NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.4

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CBSE CLASS XII Related Questions

  • 1.
    Find : \[ I = \int \frac{x + \sin x}{1 + \cos x} \, dx \]


      • 2.
        A fruit box contains 6 apples and 4 oranges. A person picks out a fruit three times with replacement. Find:
        (i) The probability distribution of the number of oranges he draws.
        (ii) The expectation of the number of oranges.


          • 3.
            If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]


              • 4.

                An amount of ₹ 10,000 is put into three investments at the rate of 10%, 12% and 15% per annum. The combined annual income of all three investments is ₹ 1,310, however, the combined annual income of the first and second investments is ₹ 190 short of the income from the third. Use matrix method and find the investment amount in each at the beginning of the year.


                  • 5.
                    Three students run on a racing track such that their speeds add up to 6 km/h. However, double the speed of the third runner added to the speed of the first results in 7 km/h. If thrice the speed of the first runner is added to the original speeds of the other two, the result is 12 km/h. Using the matrix method, find the original speed of each runner.


                      • 6.
                        The probability that a student buys a colouring book is 0.7, and a box of colours is 0.2. The probability that she buys a colouring book, given that she buys a box of colours, is 0.3. Find:
                        (i) The probability that she buys both the colouring book and the box of colours.
                        (ii) The probability that she buys a box of colours given she buys the colouring book.

                          CBSE CLASS XII Previous Year Papers

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