NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.3

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CBSE CLASS XII Related Questions

  • 1.

    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 :

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

    • 2.

      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

      \[ 2x + y \geq 8 \]

      \[ x + 2y \geq 10 \]

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


        • 3.

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


            • 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.

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

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

                  • 6.

                    Evaluate :

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

                      CBSE CLASS XII Previous Year Papers

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