NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1

CBSE CLASS XII Related Questions

  • 1.
    A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.


      • 2.
        Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]


          • 3.

            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:


              • 4.
                Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]


                  • 5.

                    The domain of \[ f(x)=\cos^{-1}(2x-5) \] is: 

                      • \([-1, 1]\)
                      • \([4, 6]\)
                      • \([-7, -3]\)
                      • \([2, 3]\)

                    • 6.
                      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.
                      CBSE CLASS XII Previous Year Papers

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