NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.4

CBSE CLASS XII Related Questions

  • 1.
    Find:

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

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

    • 2.

      Find:
      Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

        • \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
        • \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
        • \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
        • \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)

      • 3.
        Find:

        If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).

          • \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
          • \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
          • \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
          • \(p = 0, \, q = 0\)

        • 4.
          If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


            • 5.
              Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]


                • 6.

                  Evaluate:
                  \[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]

                    CBSE CLASS XII Previous Year Papers

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