NCERT Solutions for Class 12 Chapter 13 Probability Exercise 13.3

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Class 12 Maths NCERT Solutions Chapter 13 Probability Exercise 13.3 is based on Bayes’ Theorem also covering questions based on Bayes Theorem Formula.

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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.

        The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

          • \( \frac{7\pi}{12} \)
          • \( \frac{5\pi}{12} \)
          • \( -\frac{5\pi}{12} \)
          • \( \frac{\pi}{3} \)

        • 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 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.

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


                  • 6.

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

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

                      CBSE CLASS XII Previous Year Papers

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