If bigger drop 2 1

2B S

TP P

R

58. 3

2

4800 9.8 2 10

1 10

T

59. Factual Question

60. 2T T

PR d

5

2

2 75 810

0.012

TF p area A

d

dyne

61. hg = exces pressure.

2

2

/ 2

Thg

r

Tgh

d

62. wt. of the sphere = wt. of the water displaced.

3 3 34 4 49

3 3 3R r g R g

63. Let a and b be the radius of two soap babbles forms a soap babble of radius C. Then

3 3 3

0 0 0

0 0

4 4 4 4 4 4

3 3 3

43 4 0

3

P a b P P ca b c

sPV PV s

64. For the same stress, strain in wire B is more than A.

65. Tensile stress = Fcos

q / cos

.

CHEMISTRY

1. (C) Fast rate for completion.

Kc must be greater value.

Kc = ionconcentratReactant

ionconcentrat Product

More product concentration, more value of Kc, so, reaction goes to fast completion.

2. (A) H2 + I2

2HI

at equ. 5

4.0

5

4.0

5

4.2

d



Kc =

5

4.0

5

4.0

5

4.22

Kc = 4.04.0

4.24.2

Kc = 16.0

76.5

Kc = 36

3. (D)

kP = 2

3104

1

4. (A)

ng 4 1 (2 2) 1

ng

P cK k (RT)

0.03 = KC (0.082 × 700)1

KC = 523 × 10–4

5. (B)

2NOBr(g)

2NO(g) + Br2(g)

at equ. P – 9

P2 =

9

P6

9

P2

9

P

PT = 9

P6 +

9

P2 +

9

P = P

Kp = 2

2

9

P6

9

P

9

P2

= P

K P = 81

1.

6. (C)

N2 + 3H2 2NH3

t = 0

Initial 28

28

2

6 0

1 3 0

mole mole mole

at equ. t = ? 1 – x 3 – 3x 2x

2x = 17

17 2x = 1

x = 1/2

Final 1/2 3/2 1

Mole weight = 14 g 3g

7. (A)

C2H4 + H2

C2H6 H = – 32.7 K Cal

n = Pmole – Rmole = 1 – 2 = .– 1

H = – ve Exothermic reaction x T

1

Temperature increases Reaction goes toward reactant.



Thus, concentration of C2H4 increases.

8. (D)

AB(s)

A(g) + B(g)

Active mass for Solid = 1 unity

Kc = (x).(x).

Amount of AB.(s) doesn't appear in Kc, Kp

So, no change in amount of A and B

9. (D)

NH4HS (s)

NH3(g) + H2S(g)

Kp = NH3(g) ×H2S(g)

Partially pressure of NH3 and H2O doesn't affected by NH4HS(s) because NH4HS(s) is solid for

solid active mass unity.

10. (B) K decreases as increase in temp. hence exothermic H < 0

11. (A)

NH3 formed = 5 × 1000

100 = 0.5 mole

N2 + 3H2

2NH3

1.0.25 3 –0.75 0.5

KC = )25.2(75.0

5.0 2

12. (A) N2O4

2NO2

At equ. 2

2.0

2

102 3– (2 Litre)

0.1 1 × 10–3

Kc = 1.0

)101( 23–= 10

–5

13. (D) K = 2 = 1k , K2

= 4K

1, K1

= 3K

1

K1K3 = 1, 1K K4 = 1 3K = 1

14. (C)

2NH2COONH4(s)

2NH3(g) + CO2(g)

t = 0 1 0 0

at equ. t = ? 1 – x 2x x

KP = 2

Px3

x2

×

P

x3

x

(Active mass of solid is unity)

KP =

2

2

2

Px9

x4 ×

P

x3

x

KP =

3

3

3

Px27

x4

2.9 × 10–5

= 3

3

x27

x4 × P

3

78.3 × 10–5

= 4 × P3

P3 = 1.97 × 10

–4

P = (197 × 10–6

)1/3

P = 0.0582 atm.



