If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugat

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

One possible condition for the three points (a, b), (b, a) and (a2, - b2) to be collinear is

  • a - b = 2

  • a + b = 2

  • a = 1 + b

  • a = 1 - b


2.

If the mth term and the nth term of an AP are respectively 1n and 1m, then the mnth term of the AP is

  • 1mn

  • mn

  • 1

  • nm


3.

-  π2π2sin9xcos5xdx equals

  • 120

  • 20

  • 0

  • 1330


4.

The function f(x) = log1 + x1 - x satisfies the equation

  • f(x + 2) - 2f(x + 1) + f(x) = 0

  • f(x) + f(x + 1) = f{x(x + 1)}

  • f(x) + f(y) = fx + y1 + xy

  • f(x + y) = f(x)f(y)


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5.

The value of (1 - w + w2)5 + (1 + w - w2)5, where w and w2 are the complex cube roots of unity, is

  • 0

  • 32w

  • - 32

  • 32


6.

The value of limn1n + 1 + 1n + 2 + ... + 16n is

  • log2

  • log6

  • 1

  • log3


7.

limxπ2acotx - acosxcotx - cosx

  • logeπ2

  • loge2

  • logea

  • a


8.

The equation of the circle which passes through the points of intersection of the circles x2 + y2 - 6x = 0 and x2 + y2 - 6y = 0 and has its centre at 32, 32, is

  • x2 + y2 + 3x + 3y + 9 = 0

  • x2 + y2 + 3x + 3y = 0

  • x2 + y2 - 3x - 3y = 0

  • x2 + y2 - 3x - 3y + 9 = 0


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9.

If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is

  • 23

  • 25

  • 13

  • 12


C.

13

The equations of a pair of conjugate diameters of an ellipse are,

2y = x and 3y + 4x = 0

Slope of 2y = x is 12(m1)

and slope of 3y + 4x = 0 is - 43(m2)

          m1m2 = - b2a2

 12- 43 = - b2a2 - 23 = - b2a2  b2a2 = 23 Eccentricity, e = 1 - b2a2 = 1 - 23                            = 13


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10.

If t is a parameter, then x = at + 1t, y = bt - 1t represents

  • an ellipse

  • a circle

  • a pair of straight lines

  • a hyperbola


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