If f : R S, defined by  , is onto, then the interval of S is f

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 Multiple Choice QuestionsMultiple Choice Questions

11.

A particle is projected from a point O with velocity u at an angle of 60o with the horizontal. When it is moving in a direction at right angles to its direction at O, its velocity then is given by

  • u/3

  • u/2

  • 2u/3

  • 2u/3

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12.

If f : R S, defined by straight f left parenthesis straight x right parenthesis space equals space sin space straight x space minus space square root of 3 space cos space straight x space plus 1 , is onto, then the interval of S is

  • [0, 3]

  • [-1, 1]

  • [0, 1]

  • [0, 1]


D.

[0, 1]

since space minus 2 less or equal than space sin space straight x space minus square root of 3 space cos space straight x less or equal than 2
space minus 1 less or equal than space sin space straight x space minus square root of 3 space cos space straight x space plus space 1 space less or equal than space 3
Range space of space straight f left parenthesis straight x right parenthesis space equals space left square bracket negative 1 comma space 3 right square bracket
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13.

Let f(x) = x2 + 1x2 and g (x)  = x - 1x, x Ε R - {-1,0,1}.
if h(x) = f(x)g(x), then the local minimum value of h(x) is:

  • 22

  • 3

  • -3

  • -22


14.

The possible values of x, which satisfy the trigonometric equation

tan-1x - 1x - 2 + tan-1x + 1x + 2 = π4 are

  • ± 12

  • ± 2

  • ± 12

  • ± 2


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15.

If sin- 1x - x22 + x34 - x48 +  = π6, where x < 2 then the value of x is

  • 23

  • 32

  • 23

  • 32


16.

The trigonometric equation sin-1x = 2sin-12a has a real solution, if

  • a > 12

  • 122 < a < 12

  • a > 122

  • a  122


17.

The value of 2cot-112 - cot-143 is

  • - π8

  • 3π2

  • π4

  • π2


18.

If sin-1x13 + csc-11312 = π2, then the value of x is

  • 5

  • 4

  • 12

  • 11


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19.

tan-1xy - tan-1x - yx + y is equal to (where x > y > 0)

  • - π4

  • π4

  • 3π4

  • None of these


20.

If sin-1x - cos-1x = π6, then x is

  • 12

  • 32

  • - 12

  • None of these


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