NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.3 Solutions

CBSE X Related Questions

  • 1.
    If \(\alpha, \beta\) are the zeroes of the polynomial \(p(x) = x^2 - 3x - 1\), then find the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\).


      • 2.
        If the pair of linear equations : \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) is consistent and dependent, then

          • \( \frac{a_1}{a_2} \neq \frac{b_1}{b_2} \)
          • \( \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \)
          • \( \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} \)
          • \( \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \)

        • 3.
          Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
          Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

            • Both Assertion (A) and Reason (R) are true and 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.
            Prove that :
            \(\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta\).


              • 5.
                Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.


                  • 6.
                    If the quadratic equation \(9x^2 + 8kx + 16 = 0\) has real and equal roots, then the value of k is

                      • 3
                      • –3
                      • –4
                      • \(\pm 3\)

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