Set 14

  1. Observe the given Venn diagram and answer the following questions.
    1. Write the common elements of sets \(A\) and \(B\).[1]
    2. Write a proper subset of set \(A\).[1]
    3. If \(t\) is removed from set \(B\), then write the relation of sets \(A\) and \(B\) in set notation.[1]
  2. Ram obtained \(45\) marks in math subject of class \(8\) exam.
    1. Write it in scientific notation.[1]
    2. Convert it into binary number system.[2]
    3. Convert \(0.\overline{35}\) into a fraction.[1]
  3. A shopkeeper marked the price \(\text{Rs.}\,60{,}000\) for a computer and sold it with \(10\%\) discount.
    1. If marked price and discount percent are denoted by \(MP\) and \(D\%\) respectively, write the formula to find the discount amount.[1]
    2. What will be the discount amount after \(10\%\) discount?[1]
    3. Selling after \(10\%\) discount, it becomes a profit of \(\text{Rs.}\,4{,}000\). Find the cost price.[2]
  4. Roshani deposited \(\text{Rs.}\,40{,}000\) in a bank to gain interest at the rate of \(10\%\) per annum for \(18\) months.
    1. Write the formula to find interest.[1]
    2. How much interest will she gain?[2]
    3. How much amount has to be returned to her by the bank?[1]
    4. If Roshani divides the interest she got to Manisha and Anushka in the ratio \(2:3\), how much money does each get?[2]
  5. The given figure is a rectangular-shaped land belonging to Susma, and there is a swimming pool having \(14\,\text{m}\) diameter inside it. The length and breadth of the land are \(100\,\text{m}\) and \(60\,\text{m}\) respectively.
    1. Write the formula to find the area of a rectangle.[1]
    2. Find the area of the land.[1]
    3. Find the area of the land excluding the swimming pool.[2]
    4. Is a \(90\,\text{m}\) long wire enough to fence the swimming pool with \(2\) rounds of wire? Give a reason.[2]
    1. Evaluate: \((5a + x)^0\).[1]
    2. Simplify: \(\dfrac{x^2 + 2xy + y^2}{x^2 - y^2} \times \dfrac{x - y}{x + y}\).[2]
  7. Two algebraic expressions are given: \(3x^2 - 12\) and \(x^2 - 8x + 12\).
    1. Find the H.C.F. of the given expressions.[2]
    2. For what value of \(x\) does the expression \(3x^2 - 12\) become zero?[2]
  8. Two equations are given below: \(x + y = 6\) and \(x - y = 1\).
    1. Solve by using a graph.[2]
    2. What is this system of equations called?[1]
  9. In the adjoining figure, \(AB \parallel CD\).
    1. Write the name of a pair of corresponding angles.[1]
    2. Find the value of \(a\).[2]
    3. If the value of \(c\) is not \(50^\circ\), what is the relation of lines \(AB\) and \(CD\)? Write it.[1]
  10. \(\triangle ABC\) and \(\triangle PQR\) are two triangles.
    1. By which axiom are the given triangles congruent? Write it. Also write the name of a pair of corresponding angles.[2]
    2. Construct a rectangle \(PQRS\) with sides \(PQ = 8\,\text{cm}\) and \(QR = 5\,\text{cm}\).[3]
    3. What type of tessellation is given in the figure?[1]
    1. If \(A(-2,3)\), \(B(3,5)\), and \(C(6,1)\) are vertices of \(\triangle ABC\), write down the coordinates of the image of \(\triangle ABC\) after reflecting on the \(x\)-axis and sketch both figures on graph paper.[3]
    2. In the given figure, the bearing of point \(Q\) from point \(P\) is \(45^\circ\). Find the bearing of point \(P\) from \(Q\).[2]
  12. The marks secured by a student are given in the table below:
    13. Subject Nepali Math Science English
    Marks \(70\) \(40\) \(50\) \(40\)
    1. Find the mode from the above data.[1]
    2. Present it in a pie chart.[2]

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