G8_AgniSaiar Krishna VDC_8_2081

1. Study the given Venn diagram and answer the following questions:
1. From listing method, write the elements of sets \(A\) and \(B\).[1]
2. Write the improper subset from the set \(A\).[1]
3. In which condition do the given sets \(A\) and \(B\) become disjoint?[1]
1. From the Venn diagram:
   \( A = \{a, b, c\} \)
   \( B = \{c, d, e\} \)
2. The improper subset of set \(A\) is the set \(A\) itself.
   \( \{a, b, c\} \)
3. Sets \(A\) and \(B\) become disjoint when they have no common elements.
   Thus, if the element \(c\) is removed from either \(A\) or \(B\) (or both),Then
   Sets \(A\) and \(B\) become disjoint
1. Convert \(0.\overline{34}\) into fraction.[2]
2. The budget of Nepal in fiscal year 2080/081 is Rs. 1,80,00,000,000. Write down the number in scientific notation.[1]
3. Convert 75 into the binary number system.[1]
3. Mohan has deposited Rs. 2,50,000 in a bank at the rate of 8% per annum.
   1. Write the simple interest formula.[1]
   2. What does R stand for in the simple interest formula?[1]
   3. Find the interest amount obtained at the end of 3 years and 9 months.[2]
1. Simple Interest formula:
   Simple Interest (I) = \( \dfrac{P \times T \times R}{100} \)
2. Meaning of R:
   In the simple interest formula, 'R' stands for the Rate of Interest per annum.
3. Interest for 3 years and 9 months:
   Principal (P) = Rs. 2,50,000
   Rate (R) = 8%
   Time (T) = 3 years 9 months = \( 3 + \dfrac{9}{12} \) years = 3.75 years
   Thus,
   Interest (I) = \( \dfrac{2,50,000 \times 3.75 \times 8}{100} = 75,000 \)
   So, the interest amount obtained is Rs. 75,000.
1. Find the ratio of \(1\) m and \(80\) cm.[1]
2. Simplify: \(\left( \frac{x^2 y}{x y^2} \right)^3\)[2]
3. If 16 workers can do a piece of work in 25 days, how many workers can complete the same work in 20 days?[2]
4. Convert \(1101_2\) into quinary number system.[1]
5. A circular pond of radius 7 m is there inside a rectangular piece of land with length 20 m and breadth 15 m.
   1. Find the area of the land. [1]
   2. Find the area of the pond. [1]
   3. Find the area of the land excluding the pond. [2]
   4. Find the cost of fencing the land at the rate of Rs. 50 per meter. [2]
1. Area of the land
   Given: Length (\( l \)) = 20 m, Breadth (\( b \)) = 15 m
   Area (\( A_l \)) = \( l \times b = 20 \times 15 = 300 \) m²
2. Area of the pond
   Given: Radius (\( r \)) = 7 m
   Area (\( A_p \)) = \( \pi r^2 = \frac{22}{7} \times 7^2 = 154 \) m²
3. Area of land excluding the pond
   Remaining Area = Area of land - Area of pond
   or Remaining Area = \( 300 - 154 = 146 \) m²
4. Cost of fencing the land
   First, find the perimeter of the rectangular land,
   Perimeter (\( P \)) = \( 2(l + b) = 2(20 + 15) = 70 \) m
   At the rate of Rs. 50 per meter,
   Total Cost = \( 70 \times 50 = \) Rs. 3,500
1. Simplify: \(x^{a-b} \times x^{b-c} \times x^{c-a}\)[2]
2. Find the HCF of: \(x^2 + 3x + 2\) and \(x^2 - 4\)[2]
1. Factorize: \(9x^2 - 25y^2\)[1]
2. Solve by graphical method: \(x + y = 5\) \(2x - y = 4\)[2]
1. Evaluate: \(a^0 \times b^0\)[2]
2. Solve: \(x^2 - 7x + 12 = 0\)[1]
1. Write the formula to find sum of interior angles of a regular polygon.[1]
2. Find the value of \(x\) and \(y\) in the given figure.[2]
3. Find the distance between the points \(P(4,5)\) and \(Q(7,5)\).[2]
1. Construct a rectangle \(ABCD\) in which \(AB = 6\) cm and \(BC = 5\) cm.[3]
2. Find the values of \(x\) and \(y\) in the given figure.[2]
1. Reflection in x-axis to the point \(P(x, y)\).[1]
2. The bearing of B from A is \(065^\circ\). What is the bearing of A from B?[2]
3. Draw the net of cube figure.[2]
12. Study the given table and solve the problem given below:

कक्षा (Class)	1	2	3	4
विद्यार्थी सङ्ख्या (No. of Students)	40	50	60	30

1. Find the average value of the above data.[1]
2. Represent the data given above table in pie chart.[2]