Rampur_Palpa_8_2081

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  1. Study the given Venn diagram and answer the following questions.
    1. List the elements of sets \(A\) and \(B\) in listing method.[1]
    2. Write the improper subset of set \(B\).[1]
    3. If set \(A\) contains only the element ‘\(r\)’, then what type of set relation exists between \(A\) and \(B\)? Give a reason.[1]
  2. Anisha bought a scooter for \(\text{Rs.}\,3{,}00{,}000\) and sold it to Divya after \(2\) years, deducting \(20\%\) of the price. Divya sold it to Gauri at a profit of \(\text{Rs.}\,6{,}000\).
    1. Find the selling price of Anisha.[1]
    2. Compare the price of Anisha and Gauri of the scooter in the ratio form.[2]
  3. Ganesh borrowed a sum of \(\text{Rs.}\,27{,}000\) from his friend Bishnu. He paid an interest of \(\text{Rs.}\,5{,}940\) to Bishnu at the end of \(2\) years.
    1. Write the formula to find the rate of interest.[1]
    2. Find the rate of interest at which Ganesh borrowed the sum.[1]
    3. At the same rate of interest, calculate the interest for \(3\) years.[2]
    4. If Ganesh had not paid any interest till the end of \(3\) years, how much amount would be needed to clear the loan?[2]
  4. The road between Rampur to Gaidakot is \(95\) kilometers.
    1. Write the distance in scientific notation in meters.[1]
    2. If Utsab drives his bike at the rate of \(19\,\text{km/hr}\), calculate the time taken to travel from Rampur to Gaidakot.[1]
    3. Write \(35\) in the quinary number system.[1]
    4. The monthly salary of Prakash is \(\text{Rs.}\,43{,}689\). Find his expenditure and saving amount if their ratio is \(2:1\).[2]
  5. In the adjoining figure, \(LOVE\) is a square park. Inside that park, there is a circular pond. The side of the square is \(25\,\text{m}\) and the diameter of the pond is \(14\,\text{m}\).
    1. Write the formula to find the area of a circle.[1]
    2. Find the area of the circular pond.[1]
    3. Find the area of the park including the pond.[1]
    4. How much does it cost to fence the park at the rate of \(\text{Rs.}\,650\) per meter?[1]
    1. What is the value of \(\left(\dfrac{3x}{y}\right)^0\)?[1]
    2. Simplify: \(\dfrac{x^2}{x - 7} + \dfrac{49}{7 - x}\)[2]
  7. Two equations are given below: \(x + 3y = 8\) and \(2x + y = 6\).
    1. What is this system of equations called?[1]
    2. Solve the above equations using a graph.[2]
    1. Find the H.C.F. of \(x^2 - 5x + 6\) and \(x^2 - 4\).[2]
    2. At what value of \(x\) does the expression \(x^2 - 7x - 18\) become zero?[2]
  9. In the figure, \(PQ \parallel RS\). \(TR\) and \(TU\) are two transversals. If \(\angle PTR = 60^\circ\) and \(\angle QTU = 70^\circ\),
    1. Find the values of \(x^\circ\) and \(y^\circ\).[2]
    2. Experimentally verify that the angles of an equilateral triangle are equal. (Two different triangles are necessary.)[3]
    1. By which axiom are the given triangles \(\triangle ABC\) and \(\triangle PQR\) congruent?[1]
    2. Construct a parallelogram \(ABCD\) in which \(AB = 6\,\text{cm}\), \(AD = 5\,\text{cm}\), and \(\angle BAC = 60^\circ\).[3]
    3. How can the area of the parallelogram be found? Write your argument.[1]
  11. The vertices of \(\triangle ABC\) are \(A(3,2)\), \(B(5,6)\), and \(C(7,2)\).
    1. How many triangular surfaces are there in a tetrahedron?[1]
    2. In \(\triangle ABC\), if the bearing of point \(C\) from \(A\) is \(090^\circ\), find the bearing of \(A\) from point \(C\). Also, find the distance between points \(A\) and \(B\).[2]
    3. Plot \(\triangle ABC\) on a graph and find the coordinates of the image of \(\triangle ABC\) after reflection in the \(x\)-axis. Also, plot its image on the same graph.[2]
  12. The numbers of students in classes \(1\) to \(5\) in a school are given below. Study the table and answer the following questions:
    13. Class 1 2 3 4 5
    No. of students \(12\) \(18\) \(15\) \(25\) \(20\)
    1. What is the average number of students per class?[1]
    2. Present the above information in a pie chart.[2]

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