The number of non-zero integral solutions of the equation 1&

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

The equation of the circle on the common chord of the circles (x - a)2 + y2 = a2 and x2 + (y + b)2 = b2 as diameter is

  • x2 + y2 = 2ab(bx + ay)

  • x2 + y2 = bx + ay

  • (a2 + b2)(x2 + y2) = 2ab(bx - ay)

  • (a2 + b2)(x2 + y2) = 2(bx + ay)


22.

The eccentricity of the hyperbola which passes through (3, 0) and (32, 2) is

  • 13

  • 133

  • 134

  • None of these


23.

The line x - 1 = 0 is the directrix of the parabola y2 - kx + 8 = 0. Then, one of the value of k is

  • 18

  • 8

  • 4

  • 14


24.

If y = 21logx8, then x is equal to

  • y

  • y2

  • y3

  • None of these


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25.

The region of the complex plane for which z - az + a = 1, [Re (a)  0] is

  • x - axis

  • y - axis

  • the straight line x = a

  • None of the above


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26.

The number of non-zero integral solutions of the equation 1 - ix = 2x

  • infinite

  • 1

  • 2

  • None of these


B.

1

Given, 1 - ix = 2x  1 + 1x = 2x               x2 = x                x = 0, 2

Therefore, the number of non-zero integral solutions is one.


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27.

Let α, α2 be the roots of x2 + x + 1 = 0, then the equation whose roots are α31, α62 is

  • x2 - x + 1 = 0

  • x2 + x - 1 = 0

  • x2 + x + 1 = 0

  • x60 + x30 + 1 = 0


28.

If ecosx - e- cosx = 4, then the value of cosx is

  • log2 + 5

  • - log2 + 5

  • log- 2 + 5

  • None of these


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29.

If tan-1ax + tan-1bx = π2, then x is equal to

  • ab

  • 2ab

  • 2ab

  • ab


30.

A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window be 64 m, then the distance between the two houses is

  • 48 m

  • 36 m

  • 54 m

  • 72 m


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