Kathmandu_8_2081

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  1. Set \(A = \{2, 5\}\) and set \(B = \{5, 7\}\) are given.
    1. Are sets \(A\) and \(B\) overlapping or disjoint? Write it.[1]
    2. Write any two proper subsets that can be made from set \(B\).[2]
  2. As announced on December 8, 2020, the height of Mount Everest, the highest peak in the world, was \(8848.86\) meter.
    1. Write whether the number \(8848.86\) is a rational or irrational number.[1]
    2. Convert the height of Mt. Everest in centimeter and write in scientific notation.[2]
    3. Prove that: \(8848 = 240343_5\).[2]
  3. Two friends, Ramnaresh and Mahesh invested \(\text{Rs.}\,50{,}00{,}000\) in a factory in the ratio of \(3:2\).
    1. What is the difference in direct and indirect variation? Write one difference.[1]
    2. How much amount has Ramnaresh invested in the factory? Find it.[1]
    3. If Mahesh had deposited the amount invested in the industry in a bank at an annual interest rate of \(10\%\), how much simple interest would he have received after \(2\) years? Calculate.[2]
    4. If \(3:2 = x:500\), find the value of \(x\).[1]
  4. Ashim bought a machine for \(\text{Rs.}\,25{,}000\) and fixed the market price by increasing \(20\%\) on its price. He made a loss of \(\text{Rs.}\,1{,}000\) after selling the machine with some discount amount.
    1. Find the marked price of the machine.[1]
    2. At how much discount percentage was the machine sold? Find out.[2]
    3. If Ashim wants to earn a profit of \(\text{Rs.}\,2{,}000\) by selling the machine, what discount rate should be maintained?[1]
  5. In the figure, \(ABCD\) is a parallelogram where a right-angled triangle \(ADB\) with height \(AD = 5\,\text{cm}\) is formed on the semicircle having diameter \(13\,\text{cm}\).
    1. Write the formula to find the area of parallelogram.[1]
    2. Find the area of the semicircle.[1]
    3. By how much is area of right-angled triangle \(ADB\) less than the area of semicircle? Calculate it.[2]
    4. Is the area of parallelogram \(ABCD\) double the area of triangle \(ADB\)? Give logical answer.[1]
    1. Write the expanded form of \((a - b)^2\).[1]
    2. Simplify: \(x^{p(a-b)} \times x^{p(b-c)} \times x^{p(c-a)}\).[2]
  7. A rectangular garden has length \(4\) meter more than its breadth. The area of the garden is \(96\) square meter.
    1. If the breadth of the garden is \(x\) meters, what is the length? Write in terms of \(x\).[1]
    2. What are the length and breadth of the garden? Find by making quadratic equation.[2]
    1. Factorise: \(2x + xy - 2x - y\).[2]
    2. Simplify: \(\dfrac{1}{x - 3} - \dfrac{x-3}{x^2 - 9}\).[2]
  9. In the given graph, triangle \(ABC\) is shown.
    1. Which formula do you use to find the distance between two points? Write it.[1]
    2. Find the length of side \(BC\).[2]
    3. Rotate the triangle \(ABC\) a quarter turn in the positive direction and write the coordinates of the vertices of image triangle.[2]
    4. Experimentally verify that the sum of interior angles of a triangle is \(180^\circ\). (Two triangles of different measurements are required.)[3]
  10. In the figure \(PQRS\) is a rectangle in which length \(QR = 6\,\text{cm}\) and breadth \(RS = 4\,\text{cm}\).
    1. Construct the rectangle \(PQRS\) using compass according to the given dimensions.[3]
    2. Are \(\triangle QPS\) and \(\triangle QRS\) congruent to each other? Write with reason.[1]
  11. A point \(Q\), which is \(8\,\text{cm}\) away from a point \(P\), has a bearing of \(110^\circ\) in the scale \(1\,\text{cm} = 5\,\text{km}\).
    1. Draw the bearing according to the above context.[1]
    2. Compare the bearing of \(P\) from point \(Q\) and bearing of \(Q\) from \(P\).[2]
  12. The following are the marks obtained by \(7\) students of grade eight in first terminal examination in mathematics: \(23, 30, 25, 26, 23, 28, 27\).
    1. Find the mode from the above data.[1]
    2. What is the average marks obtained by the \(7\) students in first terminal examination? Find it.[1]
    3. Which among mean, median and mode divides the given data in two equal parts? Write with reason.[1]

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