NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1

CBSE CLASS XII Related Questions

  • 1.
    If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


      • 2.

        An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.  
        Based on the above information, answer the following questions :


          • 3.
            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 \(k\).

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

            • 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.

                    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 :

                      CBSE CLASS XII Previous Year Papers

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