Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

Using differentials, find the approximate value of the following up to 3 places of decimal

`(0.0037)^(1/2)`

Using differentials, find the approximate value of the following up to 3 places of decimal

`(26.57)^(1/3)`

Using differentials, find the approximate value of the following up to 3 places of decimal

`(81.5)^(1/4)`

Using differentials, find the approximate value of the following up to 3 places of decimal

`(3.968)^(3/2)`

Using differentials, find the approximate value of the following up to 3 places of decimal

`(32.15)^(1/5)`

Find the approximate value of f (5.001), where f (x) = x³ − 7x² + 15.

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

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

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 in surface area

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

A. 47.66

B. 57.66

C. 67.66

D. 77.66

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

A. 0.06 x³ m³ 

B. 0.6 x³ m³

C. 0.09 x³ m³

D. 0.9 x³ m³

Using differentials, find the approximate value of each of the following.

`(17/81)^(1/4)`

Using differentials, find the approximate value of each of the following.

`(33)^(1/5)`

Show that the function given by `f(x) = (log x)/x` has maximum at x = e.

The normal at the point (1, 1) on the curve 2y + x² = 3 is

(A) x + y = 0

(B) x − y = 0

(C) x + y + 1 = 0

(D) x − y = 1

The normal to the curve x² = 4y passing (1, 2) is

(A) x + y = 3

(B) x − y = 3

(C) x + y = 1

(D) x − y = 1

The points on the curve 9y² = x³, where the normal to the curve makes equal intercepts with the axes are

Integrate the function in x sin x.