G8_Kalaiya_8_2081

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  1. If \(A = \{1, 2, 3\}\) and \(B = \{0, 2, 3, 4\}\),
    1. How many improper subsets does set \(A\) have?[1]
    2. Find the value of \(A \cap B\).[1]
    3. Represent \(A \cap B\) in a Venn diagram.[1]
    1. A set has exactly one improper subset, which is the set itself.
    2. The intersection of sets \(A\) and \(B\) is the set of common elements
      So, \(A \cap B = \{2, 3\}\)
    3. The Venn diagram for \(A \cap B = \{2, 3\}\) is shown below.
  2. Ramu marked the price of a mobile at Rs 80000. He sold it with a \(10\%\) discount and gained a profit of Rs 4000.
    1. Write the formula for profit.[1]
    2. Find the discount amount.[1]
    3. Find the cost price of the mobile.[1]
    1. Formula for profit:
      Profit = Selling Price (SP) – Cost Price (CP)
    2. Discount amount.
      Marked Price (MP) = Rs. \(80,000\)
      Discount = \(10\%\)
      Thus
      Discount Amount = \( \dfrac{10}{100} \times 80,000 = 8,000 \)
      So, the discount amount is Rs. \(8,000\).
    3. Cost price of the mobile.
      Marked Price (MP) = Rs. \(80,000\)
      Discount = \(10\%\)
      Thus
      Selling Price (SP) = 90% of MP = \( \dfrac{90}{100} \times 80,000 = 72,000 \)
      Profit = Rs. \(4,000\)
      We know that
      CP = SP – Profit
      orCP = \(72,000 - 4,000 = 68,000\)
      So, the cost price of the mobile was Rs. \(68,000\).
  3. If principal P = Rs 10,000, time T = 4 years, and rate R = 6% per annum, then:
    1. Write the formula to find simple interest.[1]
    2. Find the interest amount.[1]
    3. Find the total amount.[1]
    1. Formula to find simple interest:
      Simple Interest (I) = \( \dfrac{P \times T \times R}{100} \)
    2. Interest amount:
      Principal (P) = Rs. 10,000
      Time (T) = 4 years
      Rate (R) = 6%
      Thus,
      Interest (I) = \( \dfrac{10,000 \times 4 \times 6}{100} = 2,400 \)
      So, the interest amount is Rs. 2,400.
    3. Total amount:
      Principal (P) = Rs. 10,000
      Interest (I) = Rs. 2,400
      Thus,
      Amount (A) = P + I = 10,000 + 2,400 = 12,400
      So, the total amount is Rs. 12,400.
    1. Write \(45{,}000\) in scientific notation.[1]
    2. Simplify: \(\sqrt{18} - 2\sqrt{18} + 2\sqrt{2}\).[2]
    3. Convert \(46\) into the quinary number system.[1]
  5. In the given figure, ABCD is a rectangle with length 10 cm and breadth 6 cm.
    1. Write the formula for the area of a rectangle. [1]
    2. Find the area of the rectangle. [1]
    3. Find the perimeter of the rectangle. [1]
    1. Area of rectangle formula
      We know that,
      Area (\( A \)) = Length (\( l \)) \(\times\) Breadth (\( b \))
    2. Area of the rectangle
      Given: Length (\( l \)) = 10 cm, Breadth (\( b \)) = 6 cm
      Area (\( A \)) = \( 10 \times 6 = 60 \) cm²
    3. Perimeter of the rectangle
      We know that,
      Perimeter (\( P \)) = \( 2(l + b) = 2(10 + 6) = 32 \) cm
    1. Find the value of \((3x)^0\).[1]
    2. Simplify: \(x^2 \times x^3 \times x^{-2}\).[2]
    3. Factorise: \(x^2 + 6x + 8\).[2]
  7. Two equations are given below: \(2x + y = 8\) and \(x + y = 5\).
    1. What is this system of equations called?[1]
    2. Solve the equations using a graph.[2]
    1. Find the L.C.M. of the algebraic expressions \(a^2 - b^2\) and \(a^2 - ab\).[2]
    2. For what value of \(x\) does the expression \(x^2 - 5x + 6\) become zero?[2]
  9. In the adjoining figure, line \(PQ\) intersects straight lines \(AB\) and \(CD\) at points \(E\) and \(F\) respectively.
    1. Write a pair of alternate angles if \(AB \parallel CD\).[1]
    2. Find the value of \(x\).[2]
    3. At what value of \(\angle BEF\) will the lines \(AB\) and \(CD\) become parallel?[2]
    1. Construct a rectangle \(ABCD\) where \(BC = 5cm\), \(BD = 10cm\), and \(\angle CBD = 60^\circ\).[3]
    2. Find the value of \(x\) in the given figure.[3]
    1. What type of triangles are required to form a regular tessellation?[2]
    2. If the bearing of point \(A\) from point \(B\) is \(080^\circ\), find the bearing of point \(B\) from point \(A\).[2]
    3. The vertices of \(\triangle PQR\) are \(P(1,3)\), \(Q(4,1)\), and \(R(3,5)\). Find the vertices of the image \(\triangle P'Q'R'\) after rotation through \(+90^\circ\) about the origin. Represent both triangles on the same graph.[3]
  12. The monthly expenditure (in Rs.) of Ram’s family is given below:
    13. Month Baishakh Jestha Ashar Shrawan
    Expenditure (Rs.) 25,000 19,000 28,000 18,000
    1. Present Ram’s family expenditure in a pie chart.[3]
    2. In a data set, \(2x = m + 77\), \(n = 10\), and mean (\(\bar{x}\)) = \(8\). Find the value of \(m\).[2]

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