NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.1

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Class 11 Maths NCERT Solutions Chapter 14 Mathematical Reasoning Exercise 14.1 are based on the following concepts:

  • Statements
  • New statements from old
  • Special words / Phrases
  • Implications
  • Validating Statements
  • Conjunction

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Chapter Related Topics
Irrational Number Prime Number Real Number

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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.

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


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


            • 4.
              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 \( \cos^{-1}(x^2) \).


                • 5.
                  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 \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).


                    • 6.
                      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 \(q\).

                        • \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
                        • \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
                        • \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
                        • \(p = 0, \, q = 0\)
                      CBSE CLASS XII Previous Year Papers

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