NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

CBSE CLASS XII Related Questions

  • 1.

    At a birthday party, children are being served orange juice in conical cups, as shown in the figure. 


    Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
    On the basis of the above information, answer the following questions :


      • 2.
        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 \(k\).

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

        • 3.
          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 \(q\).

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

          • 4.

            A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length. 


              • 5.
                Find:

                The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

                  • \(-\frac{\pi}{2}\)
                  • \(-\frac{\pi}{4}\)
                  • \(\frac{\pi}{4}\)
                  • \(\frac{\pi}{2}\)

                • 6.
                  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 \( \cos^{-1}(x^2) \).

                    CBSE CLASS XII Previous Year Papers

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