To the lines ax2 + 2hxy + by2 = 0, the lines a2x2 + 2h(a + b) xy

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

To the lines ax2 + 2hxy + by2 = 0, the lines a2x2 + 2h(a + b) xy + b2y2 = 0 are

  • equally inclined

  • perpendicular

  • bisector of the angle

  • None of these


A.

equally inclined

The equation of the bisector of the angle between the lines given by ax2 + 2hxy + by2 = 0is,

x2 - y2a - b = xyh      ...(i)

And the equation of the bisector of the angle between the lines is given by,

a2x2 + 2h(a + b)xy + b2y2 = 0 is

     x2 - y2a2 - b2 = xyha + b x2 - y2a - b = dyh      ...ii

From equation (i) and (ii), it is clear that both the pair of straight lines have the same bisector, hence the given pair of straight lines are equally inclined.

 


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2.

If R be a realtion from A = {1, 2, 3, 4} to B = {1, 3, 5} such that (a, b) ∈R  a < b, then ROR-1 is

  • {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

  • {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}

  • {(3, 3), (3, 5), (5, 3), (5, 5)}

  • {(3, 3), (3, 4), (4, 5)}


3.

If x + iy = 1 - i3100, then find (x, y).

  • 299, 2993

  • 299, - 2993

  • - 299, 2993

  • None of these


4.

For a GP, an = 3(2n), ∀ n ∈ N. Find the common ratio

  • 2

  • 1/2

  • 3

  • 1/3


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5.

If a, b, c are in HP, then ab + c, bc + a, ca + b will be in

  • AP

  • GP

  • HP

  • None of these


6.

If x2 + 2x + 72x + 3 < 6, x  R, then

  • x > 11 or x = - 32

  • x > 11 or x < - 1

  • - 32 < x < - 1

  • - 1 < x < 11 or x < - 32


7.

The number of ways of painting the faces of a cube of six different colours is

  • 1

  • 6

  • 6!

  • 36


8.

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. What is its y intercept

  • 1/3

  • 2/3

  • 1

  • 4/3


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9.

The number of common tangents to the circles x2 + y2 = 4 and x2 + y2 - 6x - 8y = 24 is

  • 0

  • 1

  • 3

  • 4


10.

If D is the set of all real x such that 1 - e(1/x) - 1 is positive, then D is equal to

  • (- , 1]

  • - , 0

  • 1, 

  • - , 0  1, 


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