If x1, x2, x3 as well as y1, y2, y3 

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 Multiple Choice QuestionsMultiple Choice Questions

201.

If a, b, c are distinct and the roots of (b - c)x2 + (c - a)x + (a - b) = 0 are equal, then a, b and c are in

  • anthmet1c progression

  • geometnc progression

  • harmonic progression

  • arithmetico-geometnc progression


202.

If the roots of x3 - kx2 + 14x - 8 = 0 are in geometric progression, then k is equal to

  • - 3

  • 7

  • 4

  • 0


203.

The number of four-digit numbers formed by using the digits 0, 2, 4, 5 and which are not divisible by 5, is

  • 10

  • 8

  • 6

  • 4


204.

If x = 15 + 1 . 35 . 10 + 1 . 3 . 55 . 10 . 5 +... ,3x2 + 6x = ?

  • 1

  • 2

  • 3

  • 4


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205.

In ABC, a + b + cb + c - a = λbc, then

  • λ < - 6

  • λ > 6

  • 0 < λ <  4

  • λ > 4


206.

The greatest positive integer which divides (n + 16)(n + 17)(n + 18)(n +19), for all positive integers n, is

  • 6

  • 24

  • 28

  • 20


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207.

If x1, x2, x3 as well as y1, y2, yare in geometric progression with the same common ratio,then the points, x1, y1, x2, y2, x3, y3 are

  • vertices of an equilateral triangle

  • vertices of a right angled triangle

  • vertices of a right angled isosceles triangle

  • collinear


D.

collinear

We have x1, x2, x3 and y1, y2, y3 are in GP with the same common ratio.

Let r be the common ratio.

 x1 = x1x2 = xr and x3 = xr2Similarly, y1 = yy2 = yr and y3 = yr2 Area of  = 12x1y11x2y21x3y31= 12xy1xryr1xr2yr21= 12xy111xryr1r2r21= 12xy111rr1r2r21 = 12 × 0 = 0  C1, C2 are identical The given points are collinear.


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208.

If 124 + 2x2 = 2433x2 - 2, then x is equal to

  • ± 1312

  • ± 145

  • ± 1213

  • ± 514


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209.

The product and sum of the roots of the equation x2 - 5x - 24 = 0 are respectively

  • - 64, 0

  • - 24, 5

  • 5, - 24

  • 0, 72


210.

The coefficient of x in the expansion of (1 - x + x2 - x3)4 is

  • 31

  • 30

  • 25

  • - 14


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