NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1

CBSE CLASS XII Related Questions

  • 1.

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

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

    • 2.

      \( \int e^{x}\left( \frac{2+\sin 2x}{1+\cos 2x} \right) dx \) is equal to :

        • \( \log \cos 2x + C \)
        • \( \sec^{2} 2x + C \)
        • \( e^{x}\tan x + C \)
        • \( e^{x}\cot x + C \)

      • 3.

        Evaluate :

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


          • 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.

                Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).


                  • 6.

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

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

                      CBSE CLASS XII Previous Year Papers

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