NCERT Solutions for Class 12 Chapter 13 Probability Exercise 13.5

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Class 12 Maths NCERT Solutions Chapter 13 Probability Exercise 13.5 is based on Bernoulli Trials and Binomial Distribution. 

Bernoulli Trials must satisfy the following conditions:

  1. There should be a finite number of trials.
  2. Trials should be conducted independently.
  3. Each trial has exactly two outcomes: success or failure.
  4. Probability of success remains the same in each trial.

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CBSE CLASS XII Related Questions

  • 1.

    Sports car racing is a form of motorsport which uses sports car prototypes.The competition is held on special tracks designed in various shapes. 

    The equation of a sports car racing track is given as: \[ f(x)= \begin{cases} x^4-4x^2+4, & 0\leq x<3,\\ x^2+40, & x\geq 3 \end{cases} \] Based on this information:


      • 2.

        Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not. 


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

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

            • 4.
              If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]


                • 5.

                  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.

                  • 6.
                    Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

                      CBSE CLASS XII Previous Year Papers

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