The equation x2 - 5xy + py2 + 

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 Multiple Choice QuestionsMultiple Choice Questions

191.

If X is a poisson variate such that a = P(X = 1) = P(X = 2), then P(X = 4) is equal to

  • 2α

  • α3

  • αe - 2

  • αe2


192.

If pth, qth, rth terms of a geometric progression are the positive numbers a, b and c respectively,then the angle· between the vectors (log(a))2i + (log(b))2j + (log(c))2k and (q - r)i + (r - p)j + (p - q)k is

  • π3

  • π2

  • sin-11a2 + b2 + c2

  • π4


193.

If x is small, so that x2 and higher powers can be neglected, then the approximate value for 1 - 2x - 11 - 3x - 21 - 4x - 3 is

  • 1 - 2x

  • 1 - 3x

  • 1 - 4x

  • 1 - 5x


194.

If 1x4 + x2 + 1 = Ax +Bx2 + x +1  + Cx + Dx2 - x +1, then C + D = ?

  • - 1

  • 1

  • 2

  • 0


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195.

If the roots of x3 - 42x2 + 336x - 512 = 0, are in increasing geometric progression, then its common ratio is

  • 2 : 1

  • 3 : 1

  • 4 : 1 

  • 6 : 1


196.

The equation of the pair of lines passing through the orign whose sum and product of slopes are respectively the arithmetic mean and geometric mean of 4 and 9 is

  • 12x2 - 13xy + 2y2 = 0

  • 12x2 + 13xy + 2y2 = 0

  • 12x2 - 15xy + 2y2 = 0

  • 12x2 + 15xy - 2y2 = 0


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197.

The equation x2 - 5xy + py2 + 3x - 8y + 2 = 0 represents a pair of straight lines. If θ is the angle between them, then sinθ is equal to

  • 150

  • 17

  • 15

  • 110


A.

150

Compairing the given equationx2 - 5xy + py2 + 3x - 8y + 2 = 0                  iwith ax2 + 2hxy + by2 + 2gx + 2fy + c = 0  iiwe geta = 1, h = - 52, b = p, g = 32, f = - 4 and c = 2Eq i represents a pair of straight lines, ifabc + 2fgh - af2 - bg2 - ch2 = 0 1 × p × 2 + 2 × - 4 × 32 × - 52 - 1 × - 42 - p × 322 - 2 × - 522 = 0 p = 6   Required angle,tanθ = 2h2 - aba + b = 2- 5 22 - 1 × 61 + 6

tanθ = 17  θ = tan-117 sinθ = 150


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198.

k = 12n + 1- 1k - 1 . k2 = ?

  • (n - 1)(2n - 1)

  • (n + 1)(2n + 1)

  • (n + 1)(2n - 1)

  • (n - 1)(2n + 1)


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199.

If a + bx - 3 = 127 + 13x + ... , then the ordered pair a, b = ?

  • (3, - 27)

  • 1, 13

  • (3, 9)

  • (3, - 9)


200.

The value of the sum 1 · 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 +  ... upto n terms is equal to

  • 16n22n2 + 1

  • 16n2 - 12n - 12n + 3

  • 18n2 + 1n2 +5

  • 14nn +1n + 2n + 3


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