NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.4

CBSE CLASS XII Related Questions

  • 1.

    Evaluate :

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


      • 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.

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

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


            • 4.

              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

              \[ 2x + y \geq 8 \]

              \[ x + 2y \geq 10 \]

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


                • 5.

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

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

                  • 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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