Set 21

  1. Two sets are given: \(A = \{1, 2, 3\}\) and \(B = \{2, 3, 4\}\).
    1. Are sets \(A\) and \(B\) disjoint sets? Give a reason.[1]
    2. Write the improper subsets of set \(A\).[1]
    3. Write the proper subsets formed from set \(B\).[1]
  2. The distance between Bhairahawa and Kathmandu is \(275{,}000\,\text{m}\).
    1. Write the distance in scientific notation.[1]
    2. Convert \(1050\) into the quinary number system.[2]
    3. The distance between Bhairahawa and Nepalgunj is \(255{,}000\,\text{m}\). Find the ratio of the distances between the two pairs of cities.[2]
  3. Pranavi bought a mobile phone of marked price \(\text{Rs.}\,12{,}000\) at a \(20\%\) discount.
    1. Write the formula to calculate the discount amount if the discount rate is \(D\%\) and the marked price is (M.P.).[1]
    2. Find the discount amount on the mobile phone.[1]
    3. Find the selling price of the mobile phone.[1]
    4. If the mobile phone is sold at a \(10\%\) loss, find the cost price.[1]
  4. Anita deposited \(\text{Rs.}\,3{,}50{,}000\) in a bank at the rate of \(12\%\) per annum for \(2\) years.
    1. Write the formula to calculate the amount.[1]
    2. How much interest does Anita get in \(2\) years?[2]
    3. \(18\) men can complete a work in \(30\) days. How many men can finish the same work in \(36\) days?[2]
  5. Manisha has a plot of land in the shape of a parallelogram. She wishes to construct a circular pond of radius \(14\,\text{m}\) inside it. The base of the parallelogram is \(150\,\text{m}\) and the height is \(18\,\text{m}\).
    1. Write the formula to calculate the area of a parallelogram and a circle.[1]
    2. Find the area of Manisha's plot.[1]
    3. What is the area of the plot excluding the pond?[2]
    4. How many meters of wire netting are needed to fence around the pond?[1]
    1. Find the H.C.F. of: \(3x^{2} - 27\) and \(2x - 6\).[2]
    2. Simplify: \(\dfrac{x^{2}}{x + y} - \dfrac{y^{2}}{x + y}\)[2]
    1. What is the value of \((9 + x)^{0}\)? Write it.[1]
    2. At what value(s) of \(x\) is the expression \(x^{2} - 3x + 2\) equal to zero?[2]
  8. Two equations are given: \(x + y = 6\) and \(x - y = 2\).
    1. What are these equations called?[1]
    2. Solve the given equations using the graphical method.[2]
  9. In the given figure, lines \(KL\) and \(MN\) are intersected by transversal \(DE\) at points \(A\) and \(C\) respectively. \(\angle KAC = 60^{\circ}\).
    1. Write one pair of alternate angles.[1]
    2. Find the value of \(x\).[2]
    3. Verify experimentally that the base angles of an isosceles triangle are equal. (Two figures of different sizes are required.)[3]
    1. Find the coordinates of the image of the line segment joining \(P(5, 3)\) and \(Q(1, 6)\) after reflection in the \(y\)-axis.[1]
    2. Find the distance between points \(P\) and \(Q\).[2]
    3. The bearing of \(P\) from \(Q\) is \(060^{\circ}\). Find the bearing of \(Q\) from \(P\).[1]
    1. Construct a rectangle \(ABCD\) with \(AB = 5\,\text{cm}\) and \(BC = 4\,\text{cm}\).[3]
    2. In the given figure, \(\angle RPQ = \angle ABC\), \(PR = BC\), and \(PQ = AB\). Prove that \(\triangle PQR \cong \triangle ABC\).[2]
  12. The marks obtained by a Grade VIII student (out of \(50\)) in four subjects are given below:
    13. Subject English Mathematics Science Social Studies
    Obtained Marks \(45\) \(30\) \(42\) \(30\)
    1. Find the mode of the given data.[1]
    2. Represent the given data in a pie chart.[2]

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