NCERT Solutions for Class 11 Maths Chapter 2 Exercise 2.2

CBSE CLASS XII Related Questions

  • 1.

    Evaluate :

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


      • 2.

        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 :

          • \(\frac{1}{2}\)
          • \(\frac{3}{5}\)
          • \(\frac{1}{5}\)
          • \(\frac{3}{10}\)

        • 3.

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


            • 4.

              Differential of \( \log \sin x \) with respect to \( \sqrt{\cos x} \) is :

                • \( -2\sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
                • \( \sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
                • \( \frac{2\sqrt{\cos x}}{\sin x} \)
                • \( \frac{1}{\sin x\sqrt{\cos x}} \)

              • 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 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

                  \[ 2x + y \geq 8 \]

                  \[ x + 2y \geq 10 \]

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

                    CBSE CLASS XII Previous Year Papers

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