Set 11

  1. If \(A = \{1, 2, 3\}\) and \(B = \{0, 2, 3, 4\}\),
    1. How many improper subsets does set \(A\) have?[1]
    2. Find the value of \(A \cap B\).[1]
    3. Represent \(A \cap B\) in a Venn diagram.[1]
  2. Ramu marked the price of a mobile at \(\text{Rs.}\,80{,}000\). He sold it with a \(10\%\) discount and gained a profit of \(\text{Rs.}\,4{,}000\).
    1. Write the formula for profit.[1]
    2. Find the discount amount.[1]
    3. Find the cost price of the mobile.[1]
  3. If principal (\(P\)) = \(\text{Rs.}\,10{,}000\), time (\(T\)) = \(4\) years, and rate (\(R\)) = \(6\%\) per annum, then
    1. Write the formula to find simple interest.[1]
    2. Find the interest amount.[1]
    3. Find the total amount.[1]
    1. Write \(45{,}000\) in scientific notation.[1]
    2. Simplify: \(\sqrt{18} - 2\sqrt{18} + 2\sqrt{2}\).[2]
    3. Convert \(46\) into the quinary number system.[1]
  5. In the given figure, \(ABCD\) is a rectangle with length \(10\,\text{cm}\) and breadth \(6\,\text{cm}\).
    1. Write the formula for the area of a rectangle.[1]
    2. Find the area of the rectangle.[1]
    3. Find the perimeter of the rectangle.[1]
    1. Find the value of \((3x)^0\).[1]
    2. Simplify: \(x^2 \times x^3 \times x^{-2}\).[2]
    3. Factorise: \(x^2 + 6x + 8\).[2]
  7. Two equations are given below: \(2x + y = 8\) and \(x + y = 5\).
    1. What is this system of equations called?[1]
    2. Solve the equations using a graph.[2]
    1. Find the L.C.M. of the algebraic expressions \(a^2 - b^2\) and \(a^2 - ab\).[2]
    2. For what value of \(x\) does the expression \(x^2 - 5x + 6\) become zero?[2]
  9. In the adjoining figure, line \(PQ\) intersects straight lines \(AB\) and \(CD\) at points \(E\) and \(F\) respectively.
    1. Write a pair of alternate angles if \(AB \parallel CD\).[1]
    2. Find the value of \(x\).[2]
    3. At what value of \(\angle BEF\) will the lines \(AB\) and \(CD\) become parallel?[2]
    1. Construct a rectangle \(ABCD\) where \(BC = 5\,\text{cm}\), \(BD = 10\,\text{cm}\), and \(\angle CBD = 60^\circ\).[3]
    2. Find the value of \(x\) in the given figure.[3]
    1. What type of triangles are required to form a regular tessellation?[2]
    2. If the bearing of point \(A\) from point \(B\) is \(080^\circ\), find the bearing of point \(B\) from point \(A\).[2]
    3. The vertices of \(\triangle PQR\) are \(P(1,3)\), \(Q(4,1)\), and \(R(3,5)\). Find the vertices of the image \(\triangle P'Q'R'\) after rotation through \(+90^\circ\) about the origin. Represent both triangles on the same graph.[3]
  12. The monthly expenditure (in Rs.) of Ram’s family is given below:
    13. Month Baishakh Jestha Ashar Shrawan
    Expenditure (Rs.) 25,000 19,000 28,000 18,000
    1. Present Ram’s family expenditure in a pie chart.[3]
    2. In a data set, \(2x = m + 77\), \(n = 10\), and mean (\(\bar{x}\)) = \(8\). Find the value of \(m\).[2]

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