NCERT Solutions for Class 12 Maths Chapter 5 Miscellaneous Exercise

Miscellaneous Exercise contains the questions based on all exercises which may require the application of formulae used in two different exercises. Get the solutions of all exercises of Class 12 Mathematics Chapter 5 main page. विविध प्रशनावली 5 में अध्याय ५ की लगभग सभी प्रश्नावलियों पर आधारित मिले जुले प्रश्न हैं। इसमें कुछ प्रश्न अवकलनीयता पर भी आधारित हैं। Join the discussion forum to ask your doubts related to NIOS or CBSE Board.

In Miscellaneous Exercise, questions are related to almost all exercises and all the concepts used in Chapter 5. Questions number 1, 2, 3, 4 and 8 are based on direct differentiation, questions 5, 6 and 13 are based on inverse trigonometry. Questions 7, 9, 10 and 11 are based on logarithm (Exercise 5.5) and question 17 is based on parametric differentiation. There is one question (question number 22) is based on differentiation of Determinants, in which we differentiate first row first and leaving the rest rows then add the next determinant differentiating second row and leaving the rest and finally adding the determinant differentiating the third row leaving the rest.

In Question 17, first find dy/dx using dy/dt and dx/dt and then find d²y/dx² keeping in mind that now we are differentiating with respect to x, so must multiply with dx/dt to get complete answer of d²y/dx². Question 20 and 21 can be done by direct differentiation with respect to any parameter assuming that A and B are related to each other with that parameter. Question 10, 14, 15, 16, 17 and 23 are important one as per the examination point of view.

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