NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.3

CBSE CLASS XII Related Questions

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


      • 2.
        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.

        • 3.
          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

          • 4.

            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:


              • 5.

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

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

                • 6.
                  The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

                    • \( e^{-3} \)
                    • \( -1 \)
                    • \( 1 \)
                    • \( -e^3 \)
                  CBSE CLASS XII Previous Year Papers

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