Set 7

  1. The elements of sets \(A\) and \(B\) are shown in the adjoining Venn diagram.
    1. Define proper subset.[1]
    2. Write the improper subset of set \(A\).[1]
    3. If \(e, i, o, u\) are the only elements of set \(B\), what type of relation exists between sets \(A\) and \(B\)? Write with reason.[1]
  2. The marked price of a book is \(\text{Rs.}\,3{,}900\).
    1. If marked price and discount are represented by \(M\) and \(D\) respectively, write the formula to find the discount percent.[1]
    2. If the discount percent is \(7\%\), how much discount is given?[1]
    3. If the shopkeeper earned a \(17\%\) profit after selling it at \(7\%\) discount, find the cost price of the book.[2]
  3. \(\text{Rs.}\,6{,}000\) is lent out at the rate of \(12\dfrac{1}{2}\%\) per annum for \(10\) months.
    1. How much interest does Sangita earn in \(10\) months?[1]
    2. How much amount will Sangita receive after \(2\) years at the same rate?[2]
    3. The ages of Sangita’s elder and younger brothers are \(12\) years and \(8\) years respectively. If she divides \(\text{Rs.}\,2{,}00{,}000\) between them in the ratio of their ages, how much more will the elder brother receive?[2]
  4. The capacity of a water tank to supply water to a village is \(37{,}200\) liters.
    1. Write the capacity of the water tank in scientific notation.[1]
    2. If a family consumes \(8{,}520\) liters in a month and the cost per liter is \(\text{Rs.}\,0.40\), how much must they pay for one month?[2]
    3. Convert \(0.\overline{34}\) into a fraction.[1]
    4. Convert the binary number \(11100_2\) into decimal.[1]
  5. A trapezium-shaped land belongs to Bimala. A circular well of diameter \(1.4\,\text{m}\) is dug inside it. The parallel sides of the land are \(45\,\text{m}\) and \(55\,\text{m}\), and the height is \(30\,\text{m}\).
    1. Write the formula to find the area of the circular well.[1]
    2. Find the area of the top of the well. (\(\pi = \dfrac{22}{7}\))[1]
    3. Find the area of the land excluding the well.[2]
    4. Bimala wants to fence the land three times. How much wire is needed?[1]
    1. Express \(\dfrac{x^m}{x^n}\) as a power of \(x\).[1]
    2. Simplify: \(\dfrac{x}{x - y} + \dfrac{y}{y - x}\).[2]
  7. Two equations are given: \(x + y = 4\) and \(3x - 2y = -13\).
    1. What is this system of equations called?[1]
    2. Solve the equations using a graph.[2]
    1. Find the H.C.F. of \(x^2 - 1\) and \(x^2 - 2x + 1\).[2]
    2. For what value of \(x\) does the expression \(x^2 - 5x + 6\) become zero?[2]
  9. In the adjoining figure, line \(EF\) intersects straight lines \(AB\) and \(CD\) at points \(G\) and \(H\) respectively.
    1. Write a pair of co-interior angles.[1]
    2. Find the value of \(x\).[2]
    3. For what value of \(\angle BGK\) will lines \(AB\) and \(CD\) be parallel?[1]
    1. Construct a rectangle \(ABCD\) with \(AB = 8\,\text{cm}\) and \(BC = 6\,\text{cm}\).[3]
    1. Which type of triangle is used to form a regular tessellation?[1]
    2. In \(\triangle ABC\), the bearing of point \(C\) from point \(B\) is \(090^\circ\). Find the bearing of point \(B\) from point \(C\).[2]
    3. Rotate \(\triangle ABC\) through \(+90^\circ\) about the origin \(O(0,0)\) and write the coordinates of the image \(\triangle A'B'C'\).[3]
  12. The monthly expenditure of a family is given below:
    13. Month Baishakh Jestha Ashar Shrawan
    Expenditure (Rs.) 25000 19000 28000 18000
    1. What is the average monthly expenditure of the family?[1]
    2. Present the family’s expenditure in a pie chart.[2]

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