NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.3 Solutions

CBSE X Related Questions

  • 1.
    Prove that \(2 + 3\sqrt{5}\) is an irrational number given that \(\sqrt{5}\) is an irrational number.


      • 2.
        A trader has three different types of oils of volume \(870 \text{ l}\), \(812 \text{ l}\) and \(638 \text{ l}\). Find the least number of containers of equal size required to store all the oil without getting mixed.


          • 3.
            Assertion (A) : If probability of happening of an event is \(0.2p\), \(p>0\), then \(p\) can't be more than 5.
            Reason (R) : \(P(\bar{E}) = 1 - P(E)\) for an event \(E\).

              • 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 Assertion (A).
              • Assertion (A) is true, but Reason (R) is false.
              • Assertion (A) is false, but Reason (R) is true.

            • 4.
              Assertion (A) : \((\sqrt{3} + \sqrt{5})\) is an irrational number.
              Reason (R) : Sum of the any two irrational numbers is always irrational.

                • 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 Assertion (A).
                • Assertion (A) is true, but Reason (R) is false.
                • Assertion (A) is false, but Reason (R) is true.

              • 5.
                A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use \(\pi = 3.14\))

                  • \(314 \sqrt{2}\) \(\text{cm}^{2}\)
                  • \(314\) \(\text{cm}^{2}\)
                  • \(\frac{3140}{3}\) \(\text{cm}^{2}\)
                  • \(3140 \sqrt{2}\) \(\text{cm}^{2}\)

                • 6.
                  An ice-cream cone of radius \(r\) and height \(h\) is completely filled by two spherical scoops of ice-cream. If radius of each spherical scoop is \(\frac{r}{2}\), then \(h : 2r\) equals

                    • \(1 : 8\)
                    • \(1 : 2\)
                    • \(1 : 1\)
                    • \(2 : 1\)

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