NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.2

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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.

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


        • 3.

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

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

          • 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.

                  The motion of a particle is described as \( S = 2t^{3} - 6t^{2} + 8 \). Its velocity \( \frac{dS}{dt} \), when the acceleration \( \frac{d^{2}S}{dt^{2}} \) vanishes is :

                    • \( -6 \) unit/sec
                    • \( 0 \) unit/sec
                    • \( 18 \) unit/sec
                    • \( 6 \) unit/sec
                  CBSE CLASS XII Previous Year Papers

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