Set 9

  1. Two sets \(M\) and \(N\) are presented below: \(M = \{a, p, l, e\}\), \(N = \{p, a, n\}\).
    1. Are the sets \(M\) and \(N\) overlapping sets? Give a reason.[1]
    2. How many subsets can be made from set \(M\)?[1]
    3. Represent the given sets \(M\) and \(N\) in a Venn diagram.[1]
  2. Kreepa marks a laptop with a price of \(\text{Rs.}\,1{,}20{,}000\).
    1. If profit percent, cost price, and selling price are denoted by \(P\%\), \(C.P.\), and \(S.P.\) respectively, write the formula to find cost price (\(C.P.\)).[1]
    2. What will be the price of the laptop if a \(15\%\) discount is given?[2]
    3. Find the cost price if the profit amount is \(\text{Rs.}\,10{,}000\).[1]
  3. Shriyansh deposited \(\text{Rs.}\,25{,}000\) in a bank at the rate of \(10\%\) per annum simple interest for \(2\) years.
    1. What do you mean by rate of interest \(10\%\) per annum?[1]
    2. Find the interest for \(2\) years.[1]
    1. Write in scientific notation: \(2{,}360{,}000\).[1]
    2. If \(2, 6, x, 27\) are in proportion, find the value of \(x\).[2]
    3. Convert \(0.\overline{34}\) into a fraction.[1]
    4. Express in the quinary number system: \((68)_{10}\).[1]
  5. A circular garden having diameter \(21\,\text{m}\) is made inside a plot which is in the shape of a square of side \(40\,\text{m}\).
    1. Write the formula to find the area of a circle.[1]
    2. Find the area of the circular garden.[1]
    3. Find the area of the land excluding the area of the circle.[2]
    4. If the garden were an equilateral triangle having a side of \(20\,\text{m}\), how much plot would remain?[1]
    1. Express \(a^3 \times a^5\) as a power of \(a\).[1]
    2. Simplify: \(x^{a^2 - b^2} \times x^{b^2 - c^2} \times x^{c^2 - a^2}\).[2]
    1. Solve: \(\dfrac{1}{x} + \dfrac{1}{x+1} = \dfrac{2}{x-1}\).[2]
    2. Find the H.C.F. of \(x^2 - 9\) and \(x^2 - 5x + 6\).[2]
    1. Write the equation of the \(x\)-axis.[1]
    2. Solve graphically: \(x + y = 7\) and \(x - y = 1\).[2]
  9. In the adjoining figure, two parallel lines \(MN\) and \(OP\) are intersected by a straight line \(XY\) at points \(A\) and \(B\) respectively.
    1. Write a pair of corresponding angles.[1]
    2. Find the value of \(x\).[2]
    3. Compare the angles \(\angle CAB\) and \(\angle ABC\).[1]
    1. Construct a parallelogram \(PQRS\) having \(PQ = 6\,\text{cm}\), \(QR = 5\,\text{cm}\), and \(\angle PQR = 75^\circ\).[3]
    2. By which axiom are \(\triangle ABC\) and \(\triangle DEF\) congruent? Also write a pair of corresponding angles.[3]
    1. Draw the net of a cylinder.[1]
    2. Write the bearing of point \(B\) from point \(A\).[1]
    3. \(A(3,4)\), \(B(2,-3)\), and \(C(6,0)\) are the vertices of \(\triangle ABC\). Find the coordinates of the image under reflection on the \(y\)-axis. Also represent \(\triangle ABC\) and its image on graph paper.[3]
  12. The monthly expenditure of a family is given below:
    13. Expenditure Food Health House Rent Education Others
    Amount (Rs.) 8000 6000 4000 12000 6000
    1. Represent the above information in a pie chart.[2]
    2. Find the average expenditure.[1]

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