Set 18

  1. The elements of sets \(A\) and \(B\) are shown in the adjoining Venn diagram.
    1. State whether the sets \(A\) and \(B\) are overlapping or disjoint. Give a reason.[1]
    2. Write two proper subsets of set \(A\).[1]
    3. What needs to be done to make the given sets disjoint?[1]
  2. Grishma has a book of \(150\) pages.
    1. Write the number of pages in scientific notation.[1]
    2. Write the number of pages in the quinary number system.[1]
    3. Write the number of pages in the binary number system.[1]
    4. If she has read \(15\) pages, find the ratio of the completed pages to the remaining pages.[1]
  3. Ganesh buys a mobile at \(\text{Rs.}\,36{,}000\). He fixed the marked price of the mobile \(30\%\) above the cost price. If he sells the mobile at a \(25\%\) discount, then
    1. What is the marked price of the mobile?[1]
    2. What is the discount amount?[1]
    3. What is the selling price of the mobile?[1]
    4. What is his profit or loss percent from that mobile? Find it.[1]
  4. Santosh borrowed a sum of \(\text{Rs.}\,27{,}000\) from his friend Roopal. He paid an interest of \(\text{Rs.}\,5{,}940\) to Roopal at the end of \(2\) years.
    1. Write the formula to find the rate of interest.[1]
    2. At which rate of interest did Santosh borrow the sum?[1]
    3. At the same rate of interest, calculate the interest for \(5\) years.[1]
    4. If Santosh had not paid any interest till the end of \(5\) years, how much amount would he need to clear the debt?[2]
  5. The perimeter of a square land is \(440\,\text{ft}\).
    1. Write the formula for the perimeter of a square.[1]
    2. Find the length of the land.[1]
    3. Find the cost of levelling the land at the rate of \(\text{Rs.}\,50\) per \(\text{ft}^2\).[2]
    4. How much does it cost to fence the land at the rate of \(\text{Rs.}\,70\) per foot?[1]
    1. For what power of \(4\) does the value become \(\dfrac{1}{64}\)?[1]
    2. If \(a = 1\), \(b = 2\), and \(c = 3\), find the value of \(a^{b} \times b^{c} \times c^{a}\).[2]
    1. For what value of \(a\), \(\dfrac{3}{a - 5}\) is undefined?[1]
    2. Simplify: \(\dfrac{4}{x^{2} + 3x + 2} \div \left( \dfrac{2}{x^{2} - 1} \right)\)[2]
  8. If two algebraic expressions are \(a^{2} - 3a + 2\) and \(a^{2} - 9a + 10\),
    1. Find the Highest Common Factor (H.C.F.).[2]
    2. Solve the equation \(x^{2} - 6x + 8 = 0\) by the factorization method.[2]
  9. From the adjoining figure,
    1. Write the name of a pair of alternate angles.[1]
    2. What is the value of \(x\)?[2]
    3. Calculate the value of \(y\).[1]
    1. Construct a square \(ABCD\) in which side \(AB = 6\,\text{cm}\).[3]
    2. In the adjoining figure, \(\angle RPQ = \angle PQS\) and \(QS = PR\). Show that \(\triangle PQR \cong \triangle QPS\).[2]
    1. Write the formula to calculate the distance between two points.[1]
    2. Find an interior angle of a regular pentagon.[2]
    3. \(A(2,1)\), \(B(-4,5)\), and \(C(2,3)\) are the vertices of \(\triangle ABC\). Find the vertices of the image \(\triangle A'B'C'\) after reflecting \(\triangle ABC\) on the \(x\)-axis using a graph.[3]
  12. Study the following table and solve the given problems:
    13. Class V VI VII VIII Total
    No. of students \(53\) \(43\) \(46\) \(50\) \(192\)
    1. Present the above information in a pie chart.[2]
    2. What is the average number of students per class?[1]

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