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

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)`.

Integrate the function in x sec² x.

Integrate the function in tan^-1 x.

Integrate the function in x (log x)².

Integrate the function in (x² + 1) log x.