NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.3

CBSE CLASS XII Related Questions

  • 1.
    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.

    • 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.

          If \[ B(\operatorname{adj} B)= \begin{bmatrix} \frac{1}{3} & 0 & 0\\ 0 & \frac{1}{3} & 0\\ 0 & 0 & \frac{1}{3} \end{bmatrix}, \] then the value of \[ \det(B^{-1}) \] is: 

            • \(\frac{1}{3}\)
            • \(\frac{1}{9}\)
            • \(3\)
            • \(9\)

          • 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.

              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:


                • 6.
                  Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]

                    CBSE CLASS XII Previous Year Papers

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