Lalitpur_8_2081

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  1. If set \(A = \{\text{even numbers up to }15\}\) and set \(B = \{\text{prime numbers up to }15\}\),
    1. Define overlapping sets.[1]
    2. Make any two proper subsets from set \(B\).[1]
    3. What change in the outcome of set \(B\) makes the two sets \(A\) and \(B\) disjoint?[1]
  2. The ratio of boys and girls of class eight of a school is \(5:7\) respectively. If the total number of students is \(60\), then
    1. How many girls are there? Find it.[1]
    2. Change the total number of students into the binary number system.[1]
    3. Write \(350{,}000\) in scientific notation.[1]
    4. Convert \(1.\overline{24}\) into a fraction.[1]
  3. Raju Lama visited a computer store to get \(5\) printers and a laptop. A set of \(5\) printers and a laptop is available for \(\text{Rs.}\,4{,}65{,}000\).
    1. If \(15\%\) discount is allowed on those machineries, find the discount amount.[2]
    2. If the shopkeeper earned \(20\%\) profit even after allowing \(15\%\) discount, at what price did the shopkeeper purchase such machineries?[2]
    3. By how much is the marked price of a laptop less or more than \(\text{Rs.}\,95{,}000\), if the price of a printer is \(\text{Rs.}\,75{,}000\)?[1]
  4. Dilliram deposited \(\text{Rs.}\,1{,}20{,}000\) in a bank at the rate of \(12\%\) per annum.
    1. Write a formula to calculate simple interest.[1]
    2. How much interest does Dilliram get after \(6\) years?[1]
    3. If he has to pay \(5\%\) of interest as income tax, how much amount will he receive after \(6\) years?[2]
  5. Mohan constructed a rectangular garden and a circular fish pond in the garden of his house with equal areas.
    1. Find the area of a triangle having base \(b\,\text{cm}\) and height \(h\,\text{cm}\).[1]
    2. Find the area of the circular fish pond.[1]
    3. Find the perimeter of the rectangular garden.[2]
    4. Which of the garden or fish pond needs more cost to fence at the same rate of cost?[1]
    1. What exponent of \(y\) will be equal to \(1\)?[1]
    2. Prove that: \((x^{a-b})^{a+b} \cdot (x^{b-c})^{b+c} \cdot (x^{c-a})^{c+a} = 1\).[2]
  7. An algebraic fraction is given: \(\dfrac{x}{x^2 + 3x + 2}\) \(\div\) \(\dfrac{2}{x^2 - 1}\).
    1. Find the L.C.M. of the denominators.[1]
    2. Simplify the given fraction and reduce it to the lowest term.[2]
  8. There are two numbers \(x\) and \(y\) such that their sum is \(8\) and difference is \(4\).
    1. Construct the simultaneous equations based on the given statements.[1]
    2. What are the numbers? Calculate by using graphical method.[2]
  9. Study the given figure and answer the following questions.
    1. Find the value of \(x\) and \(y\).[2]
    2. Compare the angles \(x\) and \(y\).[1]
    3. Draw a bearing angle of \(030^\circ\).[1]
  10. Study the given figure and answer the following questions.
    1. Define congruent figures.[1]
    2. If \(\triangle ADE \sim \triangle ABC\), find the length of \(DE\).[2]
    3. In a regular polyhedron, the number of vertices is \(8\) and the number of edges is \(12\). Calculate the number of faces by using Euler’s formula.[2]
    1. Construct a parallelogram having adjacent sides \(7\,\text{cm}\) and \(4\,\text{cm}\) and the angle between them is \(60^\circ\).[3]
    2. The vertices of \(\triangle ABC\) are \(A(-3,2)\), \(B(5,3)\), and \(C(1,6)\). Sketch it on graph paper and reflect it in the \(x\)-axis. Write down the coordinates of the image.[3]
  12. The total expenditure of a family is \(\text{Rs.}\,36{,}000\) for four months. Expenditure of each month is shown in the adjoining pie chart.
    1. Find the expenditure in each month.[2]
    2. How much is the average expenditure of such a family in one month? Calculate it.[1]

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