NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.2

CBSE CLASS XII Related Questions

  • 1.

    Evaluate :

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


      • 2.

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

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


          • 3.

            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

            • 4.

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


                • 5.

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

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

                  • 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

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