G8_Buddha Shanti_8_2081

By
  1. According to the given Venn diagram, answer the following questions:
    1. Which type of sets are \(A\) and \(B\)?[1]
    2. Make any two proper subsets from set \(A\).[1]
    3. If the members \(1\) and \(2\) are taken out from the given Venn diagram, then write the relationship between set \(A\) and set \(B\).[1]
    1. Sets \(A\) and \(B\) are overlapping sets.
      Because they share common elements \(1\) and \(2\), i.e., \(A \cap B = \{1, 2\} \neq \emptyset\).
    2. From the Venn diagram, \(A = \{1, 2, 3, 4\}\).
      Any two proper subsets of A are
      \(\{3, 4\}\) and \(\{1\}\) All proper subsets of \(A\) are listed below .
      Number of Elements Proper Subsets (examples) Count
      0 \(\emptyset\) 1
      1 \(\{1\}, \{2\}, \{3\}, \{4\}\) 4
      2 \(\{1,2\}, \{1,3\}, \{3,4\}, \{2,4\}\), etc. 6
      3 \(\{1,2,3\}, \{1,3,4\}, \{2,3,4\}\), etc. 4
      Total Proper Subsets 15
    3. If elements \(1\) and \(2\) are removed, then
      New \(A = \{3, 4\}\)
      New \(B = \{5, 7\}\)
      Now, \(A \cap B = \emptyset\).
      Therefore, sets \(A\) and \(B\) become disjoint sets.
  2. Prabin bought a mobile phone of labelled price Rs. 12,000 at 20% discount.
    1. How much is the discount price of an article whose marked price is MP and the discount percentage is \(D\%\)?[1]
    2. Find the selling price of the mobile phone.[1]
    3. If the mobile phone is sold at 20% loss, find the cost price.[2]
    1. Discount price (i.e., discount amount) of an article with marked price \(MP\) and discount percentage \(D\%\):
      Discount Amount = \( \dfrac{D}{100} \times MP \)
    2. Selling price of the mobile phone:
      Marked Price (MP) = 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 \(20\%\) loss:
      Selling Price (SP) = Rs. \(9,600\)
      Loss = \(20\%\)
      Thus
      SP=80% of CP
      \(9,600 = \dfrac{80}{100} \times \text{CP}\)
      \(\text{CP} = \dfrac{9,600 \times 100}{80} = \dfrac{960,000}{80} = 12,000\)
      So, the cost price was Rs. \(12,000\).
  3. Mina has deposited Rs. 4,00,000 in a commercial bank for 2 years at the rate of Rs. 10 interest per annum for Rs. 100.
    1. At what percent of interest rate per annum had Mina deposited the amount of money?[1]
    2. How much interest will Mina get in 2 years at the same rate of interest?[2]
    3. The ages of elder and younger daughters of Mina are 16 years and 12 years respectively. If Mina divides her Rs. 2,80,000 to her daughters based on the ratio of their ages, how much more money will the elder daughter get than the younger daughter?[2]
    1. Interest rate in percentage:
      Since interest for Rs. 100 in 1 year is Rs. 10, the rate is 10%.
      So, Rate (R) = 10% p.a.
    2. Interest for 2 years:
      Principal (P) = Rs. 4,00,000
      Time (T) = 2 years
      Rate (R) = 10%
      We know,
      Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{4,00,000 \times 2 \times 10}{100} = 80,000 \)
      So, Mina will get Rs. 80,000 interest.
    3. Division of money between daughters:
      Ratio of ages (Elder : Younger) = 16 : 12 = 4 : 3
      Sum of ratios = 4 + 3 = 7
      Total amount = Rs. 2,80,000
      Elder daughter's share = \( \dfrac{4}{7} \times 2,80,000 = 1,60,000 \)
      Younger daughter's share = \( \dfrac{3}{7} \times 2,80,000 = 1,20,000 \)
      Thus,
      Difference = 1,60,000 - 1,20,000 = 40,000
      So, the elder daughter will get Rs. 40,000 more than the younger daughter.