15. (C)

PCl5

PCl3 + Cl2

t = 0 2 0 0

at equ. 2 – x x x

Total mole = 2 + x

i = 2

x2

moleInitial

moleTotal

= 1–n

1–i =

2

x2 –

1

1

= )1–n(2

2–)x2(

n = reactant ofmole

productofmole n =

1

2

= )1–n(2

2–)x2(

= 2

2–)x2(

KC = x–2

)x( 2

(given KC = 1)

1 = x2 = 2 – x

x2 + x – 2 = 0

= b ± a2

ac4–b2

x = 1 (with –ve)

= 2

2–3 =

2

1

16. (C)

2 SO3

2SO2 + O2

H = + ve endothermic reaction

Inert gas doesn't show reaction with the reacting mixture it show effect only due to it's volume.

At constant volume doesn't effect of inert gas. Thus dissociation of SO3 unchanged.

V = constant = n = 0

No effect of inert gas

23. (A)

Meq of 0.2 M H2SO4 = 2 0.2M

100 0.04m / L1000

Meq of .2 M NaOH = 0.2

100 0.02m / L1000

Left [H+] # 0.04 – 0.02 = 0.02

Total volume = 200 = 0.02/200 = 0.0001 = 10– 4

M

pH = 4

24. (D)

3

2 4 4HC O aq PO aq

2 2

4 2 4HPO aq C O aq

Acid 1 Base 2 Base 1 Acid 2

25. (C); Conjugate acid base pair differ by a proton (H+).

HHF HF

acid base

26. (B)

2 4 2H SO 2H O 3 42H O SO

NaOH Na+ + OH

–



1 mole of H2SO4 acid gives 2 moles of H3O+ ions. So 2 moles of OH

– are required for complete

neutralization.

27. (D); HA 3H O A

At equilibrium C 1 C C

3H O C as aK

c So a

3 a

KH O C K c

c

28. (C)

23

2 62 5

1

2 4

102

NO 2 10K 10

.2N O 10

2

29. (A) Concentration of reactant and product remains constant w.r.t. time.

And, rate of [AT EQUILIBRIUM] forward reaction (rf )= rate of backward reaction (rb)

32. (A) Extent of hydrolysis decreases with increase of size of anion.

33. (C) Salt of W.A + W.B undergoes both cationic and anionic hydrolysis.

34. (A) 2CaF

2Ca 2F

For solubility ‘S’, 2 3

spK S 2S 4S

3 114S 3.2 10

3 12S 8 10

S = 42.0 10 M

35. (2)

2A B

22A B

2S S

2 sp3 3

sp sp

kk 2s .s,4s k ,s

4

36. (D) Common ion effect.

37. (B) 14

h 6 7

a b

kw 10K

k k 2 10 5 10

= 10

–2

38. (C) NaCN under go anionic hydrolysis.

39. (D) 2

2

spK Pb I

2

0.2 s 2s

40. (C)

In acidic solution, OH– ions are neutralised with H

+ ions equilibrium shift to forward direction.

41. (A)

10 10

spK 4 10 4 10 x

12

2

10

4 10x 10

4 10

42. (D)

2

2M OH M 2OH

2 3

spK x 2x 4x

OH 2x

43. (D) Eqm. Const. of a reaction depends only on temperature.

44. (C) Decrease of K with rise of temperature means that the forward reaction is exothermic or the

backward reaction (formation of HI) is endothermic. As the given reaction is exothermic,



energy of HI is greater or stability is less than H2 and I2.

45. (D) As np = nr, equilibrium will not be disturbed by pressure.

46. (A) reaction (2) is inverse of (1) and half of (1). Hence

2

2 1

1 2

1 1K or K

R K

47. (C) For the required reaction, H ve. Apply Le Chatelier principle.

48. (D) Solid + Heat liquid. Adding heat will shift the equilibrium in the forward direction.

49. (C) On adding SO2, eqm. Shifts forward. As it is exothermic, temp, will increases.

