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

Evaluate : \[\int\limits_0^\pi/4 \frac{\sin x + \cos x}{16 + 9 \sin 2x}dx\] .

Evaluate : \[\int\limits_0^{2\pi} \cos^5 x dx\] .

If |A| = 3 and \[A^{- 1} = \begin{bmatrix}3 & - 1 \\ - \frac{5}{3} & \frac{2}{3}\end{bmatrix}\] , then write the adj A .

Evaluate : \[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\] .

Find the area of a parallelogram whose adjacent sides are represented by the vectors\[2 \hat{i} - 3 \hat{k} \text { and } 4 \hat{j} + 2 \hat{k} .\]

Evaluate: \[\int\limits_{- \pi/2}^{\pi/2} \frac{\cos x}{1 + e^x}dx\] .

Evaluate : \[\int e^{2x} \cdot \sin \left( 3x + 1 \right) dx\] .

Evaluate : \[\int\frac{dx}{\sin^2 x \cos^2 x}\] .

Two schools P and Q want to award their selected students on the values of tolerance, kindness and leadership. School P wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3, 2 and 1 students, respectively, with a total award money of Rs 2,200. School Q wants to spend Rs 3,100 to award 4, 1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each value is Rs 1,200, using matrices, find the award money for each value.

`int_0^(2a)f(x)dx`

\[\int\limits_0^4 x\sqrt{4 - x} dx\]

\[\int\limits_1^2 x\sqrt{3x - 2} dx\]

\[\int\limits_1^5 \frac{x}{\sqrt{2x - 1}} dx\]

\[\int\limits_0^1 \cos^{- 1} x dx\]

\[\int\limits_0^1 \tan^{- 1} x dx\]

\[\int\limits_0^1 \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) dx\]

\[\int\limits_0^1 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) dx\]

\[\int\limits_0^{1/\sqrt{3}} \tan^{- 1} \left( \frac{3x - x^3}{1 - 3 x^2} \right) dx\]

\[\int\limits_0^1 \frac{1 - x}{1 + x} dx\]

\[\int\limits_0^{\pi/3} \frac{\cos x}{3 + 4 \sin x} dx\]