NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

CBSE CLASS XII Related Questions

  • 1.

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

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

    • 2.

      Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).


        • 3.

          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

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


            • 4.

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

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


                • 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.

                      For events A and B, if \(P(B)=\frac{3}{5}\), \(P(A/B)=\frac{1}{2}\) and \(P(A\cup B)=\frac{4}{5}\), then \(P(A)\) is :

                        • \(\frac{1}{2}\)
                        • \(\frac{3}{5}\)
                        • \(\frac{1}{5}\)
                        • \(\frac{3}{10}\)
                      CBSE CLASS XII Previous Year Papers

                      Comments


                      No Comments To Show