DMUN_8_2018

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  1. Study the Venn diagram alongside and answer the following questions.
    1. Write the sets \(M\) and \(N\) by description method and tabulation method.[1]
    2. Write the universal set \(U\).[1]
    3. Are \(M\) and \(N\) disjoint or overlapping sets? Why?[1]
    1. Which two digits are used for binary number system?[1]
    2. Convert \(1234_5\) into decimal number.[2]
    3. Convert \(0.\overline{24}\) into a fraction.[1]
    4. Divide \(\text{Rs.}\,500\) in the ratio \(7:5\).[2]
  3. A mobile set of marked price \(\text{Rs.}\,22{,}000\) is sold at \(10\%\) discount.
    1. Write the formula to find the discount amount.[1]
    2. Find the discount amount of the mobile set.[1]
    3. Find the selling price of the mobile.[1]
  4. The simple interest on \(\text{Rs.}\,4{,}000\) for \(5\) years is \(\text{Rs.}\,2{,}400\).
    1. If principal (\(P\)), time (\(T\)), and rate of interest (\(R\)) are given, write the formula to find interest (\(I\)).[1]
    2. Find the rate of interest.[2]
    3. At the same interest rate, how much will be the interest on \(\text{Rs.}\,2{,}000\) for \(4\) years?[2]
    1. Find the value of \((5x)^0\).[1]
    2. Simplify: \(x^{a-b} \times x^{b-c} \times x^{c-a}\).[2]
    1. Find the H.C.F. of \(x^2 - 16\) and \(x^2 - 8x + 16\).[2]
    2. Solve: \(x^2 - 5x + 6 = 0\).[2]
    1. Solve by graphical method: \(x + y = 6\), \(x - y = 2\).[2]
    2. Simplify: \(\dfrac{a}{a - b} - \dfrac{b}{a + b}\).[2]
  8. In the adjoining figure, \(ABCD\) is a square and point \(O\) is the centre of the circle.
    1. Find the radius of the circle.[1]
    2. Find the area of the square \(ABCD\).[2]
    3. Find the area of the circle.[2]
    4. Find the area of the shaded portion.[2]
  9. Solve the given questions from the adjoining figure.
    1. Write the relation between \(\angle AGH\) and \(\angle GHD\).[1]
    2. If \(AB \parallel CD\), find the value of \(x\).[2]
    3. Find each interior angle of a regular octagon.[1]
    1. Construct parallelogram \(PQRS\) having \(PQ = 6\,\text{cm}\), \(QR = 5\,\text{cm}\) and \(\angle PQR = 45^\circ\).[3]
    2. In the adjoining figure, if \(AO = OC\) and \(BO = OD\), prove that \(\triangle ABO \cong \triangle ODC\).[2]
    1. Write the definition of regular tessellation.[1]
    2. If the bearing of place \(D\) from place \(C\) is \(060^\circ\), find the bearing of place \(C\) from place \(D\).[2]
    3. Plot \(\triangle KLM\) with vertices \(K(6,6)\), \(L(4,5)\), and \(M(6,2)\) on graph paper. Then plot the image \(\triangle K'L'M'\) after rotation about the origin through \(+90^\circ\) on the same graph paper and write the coordinates of the vertices of \(\triangle K'L'M'\).[3]
  12. Ten students of class \(8\) have obtained the following marks in mathematics: \(50, 60, 60, 70, 80, 40, 60, 90, 50, 80\).
    1. Find the mean.[2]
    2. Find the mode.[1]

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