NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.3

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.

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


          • 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.

              The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

                • \( \frac{7\pi}{12} \)
                • \( \frac{5\pi}{12} \)
                • \( -\frac{5\pi}{12} \)
                • \( \frac{\pi}{3} \)

              • 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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