The triangle formed by the tangent to the curve f (x) = x2 +

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

Let f'(x), be differentiable a. If f(1) = - 2 and f'(x) 2  x [1, 6], then

  • f(6) < 8

  • f(6)  8

  • f(6)  5

  • f(6)  5


22.

The minimum value of xlogx is

  • e

  • 1e

  • e2

  • e3


23.

If the points (1, 2, 3) and (2, - 1, 0) lie on the opposite sides of the plane 2x + 3y - 2z = k, then

  • k < 1

  • k > 2

  • k < 1 or k > 2

  • 1 < k < 2


24.

If x = 1cosx1 - cosx1 + sinxcosx1 + sinx + cosxsinxsinx1, then 0π4xdx is equal to

  • 14

  • 12

  • 0

  • - 14


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25.

The triangle formed by the tangent to the curve f (x) = x2 + bx - b at the point (1, 1) and the coordinate axes lies in the first quadrant. If its area is 2, then the value of b is

  • - 1

  • 3

  • - 3

  • 1


C.

- 3

Given curve is y = f(x) = x2 + bx - b.

On differentiating w.r.t. x, we get

                           f'(x) = 2x + b

The equation of tangent at point (1, 1) is

                               y - 1 = dydx1, 1x - 1                          y - 1 = b + 2x - 1               2 +bx - y = 1 +b x1 + b2 + b - y1 +b = 1

So,                     OA = 1 + b2 + band                     OB = - 1 + bNow, area of AOB = 12 × 1 + b . - 1 + b2 + b = 2     42 + b + 1 + b2 = 0 8 +4b + 1 + b2 +2b = 0                  b2 + 6b + 9 = 0                         b + 32 = 0                                     b = - 3


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26.

If a plane meets the coordinate axes at A, B and C such that the centroid of the triangle is (1, 2, 4), then the equation of the plane is

  • x + 2y + 4z = 12

  • 4x + 2y + z = 12

  • x + 2y + 4z = 3

  • 4x + 2y + z = 3


27.

The volume of the tetrahedron included between the plane 3x + 4y - 5z - 60 = 0 and the coordinate planes is

  • 60

  • 600

  • 720

  • 400


28.

02πsinx + sinxdx is equal to

  • 0

  • 4

  • 8

  • 1


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29.

The value of 02x2dx, where [.] is the greatest integer function, is

  • 2 - 2

  • 2 + 2

  • 2 - 1

  • 2 - 2


30.

If l (m,n) = 01tm1 + tndt, then the expression for l (m, n) in terms of l (m + 1, n + 1) is

  • 2nm + 1 - nm + 1 . l m + 1, n - 1

  • nm + 1 . l m + 1, n - 1

  • 2nm + 1 + nm + 1 . l m + 1, n - 1

  • mn + 1 . l m + 1, n - 1


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