3tan-1a is equal to from Mathematics JEE Year 2007 Free Sol

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The maximum value of 3 cosθ + 4 sinθ is

  • 3

  • 4

  • 5

  • None of these


2.

1- 1221- 1 is equal to

  • 2- 1- 2

  • 21- 1- 2- 1142- 2

  • [- 1]

  • Not defined


3.

The domain of the function sin-1log2x22 is

  • [- 1, 2] - {0}

  • [- 2, 2] - (- 1, 1)

  • [- 2, 2] - {0}

  • [1, 2]


4.

Function f(x) = x - 1,   x <22x - 3, x  2 is a continuous function

  • for x = 2 only

  • for all real values of x such that x  2

  • for all real values of x

  • for all integral values of x only


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5.

Differential coefficient of secx is

  • 14xsecxsinx

  • 14xsecx32 . sinx

  • 12xsecx . sinx

  • 12xsecx32 . sinx


6.

The function x5 - 5x4 + 5x3 - 1 is

  • neither maximum nor minimum at x = 0

  • maximum at x = 0

  • maximum at x = 1 and minimum at x = 3

  • minimum at x = 0


7.

If the radius of a circle be increasing at a uniform rate of 2 cm/s. The area of increasing of area of circle, at the instant when the radius is 20 cm, is

  • 70 π cm2/s

  • 70 cm2/s

  • 80 π cm2/s

  • 80 cm2/s


8.

The equation of normal at the point (0, 3) of the ellipse 9x2 + 5y2 = 45 is

  • x-axis

  • y-axis

  • y + 3 = 0

  • y - 3 = 0


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9.

Let the functions f, g, h are defined from the set of real numbers R to R such that

fx = x2 - 1, gx = x2 + 1 andhx = 0, if x < 0x, if x  0

then ho(fog)(x) is defined by

  • x

  • x2

  • 0

  • None of these


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10.

3tan-1a is equal to

  • tan-13a + a31 + 3a2

  • tan-13a - a31 + 3a2

  • tan-13a + a31 - 3a2

  • tan-13a - a31 - 3a2


D.

tan-13a - a31 - 3a2

3tan-1a = 2tan-1a + tan-1a                = tan-12a1 - a2 + tan-1a                = tan-12a1 - a2 +a1 - 2a21 - a2              = tan-12a +a - a31 - a2 - 2a2              = tan-13a - a31 - 3a2


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