Set 10

  1. Answer the following questions from the given Venn diagram.
    1. Write the improper subset of the set \(P\).[1]
    2. Write the elements of set \(U\) by listing method.[1]
    3. How many subsets are formed from set \(Q\)?[1]
  2. The marked price of a bag is \(\text{Rs.}\,5{,}000\).
    1. If marked price and discount percent are represented by \(MP\) and \(D\%\) respectively, write the formula to find the discount percent.[1]
    2. How much will be the discount amount of the bag after a discount of \(5\%\) on the marked price?[1]
    3. The shopkeeper gets \(25\%\) profit after selling the bag at \(5\%\) discount. What was the cost price of the bag?[2]
  3. Ram has deposited \(\text{Rs.}\,20{,}000\) in an Agricultural Development Bank for \(5\) years at the rate of \(\text{Rs.}\,12\) interest per annum for \(\text{Rs.}\,100\).
    1. At what percent of interest rate per annum has Ram deposited the amount of money?[1]
    2. How much interest will Ram get in \(5\) years at the same rate of interest?[2]
    3. The ages of Ram’s two sons are \(8\) years and \(12\) years respectively. He divides \(\text{Rs.}\,20{,}000\) between his sons in the ratio of their ages. How much does each get?[2]
  4. The total monthly income of five families is \(\text{Rs.}\,4{,}58{,}000\).
    1. Write the total income in scientific notation.[1]
    2. What is the monthly income of a family?[1]
    3. Convert \(0.\overline{25}\) into a fraction.[1]
    4. Convert \(27\) into the binary number system.[1]
  5. A circular playground has a radius of \(100\,\text{m}\). A rectangular volleyball court of length \(18\,\text{m}\) and breadth \(9\,\text{m}\) is made inside it. (\(\pi = 3.14\))
    1. Write the formula to find the area of the playground.[1]
    2. What is the area of the volleyball court?[1]
    3. What is the area of the playground excluding the volleyball court?[2]
    4. How long should the wire be to fence the playground once?[1]
    1. Express \(\dfrac{x^6}{x^3}\) as a power of \(x\).[1]
    2. Simplify: \(\dfrac{a}{a + b} + \dfrac{b}{a - b}\).[2]
    1. Define quadratic equation.[1]
    2. Solve by graphical method: \(x + y = 5\) and \(3x + y = 9\).[2]
    1. Find the H.C.F. of \(x^2 + 7x + 12\) and \(x^2 - 16\).[2]
    2. For what value of \(x\) does the expression \(x^2 - 8x + 15\) become zero?[2]
  9. In the figure, line \(PQ\) intersects straight lines \(AB\) and \(CD\) at points \(M\) and \(N\) respectively.
    1. Write a pair of alternate angles.[1]
    2. Find the value of \(x\).[2]
    3. At what value of \(\angle DNM\) will the lines \(AB\) and \(CD\) become parallel?[1]
    1. Construct a parallelogram \(ABCD\) with \(AB = 7\,\text{cm}\), \(BC = 5\,\text{cm}\), and \(\angle ABC = 60^\circ\).[3]
    2. In the adjoining figure, if \(\angle BAD = \angle ABC\) and \(AD = BC\), prove that \(\triangle ABC \cong \triangle ABD\).[2]
    1. What is the actual distance between two places represented by \(5.5\,\text{cm}\) on a map with scale \(1\,\text{cm} = 500\,\text{m}\)?[2]
    2. What type of quadrilateral is used to make a regular tessellation?[1]
    3. The vertices of \(\triangle ABC\) are \(A(2,1)\), \(B(4,1)\), and \(C(3,4)\). Find the coordinates of the image \(\triangle A'B'C'\) after reflecting \(\triangle ABC\) on the \(x\)-axis. Also draw the graph of the reflection.[3]
  12. The monthly expenditure of a family is given below:
    13. Title of expenditure Amount (Rs.)
    Food 20,000
    Education 10,000
    Health 6,000
    1. Calculate the average expenditure.[1]
    2. Represent the above data in a pie chart.[2]

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