Set 24

  1. Given a Venn diagram.
    1. Define subset.[1]
    2. Write all the subsets of \(A\) having a single element.[1]
    3. Which elements of set \(B\) are to be removed to make the sets \(A\) and \(B\) disjoint sets? Write it.[1]
  2. The marked price of a laptop is \(\text{Rs.}\,80{,}000\). The shopkeeper allows a \(15\%\) discount on it.
    1. If marked price and discount are represented by (M.P.) and (\(D\)) respectively, write the formula to find the discount percentage.[1]
    2. Find the discount amount given on the laptop.[1]
    3. Find the profit or loss of the shopkeeper if he bought the laptop at \(\text{Rs.}\,65{,}000\).[2]
  3. A man deposited \(\text{Rs.}\,60{,}000\) in a bank. If he received \(\text{Rs.}\,16{,}200\) as interest from the bank after \(3\) years,
    1. Find the total amount he received from the bank.[1]
    2. Find the rate of interest.[2]
    3. If he divided the received interest between two daughters Rusmita and Susmita in the ratio \(2:3\), then how much money did Rusmita and Susmita get?[2]
  4. There are \(530\) students in a school.
    1. Express the total number of students in scientific notation.[1]
    2. Find the total number of copies required to distribute to all students at the rate of \(3\) copies per student.[1]
    3. Convert \(0.94\) into a fraction.[1]
    4. A teacher writes his salary in quinary number in the expanded form as \[ 2 \times 5^{6} + 1 \times 5^{5} + 4 \times 5^{4} + 2 \times 5^{3} + 3 \times 5^{2} + 0 \times 5^{1} + 0 \times 5^{0}. \] Write the short form of his salary in the quinary system.[1]
  5. In the figure, a rectangular field is shown and a square cottage is constructed in its one corner.
    1. Write the formula to find the area of a rectangle.[1]
    2. Find the area of the cottage.[1]
    3. Find the area of the field excluding the cottage.[2]
    4. How much does it cost to fence the field at the rate of \(\text{Rs.}\,50\) per meter?[1]
    1. Express \(\dfrac{x^{m}}{x^{n}}\) as a power of \(x\).[1]
    2. Simplify: \(\dfrac{a}{a - b} - \dfrac{a}{a + b}\)[2]
  7. Let \(x\) and \(y\) be two numbers whose sum is \(4\) and difference is \(2\).
    1. Form the linear equations to represent the given statements.[1]
    2. Solve the equations using the graphical method.[2]
  8. If two algebraic expressions are \(x^{2} + x - 20\) and \(x^{2} - 25\),
    1. Find the Highest Common Factor (H.C.F.) of the given algebraic expressions.[2]
    2. At what values of \(x\) is the expression \(x^{2} + x - 20\) equal to zero?[2]
  9. In the adjoining figure, lines \(DE \parallel BC\). Also, \(\angle BAC = 70^{\circ}\), \(\angle ABC = 3x\), \(\angle ACB = 2x\), and \(\angle EAC = y\) are given.
    1. Write the alternate angle of \(\angle DAB\).[1]
    2. Find the values of \(x\) and \(y\) from the figure.[2]
    3. Compare the values of \(x\) and \(y\).[1]
    1. Construct a parallelogram \(ABCD\) with \(AB = 8\,\text{cm}\), \(BC = 6\,\text{cm}\), and \(\angle ABC = 45^{\circ}\).[3]
    2. In the given figure, if \(AB \parallel CD\), prove that \(\triangle ADB \sim \triangle COD\).[2]
    1. Write down the bearing of point \(P\) from point \(O\).[1]
    2. Find the value of \(m\) if the distance between \(A(2, -1)\) and \(B(m, -5)\) is \(4\sqrt{2}\) units.[2]
    3. Draw a triangle \(ABC\) with vertices \(A(4, 2)\), \(B(3, 5)\), and \(C(6, 5)\) on graph paper. Rotate it through \(+90^{\circ}\) about the origin and show the image on the same graph paper.[3]
  12. The annual budget of a family is given below:
    13. Headings House Rent Business Agriculture Salary Others
    Expenses (Rs.) \(\text{Rs.}\,15{,}000\) \(\text{Rs.}\,17{,}000\) \(\text{Rs.}\,12{,}000\) \(\text{Rs.}\,25{,}000\) \(\text{Rs.}\,3{,}000\)
    1. Represent the given data in a pie chart.[2]
    2. What is the average annual budget? Find it.[1]

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