Set 25

  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]
  2. Sagar went to the utensil shop to buy a rice cooker. The marked price of a rice cooker is \(\text{Rs.}\,5{,}000\).
    1. If marked price (M.P.) and discount (\(D\)) are represented by (M.P.) and (\(D\)) respectively, write the formula to find the selling price (S.P.).[1]
    2. How much discount did Sagar get while buying a rice cooker on a discount of \(15\%\)?[1]
    3. The shopkeeper got \(15\%\) profit after selling it at a \(15\%\) discount. What was the cost price of the rice cooker?[2]
  3. Elisza took a loan of \(\text{Rs.}\,80{,}000\) 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]
  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 \(84\,\text{m}\) 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 \(144\,\text{m}\), 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 \(\text{Rs.}\,40{,}000\). But \(\text{Rs.}\,530\) was not enough to fence the land. What was the cost of fencing the land per meter? Find it.[2]
    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 \(6\,\text{cm}\) and \(4\,\text{cm}\), 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]

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