The function x5 - 5x4 + 5x3 - 1 is from Mathematics Application

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

211.

The function f(x) = log1 + x - 2x2 + x is increasing on

  • - 1, 

  • - , 0

  • - , 

  • None of these


212.

The minimum value of x2 + 11 + x2 is at

  • x = 0

  • x = 1

  • x = 4

  • x = 3


213.

The maximum value of 3 cosθ + 4 sinθ is

  • 3

  • 4

  • 5

  • None of these


Advertisement

214.

The function x5 - 5x4 + 5x3 - 1 is

  • neither maximum nor minimum at x = 0

  • maximum at x = 0

  • maximum at x = 1 and minimum at x = 3

  • minimum at x = 0


C.

maximum at x = 1 and minimum at x = 3

Let fx = x5 - 5x4 + 5x3 - 1On differentiating w.r.t. x, we get     f'x = 5x4 - 20x3 + 15x2For maximum or minimum, put f'(x) = 0      5x4 - 20x3 + 15x2 = 0 x25x2 - 20x + 15 = 0    5x2x - 1x - 3 = 0         x = 0,1, 3Again differentiating w.r.t. x, we getf''x = 54x3 - 12x2 + 6xAt x = 1, f''1 = 54 - 12 + 6         = - 10 < 0, maximumAt x = 3, f''3 = 54 × 27 - 12 × 9 + 6 × 3        = 90 > 0, minimumAt x = 0, f''0 = 50 - 12 × 0 + 6 × 0 = 0,we have further check     f'''x = 512x2 - 24x + 6 f'''0 = 30  0       Inflexion fx is maximum at x = 1 and minimum at x = 3.


Advertisement
Advertisement
215.

If the radius of a circle be increasing at a uniform rate of 2 cm/s. The area of increasing of area of circle, at the instant when the radius is 20 cm, is

  • 70 π cm2/s

  • 70 cm2/s

  • 80 π cm2/s

  • 80 cm2/s


216.

The equation of normal at the point (0, 3) of the ellipse 9x2 + 5y2 = 45 is

  • x-axis

  • y-axis

  • y + 3 = 0

  • y - 3 = 0


217.

The maximum value of x1/x is :

  • 1/ee

  • e

  • e1/e

  • 1/e


218.

The function f defined by f(x) = 4x4 - 2x + 1 is increasing for :

  • x < 1

  • x > 0

  • x < 1/2

  • x > 1/2


Advertisement
219.

A particle moves in a straight line so that s = t, then its acceleration is proportional to :

  • (velocity)3

  • velocity

  • (velocity)2

  • (velocity)3/2


220.

If the line ax + by + c = 0 is a normal to the curve y =1, then :

  • a > 0, b > 0

  • a > 0, b < 0

  • a < 0, b < 0

  • Data is insufficient


Advertisement