NCERT Solutions Class 11 Maths Chapter 1 Sets Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.

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


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


              • 4.

                Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \] 


                  • 5.
                    Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]


                      • 6.

                        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.
                        CBSE CLASS XII Previous Year Papers

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