Amarghadhi_8_2081

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  1. Two subsets of the universal set \(U = \{a, e, i, o, u\}\) are \(A = \{e, o, u\}\) and \(B = \{a, c, i\}\).
    1. What types of sets are \(A\) and \(B\)—overlapping or disjoint? Write it.[1]
    2. Write one proper and one improper subset of \(A\).[1]
    3. If \(e\) is eliminated from sets \(A\) and \(B\), then what types of sets are \(A\) and \(B\)? Write with a reason.[1]
  2. The binary and decimal number systems are illustrated in the table below, where the binary representation of \(15\) is blank.
    3. Binary number system \(0_2\) \(1_2\) \(10_2\) \(11_2\) \(100_2\) ?
    Decimal number system \(0\) \(1\) \(2\) \(3\) \(4\) \(15\)
    1. Write the digits used in the binary number system.[1]
    2. Which binary number should be placed in the blank?[2]
    3. Convert the distance of \(240{,}000\) miles from the Earth to the Moon into scientific notation.[2]
  3. Ashok Mahato went to a stationery shop to buy a ball. He saw two balls \(A\) and \(B\). The ratio of their marked prices is \(3:2\). The marked price of ball \(A\) is \(\text{Rs.}\,3{,}750\), and that of ball \(B\) is \(\text{Rs.}\,2{,}500\). A discount of \(5\%\) is offered.
    1. Write the marked prices of balls \(A\) and \(B\) in proportion.[1]
    2. If Ashok Mahato decided to buy ball \(B\), what amount should he pay for it? Find it.[2]
    3. If the shopkeeper wanted to earn a \(10\%\) profit by selling ball \(B\) after the discount, at what price did he buy ball \(B\)?[2]
  4. Bhargab deposited \(\text{Rs.}\,50{,}000\) in a bank. After \(2\) years, he received simple interest of \(\text{Rs.}\,10{,}000\).
    1. What is the amount after \(2\) years? Find it.[1]
    2. Find the rate of interest per annum.[2]
    3. If Bhargab had deposited the same amount for only \(1\) year, how much less interest would he have received?[1]
  5. A wire of length \(39.6\,\text{m}\) is bent to form an equilateral triangle on a plane surface.
    1. Write the formula to find the area of an equilateral triangle.[1]
    2. What is the radius of the circle if the same wire is bent into a circle? Find it.[1]
    3. Find the area of the equilateral triangle.[2]
    4. How much more or less is the area of the circle compared to the area of the equilateral triangle when the same wire is used? Find it.[2]
    1. Find the value of: \((2a)^0\)[1]
    2. Simplify: \(x^{a-b} \times x^{b-c} \times x^{c-a}\)[2]
  7. Two algebraic expressions are \(x^{2} - 16\) and \(x^{2} - 9x + 20\).
    1. Find the Highest Common Factor (H.C.F.) of the given algebraic expressions.[2]
    2. What is the value of \(x\) when the expression \(x^{2} - 16\) is zero?[2]
  8. Two equations are given: \(x + 2y = 7\) and \(x + y = 5\).
    1. What type of equations are these?[1]
    2. Solve the above equations using the graphical method.[2]
  9. In the figure, straight lines \(AB\) and \(CD\) are cut by transversal \(EF\) at points \(G\) and \(H\) respectively. \(\angle BGH = (3y - 70)^{\circ}\) and \(\angle DHF = (2x - 9)^{\circ}\). Also, \(\angle AGH = 109^{\circ}\).
    1. What are \(\angle BGH\) and \(\angle DHF\) called in the figure?[1]
    2. Find the value of \(y\) from the figure.[2]
    3. At what degree value of \(x\) will the straight lines \(AB\) and \(CD\) be parallel? Write with reasons.[2]
    1. What is the sum of the interior angles of a regular polygon having \(n\) sides?[1]
    2. Construct a parallelogram with adjacent sides \(7\,\text{cm}\) and \(4\,\text{cm}\), and one diagonal \(8\,\text{cm}\), using compasses.[3]
    3. Measure the opposite sides of the parallelogram and write the conclusion based on your measurement.[1]
    1. What type of tessellation is shown in the given figure?[1]
    2. A man walks \(3\,\text{m}\) north and then turns east and walks \(4\,\text{m}\). What is the shortest distance between his starting point and final position? Calculate it.[1]
    3. \(A(2, 2)\), \(B(4, 6)\), and \(C(6, 3)\) are the vertices of \(\triangle ABC\). Draw \(\triangle ABC\) on graph paper and also plot its image obtained by reflecting it in the \(x\)-axis.[3]
  12. There are \(50\) students in Grade VIII of a school. The pie chart below shows their preferences for Mathematics and Science & Technology.
    13. (Pie chart: Mathematics = \(144^{\circ}\), Science & Technology = \(216^{\circ}\))
    1. Find the number of students who liked Science and Technology.[2]
    2. Write the name of the subject that represents the mode value.[1]

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