Godawari_Kailali_8_2081

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  1. Universal set \(U = \{1, 2, 3, 4, 5, 6\}\), set \(A = \{1, 3, 5\}\), and set \(B = \{3, 5, 6\}\) are given.
    1. Are the sets \(A\) and \(B\) overlapping or disjoint? Write it.[1]
    2. Write any two proper subsets from the set \(A\).[1]
    3. Show the sets \(A\) and \(B\) in a Venn diagram.[1]
  2. The marked price of a watch is \(\text{Rs.}\,1{,}500\). The shopkeeper sold the watch after a \(10\%\) discount.
    1. Write the formula to find the discount percentage.[1]
    2. Find the discount amount.[1]
    3. If the shopkeeper sold the watch to make a \(5\%\) profit, then find the cost price of the watch.[2]
  3. Anu had borrowed a loan of \(\text{Rs.}\,6{,}000\) from a bank \(4\) years ago. She paid a total amount of \(\text{Rs.}\,9{,}000\) and cleared the loan.
    1. Find the simple interest.[2]
    2. What was the rate of interest?[2]
    3. In how many years will the principal and interest be equal?[1]
    1. Write the decimal number \(0.000063\) in scientific notation.[1]
    2. If the cost of \(10\,\text{kg}\) of oranges is \(\text{Rs.}\,1{,}250\), what will be the cost of \(6\,\text{kg}\) of oranges?[1]
    3. Convert \(0.\overline{17}\) into a fraction.[2]
    4. Convert the binary number \(10111_2\) into the decimal number system.[1]
  5. A circular pond of diameter \(14\,\text{m}\) is inside a rectangular piece of land of length \(40\,\text{m}\) and breadth \(35\,\text{m}\).
    1. Find the area of the pond.[1]
    2. Find the total area of the land and pond.[1]
    3. Find the area of the land excluding the pond.[1]
    4. Find the cost of fencing the land at the rate of \(\text{Rs.}\,200\) per meter.[2]
    1. Simplify by using rules of indices: \(x^{3} \times x^{-3}\)[1]
    2. Simplify: \(\dfrac{y^{2}}{y - 2} - \dfrac{4}{y - 2}\)[2]
    1. Factorize: \(a^{2} - 64b^{2}\)[2]
    2. Solve graphically: \(x + y = 6\) and \(y = x + 4\)[2]
    1. Find the H.C.F. of the expressions: \(a^{2} - 25\) and \(a^{2} - 12a + 35\).[2]
    2. Solve: \(a^{2} + 7a + 12 = 0\)[2]
  9. In the given figure, \(\angle AEB = 60^{\circ}\), and lines are as shown.
    1. Find the values of \(y\) and \(z\) from the given figure.[2]
    2. Write the formula to find the measure of each exterior angle of a regular polygon.[1]
    3. Find the distance between the points \(P(1, 7)\) and \(Q(1, 1)\).[1]
    1. Construct a rectangle \(ABCD\) in which \(AB = 7\,\text{cm}\) and \(AD = 4\,\text{cm}\).[3]
    2. Verify experimentally that the base angles of an isosceles right-angled triangle are equal to \(45^{\circ}\). (Two figures of different sizes are required.)[2]
    1. Draw a net of a cylinder.[1]
    2. If \(A(2, 1)\), \(B(5, 1)\), and \(C(4, 4)\) are the vertices of \(\triangle ABC\), find the image \(\triangle A'B'C'\) after reflecting on the \(y\)-axis and show both triangles on the same graph.[3]
    3. If the bearing of \(B\) from \(A\) is \(060^{\circ}\), find the bearing of \(A\) from \(B\).[2]
    1. Find the mode of the given data: \(30, 40, 60, 80, 30\).[1]
    2. Represent the following data in a pie chart:
      Gases Nitrogen Oxygen Others
      Percentage \(78\%\) \(21\%\) \(1\%\)
      [2]

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