50. (B) Eqm. Const. is constant at constant temperature.

51. (B) Eqm. Shifts forward.

52. (A) Eqm. Shifts backward by Le Chatelier principle.

53. (D) 2 2

31 22 3

2 2 2 2

[NH ] [NO]K .K

[N ] [H ] [N ][O ]'

1/2

2 23

2

[H ][O ]K

[H O]

Aim: 32 3

2 32

2 5/2

3 2 1

K H[NO] [H O]K .Thus K

[NH ] [O ] K

54. (B) Reaction is reversed. Hence

3 2K 1/ (2.4 10 ) 4.2 10

55. (B)

2XY XY Y

Initial 600mm

At eqm. 600 p p p

Total 600 p 800

Actual values 400 200

or p 200mm

200 200K 100

400

56. (C)

A B C D

At eqm. a a 2a 2a

2a 2aK 4

a a

57. (D) n

g p cn 4 3 1, K K (RT)

c0.05 K (1000 R)

58. (A) [H+] for the solution of pH = 3 = 1 × 10

–3

[H+] for the solution of pH 5 = 1 × 10–5

Let V volumes of both the solutions are added, then concentration of H

+ in final mixture is

3 51 10 V 1 10 V

[H ]V V

3 5V(1 10 1 10 )

2V



3

41.01 105.05 10

2

pH of resultant = – log [H+]

= – log(5.05 × 10–4

)

3.29 3.3

59. (A) 0.365 g of HCl0.365

36.5 =0.01 moles of HCl

0.2 M NaOH in 100 cm3 =

0.2 1000.02

1000

moels of NaOH

0.01 moles of HCl get neutralized with 0.01 moles of NaOH, thus resulting solution contains

0.01 moels of NaOH in 100 cm3 solution.

Concentration of NaOH = 0.01

1000 0.1M100

1 14[OH ] 0.1M 10 M,[H ][OH ] 10

13pH log10 13

60. (D) pH of buffer does not change on dilution

61. (C) Let the solubility of Ni(OH)2 be equal to S, dissolution of S mol/L of Ni(OH)2 provides S

mnol/L of Ni2+

and 2S mol/L of OH–, but the total concentration of OH

– = (0.10 + 2S) mol/L

because the solution already contsins 0.10 mol/L of OH–

from NaOH

15 2 2

spK 2.0 10 [Ni ][OH ]

2(S)(0.10 2S)

As Ksp is small, 2S << 0.10,

Thus, (0.10 + 2S) 0.10

Hence,

15 22.0 10 S(0.10)

13 2S 2.0 10 M [Ni ]

62. (A)A know fact

63. (D)As Ka = Kb, the solution is neutral.

64. (B) In (b), after mixing, [Ca2+

] [F–]2 > Ksp.

65. (B) NH4OH + HCl forms NH4Cl which gives acidic solution with pH < 7.

66. (D) CH3COONa is a salt of weak acid, CH3COOH and strong base, NaOH.

67. (D) Anionic hydrolysis means anion reacting with water

2 3 2 2 3(Na CO 2H O 2NaOH H CO or

2

3 22Na CO 2H O 2Na 2OH

2

2 3 3 2 2 3H CO or CO 2H O 2OH H CO )

68. (B) For pure water, [H3O+] = [OH

–].

Hence Kw = 10–12

.

69. (B) Total [I–] = 10

–4 + 10

–16 – 10

–4 M

[Ag+] [I

–] = Ksp [Ag

+] (10

–4) = 1.0 × 10

–16

or [Ag+] = 10

–12.

70. (C) HA H A ,

3H 10 M

[A–] = 10

–3 M. Hence

3 3

5

a

10 10K 10

0.1



71. (D) As the solution is acidic, pH < 7. This is because [H+] from H2O (10

–7 M) cannot be

neglected in comparison to 10–8

.

72. (D)

2 3

3 4 42Ca PO 3Ca 2PO ,

x 3x 2x

3 2 5

spK 3x 2x 108x .

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