Nepalganj_8_2081

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  1. The subsets \(A\) and \(B\) of the universal set \(U\) are presented in the Venn diagram.
    1. Identify and write whether the sets \(A\) and \(B\) are overlapping or disjoint.[1]
    2. Write the improper subset that can be made from set \(B\).[1]
    3. How many more or less proper subsets can be made from set \(B\) than from set \(A\)?[1]
  2. The marked price of a watch is \(\text{Rs.}\,1{,}500\). A shopkeeper sold it at \(10\%\) discount.
    1. Write the formula to calculate discount percentage.[1]
    2. Find the discount amount.[1]
    3. If the shopkeeper earns a profit of \(8\%\) by selling the watch, at what price did he buy the watch?[2]
  3. If Karuna has deposited \(\text{Rs.}\,35{,}000\) in a bank at \(12\%\) rate of interest per year for \(2\) years,
    1. Express the simple interest in the form of \(P\), \(T\), and \(R\).[1]
    2. Find the interest.[1]
    3. Divide the interest in the ratio \(1:2\).[2]
    1. Convert the quinary number \(123_5\) into the decimal number system.[1]
    2. If \(16\) workers can complete a work in \(25\) days, how many workers can complete the same work in \(20\) days?[2]
    3. Write the decimal number \(0.0000045\) in scientific notation.[1]
    4. If \(3, x, 6, 8\) are in proportion, find the value of \(x\).[1]
  5. There is a rectangular plot with a length of \(20\,\text{m}\) and width of \(15\,\text{m}\), and within it there is a circular pond with radius \(7\,\text{m}\).
    1. Find the area of the land.[1]
    2. Find the area of the land excluding the pond.[2]
    3. Find the cost of fencing the land at the rate of \(\text{Rs.}\,175\) per meter.[1]
    1. Simplify: \(x^{a-b} \times x^{b-c} \times x^{c-a}\).[1]
    2. Simplify: \(\left(\dfrac{xy}{z}\right)^{-1} \times \left(\dfrac{z}{xy}\right)^{-2}\).[2]
    3. Simplify: \(\dfrac{1}{a + b} + \dfrac{1}{a - b} + \dfrac{2b}{a^2 - b^2}\).[2]
    1. Factorise: \(9x^2 - 25y^2\).[2]
    2. Find the H.C.F. of \(x^2 - 5x + 6\) and \(x^2 - 9\).[2]
    1. Write the expanded form of \((a - 5)^3\).[2]
    2. Solve: \((x - 7)^2 - 64 = 0\).[2]
    1. Find the value of \(x\) in the given figure.[2]
    2. In \(\triangle ABC\), \(\angle B = 90^\circ\), \(AB = 4\,\text{cm}\), and \(BC = 3\,\text{cm}\). Find the length of \(AC\).[2]
    3. What is the measure of each interior angle of a regular pentagon?[1]
    1. Construct a rectangle \(ABCD\) having adjacent sides \(AB = 8\,\text{cm}\), \(BC = 6\,\text{cm}\), and diagonal \(AC = 10\,\text{cm}\).[3]
    2. In the given figure, if \(\triangle PQC \sim \triangle ABC\), find the value of \(QC\).[2]
    1. Find the distance between the points \(P(-2,-4)\) and \(Q(10,1)\).[1]
    2. If the bearing of a place \(S\) from the place \(R\) is \(050^\circ\), what is the bearing of place \(R\) from place \(S\)?[2]
    3. Verify from at least \(2\) experiments that the sum of interior angles of a triangle is \(180^\circ\).[3]
  12. The monthly expenditure of a family is given in the table below:
    13. Title Food Education Clothing Other expense
    Expenditure Amount (Rs.) 3600 2000 1000 600
    1. Represent the above data in a pie chart.[2]
    2. If the mean of \(4, 10, 3, 6, a, 9, 10\) is \(7\), find the value of \(a\).[1]

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