NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.4

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CBSE CLASS XII Related Questions

  • 1.
    Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).


      • 2.
        Find:

        The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

          • \(-\frac{\pi}{2}\)
          • \(-\frac{\pi}{4}\)
          • \(\frac{\pi}{4}\)
          • \(\frac{\pi}{2}\)

        • 3.
          If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


            • 4.
              Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]


                • 5.

                  An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.  
                  Based on the above information, answer the following questions :


                    • 6.
                      Find:

                      If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

                        • \(0\)
                        • \(-2\)
                        • \(-1\)
                        • \(2\)
                      CBSE CLASS XII Previous Year Papers

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