If a, b, c are in HP, then ab + c, bc +&

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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


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


C.

HP

Since a, b, c are in HP.

 1a, 1b, 1c are in AP. a + b + ca, a + b + cb, a + b + cc are in AP. 1 + b + ca, 1+ a + cb, 1 + a + bc are in AP. b + ca, a + cb, a + bc are in AP. ab + c, bc + a, ca + b are in HP.


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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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