NCERT Solutions for Class 12 Maths Chapter 13 Probability Miscellaneous Exercises

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Class 12 Maths NCERT Solutions Chapter 13 Probability Miscellaneous Exercises cover all important concepts of Chapter 13. 

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CBSE CLASS XII Related Questions

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


      • 2.
        For a square matrix \(A\), \[ (3A)^{-1}= \]

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

        • 3.

          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.

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


              • 5.
                Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]


                  • 6.

                    Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not. 

                      CBSE CLASS XII Previous Year Papers

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