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Creative important question for all chapter

8th Standard EM

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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)

    quadrilateral

    (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.

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