NCERT Solutions for Class 12 Chapter 9 Differential Equations Miscellaneous Exercises

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Class 12 Maths NCERT Solutions Chapter 9 Differential Equations Miscellaneous Exercises are provided in the article. Class 12 Chapter 9 Differential Equations Exercises cover miscellaneous questions from the entire chapter. 

The exercises are thus based on following concepts:

  • Introduction to Differential Equations
  • Basic Concepts of Differential Equation
  • General and Particular Solutions of a Differential Equation
  • Formation of a Differential Equation whose General Solution is given
  • Methods of Solving First Order, First Degree Differential Equations

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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:

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

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

        • 3.

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


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


                    • 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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