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.

Application of Derivatives

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Multiple Choice Questions

391.

If f (x) = 3x² + 15x + 5, then find the approximate value of f (3.02) is

47.66
57.66
67.66
67.66

81 Views

Short Answer Type

392.

Find the approximate change in the volume V of a cube of side v meters caused by increasing the side by 2%.

78 Views

393.

Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

90 Views

394. Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.

95 Views

395.

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its volume.

118 Views

396.

If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.

93 Views

397.

If the radius of a sphere is measured as 9 m with an error of 0.03 m. then find the approximate error in calculating its surface area.

100 Views

398.

A circular disc of radius 3 cm is being heated. Due to expanison, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm.

84 Views

Multiple Choice Questions

399. The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is

0.06 x³ m³

0.6 x³ m³
0.09 x³ m³
0.09 x³ m³

0.09 x³ m³

Let V be volume of cube of side x metre.
$therefore space space space space space space space space space space space space space space space straight V space equals space straight x cubed Now comma space space space space space space space space dV space equals space open parentheses dV over dx close parentheses increment straight x space equals space left parenthesis 3 straight x squared right parenthesis space increment straight x space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis 3 straight x squared right parenthesis thin space. space left parenthesis 0.03 space straight x right parenthesis space space space space space space space space space space space space space space space space open square brackets because space space space 3 percent sign space of space straight x space equals space 0.03 space straight x close square brackets space space space space space space space space space space space space space space space space space dV space equals space 0.09 space straight x cubed straight m cubed therefore space space space approximate space change space in space voume space space equals space 0.09 space straight x cubed space straight m cubed therefore space space space space left parenthesis straight C right parenthesis space is space correct space answer.$

81 Views

Long Answer Type

400.

If the sum of the lengths of hypotenuse and a side of a right angled triangle is given, show that the area is maximum when the angle between them is 60°.

94 Views