NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.
    Find the differential of \( x^{\cot x} + \frac{2x^2-3}{2x^2-x+2} \) with respect to \( x \).


      • 2.
        The volume of a wooden block in the shape of a cube increases at a constant rate as the air becomes moist during the rainy season. Show that the rate of change of its surface area varies inversely as the length of edge of the cube.


          • 3.
            If \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) are unit vectors, then prove that \( |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \leq 9 \).


              • 4.
                Find the value of \( p \) if the shortest distance between the lines \( \vec{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} - \hat{j} + \hat{k}) \) and \( \vec{r} = (p\hat{i} - \hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + 2\hat{k}) \) is \( \frac{3}{\sqrt{2}} \) units.


                  • 5.
                    Solve the differential equation \( (x - \sin y) \, dy + \tan y \, dx = 0 \).


                      • 6.
                        Let three toys A, B and C be placed in the same straight line. If the position vectors of A, B and C are \( 55\hat{i} - 2\hat{j} \), \( 5\hat{i} + 8\hat{j} \) and \( a\hat{i} - 52\hat{j} \) respectively, find the value of ‘a’.

                          CBSE CLASS XII Previous Year Papers

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