NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2

CBSE CLASS XII Related Questions

  • 1.

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

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


      • 2.

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

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

        • 3.

          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

          \[ 2x + y \geq 8 \]

          \[ x + 2y \geq 10 \]

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


            • 4.

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


                • 5.

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


                    • 6.

                      Evaluate :

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

                        CBSE CLASS XII Previous Year Papers

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