NCERT Solutions for Class 11 Maths Chapter 8 Exercise 8.2

CBSE CLASS XII Related Questions

  • 1.

    Evaluate :

    \[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]


      • 2.

        For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :

        Minimize \(Z = 18x + 10y\)

        subject to constraints

        \[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]


          • 3.

            Differential of \( \log \sin x \) with respect to \( \sqrt{\cos x} \) is :

              • \( -2\sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
              • \( \sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
              • \( \frac{2\sqrt{\cos x}}{\sin x} \)
              • \( \frac{1}{\sin x\sqrt{\cos x}} \)

            • 4.

              Find the value of \(x\) if \(A = B\), where

              \[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]


                • 5.

                  For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.

                  Minimize \(Z = 5x + 7y\)

                  subject to constraints

                  \[ 2x + y \geq 8 \]

                  \[ x + 2y \geq 10 \]

                  \[ x,\ y \geq 0. \]


                    • 6.

                      Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

                        CBSE CLASS XII Previous Year Papers

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