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#### Creative important question for all chapter

8th Standard EM

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 100

#### Multiple Choice Question

14 x 1 = 14
1. $\frac{5}{6}\div\frac{6}{2}$ is

(a)

$\frac{5}{2}$

(b)

$\frac{2}{5}$

(c)

$\frac{5}{18}$

(d)

$\frac{30}{12}$

2. $\frac { 1 }{ 2 } \times \left( \frac { 2 }{ 3 } +\frac { 6 }{ 4 } \right) =\left( \frac { 1 }{ 2 } +\frac { 2 }{ 3 } \right) +\left( \frac { 1 }{ 2 } \times \_ \_ \right)$

(a)

$\frac{1}{2}$

(b)

$\frac{2}{3}$

(c)

$\frac{4}{6}$

(d)

0

3. Multiplicative identity is _______.

(a)

1

(b)

0

(c)

the given number itself

(d)

reciprocal of the given number

4. In if the faces shows the area in the net, then the shape mentioned is

(a)

pyramid

(b)

Cube

(c)

cuboid

(d)

prism

5. If V = 6, E = 12 then the faces of the polyhedron is

(a)

6

(b)

7

(c)

8

(d)

9

6. A part of the circumference of a circle is called

(a)

circular arc

(b)

segment

(c)

sector

(d)

chord

7. Perimeter of a sector is

(a)

$\frac{lr}{2}$

(b)

$\frac{l+r}{2}$

(c)

l+2r

(d)

$\pi$+2

8. A closed plane figure formed by three or more sides is called a

(a)

(b)

pentagon

(c)

triangle

(d)

polygon

9. Volume of the rectangle 1= 2ab, b = 3ac and h = 2ac is _________.

(a)

12a2bc2

(b)

12a2bc

(c)

12a2 bc

(d)

2ab + 3ac + 2 ac

10. Product of 6a2 - 7b + ab and 2ab is __________.

(a)

12a3b - 14ab2 + 10 ab

(b)

12a3b - 14ab2 + 10 a2b2

(c)

6a2b - 7b2 + 7 ab

(d)

12a2b -7ab2 + 10 ab

11. Square of (3x - 4y) is _______.

(a)

9x2-16y2

(b)

6x2-8y2

(c)

9x2+ 16y2 + 24xy

(d)

9x2 + 16y2-24xy

12. On dividing 57pqr by 114 pq we get __________.

(a)

$\frac{1}{4}$pr

(b)

$\frac{3}{4}$pr

(c)

$\frac{1}{2}$pr

(d)

2pr

13. Common factor of 3ab and 2pq is _________.

(a)

1

(b)

-1

(c)

a

(d)

c

14. (a) $\frac { x }{ 2 }$=10     (i) x = 4
(b) 20= 6x – 4   (ii) x = 1
(c) 2x – 5 = 3 – x  (iii) x = 20
(d) 7x – 4 – 8x = 20  (iv) x =$\frac { 8 }{ 3 }$
(e) $\frac { 4 }{ 11 }$- x = $\frac { -7 }{ 11 }$   (v) x = –24

(a)

(i),(ii), (iv) ,(iii),(v)

(b)

(iii), (iv) , (i) ,(ii), (v)

(c)

(iii),(i) ,(iv), (v), (ii)

(d)

(iii) , (i) , (v) ,(iv) ,(ii)

15. #### Fill in the blanks

11 x 1 = 11
16. The additive inverse of -2 is __________.

()

+2

17. Addition of rational numbers commutative, so a + b =_______.

()

b+a

18. If the difference between the circumference and radius of a circle is 37cm then find the circumference of the circle.

()

44

19. If a wire is bent to the shape of a square, the area of the square is 81cm2. If it is bent to a semi-circle then find the area of the semicircle?

()

77 cm2

20. The radius of a wheel is 0.25m, how many revolutions are needed to travel a distance of 11 km?

()

7000

21. The circumference of a circle is 100 cm. Find the side of the square inscribed in the circle.

()

$\frac{50\sqrt2}{\pi}$

22. Find the area of the larger triangle that can be inscribed in a semi circle of radius' r' cm.

()

r2

23. The area of the circle is 220 cm2. What is the area of the square inscribed in it?

()

140 cm2

24. On simplificaiton  $\frac{3x+3}{3}$=________.

()

x+1

25. The factorization of 2x + 4y is ________.

()

2(x+2y)

26. Factorisation of 18 mn + 10 mnp is = ___________.

()

2mn(9+5p)

27. #### True or False

7 x 1 = 7
28. $\frac { 5 }{ 6 } -\frac { 11 }{ 12 } =\frac { -1 }{ 12 }$

(a) True
(b) False
29. $\frac { 4 }{ 3 } \times \frac { 3 }{ 11 } =\frac { 12 }{ 11 }$

(a) True
(b) False
30. (a + b)2 = a2 + b2

(a) True
(b) False
31. Product of two negative terms is a negative term

(a) True
(b) False
32. p2q + q2 r + r2 is a binomial

(a) True
(b) False
33. (a+b)(a-b) = a2 - b2

(a) True
(b) False
34. Common factor of 12a2b2+ 4ab2 - 32 is 4.

