The height of the cylinder of maximum volume inscribed in a spher

Subject

Mathematics

Class

JEE Class 12

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

1.

If tan-1x + 1x - 1 + tan-1x - 1x = tan-1- 7, then the value of x is

  • zero

  • - 2

  • 1

  • 2


2.

Let the function f : R R be defined by f(x) = 2x + cos(x), then f

  • has maximum at x = 0

  • has minimum at x = π

  • is an increasing function

  • is a decreasing


3.

If cos-1p + cos-11 - p +cos-11 - q = 3π4, then the value of q is

  • 22

  • 1

  • 1/2

  • 1/3


4.

If 5 is one root of the equations x372x- 278x = 0, then the other two roots of the equation are

  • - 2, - 7

  • - 2, 7

  • 2, - 7

  • 2, 7


Advertisement
5.

The equation to the tangent to the curve y = be- x/a at the point where it crosses the Y-axis is

  • ax + by = 1

  • xa - yb = 1

  • xa + yb = 1

  • ax - by = 1


6.

If w = - 12 + 3i2, the value of the determinant 1ww2ww21w21w is

  • zero

  • 3

  • - 1

  • 1


Advertisement

7.

The height of the cylinder of maximum volume inscribed in a sphere of radius 'a' is

  • 3a2

  • 2a3

  • a3

  • 2a3


D.

2a3

Let a be the radius and h the height from figurer2 + h24 = a2 h2 = 4a2 - r2Now, v = πr2h = πa2 - h24h           = πa2h - h34 dvdh = πa2 - 3h24 = 0for maximum or minimum h = 2a3 d2vdh2 = - 6h4 < 0 v i s maximum when h = 2a3


Advertisement
8.

If f(x) = sinxcosxtanxx3x2x2x11, then limx0fxx2 is

  • - 1

  • 3

  • 1

  • zero


Advertisement
9.

If for a triangle ABC, 1ab1ba1cc = 0, then the value of sin2A + sin2B + sin2C is

  • 49

  • 94

  • 1

  • 332


10.

Let f(x) = sinπx5x, x 0k,           x = 0. If f(x) continuous at x = 0, the value of k is

  • 5π

  • π5

  • zero

  • 1


Advertisement