If fx = 1x2∫3x2t - 3f tdt, then

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

61.

If G is the centroid of the ABC, then GA + BG + GC is equal

  • 2GB

  • 2GA

  • 0

  • 2BG


62.

If the vectors i^ + 3j^ + 4k^,  λi^ - 4j^ + k^ are orthogonal to each other, then λ is equal to

  • 5

  • - 5

  • 8

  • - 8


63.

The vector c . (b + c) x (a + b + c) is equal to

  • c . b x a

  • 0

  • c . a x b

  • a . c x b


64.

If 3i^ + 3j^ + 3k^, 3i^ + 3j^ + λk^ are coplaner, then λ is equal to

  • 1

  • 2

  • 3

  • 4


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65.

If X is a poisson variate with P(X = 0) = 0.8, then the variance of X is

  • loge20

  • log1020

  • loge54

  • 0


66.

If the direction ratio of two lines are given by l + m + n = 0, mn - 2ln + lm = 0, then the angle between the lines is

  • π4

  • π3

  • π2

  • 0


67.

If (2, - 1, 3) is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

  • 2x + y - 3z + 6 = 0

  • 2x - y + 3z - 14 = 0

  • 2x - y + 3z - 13 = 0

  • 2x + y + 3z - 10 = 0


68.

If the plane 3x - 2y - z - 18 = 0 meets the coordinate axes in A, B, C then the centroid of ABC is

  • (2, 3, - 6)

  • (2, - 3, 6)

  • (- 2, - 3, 6)

  • (2, - 3, - 6)


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69.

If fx = 1x23x2t - 3f'tdt, then f't, then f'(3) is equal to

  • - 1 2

  • - 13

  • 12

  • 13


C.

12

Given that,fx = 1x23x2t - 3f'tdt + 3x2t - 3f'tdtOn differentiating both sides w. r. t. x, we getf'x = 1x2ddx3x2t - 3f'tdt + 3x2t - 3f'tdtddx1x2 f'x = 1x22t - 3f't - 2x33x2t - 3f'tdtAt x = 3 f'3 = 1326 - 3f'3 - 0 4 f'33 = 23   f'3 = 12


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70.

dxx + 100x + 99 = fx + c  fx

  • 2(x + 100)1/2

  • 3(x + 100)1/2

  • 2tan-1x + 99

  • 2tan-1x + 100


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