(a) True
(b) False
35. #### 2 Marks

67 x 2 = 134
36. Add $\frac{3}{5}$ and $\frac{13}{5}$

37. Add $\frac{7}{9}$ and $\frac{-12}{9}$

38. Subtract $\frac{3}{4}$ and $\frac{7}{4}$

39. Subtract $\frac{6}{17}$ and $\frac{7}{4}17$

40. Divide 1 by $\frac{1}{2}$

41. Divide $\frac{2}{3}$ by $\frac{-7}{12}$

42. Verify addition of rational numbers is closed using $\frac{1}{4}$ and $\frac{2}{3}$.

43. Is subtraction is commutative for rational numbers. Give an example,

44. Add $\frac{31}{-4}$and $\frac{-5}{8}$

45. $\frac { 5 }{ 9 } +\frac { -11 }{ 6 }$.

46. Subtract $\frac{-2}{3}$from $\frac{5}{6}$

47. Evaluate $\frac { -6 }{ 13 } -\frac { -7 }{ 13 }$

48. Multiply $\frac{-11}{13}$by$\frac{-21}{7}$

49. What should we multiply with $\frac{-1}{6}$to get $\frac{-23}{9}?$

50. What should we multiply with $\frac{-15}{28}$to get $\frac{-5}{7}?$

51. The given circular figure is divided into six equal parts. Can we call the parts as sectors? Why?

52. Fill the central angle of the shaded sector (each circle is divided into equal sectors)

53. If the radius of a circle is doubled, what will the area of the new circle so formed?

54. All the sides of a rhombus are equal. Is it a regular polygon?

55. In the above example split the given mat as into two trapeziums and verify your answer

56. If π = $\frac{22}{7}$ show that the area of the unshaded part of a square of side 'a' units is approximately $\frac{3}{7}$ a2 sq. units and that of the shaded part is approximately $\frac47$ a2 sq. units for the given figure.

57. List out atleast three objects in each category which are in the shape of cube, cuboid, cylinder, cone and sphere.

58. Tabulate the number of faces(F), vertices (V) and edges(E) for the following polyhedron. Also find F+V-E

59. Find the area of the given nets.

60. Find the length of arc if the perimeter of a sector is 65 cm and radius is 20 cm.

61. Find the area of the sector whose arc length is 20 cm and radius is 7 cm

62. What is the least number of planes that can enclose a solid? What is the name of the solid?

63. Find the product of the following: (x,y)

64. Find the product of the following.
(10x,5y)

65. Find the product of the following
(2x2,5y2)

66. Find the product of the following
(4a,3a2)

67. Find the product of the following
(3mn, 4np)

68. Divide:12x3y3 by 3x2y

69. Divide. -15a2 bc3 by 3ab

70. Divide :25x3y2 by -15x2y

71. Divide. -72x2yz by -12yz

72. Divide 6x3y2z2 by 3x2yz

73. Evaluate:
(2x+3y)2

74. Evaluate:
(2x-3y)2

75. Evaluate :
(2x+3y)(2x-3y)

76. Factorize:7(2x + 5) + 3 (2x + 5)

77. Factorize :12x3y4+16x2y5-4x5y2

78. Factorize:x2+xy+8x+8y

79. Factorize:9a2 -16b2

80. Multiply (p + 6), (q - 7).

81. Multiply (pz - 2r) (pq - 2r)

82. Simplify (ab - q)2+ 2abc

83. Expand (xy +yx)2

84. (7x - 5)2 Expand

85. Expand 9a2 - 16b2

86. Evaluate 992 using identity

87. Factorize 6 ab + 12 bc

88. Factorize - xy - ay

89. Factorize 6x3 - 92 + 3x

90. Simplify (pq - qr)2 + 4pq2r

91. (x2- 4) + (x2 + 4) + 16. Simplify

92. Simplify (-2x - 2y - 10) + (x +Y + 5)

93. Identify the pairs of shapes which are similar and congruent and write the letter pairs.

94. Match the following by their congruence

 S.No. A B 1. (i) RHS 2. (ii) SSS 3. (iii) SAS 4. (iv) ASA
95. In the figure, DA =DC and BA= BC. Are the triangles DaA and DBC congruent? Why?

