The perimeter of a sector is a constant. If its area is to be max

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 Multiple Choice QuestionsMultiple Choice Questions

321.

The radius of a circular plate is increasing at the rate of 0.01 cm/s when the radius is 12 cm. Then, the rate at which the area increases, is

  • 0.24 π cm/s

  • 60 π sq cm/s

  • 24π sq cm/s

  • 1.2π sq cm/s


322.

Observe the following statements

A: f(x) = 2x3 - 9x2 + 12x - 3 is increasing outside the interval (1, 2)

R : f'(x) < 0 for x  (1, 2).

Then, which of the following is true ?

  • Both A and R are true, and R is not the correct reason for A

  • Both A and R are true, and R is the correct reason for A

  • A is true but R is false

  • A is false but R is true


323.

If θ is the angle between the curves xy = 2 and x2 + 4y = 0 and x2 + 4y = 0, then tanθ is equal to :

  • 1

  • - 1

  • 2

  • 3


324.

In the interval(- 3, 3) the function f(x) = x3 + 3x, x  0 is

  • increasing

  • decreasing

  • neither increasing nor decreasing

  • partly increasing and partly decreasing


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325.

The perimeter of a sector is a constant. If its area is to be maximum, the sectorial angle is :

  • πc6

  • πc4

  • 4c

  • 2c


D.

2c

Let length of sectors is l and radius of sector is r. l = 2πrθ360° + 2r P = 2πθ360° + 2r  r = P2πθ360° + 2 A = πr2θ360°A = π360°P22πθ360° + 22θA = πP2360°θ2πθ360° + 22dA = πP2360°2πθ360° + 22 - θ . 22πθ360° + 2π360°2πθ360° + 24put  dA =0, for maxima or minima2πθ360° + 2 - 4θπ360° = 0πθ180° = 2  θ = 2 × 180° π = 2 radThus area of sector will be maximum, if sectorial angle is of 2rad.


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326.

The lengths of tangent, subtangent, normal and subnormal for the curve y = x2 + x - 1 at (1, 1) are A, B, C and D respectively, then their increasing order is

  • B, D, A, C

  • B, A, C, D

  • A, B, C, D

  • B, A, D, C


327.

The condition f(x) = x+ px+ qx + r(x ∈ R) to have no extreme value, is

  • p2 < 3q

  • 2p2 < q

  • p2 < 14q

  • p2 > 3q


328.

The circumference of a circle is measured as 56cm with an error 0.02 cm. The percentage error in its area is

  • 17

  • 128

  • 114

  • 156


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329.

Observe the statements given below :

Assertion (A) : f(x) = xe- x has the maximum at x =1

Reason (R) : f'(1) = 0 and f'(1) < 0

Which of the following is correct ?

  • Both (A) and (R) are true and (R) is the correct reason for (A)

  • Both (A) and (R) are true, but (R) is not the correct reason for (A)

  • (A) is true, (R) is false

  • (A) is false, (R) is true


330.

The equation of the normal to the curve y4 = ax3 at (a, a) is

  • x + 2y = 3a

  • 3x - 4y + a = 0

  • 4x + 3y = 7a

  • 4x - 3y = 0


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