Set 3

  1. Study the given Venn diagram and answer the following questions.
    1. Define disjoint sets.[1]
    2. Write any one proper subset of set \(P\).[1]
    3. If the common element \(5\) is removed from the Venn diagram, then what will be the relation between sets \(P\) and \(Q\)? Write it.[1]
  2. The marked price of a television is \(\text{Rs.}\,24{,}000\). If the shopkeeper got \(\text{Rs.}\,2{,}400\) profit after selling it with \(15\%\) discount, then
    1. If marked price and discount amount are represented by \(MP\) and \(D\) respectively, write the formula to find the selling price after discount.[1]
    2. How much discount had been given by the shopkeeper to sell the television? Find it.[2]
    3. Find the cost price of the television.[2]
  3. Sunil has deposited \(\text{Rs.}\,3{,}00{,}000\) in Rastriya Banijya Bank for \(3\) years at the rate of \(\text{Rs.}\,12\) simple interest per annum for every \(\text{Rs.}\,100\).
    1. At what percent of interest rate per annum had Sunil deposited the amount?[1]
    2. After \(3\) years, how much total money does Sunil get with principal and interest? Calculate it.[1]
    3. If Sunil decides to distribute \(\text{Rs.}\,3{,}00{,}000\) to his brothers Chandan and Ram in the ratio \(2:3\), then compare the amount received by Chandan and Ram.[2]
  4. Raju takes a bus to Dharan from Biratnagar. The wheel of the bus rotates \(35{,}750\) times in an hour.
    1. Write \(35{,}750\) in scientific notation.[1]
    2. How many times will the wheel rotate in \(90\) minutes?[1]
    3. Find the value of \(\sqrt{48} + \sqrt{75} - \sqrt{3}\).[2]
    4. Convert \(0.\overline{24}\) into a fraction.[1]
  5. In the given figure, \(ABCD\) is a square and a circle is drawn inside it.
    1. Write the formula to find the area of a circle.[1]
    2. How much is the radius of the circle?[1]
    3. Find the area of the shaded region.[2]
    4. Compare the circumference of the circle and the perimeter of the square.[1]
    1. Express \(x^m \times x^{-1}\) as a power of \(x\).[1]
    2. Simplify: \(\dfrac{a}{(a - b)^2} + \dfrac{b}{(a - b)^2}\).[2]
  7. Two equations are given: \(x + y = 6\) and \(x - y = 2\).
    1. What is meant by simultaneous equations?[1]
    2. Solve the given equations by using a graph.[2]
    1. Find the L.C.M. of the algebraic expressions: \(x^2 - 7x + 12\) and \(3x^2 - 27\).[2]
    2. Find the quadratic equation in which the values of \(x\) are \(2\) and \(3\).[2]
  9. In the adjoining figure, when \(XY\) and \(XZ\) meet the line segments \(PQ\) and \(RS\), a \(\triangle XYZ\) is formed.
    1. Write the relation between \(\angle XYZ\) and \(\angle XZY\).[1]
    2. Find the value of \(x\).[2]
    3. At which value of \(\angle PXY\) will the line segments \(PQ\) and \(RS\) be parallel?[1]
    1. Construct a rectangle \(ABCD\) in which \(AB = 7\,\text{cm}\) and \(BC = 5\,\text{cm}\).[3]
    2. In rectangle \(ABCD\), prove that \(\triangle ABC \cong \triangle ACD\) by drawing diagonal \(AC\).[2]
    1. What is meant by regular tessellation?[1]
    2. In the adjoining figure, if the bearing of point \(S\) from point \(R\) is \(060^\circ\), find the bearing of point \(R\) from point \(S\).[2]
    3. Find the coordinates of the images \(M'\), \(N'\), and \(O'\) of \(\triangle MNO\) with vertices \(M(2,1)\), \(N(4,3)\), and \(O(-1,2)\) after reflection on the \(x\)-axis.[3]
  12. The monthly expenses of Shital's meals are given in the table below:
    13. Month Ashoj Kartik Mangsir Poush Magh
    Expenditure (Rs.) 4000 2500 2000 1700 1800
    1. What is the monthly average expenditure of Shital on her meals?[1]
    2. Present Shital’s expenditure in a pie chart.[2]

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