Creative Questions Part-VI

10th Standard

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Maths

Time : 01:30:00 Hrs
Total Marks : 100

    Part-A

    10 x 1 = 10
  1. If f(x) = ax - 2, g(x) = 2x - 1 and fog = gof, the value of a is ___________

    (a)

    3

    (b)

    -3

    (c)

    \(\frac { 1 }{ 3 } \)

    (d)

    13

  2. In the arithemetic series Sn = k + 2k + 3k +...+ 100, k is positive integer and k is a factor 100 then Sn is ____________

    (a)

    \(1000\frac { 10 }{ k } \)

    (b)

    \(5000\frac { 50 }{ k } \)

    (c)

    \(\frac { 1000 }{ k } +10\)

    (d)

    \(\frac { 5000 }{ k } +50\)

  3. If \(A=\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right] _{ 3\times 2 }\) \(B=\left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix} \right] _{ 2\times 3 }\) then which of the following products can be made from these matrices 
    (i) A2
    (ii) B2
    (iii) AB
    (iv) BA

    (a)

    (i) only

    (b)

    (ii) and (iii) only

    (c)

    (iii) and (iv) only

    (d)

    all the above

  4. In the given figure if OC = 9 cm and OB = 15 cm then OB + BD is equal to ____________

    (a)

    23 cm

    (b)

    24 cm

    (c)

    27 cm

    (d)

    30 cm

  5. Two concentric circles if radii a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is ____________

    (a)

    \(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)

    (b)

    \(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)

    (c)

    \(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)

    (d)

    \(2\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)

  6. The area of triangle formed by the points (a, b+c), (b, c+a) and (c, a+b) is ____________

    (a)

    a+b+c

    (b)

    abc

    (c)

    (a+b+c)2

    (d)

    0

  7. If cos θ + cos2θ = 3 then tan2θ + cot2θ is equal to ___________

    (a)

    4

    (b)

    7

    (c)

    6

    (d)

    9

  8. The radio of base of a one 5 cm and to height 12 cm. The slant height of the cone ___________

    (a)

    12 cm

    (b)

    17 cm

    (c)

    7 cm

    (d)

    60 cm

  9. If S1 denotes the total surface area at a sphere of radius ૪ and S2 denotes the total surface area of a cylinder of base radius ૪ and height 2r, then ___________

    (a)

    S= S2

    (b)

    S> S2

    (c)

    S< S2

    (d)

    S= 2S2

  10. Th4e batsman A is more consistent than batsman B if ___________

    (a)

    C.V of A > C.V of B

    (b)

    C.V of A < C.V of B

    (c)

    C.V of a =C.V of B

    (d)

    C.V of A≥C.V of B

  11. Part-B

    8 x 2 = 16
  12. Let A =  {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} \(\subseteq \) A x B bea relation. Show that R is a function and find its domain, co-domain and the range of R.

  13. Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

  14. Using quadratic formula solve the following equations.9x2-9(a+b)x+(2a2+5ab+2b2)=0

  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. Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

  17. Simplify (1+tan2θ)(1-sinθ)(1+sinθ)

  18. Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m x 16 m x 11 m.

  19. Find the standard deviation for the following data. 5, 10, 15, 20, 25. And also find the new S.D. if three is added to each value.

  20. Part-C

    8 x 5 = 40
  21. A functionf: [-7,6) \(\rightarrow\) R is defined as follows.

    f(-7) - f(-3)

  22. Determine the AP whose 3rd term is 5 and the 7th term is 9.

  23. A chess board contains 64 equal squares and the area of each square is 6.25 cm2, A border round the board is 2 cm wide.

  24. Prove that in a right triangle, the square of 8. the hypotenure is equal to the sum of the squares of the others two sides.

  25. If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

  26. P.T (1+tan∝tan∝tanβ)2 +(tan∝-tanβ)2 =sec2 ∝sec2β.

  27. Find the number of coins, 1.5 cm is diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

  28. C.V. of a data is 69%, S.D. is 15.6, then find its mean.

  29. Part-D

    8 x 8 = 64
  30. A functionf: (1,6) \(\rightarrow\)R is defined as follows:

    Find the value of f(2) - f( 4).

  31. How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?

  32. A two digit number is such that the product of its digits is 18, when 63 is subtracted from the number, the digits interchange their places. Find the number.

  33. In \(\angle ACD={ 90 }^{ 0 }\) and \(CD\bot AB\) Prove that \(\cfrac { { BC }^{ 2 } }{ { AC }^{ 2 } } =\cfrac { BD }{ AD } \)

  34. Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).

  35. Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

  36. A wooden article was made by scooping out a hemisphere from each end of a cylinder as shown in figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm find the total surface area of the article.

  37. Final the probability of choosing a spade or a heart card from a deck of cards.

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