NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.2

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CBSE CLASS XII Related Questions

  • 1.

    For two vectors \(\vec{a}\) and \(\vec{b}\):  

    Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

      • 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, but Reason (R) is false.
      • Assertion (A) is false, but Reason (R) is true.

    • 2.
      If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]


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

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

          • 4.
            The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

              • \( e^{-3} \)
              • \( -1 \)
              • \( 1 \)
              • \( -e^3 \)

            • 5.

              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: 

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

              • 6.
                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.

                  CBSE CLASS XII Previous Year Papers

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