NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.2

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


          • 3.

            The domain of \[ f(x)=\cos^{-1}(2x-5) \] is: 

              • \([-1, 1]\)
              • \([4, 6]\)
              • \([-7, -3]\)
              • \([2, 3]\)

            • 4.
              Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]


                • 5.
                  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.

                  • 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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