Bharatpur_8_2081

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  1. Two subsets of universal set \(U = \{a, e, i, o, u\}\) are \(A = \{e, o, u\}\) and \(B = \{a, e, i\}\).
    1. What type of sets are \(A\) and \(B\)—overlapping or disjoint? Write it.[1]
    2. Write one proper and one improper subset of set \(A\).[1]
    3. If the element \(e\) is removed from both sets \(A\) and \(B\), then what type of sets are \(A\) and \(B\)? Write with reason.[1]
  2. In the numeration system, the following sets are given: \(B_{10} = \{0, 1, 2, 3, \ldots, 8, 9\}\), \(B_2 = \{0, 1\}\), \(B_5 = \{0, 1, 2, 3, 4\}\).
    1. Which number system’s digits are used while opening and closing the switch of an electric circuit?[1]
    2. Convert \(35\) into the binary number system.[2]
    3. What is the relation between \(1010_2\) and \(20_5\)? Evaluate.[1]
    4. Convert \(0.\overline{24}\) into a fraction.[1]
  3. Ashok Mahato went to a stationery shop to buy a ball. He saw two balls \(A\) and \(B\) as shown in the figure. The ratio of marked prices of ball \(A\) and ball \(B\) is \(3:2\). The marked price of ball \(A\) is \(\text{Rs.}\,3{,}750\); the marked price of ball \(B\) is \(\text{Rs.}\,2{,}500\), and a \(5\%\) discount 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.[1]
    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. Sarita invested \(\text{Rs.}\,5{,}000\) as a loan and lent it to Mansur for \(3\) years at \(10\%\) simple interest per annum.
    1. How much interest is obtained by Sarita?[1]
    2. How long should Sarita wait to get double the invested sum?[2]
    3. What will be the interest on \(\text{Rs.}\,12{,}000\) at the same rate and for the same time?[1]
  5. In the figure, \(ABCD\) is a kite-shaped plot where diagonals \(AC = 6\,\text{m}\) and \(BD = 5\,\text{m}\). Inside it, there is a circular well of radius \(50\,\text{cm}\).
    1. Write the formula to find the area of the kite.[1]
    2. Calculate the area of the kite-shaped land.[1]
    3. Find the area and circumference of the circular well.[2]
    4. What is the difference in area between the circular well and the kite-shaped plot? Find it by calculation.[1]
    1. Which geometrical figure's area is represented by \(x^2\)?[1]
    2. Simplify: \(\left(\dfrac{x^3 y^2}{x^4 y}\right)^2\).[2]
  7. Two algebraic expressions are given: \(x^2 - 16\) and \(x^2 - 9x + 20\).
    1. Find the Highest Common Factor (H.C.F.) of the given expressions.[2]
    2. For what value of \(x\) does the expression \(x^2 - 16\) become zero?[2]
    1. What type of equation is \(ax + by + c = 0\)?[1]
    2. Find the quotient when \(\dfrac{m^2 - n^2}{n^2}\) is divided by \(\dfrac{m^2 + mn}{mn}\).[2]
  9. In the given figure, \(RS \parallel MN\), \(\angle PQM = 55^\circ\), \(\angle QMR = y\), \(\angle MRS = (2x + 3)^\circ\), and \(\angle RMN = 73^\circ\).
    1. If \(y = 55^\circ\), write the relation between line segments \(PQ\) and \(MR\).[1]
    2. Find the value of \(x\).[1]
    3. Experimentally verify that the base angles of an isosceles triangle are equal. (Two figures of different sizes are necessary.)[3]
  10. The given figure \(ABCDEF\) is a regular polygon. \(ACDF\) is a rectangle where \(AC = 5.5\,\text{cm}\) and \(AF = 3.6\,\text{cm}\). Side \(FE\) is produced to a point \(G\) such that \(\angle GED = m\).
    1. Find the sum of interior angles of the given regular polygon.[2]
    2. Construct another rectangle having the same dimensions as rectangle \(ACDF\).[3]
    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 and ending points? 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 after reflection on the \(x\)-axis.[3]
  12. The adjoining pie chart presents the number of animals in Devchuli Animal Husbandry:
    13. Animal Buffalo Goat Cow Chicken
    Number 50 200 450 200
    1. Write the names of animals that represent the mode value.[1]
    2. Find the average number of animals.[2]

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