Creative Questions Part-IV

10th Standard

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Maths

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

    Part-A

    10 x 1 = 10
  1. If the order pairs (a, -1) and (5, b) blongs to {(x, y) | y = 2x + 3}, then a and b are __________

    (a)

    -13, 2

    (b)

    2, 13

    (c)

    2, -13

    (d)

    -2,13

  2. 44 ≡ 8 (mod12), 113 ≡ 85 (mod 12), thus 44 x 113 ≡______(mod 12):

    (a)

    4

    (b)

    3

    (c)

    2

    (d)

    1

  3. The real roots of the quardractic equation x2-x-1 are ___________

    (a)

    1, 1

    (b)

    -1, 1

    (c)

    \(\frac { 1+\sqrt { 5 } }{ 2 } ,\frac { 1-\sqrt { 5 } }{ 2 } \)

    (d)

    None

  4. If the angle between two radio of a circle is o, the angle between the tangents at the end of the radii is ____________

    (a)

    50o

    (b)

    90o

    (c)

    40o

    (d)

    70o

  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 tan θ + cot θ = 3 then tan2θ + cot2θ is equal to ___________

    (a)

    4

    (b)

    7

    (c)

    6

    (d)

    9

  8. A spherical steel ball is melted to make 8 new identical balls. Then the radius each new ball is how much times the radius of the original ball?

    (a)

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

    (b)

    \(\frac { 1 }{ 4 } \)

    (c)

    \(\frac { 1 }{ 2 } \)

    (d)

    \(\frac { 1 }{ 8 } \)

  9. A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is

    (a)

    45%

    (b)

    56%

    (c)

    67%

    (d)

    75%

  10. If the observations 1, 2, 3, ... 50 have the variance V1 and the observations 51, 52, 53, ... 100 have the variance V2 then \(\frac { { V }_{ 1 } }{ { V }_{ 2 } } \) is ___________

    (a)

    2

    (b)

    1

    (c)

    3

    (d)

    0

  11. Part-B

    8 x 2 = 16
  12. State whether the graph represent a function. Use vertical line test.

  13. Find the LCM and HCF of 6 and 20 by the prime factorisation method.

  14. Solve the following system of linear equations in three variables.
    x + y + z = 6; 2x + 3y + 4z = 20;
    3x + 2y + Sz = 22

  15. In figure OA· OB = OC·OD
    Show that \(\angle A=\angle C\ and\ \angle B=\angle D\)

  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. \(\sqrt3\)1 (3-cot30o)=tan3 60o-2sin60o

  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.

    find 2f(-4) + 3f(2)

  22. Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
    -2, 2, -2, 2, -2

  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. In \(AD\bot BC\) prove that AB+ CD2 = BD+ AC2

  25. Find the area of a triangle vertices are(1, -1), (-4, 6) and (-3, -5).

  26. If sin 3A = cos (A - 26°), where 3A is an acute angle, find the value at A.

  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. Find the co-efficient of variation for the following data: 16, 13, 17,21, 18.

  29. Part-D

    8 x 8 = 64
  30. If R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function, find the values of a, b, c and 

  31. Find the sum of first 24 terms of the list of numbers whose nth term is given by a= 3 + 2n.

  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 figure 0 is any point inside a rectangle ABCD. Prove that OB2 + OD2 = OA+ OC2

  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 spherical ball of iron has been melted and made into small balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

  37. S.D. of a data is 2102, mean is 36.6, then find its C.V.

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