96. Is it possible to construct a quadrilateral PQRS with PQ = 5 cm, QR = 3 cm, RS = 6 cm, PS = 7 cm and PR = 10 cm. If not, why?

97. In the given figure if $\frac { AO }{ OC } =\frac { BO }{ OD } =\frac { 1 }{ 2 }$ and AB=5cm. Find the value of DC.

98. In the given figure if $\angle$A =$\angle$C then prove that $\triangle$AOB ~$\triangle$COD

99. In the figure AB$\bot$ BC and DE$\bot$AC prove that $\triangle$ABC ~$\triangle$AED.

100. In the given figure if $\angle$P =$\angle$RTS, prove that $\triangle$RPQ ~$\triangle$ RTS.

101. A fast food restaurant has a meal special Rs.50 for a drink, sandwich, side item and dessert. The choices are Sandwich : Grilled chicken, AU beef patty, Vegeburger and Fill filet.
Side: Regular fries, cheese fries, potato fries
Dessert: Chocolate chip cookie or Apple pie.
Drink: Fanta, Dr. Pepper, Coke, Diet coke and sprite.
How may meal combos are possible?

102. A company puts a code on each different product they sell. The code is made up of 3 numbers and 2 letters. How many different codes are possible?

103. #### 3 Marks

47 x 3 = 141
104. Add $\frac{4}{-3}$ and $\frac{8}{15}$

105. What number should be subtracted from $\frac{7}{3}$ to get $\frac{5}{4}?$

106. The product of two rational numbers is $\frac{-28}{81}$. If one of the number is $\frac{14}{27}$. find the other number.

107. Add and simplify in mixed fraction $\frac{-12}{5}$and $\frac{43}{10}$

108. Simplify 1+$\frac{-4}{5}$

109. Simplify $\frac { 2 }{ 5 } +\frac { 8 }{ 3 } +\frac { -11 }{ 15 } +\frac { 4 }{ 5 } +\frac { -2 }{ 3 }$

110. What number should be subtracted from $\frac{-5}{3}$ to get $\frac{5}{6}$?

111. Simplify $\left( \frac { 13 }{ 7 } \times \frac { 11 }{ 26 } \right) -\left( \frac { -4 }{ 3 } \times \frac { 5 }{ 6 } \right)$

112. Find the length of arc whose radius is 42 cm and central angle is 600

113. Verify Euler's formula for a pyramid.

114. Verify Eulers formula for a triangular prism

115. Find the length of an arc if the radius of the circle is 14 cm and area of the circle is 63 cm2.

116. A circular arc whose radius is 12 cm makes an angle 30° at the center. Find the perimeter of the sector formed (ㅠ = 3.14)

117. Find r1 + r2 if the sum of the areas of two circles with radii r1 and r2 is equal to the area of a circle of radius r.

118. If the perimeter of a semicircle is 36 cm find its diameter.

119. Find the product of the following
3ab2c3 by 5a3b2c

120. Find the product of the following
${ 4x }^{ 2 }yzby\cfrac { 3 }{ 2 } { x }^{ 2 }{ yz }^{ 2 }$

121. Find the product of the following.
$\cfrac { -8 }{ 5 } { x }^{ 2 }{ yz }^{ 2 }by-\cfrac { 3 }{ 4 } { xy }^{ 2 }z$

122. Find the product of the following
$\cfrac { 3 }{ 14 } { x }^{ 2 }yby\cfrac { 7 }{ 2 } { x }^{ 4 }y$

123. Find the product of the following.
2.1 a2bc by 4ab2

124. Divide 15m2n3 by 5m2n2

125. Divide 24a3b3 by -8ab

126. Divide -21abc2 by 7abc

127. Divide 72xyz2  by-9xz

128. Divide -72a4b5c8 by -9a2b2c3

129. Divide 16m3y by 4m2y

130. Divide 32m2n3p2 by 4mnp

131. Evaluate the following (2x-3)(2x+5)

132. Evaluate the following (y-7)(y+3)

133. Evaluate the following
107X103

134. Evaluate the following
56X48

135. Evaluate the following 95 x 97

136. Factorize
81a2-121b2

137. Factorize
x2+8x+16

138. Factorize
4a2 - 4a + 1

139. Factorize
4x2-4xy+y2-9z2

140. Find the length of breadth of a rectangle with area x2- 3x + 2.

141. Divide 76x 5y3 z3 $\div$19x2y2

142. Divide (3x4 - 1875) $\div$ by (3x2-75)

143. Divide -121p4 q2r2 $\div$ (-11pqr)

144. Factorize r2 - 12x + 20

145. Factorize x2 -7x- 8

146. Factorize x2 -6x- 8

147. D is a point on the side BC. Such that $\angle$ADC = $\angle$BAC. Prove that $\frac { CA }{ CD } =\frac { CB }{ CA }$ or CA= CBXCD.

