NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.3

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.

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

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

            • 5.

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


                • 6.

                  Solve the differential equation \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \).

                    CBSE CLASS XII Previous Year Papers

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