  4. In a shop, the price of articles is attached in binary number.
    1. If the price of a copy is written Rs. \(11111_2\), then write the price of the copy in decimal number system.[1]
    2. What is the price of the copy in quinary number system?[1]
    3. Convert \(0.\overline{41}\) into fraction.[1]
    4. In a month of 30 days, there are 25,92,000 seconds. Write the given seconds in scientific notation.[1]
  5. A school has a circular swimming pool and a rectangular garden. Their areas are equal.
    1. Write the formula to calculate the area of a circle. [1]
    2. Find the area of the circular swimming pool. [1]
    3. Calculate the perimeter of the rectangular garden. [2]
    4. Which of the garden or swimming pool needs more cost to fence? [1]
    1. Area of circle formula
      We know that,
      Area (\( A \)) = \( \pi r^2 \)
    2. Area of swimming pool
      Given,
      Radius (\( r \)) = 28 cm
      Using the formula,
      Area (\( A_c \)) = \( \frac{22}{7} \times 28^2 = 2464 \) cm²
    3. Perimeter of the rectangular garden
      According to the question, Area of garden = Area of pool = 2464 cm²
      Length of garden (\( l \)) = 77 cm
      We know, Area (\( A \)) = \( l \times b \)
      \( 2464 = 77 \times b \)
      or \( b = \frac{2464}{77} = 32 \) cm
      Now, calculating the perimeter,
      Perimeter (\( P \)) = \( 2(l + b) = 2(77 + 32) = 218 \) cm
    4. Comparison of fencing cost
      Fencing cost depends on the perimeter/circumference.
      Perimeter of garden = 218 cm
      Circumference of pool (\( C \)) = \( 2\pi r = 2 \times \frac{22}{7} \times 28 = 176 \) cm
      Since the perimeter of the garden is greater than the circumference of the pool (\( 218 > 176 \)),
      the garden needs more cost to fence.
    1. If \(x = y^0 + 4\), find the value of \(x\).[1]
    2. Simplify: \(\frac{x^2}{x+y} \times \frac{y^2}{x+y}\)[2]
  7. Simultaneous linear equations \(x + y = 8\) and \(x - y = 2\) are given.
    1. If \(x = 5\) is in the equation \(x + y = 8\), then what will be the value of \(y\)?[1]
    2. Solve the given equations by graphical method.[2]
  8. Two algebraic expressions \(x^2 + x - 20\) and \(x^2 - 25\) are given.
    1. Find the H.C.F. of the given expressions.[2]
    2. What is the value of \(x\) when the expression \(x^2 + x - 20\) is zero?[2]
  9. In the given figure, \(AB \parallel CE\), \(\angle BAC = 50^\circ\), \(\angle ECD = 60^\circ\), and \(\angle ACB = x\).
    1. Write an angle alternate to \(\angle BAC\).[1]
    2. Find all the angles of \(\triangle ABC\).[2]
    3. Compare all the angles of \(\triangle ABC\).[1]
    1. Construct a parallelogram \(ABCD\) with \(AB = 8\) cm, \(BC = 6\) cm and \(\angle ABC = 75^\circ\).[3]
    2. Construct two triangles \(ABC\) and \(ACD\) from the parallelogram \(ABCD\). Prove that \(\triangle ABC \cong \triangle ACD\).[2]
    1. Write the name of tessellation which uses only one type of regular geometrical shape.[1]
    2. In the graph, the bearing of point \(C\) from point \(B\) is \(090^\circ\). What is the bearing of point \(B\) from point \(C\)?[2]
    3. In the graph, translate the triangle \(\triangle ABC\) by 2 units right and 5 units down. Write the coordinates of the image.[3]
  12. The monthly budget of a family is given below:
    13. Heading Food Clothing Education Medicine Others
    Expenditure (Rs.) 6,000 8,000 3,000 1,200 1,000
    1. Represent the given data in a pie chart.[2]
    2. What is the average annual budget?[1]

No comments:

Post a Comment