NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.3 Solutions 

CBSE CLASS XII Related Questions

  • 1.
    Which of the following equations is NOT a Linear Differential Equation?

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

    • 2.
      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 \(q\).

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

      • 3.

        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 \(A'\).

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

        • 4.
          Find:

          The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]


            • 5.
              If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


                • 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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