The lines 2x + 3y = 6 , 2x + 3y = 8 cut the X-axis at A and B, re

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 Multiple Choice QuestionsMultiple Choice Questions

151.

If a, b, c are in arithmetic progression, then abc, 1c, 2b will be in

  • arithmetic proression

  • geometric progression

  • harmonic progresssion

  • None of the above


152.

If G is the geometric mean of x and y, then 1G2 - x2 + 1G2 - y2 will be

  • - G2

  • - 1G2

  • 1G2

  • G2


153.

If a > 1, b > 1 and c > 1 are in geometric progression, then 11 + logea, 11 + logeb, 11 + logec will be in

  • arithmetic proression

  • geometric progression

  • harmonic progresssion

  • None of the above


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154.

The lines 2x + 3y = 6 , 2x + 3y = 8 cut the X-axis at A and B, respectively. A line L drawn through the point (2, 2) meets the X-axis as C in such away that abscissae of A, B and C are in arithmetic progression. Then, the equation of the line L is

  • 2x + 3y = 10

  • 8x + 2y = 10

  • 2x - 3y = 10

  • 8x - 2y = 10


A.

2x + 3y = 10

Given lines are,

      2x + 3y = 6

and 2x + 3y = 8

These lines meet the X-axis at A(3, 0) and B(4, 0)

The line L passes through (2, 2) cuts X-axis at C, such that x-coordinate of A, B, C are in ap i.e. 3, 4, x1.

 2.4 = 3 + x1   x1 = 8 - 3 = 5

To coordinates of C are (5, 0).

A line L passing through the points (2, 2) and (5, 0), is

y - 0 = 0 - 25 - 2x - 5   y = - 23x - 5 3y = - 2x + 10 2x +3y = 10


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155.

If the polar of a point on the circle x2 + y2 = p2 with respect to the circle x2 + y2 = q2 touches the circle x2 + y2 = r, then p, q, r are in

  • AP

  • GP

  • HP

  • AGP


156.

If 23 + 43 + 63 + ... + 2(n)3 = hn2(n + 1)2, then h is equal to

  • 12

  • 1

  • 32

  • 2


157.

1 + 14 + 14 . 38 + 14 . 38 . 512  + . . . is equal to 

  • 2

  • 12

  • 3

  • 13


158.

22! + 2 + 43! + 2 + 4 + 64! +  ...is equal to

  • e

  • e - 1

  • e - 2

  • e - 3


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159.

The roots of the equation x3 - 14x2 + 56x - 64 = 9 are in

  • AGP

  • HP

  • AP

  • GP


160.

1 + 1 + 22! + 1 + 2 + 223! + ... is equal to

  • e2 + e

  • e2

  • e2 - 1

  • e2 - e


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