NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.3

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CBSE CLASS XII Related Questions

  • 1.
    Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]


      • 2.
        Solve the following linear programming problem graphically: Maximise \( Z = x + 2y \) Subject to the constraints: \[ x - y \geq 0 \] \[ x - 2y \geq -2 \] \[ x \geq 0, \, y \geq 0 \]


          • 3.
            Solve the differential equation: \[ x^2y \, dx - (x^3 + y^3) \, dy = 0. \]


              • 4.
                Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:

                  • $x^3 + 3x^2 + \frac{2}{x^2} + 5x + 11$
                  • $x^3 + 3x^2 + \frac{2}{x^2} + 5x - 11$
                  • $x^3 + 3x^2 - \frac{2}{x^2} + 5x - 11$
                  • $x^3 - 3x^2 - \frac{2}{x^2} + 5x - 11$

                • 5.
                  The diagonals of a parallelogram are given by \( \mathbf{a} = 2 \hat{i} - \hat{j} + \hat{k} \) and \( \mathbf{b} = \hat{i} + 3 \hat{j} - \hat{k}\) . Find the area of the parallelogram.


                    • 6.
                      The values of $\lambda$ so that $f(x) = \sin x - \cos x - \lambda x + C$ decreases for all real values of $x$ are :

                        • $1<\lambda<\sqrt{2}$
                        • $\lambda \geq 1$
                        • $\lambda \geq \sqrt{2}$
                        • $\lambda<1$
                      CBSE CLASS XII Previous Year Papers

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