Full Portion Two Marks Question Paper

10th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    25 x 2 = 50
  1. If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

  2. The arrow diagram shows a relationship between the sets P and Q. Write the relation in
    (i) Set builder form
    (ii) Roster form
    (iii) What is the domain and range of R.

  3. A plane is flying at a speed of 500 km per hour. Express the distanced travelled by the plane as function of time t in hours.

  4. If f(x) = 3x - 2, g(x) = 2x + k and if f o g = f o f, then find the value of k..

  5. State whether the graph represent a function. Use vertical line test.

  6. Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f : A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

  7. Find the square root of \(1+\frac { 1 }{ { x }^{ 6 } } +\frac { 2 }{ { x }^{ 3 } } \)

  8. Determine the nature of the roots for the following quadratic equations
    \(\sqrt { 2 } { t }^{ 2 }-3t+3\sqrt { 2 } \) = 0

  9. In the matrix A = \(\left[ \begin{matrix} 8 \\ -1 \\ \begin{matrix} 1 \\ 6 \end{matrix} \end{matrix}\begin{matrix} 9 \\ \sqrt { 7 } \\ \begin{matrix} 4 \\ 8 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \frac { \sqrt { 3 } }{ 2 } \\ \begin{matrix} 3 \\ -11 \end{matrix} \end{matrix}\begin{matrix} 3 \\ 5 \\ \begin{matrix} 0 \\ 1 \end{matrix} \end{matrix} \right] \), write The order of the matrix

  10. Using quadratic formula solve the following equations.
    p2x2 + (P2 -q2) X - q2 = 0

  11. In the Figure, AD is the bisector of \(\angle\)BAC, if A = 10 cm, AC = 14 cm and BC = 6 cm. Find BD and DC.

  12. \(\triangle\) LMN is a right angled triangle with\(\angle\)L = 90o. A circle is inscribed in it. The lengths of the sidescontaining the right angle are 6 cm and 8 cm. Find the radius of the circle.

  13. In fig. if PQ || BC and PR || CD prove that

    \(\frac { QB }{ AQ } =\frac { DR }{ AR } \)

  14. In figure if PQ || RS Prove that \(\Delta POQ\sim \Delta SOQ\)

  15. In figure the line segment xy is parallel to side AC of \(\Delta ABC\) and it divides the triangle int two parts of equal areas. Find the ratio \(\cfrac { AX }{ AB } \)

  16. If the three points (3, - 1) , (a, 3) and (1, - 3) are collinear, find the value of a.

  17. Find the equation of a straight line parallel to Y axis and passing through the point of intersection of the lines 4x + 5y = 13 and x - 8y + 9 = 0

  18. Find the equation of a line through the given pair of points (2, 3) and (-7, -1)

  19. prove the following identity.
     \(\sqrt { \frac { 1+sin\theta }{ 1-sin\theta } } =sec\theta +tan\theta\)

  20. calculate \(\angle \)BAC inthe given triangles ( tan 69.4° = 2.6604 )

  21. If 2sin2θ-cos2θ=2, then find the value θ.

  22. A metallic sphere of radius 16 cm is melted and recast into small spheres each of radius 2 cm. How many small spheres can be obtained?

  23. If the radii of the circular ends of a conical bucket which is 45 cm high are 28 cm and 7 cm, find the capacity of the bucket. (Use π = \(\frac{22}{7}\))

  24. Find the range and coefficient of range of the following data.
    43.5, 13.6, 18.9, 38.4, 61.4, 29.8

  25. The marks scored by 5 students in a test for 50 marks are 20, 25, 30, 35, 40. Find the S.D for the marks. If the marks are converted for 100 marks, find the S.D. for newly obtained marks.

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