If the area of a rectangle is 64 sq unit, find the minimum value

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

31.

The minimum value of the function f (x) = 2x - 1 + x - 2 is

  • 0

  • 1

  • 2

  • 3


32.

Maximum value of the function f(x) = x8 + 2x on the interval [1, 6] is

  • 1

  • 98

  • 1312

  • 178


33.

For  - π2 < x < 3π2, the avlue of ddxtan-1cosx1 + sinx is equal to

  • 12

  • 12

  • 1

  • sinx1 + sinx2


 Multiple Choice QuestionsShort Answer Type

Advertisement

34.

If the area of a rectangle is 64 sq unit, find the minimum value possible for its perimeter


Let the dimensions be a and b.

 Area = ab  64 = ab

Perimeter = 2(a + b)

 P = 2a + 64a dPda = 21 - 64a2

For maxima and minima, put dPda = 0

 21 - 64a2 = 0 a2 = 64  a = ± 8Now, d2Pda2 = 2+ 128a3At a = 8,d2Pda2 = 212883 = 12 > 0, minima Minimum value is P(8) = 28 + 648 = 32


Advertisement
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

35.

Let f(x) = x3e- 3x, x > 0. Then, the maximum value of f(x) is

  • e- 3

  • 3e- 3

  • 27e- 9


36.

The point in the interval [0, 2π], where f(x) = ex sin(x) has maximum slope, is

  • π4

  • π2

  • π

  • 3π2


37.

The minimum value of f(x) = ex4 - x3 + x2

  • e

  • - e

  • 1

  • - 1


38.

If the line ax + by + c = 0 is a tangent to the curve xy = 4, then 

  • a < 0, b > 0

  • a  0, b > 0

  • a < 0, b < 0

  • a  0, b < 0


Advertisement
39.

If the normal to the curve y = f(x) at the point (3, 4) make an angle 3π/4 with the positive x-axis, then f'(3) is

  • 1

  • - 1

  • 34

  • 34


40.

The equation of normal of x+ y2 - 2x + 4y - 5 = 0 at (2, 1) is

  • y = 3x - 5

  • 2y = 3x - 4

  • y = 3x + 4

  • y = x + 1


Advertisement