NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2

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CBSE CLASS XII Related Questions

  • 1.
    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 \(k\).

      • \(0\)
      • \(-2\)
      • \(-1\)
      • \(2\)

    • 2.

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


        • 3.
          Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]


            • 4.
              Find the vector and cartesian equations of the line passing through the point of intersection of the lines \( \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) \) and \( \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) \) and parallel to the line \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).


                • 5.
                  Which of the following equations is NOT a Linear Differential Equation?

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

                  • 6.
                    A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is

                      • Reflexive only
                      • Reflexive and Transitive
                      • Symmetric and Transitive
                      • Symmetric only
                    CBSE CLASS XII Previous Year Papers

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