The normal to the curve x = acosθ + sinθ, y

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 Multiple Choice QuestionsMultiple Choice Questions

201.

Let P(x) = a0 + a1x2 + a2x2 + a3x6 + ... + anx2n be a polynomial in a real variables with 0 < a0 < a1 < a2 < .... < an. The function P(x) has

  • neither a maxima nor a minima

  • only one maxima

  • both maxima and minima

  • only one minima


202.

The maximum value of f(x) = 2sinx + cos2x, 0  x  π2 occurs at x is equal to

  • 0

  • π6

  • π2

  • None of these


203.

The equation of tangent of the curve y = be-x/a at the point, where the curve meet y-axis is

  • bx + ay - ab = 0

  • ax + by - ab = 0

  • bx - ay - ab = 0

  • ax + by - ab = 0


204.

If y = 4x - 5 is a tangent to the curve y2 = px3 + q at (2, 3), then

  • p = 2, q = - 7

  • p = - 2, q = 7

  • p = - 2, q = - 7

  • p = 2, q = 7


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205.

On which of the following intervals is the function f(x) = 2x2 - logx, x  0 increasing 2.

  • 12, 

  • - , - 12  12, 

  • - , - 12  0, 12

  • - 12, 0  12, 


206.

The length of the normal to the curve x = aθ + sinθ, y =  a1 - cosθ at θ = π2 is

  • 2a

  • a2

  • a2

  • 2a


207.

The maximum value of logxx is

  • e

  • 2e

  • 1e

  • 2e


208.

The smallest circle with centre on y-axis and passing through the point (7, 3) has radius

  • 58

  • 7

  • 3

  • 4


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209.

If sum of two numbers is 6, the minimum value of the sum of their reciprocals is

  • 65

  • 34

  • 23

  • 12


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210.

The normal to the curve x = acosθ + sinθ, y = asinθ - θcosθ at any point θ is such that

  • it makes a constant angle with x-axis

  • it passes through origin

  • it is at a constant distance from origin

  • None of the above


C.

it is at a constant distance from origin

Given curves arex = acosθ + sinθy = asinθ - θcosθOn differentiating w.r.t. θ respectively, we getdx = a- sinθ + sinθ + θcosθdy = acosθ - cosθ + θsinθ dx = aθcosθ     dy = aθsinθ dydx = sinθcosθ Equation of normal isy - asinθ + aθcosθ = - cosθsinθ ysinθ - asin2θ + aθcosθsinθ     = - xcosθ + acos2θ + aθsinθcosθ xcosθ + ysinθ = a

Which is always a constant distance ' a' from the origin.


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