NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1

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CBSE CLASS XII Related Questions

  • 1.

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

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

    • 2.

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

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

      • 3.

        Evaluate :

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


          • 4.

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


              • 5.

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

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


                  • 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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