NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

CBSE CLASS XII Related Questions

  • 1.

    If \(y = \sqrt{\log \left\{ \sin \left( \dfrac{x^2}{3} + 1 \right) \right\}}\), then show that

    \[ \frac{dy}{dx} = \frac{x \cot \left( \dfrac{x^2}{3} + 1 \right)}{3y}. \]


      • 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.

            Evaluate :

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


              • 4.

                If \(P(A) = 0.3\), \(P(B) = 0.7\) and \(P(B/A) = 0.5\), then \(P(A \cup B)\) is :

                  • \(0.35\)
                  • \(0.85\)
                  • \(0.5\)
                  • \(0.21\)

                • 5.

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

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


                    • 6.

                      Solve the differential equation \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \).

                        CBSE CLASS XII Previous Year Papers

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