NCERT Solutions for Class 12 Maths Chapter 8 Applications of Integrals Miscellaneous Exercise Solutions

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Class 12 Maths NCERT Solutions Chapter 8 Applications of Integrals Miscellaneous Exercises are provided in the article. Class 12 Chapter 8 Applications of Integrals Miscellaneous Exercises are important for both CBSE Term II exam and for competitive exams. Key topics covered in this chapter are Area Between Two Curves, lines, parabolas; area of circles/ellipses.

Download PDF: NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercises

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CBSE CLASS XII Related Questions

  • 1.

    Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \] 


      • 2.

        Sports car racing is a form of motorsport which uses sports car prototypes.The competition is held on special tracks designed in various shapes. 

        The equation of a sports car racing track is given as: \[ f(x)= \begin{cases} x^4-4x^2+4, & 0\leq x<3,\\ x^2+40, & x\geq 3 \end{cases} \] Based on this information:


          • 3.
            Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]


              • 4.
                For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

                  • local maximum value is 2
                  • local minimum value is \( -2 \)
                  • local maximum value is \( -2 \)
                  • local minimum value \( < \) local maximum value

                • 5.
                  Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
                  Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

                    • Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
                    • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
                    • Assertion (A) is true and Reason (R) is false.
                    • Assertion (A) is false and Reason (R) is true.

                  • 6.

                    Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not. 

                      CBSE CLASS XII Previous Year Papers

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