NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1

CBSE CLASS XII Related Questions

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


      • 2.
        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.


          • 3.
            For a square matrix \(A\), \[ (3A)^{-1}= \]

              • \( 3A^{-1} \)
              • \( 9A^{-1} \)
              • \( \frac{1}{3} A^{-1} \)
              • \( \frac{1}{9} A^{-1} \)

            • 4.
              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.

              • 5.
                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

                • 6.

                  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:

                    CBSE CLASS XII Previous Year Papers

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