NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.2

CBSE CLASS XII Related Questions

  • 1.

    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 :


      • 2.
        Which of the following equations is NOT a Linear Differential Equation?

          • \((1 + x^2) \, dy + 2xy \, dx = \cot x \, dx\)
          • \(y + \frac{d}{dx}(xy) = x(\sin x + \log x)\)
          • \(x(1 + y^2) \, dx - y(1 + x^2) \, dy = 0\)
          • \(y \, dx - (x + 3y^2) \, dy = 0\)

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


            • 4.
              Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).


                • 5.

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


                    • 6.

                      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 \(A'\).

                        • \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
                        • \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
                        • \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
                        • \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)
                      CBSE CLASS XII Previous Year Papers

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