NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.3

CBSE CLASS XII Related Questions

  • 1.
    The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

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

    • 2.

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

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

      • 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.
          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.

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


              • 6.

                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 \[ 3q(x)-\pi. \] 

                  CBSE CLASS XII Previous Year Papers

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