NCERT Solutions for Class 11 Maths Chapter 15 Miscellaneous Exercises

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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.

      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 :

        • \(\frac{1}{2}\)
        • \(\frac{3}{5}\)
        • \(\frac{1}{5}\)
        • \(\frac{3}{10}\)

      • 3.

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


          • 4.

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


              • 5.

                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

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


                  • 6.

                    Solve the differential equation \( (x+y)\,dy + (x-y)\,dx = 0 \), given that \( y(1) = 1 \).

                      CBSE CLASS XII Previous Year Papers

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