G8_Bardiya_8_2081

By
  1. Given a Venn diagram.
    1. What types of sets are \(A\) and \(B\), overlapping or disjoint sets?[1]
    2. Write the improper subset of \(B\).[1]
    3. If \(m\) and \(n\) are only the members of set \(A\), then what type of sets are \(A\) and \(B\)? Write with reason.[1]
    1. Sets \(A\) and \(B\) are overlapping sets.
      Because they share common elements \(p\) and \(q\).
    2. The improper subset of set \(B\) is the set \(B\) itself.
      \( B = \{p, q, x, y\} \)
    3. If \(m\) and \(n\) are the only members of set \(A\), then \(A = \{m, n\}\) and \(B = \{x, y, p, q\}\).
      In this case, \(A\) and \(B\) would be disjoint sets because they have no common elements
      i.e., \(A \cap B = \emptyset\).
  2. Sagar went to the utensil shop to buy a rice cooker. The marked price of a rice cooker is Rs 5000.
    1. If marked price MP and discount D are represented by MP and D respectively, write the formula to find the selling price SP[1]
    2. How much discount did Sagar get while buying a rice cooker on a discount of \(8\%\)?[1]
    3. The shopkeeper got \(15\%\) profit after selling it at a \(8\%\) discount. What was the cost price of the rice cooker?[2]
    1. Formula to find the selling price (SP) is
      SP = MP – D
    2. Finding the discount amount
      Marked Price (MP) = Rs. \(5,000\)
      Discount = \(8\%\) of MP
      Therefore
      Discount = \( \dfrac{8}{100} \times 5,000 = 400 \)
      So, Sagar got a discount of Rs. \(400\).
    3. Finding the cost price (CP)
      Selling Price (SP) = MP – Discount = \(5,000 - 400 = 4600\)
      Profit=\(15\%\)
      We know
      \( SP=115\% \text{ of CP} \)
      or\( 4600 = \dfrac{115}{100} \times \text{CP} \)
      or\( \text{CP} = \dfrac{4600 \times 100}{115} = \dfrac{460,000}{115} =4000 \)
      So, the cost price of the rice cooker was approximately Rs. \(4000\).
  3. Elisza took a loan of Rs 80,000 from Nabil Bank for 4 years at the rate of 10% p.a. simple interest.
    1. Write amount (A) in terms of principal (P) and interest (I).[1]
    2. How much interest should she pay in 4 years? Calculate it.[2]
    3. Find the amount.[1]
    1. Amount (A) in terms of P and I:
      Amount (A) = Principal (P) + Interest (I)
    2. Interest for 4 years:
      Principal (P) = Rs. 80,000
      Time (T) = 4 years
      Rate (R) = 10%
      We know,
      Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{80,000 \times 4 \times 10}{100} = 32,000 \)
      So, she should pay Rs. 32,000 as interest.
    3. Find the amount:
      Principal (P) = Rs. 80,000
      Interest (I) = Rs. 32,000
      Thus,
      Amount (A) = P + I = 80,000 + 32,000 = 1,12,000
      So, the amount is Rs. 1,12,000.
  4. The distance between Jayanagar to Kohalpur is \(32{,}000\,\text{m}\).
    1. Write the number \(32{,}000\) in scientific notation.[1]
    2. Write \(320\) in quinary number system.[2]
    3. Convert the decimal number \(0.\overline{3}\) into a fraction.[2]
    4. If the cost of \(10\,\text{kg}\) of apples is \(\text{Rs.}\,1{,}200\), what will be the cost of \(14\,\text{kg}\) of apples?[1]
  5. Bimala decided to exchange her square land of side length 84 m with a rectangular land of equal area.
    1. What was the area of her square land? [1]
    2. If the length of the rectangular land which she wants to exchange is 144 m, find the breadth of the land. [1]
    3. What will be the required length of the wire to fence the rectangular land three times? [2]
    4. Bimala wanted to fence the rectangular land one time with Rs 40000. But Rs 530 was not enough to fence the land. What was the cost of fencing the land per meter? Find it. [2]
    1. Area of square land
      Given that,
      (\( l \)) = 84 m
      Therefore,
      Area (\( A \)) = \( l^2 = 84^2 = \) 7056 m²
    2. Breadth of rectangular land
      We know that,
      Area (\( A \)) = 7056 m²
      Length (\( l \)) = 144 m
      Now using the formula, we get
      \( l \times b = A \)
      or \( 144 \times b = 7056 \)
      or \( b = \frac{7056}{144} = \) 49 m
    3. Total length of wire required
      We know that,
      Perimeter (\( P \)) = \( 2(l + b) = 2(144 + 49) = 2 \times 193 = \) 386 m
      According to the question,
      Wire needed for 3 rounds is:
      3P = \( 3 \times 386 = \) 1158 m
    4. Cost of fencing per meter
      According to the question,
      Total actual cost = \( 40000 + 530 = \) Rs 40,530
      We know that,
      Perimeter (\( P \)) = 386 m
      Thus,
      Cost per meter = \( \frac{40530}{386} = \) Rs 105
    1. Factorize: \(9y^{2} - 25\)[1]
    2. Simplify: \(\left( \dfrac{x^{a}}{x^{b}} \right)^{a+b} \times \left( \dfrac{x^{b}}{x^{c}} \right)^{b+c} \times \left( \dfrac{x^{c}}{x^{a}} \right)^{c+a}\)[2]
    1. Simplify: \(\dfrac{a^{2}}{a+b} - \dfrac{b^{2}}{a+b}\)[2]
    2. Find the H.C.F. of: \(x^{2} - 16\) and \(x^{2} + 8x + 16\)[2]
    1. Solve: \(x^{2} - 49 = 0\)[2]
    2. Solve graphically: \(x + y = 5\) and \(x - y = 1\)[2]
  9. In the given figure, \(AB \parallel CD\).
    1. Which is the alternate angle of \(\angle AGH\)?[1]
    2. Find the value of \(x\) in the given figure.[2]
    3. Find the values of \(x\) and \(y\) from the given parallelogram.[2]
    1. By which axiom are the given triangles congruent?[1]
    2. Construct a parallelogram having measures of adjacent sides \(6cm\) and \(4cm\), and the angle between them is \(60^{\circ}\).[3]
    1. For regular tessellation, what types of triangles are required?[1]
    2. Find the unknown side of the given right-angled triangle.[2]
    3. Draw a triangle with vertices \(A(3,1)\), \(B(2,5)\), and \(C(6,5)\) on a graph paper. Reflect it on the \(y\)-axis and show the image on the same paper.[3]
  12. The monthly expenditure of Jiban's family is given below:
    13. Bhadra Asoj Kartik Mansir
    \(\text{Rs.}\,15{,}000\) \(\text{Rs.}\,19{,}000\) \(\text{Rs.}\,15{,}000\) \(\text{Rs.}\,16{,}000\)
    1. What is the monthly average expenditure of Jiban's family?[1]
    2. Present Jiban's family expenditure in a pie chart.[2]

No comments:

Post a Comment