The combined equation of the asymptotes of the hyperbola 2x2 + 5x

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The normal at (a, 2a) on y2 = 4ax, meets the curve again at (at, 2at ), then the value of t is

  • - 1

  • 1

  • - 3

  • 3


2.

The value of 2cos56°15' +isin56°15'8

 

  • - 16i

  • 16i

  • 8i

  • 4i


3.

If α is an nth root of unity, then 1 + 2α + 3α2 + ... + n - 1equals

  • - n1 - α

  • - n1 + α2

  • n1 - α

  • None of these


4.

Given, fx = log1 + x1 - x and gx = 3x + x31 +3x2, then fog(x) equals

  • [f(x)]3

  • - f(x)

  • 3f(x)

  • None of these


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5.

If a set A contains n elements, then which of the following. cannot be the number of reflexive relations on the set A?

  • 2n + 1

  • 2n - 1

  • 2n

  • 2n2 - 1


6.

The relation on the set A = {x : x < 3, x  Z} is defined by R = {(x, y) : y = x, x  - 1} Then, the number of elements in the power set of R is

  • 8

  • 16

  • 32

  • 64


7.

Which of the following proposition is a tautology?

  • ~ P  ~ q  p  ~ q

  • ~ q  p  ~ q

  • ~ P   p  ~ q

  • ~ P  ~ q  p  ~ q


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8.

The combined equation of the asymptotes of the hyperbola 2x2 + 5xy + 2y2 + 4x + 5y = 0 is

  • 2x2 + 5xy + 2y2 + 4x + 5y - 2 = 0

  • 2x2 + 5xy + 2y= 0

  • 2x2 + 5xy + 2y2 + 4x + 5y + 2 = 0

  • None of the above


C.

2x2 + 5xy + 2y2 + 4x + 5y + 2 = 0

Let the equation of asymptotes be,

2x2 + 5xy + 2y2 + 4x + 5y + λ = 0            ...(i)

The above equation represents a pair of straight lines.

Therefore, abc + 2fgh - af2 - bg2 - ch2 = 0

Here, a = 2, b = 2, h = 52, g = 2, f = 52

and c = λ,

 4λ + 25 - 252 - 8 - 254λ = 0 - 9λ4 + 92 = 0                  λ = 2

On putting the value of λ in Eq. (i), we get

2x2 + 5xy + 2y2 + 4x + 5y + 2 = 0

which is the equation of the asymptotes.


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9.

A point on the ellipse : x216 + y29 = 1 at a distance equal to the mean of length of the semi-major and semi-minor axes from the centre, is

  • 2917, - 39114

  • - 21057, 9114

  • - 21057, - 39114

  • 2917, 310514


10.

The parametric coordinates of any point on the parabola whose focus is (0, 1) and the directrix is x + 2 = 0, are

  • (t2 - 1, 2t + 1)

  • (t2 + 1, 2t + 1)

  • (t2, 2t)

  • (t2 + 1, 2t - 1)


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