Waling, Syanja_8_2081

1. Given a Venn diagram.
1. Define improper subset.[1]
2. Write the improper subset of set \(A\).[1]
3. If \(x\) and \(y\) are only the members of set \(B\), then what type of sets are \(A\) and \(B\)?[1]
2. Janak marked the price of a watch as \(\text{Rs.}\,400\). He sold it allowing a discount of \(10\%\) and made a profit of \(\text{Rs.}\,40\).
1. What do you understand by \(10\%\) discount?[1]
2. Find the discount amount.[1]
3. Find the cost price of the watch.[2]
3. Radhika has deposited \(\text{Rs.}\,4{,}00{,}000\) in a commercial bank for \(2\) years at the rate of \(\text{Rs.}\,10\) interest per annum for every \(\text{Rs.}\,100\).
1. At what percent of interest rate per annum had Radhika deposited the amount of money?[1]
2. How much interest will Radhika get in \(2\) years at the same rate of interest?[2]
3. The ages of Radhika’s elder and younger daughters are \(10\) years and \(6\) years respectively. If Radhika divides the obtained interest between her daughters in the ratio of their ages, how much more money will the elder daughter get than the younger daughter?[2]
4. In a month of \(30\) days, there are \(25{,}92{,}000\) seconds.
1. Which of the following is correct for its scientific notation?
   i) \(25.92 \times 10^{4}\,\text{sec}\)
   ii) \(2.592 \times 10^{6}\,\text{sec}\)
   iii) \(2.59 \times 10^{7}\,\text{sec}\)
   iv) \(259.2 \times 10^{3}\,\text{sec}\)[1]
2. Write \(2592\) in the quinary number system.[1]
3. Convert \(0.\overline{34}\) into a fraction.[1]
4. If \(\blacksquare\) and \(\square\) denote \(1\) and \(0\) respectively, which of the following blocks should be shaded to represent \(25\) in binary number system? \(\square\) \(\square\) \(\square\) \(\square\) \(\square\)[1]
5. The circumference of a circular ground is \(132\,\text{m}\).
1. Write the formula to find the circumference of a circle.[1]
2. Calculate the radius of the ground.[1]
3. Find its area.[2]
4. At the centre of the ground, there is a rectangular pond of dimensions \(40\,\text{m} \times 30\,\text{m}\). Find the area of the pond.[1]
1. Write the expanded form of \((2x + 1)^{2}\).[1]
2. Simplify: \(\dfrac{x^{2} - y^{2}}{x - y} \div \dfrac{x - y}{x + y}\)[2]
7. If the sum of two numbers is \(8\) and the difference between them is \(6\),
1. Express the above information in the form of equations using \(x\) and \(y\).[1]
2. Find the values of \(x\) and \(y\) using the graphical method.[2]
1. Find the H.C.F. of the given algebraic expressions: \(5x - 20\) and \(x^{2} - 16\).[2]
2. In the given triangle, find the value of \(x\).[2]
9. In the adjoining figure, line \(MN\) intersects straight lines \(AB\) and \(CD\) at points \(E\) and \(F\) respectively.
1. Write a pair of alternate angles in the figure.[1]
2. What type of triangle is \(\triangle EFG\) according to the angles of the triangle?[2]
3. At what value of \(\angle BEG\) will the line segments \(AB\) and \(CD\) be parallel?[1]
1. Construct a parallelogram \(PQRS\) with \(PQ = 8\,\text{cm}\), \(PS = 5.5\,\text{cm}\), and \(\angle SPQ = 60^{\circ}\).[3]
2. Construct two triangles \(\triangle PQS\) and \(\triangle QRS\) from the parallelogram \(PQRS\). Prove that \(\triangle PQS \cong \triangle QRS\).[2]
1. Which type of triangle is used to make regular tessellation?[1]
2. \(P(4, 3)\), \(Q(7, 3)\), and \(R(4, -3)\) are the vertices of a right-angled triangle. Draw the triangle and its image on graph paper after reflecting it in the \(y\)-axis.[3]
3. Find the perpendicular distance of the line joining the points \(A(4, 1)\) and \(B(4, 5)\) from the \(y\)-axis.[1]
12. The monthly expenditure of Anup's family is shown in the table below:

Item	Food	Education	Rent	Others
Expenditure (Rs.)	\(\text{Rs.}\,2{,}000\)	\(\text{Rs.}\,2{,}500\)	\(\text{Rs.}\,3{,}000\)	\(\text{Rs.}\,2{,}500\)

1. What is the monthly average expenditure of Anup's family?[1]
2. Show the expenditure of Anup's family in a pie chart.[2]