Dharan_8_2081

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  1. Study the given Venn diagram and answer the following questions.
    1. Write the set notation for the shaded region.[1]
    2. Write all the possible subsets formed from set \(B\).[1]
    3. Which elements must be removed from both sets to make them disjoint sets?[1]
  2. The cost of \(16\,\text{kg}\) apples is \(\text{Rs.}\,4{,}800\).
    1. Write the cost of \(16\,\text{kg}\) apples in scientific notation.[1]
    2. What is the cost of \(1\,\text{kg}\) apple in the quinary number system?[1]
    3. How many kg of apples can be bought for \(\text{Rs.}\,5{,}100\)? Find it.[1]
  3. The cost of a mobile is \(\text{Rs.}\,12{,}800\). However, the mobile's marked price is \(20\%\) above the cost price. The shopkeeper sold the mobile, allowing a \(10\%\) discount.
    1. Find the marked price of the mobile.[2]
    2. Find the selling price of the mobile.[2]
    3. What is the shopkeeper's profit or loss percent from the mobile? Find it.[1]
  4. Ramesh gave Suresh a loan of \(\text{Rs.}\,24{,}500\) at a fixed simple interest rate for \(2\) years. After the term ended, Suresh repaid a total amount of \(\text{Rs.}\,30{,}380\).
    1. Write the formula to find simple interest when principal (\(P\)), time (\(T\)), and rate of interest (\(R\)) are given.[1]
    2. Find the interest rate paid by Suresh.[1]
    3. How much amount is returned by Suresh to Ramesh, if he paid at the end of \(3\) years?[2]
    4. If Ramesh distributes the total amount he received in two years between Ganesh and Mahesh in the ratio \(3:7\), who will receive how much more?[2]
  5. The length and width of the floor of a rectangular room are \(5\,\text{m}\) and \(4\,\text{m}\) respectively. \(500\) circular tiles with a diameter of \(20\,\text{cm}\) have been installed on it.
    1. Write the formula to find the area of a rectangle.[1]
    2. How much square cm space of floor does a tile cover? (\(\pi = 3.14\))[1]
    3. Calculate the area of the room's floor excluding the tiles.[2]
    4. If a circular tile is being replaced with a square tile that has a side length of \(25\,\text{cm}\), calculate the total cost of tiling the room where each tile costs \(\text{Rs.}\,20\).[1]
    1. What is the value of \((30x^3)^0\)?[1]
    2. Simplify: \(\dfrac{1}{a + b} + \dfrac{2b}{a^2 - b^2}\).[2]
    1. What value should be written in the blank space of \(x + \ldots + y^2\) to make a perfect square?[1]
    2. Find the H.C.F. of the given algebraic expressions: \(4x^2 - 9\) and \(2x^2 + x - 3\).[2]
    1. Solve: \(\dfrac{x + 15}{15x + 25} = \dfrac{1}{x}\).[2]
    2. Solve the given equations by using graphical method: \(2x + y = 7\) and \(x - 2y = -4\).[2]
  9. In the adjacent figure, the line \(CR\) intersects the straight lines \(EF\) and \(GH\) at points \(A\) and \(C\), while the line \(TS\) intersects the straight lines \(EF\) and \(GH\) at points \(B\) and \(C\).
    1. Write a pair of co-interior angles from the figure.[1]
    2. Find the value of \(x\).[2]
    1. Construct a parallelogram \(ABCD\) with \(AB = 6.7\,\text{cm}\), \(\angle ABC = 60^\circ\), and \(BC = 5.6\,\text{cm}\).[3]
    2. In the adjoining figure, if \(\triangle PMN \sim \triangle PQR\), find the length of \(MN\).[2]
    3. Construct two triangles \(\triangle ABC\) and \(\triangle ADC\) from parallelogram \(ABCD\) and prove that \(\triangle ABC \cong \triangle ADC\).[2]
    1. Which type of triangle is used to make a regular tessellation?[1]
    2. In the adjoining figure, the bearing of \(B\) from \(A\) is \(106^\circ\). Find the bearing of \(A\) from \(B\).[2]
    3. The triangle \(\triangle ABC\) with vertices \(A(2,3)\), \(B(5,6)\), and \(C(6,1)\) is reflected on the \(y\)-axis. Find the coordinates of the image triangle \(\triangle A'B'C'\).[3]

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