If the line y = mx + 73 is normal to the hyperbola x224

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If the function f : R - 1, - 1  A defined by fx = x21 - x2, is surjective, then A is equal to :

  • R - (- 1, 0)

  • R - [- 1, 0)

  • - {- 1}

  • [0, )


2.

If the function f defined on π6, π3 by f(x) = 2cosx - 1cotx - 1, x  π4k,                       x = π4 is continuous, then k is equal to :

  • 2

  • 12

  • 12

  • 1


3.

Let α and β be the roots of the equation x2 + x + 1 = 0 . Then for y  0 in R, y + 1αβαy +β1β1y + α is equal to :

  • y(y2 - 1)

  • y3

  • y(y2 - 3)

  • y3 - 1


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4.

If the line y = mx + 73 is normal to the hyperbola x224 - y218 = 1, then a value of m is :

  • 52

  • 152

  • 215

  • 315


C.

215

Use a2l2 - b2m2 = a2 + b22n2Here a2 = 24, b2 = 18, l = m, m = - 1, n = 73On simplifying, we getm = 25


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5.

Let k = 10fa + k = 16210 - 1, where function satisfies f(x + y) = f(x)f(y) for all natural numbers x, y and f(1) = 2 . Then the natural number ‘a’ is

  • 16

  • 22

  • 20

  • 25


6.

If the tangent to the curve, y = x3 + ax - b at the point (- 1, - 5) is perpendicular to the line, - x + y + 4 = 0, then which one of the following points lies on the curve ?

  • (2, - 1)

  • (- 2, 2)

  • (2, - 2)

  • (- 2, 1)


7.

If 110112011301 ... 1n - 101 = 17801 then the inverse of 1n01 is

  • 11201

  • 10121

  • 10131

  • 1- 1301


8.

Let f(x) = 15 - x - 10 ; x  R. Then the set of all values of x, at which the function, g(x) = f(f(x) is not differentiable, is:

  • {5, 10, 15}

  • {10}

  • {10, 15}

  • {5, 0, 15, 20}


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9.

Let α = 3i^ + j^ and β = 2i^ - j^ + 3k^. If β = β1 - β2, where β1 is paralle to α and β2 is perpendicular to α, then β1 × β2

  • 12- 3i + 9j + 5k

  • 123i - 9j + 5k

  • 3i - 9j - 5k

  • - 3i + 9j + 5k


10.

The value of 0π2sin3xsinx + cosxdx is :

  • π - 24

  • π - 28

  • π - 14

  • π - 12


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