148. In the figure with respect to $\triangle$BEP and $\triangle$CPD prove that BP x PD = EP x PC.

149. Two triangles BAC and BDC right angled at A and D respectively are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P. Prove that AP x PC = DP x PB.

150. Colour the graph with minimum number of colours and no two adjacent vertices should have the same colour.

151. #### 3 Marks

36 x 5 = 180
152. Simplify $=\frac { -12 }{ 10 } +\left( \frac { -90 }{ 15 } \right) -\left( \frac { 3 }{ 8 } \right)$

153. Simplify $\left( \frac { -7 }{ 18 } \times \frac { 15 }{ -7 } \right) -\left( 1\times \frac { 1 }{ 4 } \right) +\left( \frac { 1 }{ 2 } \times \frac { 1 }{ 4 } \right)$

154. Verify associative property for addition of rational numbers for $a=\frac{5}{6}, b=\frac{-3}{4},c=\frac{4}{7}$

155. Rearrange suitably and apply the properties to simplify $\left( \frac { 6 }{ 7 } \times \frac { 2 }{ 3 } \right) +\left( \frac { 9 }{ 11 } +\frac { 2 }{ 3 } \right) +\left( \frac { 2 }{ 3 } \times \frac { 4 }{ 9 } \right)$

156. Find three rational numbers between -2 and 5 by average method.

157. Divide the sum of $\frac{-13}{5}$ and $\frac{12}{7}$ by the product of $\frac{-31}{7}$ and $\frac{-1}{2}$.

158. The cost of 2$\frac{1}{3}$metres of cloth is 275 $\frac{1}{4}$. Find the cost cloth meter.

159. A sector is cut from a circle of radius 21 cm. The angle of the sector is 150°. Find the length of its arc and area of the sector,

160. An arc of a circle is of length 5π cm and the sector it bounds has an area of 20π cm2 Find the radius of the circle.

161. PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal semi-circles drawn on PQ and QS as diameters. Find the perimeter and area of the shaded region

162. In the figure AOBCA represents a quadrant of a circle of radius 3.5cm D with center 'O' calculate the area of the shaded portion $\left( \pi =\frac { 22 }{ 7 } \right)$

163. Find the area of the shaded region in the figure.

164. An athletic track 14m wide consists of two straight sections 120m long joining semicircular ends whose inner radius is 35 m. Calculate the area of the shaded region.

165. Find the area of the shaded portion.

166. Find the area of the shaded region.

167. Simplify (3x-2)(x-1)(3x+5).

168. Simplify (5 -x) (3 - 2x) (4 - 3x).

169. Divide.9m5+12m4-6m2 by 3m2

170. Divide 24x3y+20x2y2-4xy by 2xy

171. Divide.6x2yz-3xy3z+8x2yz4 by 2xyz

172. Divide
$\cfrac { 2 }{ 3 } { a }^{ 2 }{ b }^{ 2 }{ c }^{ 2 }+\cfrac { 4 }{ 3 } { ab }^{ 2 }{ c }^{ 3 }-\cfrac { 1 }{ 5 } { ab }^{ 3 }{ { c }^{ 2 } }by\cfrac { 1 }{ 2 } abc$

173. If x+y=12 and xy=14 find x2+y2

174. If 3x + 2y = 12 and xy = 6 find the value of 9x2+4y2

175. Factorize
x2+2xy+y2-a2+2ab-b

176. Factorize
9-a6+2a3-b6

177. Factorize
x16-y16+x8+y8

178. Factorize
(p + q)2 - (a - b)2 + P + q - a + b

179. Factorize
100 (x +y)2 - 81 (a + b)2

180. Factorize
(x+1)2-(x-2)2

181. The area of a square is 4x2- + 12xy + 9y2-. Find its side.

182. If p + q = 12 and pq = 22 find p2 + q2

183. If a + b = 25, a2+ b2 = 225 find ab

184. If (x +y) = 13 and xy = 28, find x2+y2

185. If m - n = 16 and m2 + n2 = 400 find mn.

186. P and Q are points on sides AB and AC respectively of $\triangle$ABC. If AP = 3 cm PB = 6cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.

187. In the given figure if $\frac { QT }{ PR } =\frac { QR }{ QS }$ and $\angle$1 = $\angle$2.Prove that $\triangle$PQS ~$\triangle$TQR.