Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

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.

Integrate the function in x sin 3x.

Integrate the function in `x^2e^x`.

Integrate the function in x log x.

Integrate the function in x log 2x.

Integrate the function in x² log x.

Integrate the function in x sin⁻¹ x.

Integrate the function in x tan^-1 x.

Integrate the function in x cos^-1 x.

Integrate the function in (sin^-1x)².

Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.