NCERT Solutions for Class 11 Maths Chapter 14 Miscellaneous Exercises

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

  • New statements from old statements
  • Implications
  • Validating Statements
  • Conjunction

Download PDF NCERT Solutions for Class 11 Chapter 14 Mathematical Reasoning Miscellaneous Exercises

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Chapter Related Topics
Irrational Number Prime Number Real Number

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CBSE CLASS XII Related Questions

  • 1.

    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. 


      • 2.
        If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


          • 3.
            Find:

            The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]


              • 4.
                Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).


                  • 5.

                    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 :


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

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