If x - 5x - 7dx = Ax2 -&n

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

Let PQRS be a quadrilateral. If M and N are the mid-points of the sides PQ and RS respectively, then PS + QR =

  • 3 MN

  • 4 MN

  • 2 MN

  • 2 NM


22.

If vector r with dc's l, m, n is equally inclined to the coordinate axes, then the total number of such vectors is

  • 4

  • 6

  • 8

  • 2


23.

1x2 + 4x2 + 9dx = Atan-1x2 + Btan-1x3 + C, then A - B =

  • 16

  • 130

  • - 130

  • - 16


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24.

If x - 5x - 7dx = Ax2 - 12x +35 + logx - 6 + x2 - 12x + 35 + C, then A =

  • - 1

  • 12

  • - 12

  • 1


D.

1

Let  I = x - 5x - 7dx        = x - 5x - 5x - 7x - 5dx     rationalising        = x - 5x2 - 5x - 7x + 35dx        = x - 5x2 - 12x + 35        = 122x - 10x2 - 12x + 35dx       = 122x - 12 + 2x2 - 12x + 35dx       = 122x - 12x2 - 12x + 35dx + 1x2 - 12x + 35dx       = x2 - 12x + 35 + 1x2 - 12x + 36 - 1 + C          Let x2 - 12x + 35 = t   2x - 12dx = dt       = x2 - 12x + 35 + 1x - 62 - 12dx + C       = x2 - 12x + 35 + logx - 6 + x2 - 12x + 35 + C I = Ax2 - 12x +35 + logx - 6 + x2 - 12x + 35 + C      = 1 . x2 - 12x +35 +  logx - 6 + x2 - 12x + 35 + COn comparing both sides, we get A= 1.


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25.

At random variable X ~ B(n, p), if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are

  • 54

  • 55

  • 12

  • 18


26.

The area of the region bounded by the lines y = 2x + 1, y = 3x + 1and x = 4 is

  • 16 sq unit

  • 1213 sq unit

  • 1216 sq unit

  • 8 sq unit


27.

The differential equation of all parabolas whose axis is Y-axis, is

  • xd2ydx2 - dydx = 0

  • xd2ydx2 + dydx = 0

  • d2ydx2 - y = 0

  • d2ydx2 - dydx = 0


28.

03xdx = ..., where [x] is greatest integer function

  • 3

  • 0

  • 2

  • 1


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29.

The objective function of LPP defined over the convex set attains it optimum value at

  • atleast two of the corner points

  • all the corner points

  • atleast one of the corner points

  • None of the corner points


30.

The equation of the plane through (- 1, 1, 2) whose normal makes equal acute angles with coordinate axes is

  • r. i^ + j^ + k^ = 2

  • r. i^ + j^ + k^ = 6

  • r. 3i^ - 3j^ + 3k^ = 2

  • r. i^ - j^ + k^ = 3


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