NCERT Solutions Class 11 Maths Chapter 1 Sets Miscellaneous Exercises

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


            • 4.
              Which of the following equations is NOT a Linear Differential Equation?

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

              • 5.

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


                  • 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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