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

Differentiate the following w.r.t. x:

cos (log x + e^x), x > 0

Differentiate the function with respect to x:

(log x)^{log x}, x > 1

Differentiate the function with respect to x:

cos (a cos x + b sin x), for some constant a and b.

Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.

Find the scalar components and magnitude of the vector joining the points `P(x_1, y_1, z_1) and Q (x_2, y_2, z_2).`

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.