Jaljala_8_2081

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  1. Given Venn diagram:
    1. Define overlapping subset.[1]
    2. Make a proper subset of set \(M\).[1]
    3. If the element \(b\) is removed from the above Venn diagram, which type of set relation will exist between \(L\) and \(M\)? Write with reason.[1]
  2. Suman went to the furniture shop to buy a set of a table and chairs. The marked price of a set of a table and 4 chairs was \(\text{Rs.}\,12{,}000\).
    1. If the price of a table is \(\text{Rs.}\,6{,}000\), then how much is the cost for 4 chairs?[1]
    2. Suman gets \(5\%\) discount on the set of table and chairs. Find the price after discount.[2]
    3. If the shopkeeper earned \(5\%\) profit even after offering \(5\%\) discount, at what price did the shopkeeper purchase the set?[2]
  3. A hotel of Mardi Himal has deposited \(\text{Rs.}\,5{,}00{,}000\) in bank \(A\) and \(\text{Rs.}\,3{,}00{,}000\) in bank \(B\) at the rate of \(6\%\) per annum.
    1. Write the formula to find simple interest.[1]
    2. How much interest does the hotel earn in \(4\) years from bank \(A\)?[1]
    3. Find the ratio of interest received from bank \(A\) and bank \(B\) in \(4\) years.[2]
  4. There are two tanks. The first tank contains \(2.64 \times 10^3\) liters and the second contains \(3.56 \times 10^2\) liters of water.
    1. How much water is there altogether from both tanks? Express in scientific notation.[1]
    2. How much water should be added to the second tank to make it equal to the first tank?[1]
    3. Convert \(0.57\) into a fraction.[1]
    4. Prove that \(2081 = 3131_5\).[2]
  5. There is a football ground with \(90\,\text{m}\) length and \(60\,\text{m}\) width inside a circular stadium with diameter \(140\,\text{m}\).
    1. Write the formula to find the radius when diameter is given.[1]
    2. Find the area of the football ground.[1]
    3. Find the area of the circular stadium excluding the football ground.[2]
    4. Find the cost of planting grass on the football ground at the rate of \(\text{Rs.}\,250\) per \(\text{m}^2\).[1]
    1. Express \(\dfrac{x^a}{x^{-b}}\) as a power of \(x\).[1]
    2. Simplify: \(\dfrac{x^2 + 5x + 6}{x^2 - 9} \times \dfrac{x - 3}{x + 3}\)[2]
  7. Two equations are given below: \(x + y = 6\) and \(2x + y = 9\).
    1. What is this system of equations called?[1]
    2. Solve the above equations using a graph.[2]
    1. Find the Highest Common Factor (H.C.F.) of \(x^2 - 7x + 10\) and \(x^2 - 4\).[2]
    2. At what value of \(m\) does the expression \(m^2 - 5m + 6\) become zero?[2]
  9. In the figure, \(AB \parallel CD\) and \(QR\) is a transversal.
    1. Write the alternate angle of \(\angle BIJ\).[1]
    2. What type of triangle is \(\triangle IKJ\) according to its angles?[2]
    3. At what value of \(\angle AIK\) will the lines \(AB\) and \(CD\) be parallel?[1]
    1. In the given figure, \(AB = CD\) and \(AB \parallel CD\). Prove that \(\triangle AOB \cong \triangle COD\).[2]
    2. Construct a rectangle \(ABCD\) in which \(AB = 7\,\text{cm}\) and \(AD = 4\,\text{cm}\).[3]
  11. Answer the following questions:
    1. What type of quadrilateral is used to make a regular tessellation?[1]
    2. From the given figure, write the bearing of point \(B\) from point \(A\) and the bearing of point \(A\) from point \(B\).[2]
    3. Find the vertices of the image square \(A'B'C'D'\) formed by reflecting square \(ABCD\) with vertices \(A(2,3)\), \(B(6,3)\), \(C(6,7)\), and \(D(2,7)\) in the \(x\)-axis. Also draw the graph of the reflection.[3]
    1. In a class test of mathematics, 10 students obtained the following marks: \(10, 15, 12, 15, 14, 12, 15, 14, 15, 10\). Find its mode.[1]
    2. A man with a monthly income of \(\text{Rs.}\,30{,}000\) plans his budget as follows:
      Items Food Education Miscellaneous
      Expenditure (Rs.) 15000 6000 9000
      Present the above data in a pie chart.[2]

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