Mahalaxmi Lalitpur_8_2081

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  1. Two sets \(P\) and \(Q\) are shown in the adjoining Venn diagram.
    1. Define subset.[1]
    2. Write an improper subset of set \(P\).[1]
    3. If two elements \(a\) and \(e\) are removed from set \(P\), then what type of sets are \(P\) and \(Q\)? Write with reason.[1]
  2. Sundar sold a piano of marked price \(\text{Rs.}\,20{,}000\) at \(15\%\) discount.
    1. How much is the discount amount of the article whose marked price is \(MP\) and discount percentage is \(D\%\)?[1]
    2. Find the selling price of the piano.[1]
    3. If the piano is sold at \(20\%\) loss, find the cost price.[2]
    4. If the discount was not allowed, then what would be the profit or loss? Find in percentage.[2]
  3. The interest on \(\text{Rs.}\,5{,}040\) in \(5\) years is \(\text{Rs.}\,2{,}520\).
    1. Write the formula to find the simple interest if the amount (\(A\)) and principal (\(P\)) are given.[1]
    2. Find the rate of interest.[2]
    3. In how many years will the principal and interest be equal? Write with reason.[1]
  4. There are \(2{,}075\) lemon plants in Numa's garden.
    1. Write the number of plants in scientific notation.[1]
    2. If the cost of one plant was \(\text{Rs.}\,70\), then find the total cost.[1]
    3. Express the number of plants in the quinary number system.[2]
  5. As shown in the figure, inside a circular ground having diameter \(42\,\text{m}\), a rectangular pond having length \(20\,\text{m}\) and breadth \(10\,\text{m}\) is made.
    1. Write the formula to calculate the area of the pond.[1]
    2. What is the area of the circular ground? Find it.[1]
    3. Find the area of the remaining ground excluding the pond.[2]
    4. How much will it cost to plant dubo at the rate of \(\text{Rs.}\,25\) per \(\text{m}^2\) in the remaining part of the ground?[1]
    1. Write the expanded form of \(x^2 - y^2\).[1]
    2. Simplify: \(\left(\dfrac{x^a}{x^b}\right)^{a+b} \times \left(\dfrac{x^b}{x^c}\right)^{b+c} \times \left(\dfrac{x^c}{x^a}\right)^{c+a}\)[2]
  7. An equation \(x^2 - 7x + 12 = 0\) is given.
    1. What is the degree of the given equation? Write it.[1]
    2. For what values of \(x\) is the expression \(x^2 - 7x + 12 = 0\) equal to zero?[2]
    1. Find the Highest Common Factor (H.C.F.) of \(2a^2 - 9a + 10\) and \(5(a - 2)\).[2]
    2. Simplify: \(\dfrac{p - 2}{p + 2} - \dfrac{p - 2}{p^2 - 4}\)[2]
  9. In the adjoining figure, \(AB\) intersects straight lines \(LM\) and \(PQ\) at points \(E\) and \(F\) respectively.
    1. Write the name of a pair of co-interior angles.[1]
    2. Find the value of \(x\).[2]
    3. At what value of \(\angle MEG\) will the lines \(LM\) and \(PQ\) become parallel?[1]
    1. Construct a square \(PQRS\) having side length \(6\,\text{cm}\).[3]
    2. In the adjoining figure, \(ABCD\) is a parallelogram. Prove that \(\triangle ABD \cong \triangle CDB\).[2]
    1. A tessellation is formed by regular octagons and squares. Write the type of tessellation.[1]
    2. In \(\triangle ABC\), if the bearing of point \(B\) from point \(A\) is \(075^\circ\), find the bearing of point \(A\) from point \(B\).[2]
    3. Reflect \(\triangle ABC\) (shown on graph paper) on the \(y\)-axis and write the coordinates of the vertices of the image triangle.[3]
  12. The ages (in years) of \(10\) students of grade \(8\) are given below: \(13, 14, 12, 14, 13, 14, 13, 12, 14, 16\).
    1. What is the mode of the above data? Write it.[1]
    2. Find the average age (in years) of the students from the above data.[2]

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