G8_Chhatrakot Municipality_2081

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  1. Study the Venn diagram and answer the following questions:
    1. List the elements of set R and S by listing method.[1]
    2. Write the improper subset formed from the set R.[1]
    3. In which condition do the given sets R and S become disjoint sets?[1]
    1. From the Venn diagram:
      \( R = \{a, b, c\} \)
      \( S = \{c, d, e\} \)
    2. The improper subset formed from set \(R\) is the set \(R\) itself.
      \( \{a, b, c\} \)
    3. Sets \(R\) and \(S\) become disjoint when they have no common elements.
      Therefore, if the element \(c\) is removed from either \(R\) or \(S\) (or both), then
      \(R\) and \(S\) become disjoint set.
  2. Anup bought a mobile phone labelled at Rs. 12,000 at a 20% discount.
    1. How much is the discount price of an article whose marked price is (M.P.) and discount percentage is (D%)?[1]
    2. Find the selling price of the mobile phone.[1]
    3. If the mobile phone is sold at a 20% loss, find the cost price.[2]
    1. Discount amount of an article with marked price (M.P.) and discount percentage (D%):
      Discount Amount = \( \dfrac{D}{100} \times \text{M.P.} \)
    2. Selling price of the mobile phone.
      Marked Price (M.P.) = Rs. \(12,000\)
      Discount = \(20\%\)
      Thus
      SP=80% of MP = \( \dfrac{80}{100} \times 12,000 = 9,600\)
      So, the selling price is Rs. \(9,600\).
    3. Cost price if the mobile phone is sold at a \(20\%\) loss.
      Selling Price (SP) = Rs. \(9,600\)
      Loss=20%
      Thus
      SP=\(80\%\) of Cost Price (CP).
      or\(9,600 = \dfrac{80}{100} \times \text{CP}\)
      or\(\text{CP} = \dfrac{9,600 \times 100}{80} = \dfrac{960,000}{80} = 12,000\)
      So, the cost price was Rs. \(12,000\).
  3. If Anju deposited Rs. 35,000 in a bank at the rate of 12% per year for 2 years.
    1. Write the formula to find Principal.[1]
    2. What interest does Anju get in 2 years?[1]
    3. Find the amount.[1]
    1. Formula to find Principal:
      Principal (P) = \( \dfrac{I \times 100}{T \times R} \)
    2. Interest for 2 years:
      Principal (P) = Rs. 35,000
      Time (T) = 2 years
      Rate (R) = 12%
      Thus,
      Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{35,000 \times 2 \times 12}{100} = 8,400 \)
      So, Anju gets Rs. 8,400 as interest.
    3. Find the amount:
      Principal (P) = Rs. 35,000
      Interest (I) = Rs. 8,400
      Thus,
      Amount (A) = P + I = 35,000 + 8,400 = 43,400
      So, the amount is Rs. 43,400.
  4. Hari bought a car at Rs. 42,000.
    1. Write the cost of car in scientific notation.[1]
    2. Find the ratio \(1\) meter and \(80\) cm.[1]
    3. Express \(0.\overline{34}\) into fraction.[2]
    4. \(101010_2\) is a binary number. Convert the number into decimal number system.[2]
  5. The length of rectangular surface is 10 m. and perimeter is 32 m.
    1. Write the formula to find perimeter of rectangle. [1]
    2. Find the breadth of surface. [1]
    3. How much does it cost to color the surface at the rate of Rs.100 per square meter? Calculate. [2]
    4. Compare the length and breadth of the surface. [1]
    1. Perimeter of rectangle formula
      We know that,
      Perimeter (\( P \)) = \( 2(l + b) \)
    2. Breadth of the surface
      Given: Perimeter (\( P \)) = 32 m and Length (\( l \)) = 10 m
      Using the formula,
      \( 32 = 2(10 + b) \)
      or \( 16 = 10 + b \)
      or \( b = 16 - 10 = 6 \) m
    3. Cost of coloring the surface
      First, calculate the area of the surface,
      Area (\( A \)) = \( l \times b = 10 \times 6 = 60 \) m²
      At the rate of Rs. 100 per sq. meter,
      Total Cost = \( 60 \times 100 = \) Rs. 6,000
    4. Comparison of length and breadth
      Here, Length = 10 m and Breadth = 6 m.
      Comparing them, the length is \( 10 - 6 = 4 \) m longer than the breadth.
    1. What should be the index of \(x\), so that its value will be \(1\)?[1]
    2. Simplify: \(\frac{a}{a-b} - \frac{a}{a+b}\)[2]
  7. Two equations are given as: \(x + y = 8\) and \(x - y = 4\).
    1. What is the system of given equation called?[1]
    2. Solve the above equation by using graph.[2]
    1. Find the H.C.F. of \(x^2 - 4\) and \(x^2 - 6x - 16\).[2]
    2. For what value of \(x\) the value of \(x^2 - x - 12\) is zero?[2]
  9. In the given figure \(\triangle ABC\) is formed between \(PQ \parallel XY\). \(\angle BAC = 65^\circ\) and \(\angle CBY = 60^\circ\) are given.
    1. What is the value of \(x\)?[1]
    2. What is the value of \(y\)?[1]
    3. Verify experimentally that the sum of internal angles of a triangle is \(180^\circ\).[2]
    1. Construct a parallelogram \(PQRS\) with \(PQ = 8\) cm, \(QR = 6\) cm and \(\angle PQR = 30^\circ\).[3]
    2. If \(\triangle ABC \cong \triangle DEF\), find the value of \(x\).[2]
    1. Draw the net of a cube.[1]
    2. If the bearing of a place B from place A is \(060^\circ\), find the bearing of A from B.[2]
    3. Find the vertices of the image triangle \(\Delta P'Q'R'\) of \(\Delta PQR\) with vertices \(P(6,8)\), \(Q(4,5)\) and \(R(6,2)\) after rotation through \(+90^\circ\) about origin. Represent \(\Delta PQR\) and \(\Delta P'Q'R'\) in same graph.[3]
  12. The monthly expenditure of a family is given in the table below:
    13. (Title) (Food) (Education) (Clothing) (Other Expenses)
    (Expenditure Rs.) 18,000 10,000 5,000 3,000
    1. Show the given data in pie-chart.[2]
    2. Find the median of the given data: \(14, 15, 20, 37, 18, 17, 46, 19, 25, 22, 21, 23, 24\).[1]

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