A

B C

A'

B' C'

20 cm

6 cm

8 cm

2 4

50. Simplify : a2

(a−b )(a−c )+ b2

(b−a )(b−c)+ c2

(c−b )(c−a)51.a) A solid metallic sphere of radius 7 cm is cut into two halves. Find the total surface area of the two hemispheres so formed.b) The total surface area and the curved surface area of a cone are 704 sq.cm and 550 sq.cm respectively. Find the slant height of the cone.

52. a Evaluate: b. Simplify:

c) Solve:2 y+3√3−1

=√3+13

53. Find the HCF of x3-8, x4+4x2+16, x3+2x2+4x.

54. Simplify:1y+ p

− 2 yy2+p2

+ 8 y7

y 8−p8− 4 y3

y4+p4

55. a) Evaluate -: 6x+2– 18 .6x−1

11 .6x b) Simplify: 4−√15+ 1

4−√15

56. a)Solve: √ x+1=3−√ x+12

b)The lateral surface area of the prism shown in the figure is 420 cm2. Find the measure of AC.

57.Solve: 22x+3 – 9.2x + 1 = 0

58. Calculate the lateral surface area of given traingular prism.

59. Find the volume of given solid:

60. `Find the HCF of following expression given below:

9m2-4n2-4nr-r2, r2-4n2-9m2-12mn and 9m2 + 6mr+ r2 – 4n2

61. In the given adjoining figure, area of base of the cylinder is 64 cm2 and the height of cylinder is 4 cm. If the volume of solid is 320cm3, find the height of the solid.

1. a) Simplify: 13x+2−65×13x−1

13x×41

b) Simplify: 1

1+ xa−b+ 1

1+xb−a

2. a) Simplify: 5−√24+ 15−√24

b) Evaluate: (√ 3√ 72964 )

−1

3. a) Solve: √ x−3= 1

√ x+3b) Solve: 3√ x2−1−2=0c) Find the lateral surface area of given triangular prism.

4. Find HCF of: 2a2−5 a+2 ,3a2−8a+4 , a4−8 a5. Simplify:

y−2

y2−2 y+4+ y+2

y2+2 y+4− 16

y4+4 y2+166. If pqr = 1 then prove that:

1

1+ p+q−1+ 1

1+q+r−1+ 1

1+r + p−1=1

7. Solve: 8x+8− x=64

164

8. a) Simplify:(64 x3÷27a−3 )−23

2

5cm

3 cm

4cm

15cm

12cm

70cm

75cm

26cm

A

B

C

D

E

F20cm

8cm

6cm

24cm

6cm

14cm

b)Simplify:2 3√32+2 3√108− 3√256−3√500

9. a) Solve: y+2√ y+1=0b)Find the volume of given triangular prism.

10. a)A cone has curved surface area is 20πcm2 and slant height is 5cm, find the radius.b)A solid metallic sphere of radius 7cm is cut into two halves. Find the total surface area of the two hemispheres so formed.

11. Find HCF of: x2+ y2+2xy−1, y2−x2+2 y−1 , x2− y2+2 x+1

12. Solve: x−1√x+1

=4+ √x−12

13. Simplify: aa−b

+ aa+b

− 6a2

a2−b2 +8a4

a4−b4

14. a) Simplify:

6n+2−6n

6n+1−66

b)

Evaluate: [ a√ x÷2 a√ x3]−2a

15. a) Solve: √√x+25+√x=5b) The area of lateral faces of prism shown in the figure is 288cm2. Find the measures of base side and the base area.

18. a) The total surface area of a cone is 4928 square cm. If the sum of the radius and slant height of the cone is 32cm, find the radius of its base.

b) Three spheres of diameters 6cm, 8cm and 10cm are melted and formed a single sphere. Find the diameter of the sphere.

19. Calculate the total surface area of given adjoining solid figure.

20. Find the HCF of; x2+5x+6, x2+3x+2, x2-4

21. Solve: 4 x+ 1

4 x=16

116

22. Simplify: 1

4 (a+x )− 1

4 (a−x )+ x

2( x2−a2 )+ x3

a4−x4

23. Calculate the volume of the given solid.

24. a) Evaluate : 3.2x+1+5. 2x+2

4.2x−1+15.2x

b) Simplify: 23x-5 . ax-2 = 2x-2 . a1-x

25. a) Solve: 2 3√5 x−35=5 3√2x−7

b) Find the volume of the given triangular prism.

26= a) If the volume of the cone is 1848 cm3 and its radius is 14 cm then find its height.

b) A cylindrical water tank contains 46200lt of water. If its radius is 3.5m, find its height.

27. Find the L.C.M.1+4x+4x2-16x4, 1+2x-8x3-16x4

28= If p+q+r=0, then prove that:

1

1+ xp+x−q+ 1

1+xq+x−r+ 1

1+xr+x−p=1

29. Simplify : m+n

m2+mn+n2 +m−n

m2−mn+n2 +2n3

m4+m2n2+n4

30. Given figure is a object composed of a cylinder and a cone. If the height of the cylinder is 24cm, height of cone is 6cm and the diameter of the base 14cm then find the volume of the solid object.

31. a) The total surface area of a cone is 4928 square cm. If the sum of the radius of the base and the slant height of the cone is 32cm, find the radius of its base.

b) If the volume of a spherical object is4 π3cm3

, find its surface area.

32. Find HCF of x3+2x2 y−x y2−2 y3∧x3− y3 , x3−x y2

33. If p+q+r=0, then prove that: 1

1+ xp+x−q+ 1

1+xq+x−r+ 1

1+xr+x−p=1

34. Simplify: 1

4 a3(a+x )− 1

4a3(x−a)+ 1

2a2(a2+ x2)− a4

a8−x8

66 cm

14 c

m

25 cm

6cm

24cm

14cm

6cm

10cm

35. If the height of the cylinder is 24cm, height of cone 6cm and the diameter of the base 14cm, find the volume of the solid object.

35. a)Solve for x: ax−2=2x−2

b) Evaluate: 13√a−1×( 1

a )−3

36. a) Evaluate :

3n+2+5 .3n

3n . 5−3n−1

b) Simplify: 3√16+ 3√54−3√250

37. a) Solve: 1−√x+7=−√x b) Find the volume of given prism.38. a) If the volume of hemi-sphere is 19404cm3, find its radius

b) A cone has radius of base is 12cm and slant height is 13cm, find the volume of the cone.

39. Find the LCM of ; x4+x2+1, x4−x, x3+x2+x40. Solve: 4 x−6.2x+1+32=0