Set 27

  1. Sets \(P\) and \(Q\) are shown in a Venn diagram.
    1. Define subset.[1]
    2. Write the improper subset of set \(Q\).[1]
    3. If \(1, 3, 5\) are the only members of set \(P\), then what types of sets are \(P\) and \(Q\)? Write with reasons.[1]
  2. The highway distance between Kathmandu to Narayanghat is \(140{,}000\) m.
    1. Write the distance in scientific notation.[1]
    2. Convert \(1050\) into the quinary number system.[1]
    3. Convert \(0.\overline{34}\) into a fraction.[2]
  3. Anish marked the price of a radio Rs. \(3{,}000\). If he sold it allowing a discount of \(15\%\) and made a profit of Rs. \(500\).
    1. If marked price (MP) and discount (D) are represented by (MP) and (D) respectively, write the formula to find the selling price.[1]
    2. What is the selling price of the radio?[1]
    3. If the discount was not allowed, then what would be the profit?[2]
  4. Rajan deposited Rs. \(60{,}000\) at the rate of \(10\%\) p.a. in a savings account. After 5 years, he withdrew Rs. \(40{,}000\) and the total interest of 5 years.
    1. If interest (\(I\)), rate (\(R\)), and time (\(T\)) are given, write the formula to calculate the principal.[1]
    2. Find the interest of 5 years.[2]
    3. How long should he keep the remaining balance in the bank to get a total interest of Rs. \(40{,}000\) from the beginning?[2]
  5. The length of a rectangular field is twice the breadth. A circular garden of radius \(35\) m is constructed in the field. The length of the field is \(100\) m.
    1. Write the formula to find the area of the rectangular field.[1]
    2. Calculate the area of the circular garden.[1]
    3. What is the area of the field excluding the garden?[2]
    4. Compare the perimeter of the field and the garden.[2]
    1. Write the combined form of \((m+n)(m-n)\).[1]
    2. Simplify: \(\left( \frac{m^a}{m^b} \right)^{a+b} \times \left( \frac{m^b}{m^c} \right)^{b+c} \times \left( \frac{m^c}{m^a} \right)^{c+a}\)[2]
  7. Two equations are given as: \(x + y = 4\) and \(x - y = 2\).
    1. What are the system of equations called?[1]
    2. Solve the above equations by using graph.[2]
  8. If two algebraic expressions are \(x^2 - 5x + 6\) and \(x^2 - 9\).
    1. Find the H.C.F. of the given algebraic expressions.[2]
    2. At what value of \(x\) is the value of the expression \(x^2 - 5x + 6\) equal to zero?[2]
  9. In the adjoining figure, line \(l\) intersects straight lines \(AB\) and \(CD\) at points \(G\) and \(E\) respectively. \(\angle GHE = 45^\circ\).
    1. Write a pair of co-interior angles in the figure.[1]
    2. What type of triangle is \(\triangle GHE\) according to its angles?[2]
    3. At what value of \(\angle GED\) will the given line segments \(AB\) and \(CD\) be parallel?[1]
    1. Construct a parallelogram \(ABCD\) where \(AB = 7\) cm, \(AD = 6\) cm and \(\angle BAC = 75^\circ\).[3]
    2. In the given figure, \(\triangle ABC \sim \triangle AXY\). If \(AB = 4\) cm, \(AX = 6\) cm, and \(BC = 12\) cm, find the value of \(XY\).[2]
    1. Define regular tessellation.[1]
    2. In the given figure, the bearing of point \(B\) from point \(A\) is \(075^\circ\). What is the bearing of point \(A\) from point \(B\)?[2]
    3. \(A(-3, 2)\), \(B(-5, 4)\), and \(C(-2, 6)\) are the vertices of \(\triangle ABC\). Plot \(\triangle ABC\) on a graph and reflect it in the \(x\)-axis. Then, write the coordinates of the image points \(A'\), \(B'\), and \(C'\).[3]
  12. The monthly expenditure of Ramesh's family is given below:
    13. Baishakh Jestha Asar Shrawan
    Rs. 8,000 Rs. 12,500 Rs. 9,000 Rs. 4,500
    1. What is the monthly average expenditure of Ramesh's family?[1]
    2. Present Ramesh's family expenditure in a pie chart.[2]

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