NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.3

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Jasmine Grover

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NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.3 is covered in this article with a detailed explanation. Chapter 1 Real Numbers Exercise 1.3 deals with proving that root p is irrational. The 3 questions of the exercise cover the concept of irrational numbers

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CBSE X Related Questions

  • 1.
    Prove that : \(\sqrt{\frac{1 - \cos A}{1 + \cos A}} = \frac{\tan A}{\sec A + 1}\).


      • 2.
        If \( 2 \sin A = 1 \), then the value of \( \tan A + \cot A \) is :

          • \( \sqrt{3} \)
          • \( \frac{4}{\sqrt{3}} \)
          • \( \frac{\sqrt{3}}{2} \)
          • \( 1 \)

        • 3.
          Find the H.C.F. and L.C.M. of 408 and 312.


            • 4.
              There are many varieties of mushrooms available in the world. One such mushroom ‘Amanita muscaria’ has a upper part which is like red cap (hemispherical) and lower part is like white stem (cylindrical). The hemispherical cap’s radius = 3 cm and cylindrical stem is 2 cm high with diameter 1.4 cm. Considering mushroom a solid object, answer the following questions:

              36(i) What is the total height of a mushroom ?


                • 5.
                  In a circular museum hall of radius 14 m, some statues are displayed. Statues are kept inside the inner concentric circle of radius 7 m. One such statue lying in sector OAB, is fenced along line segments OA, AP, PB and BO where P is a point on outer circle. Based on above information, answer the following questions:

                  37(i) Find \(m\angle AOP\).


                    • 6.
                      In the given figure, PQ is a tangent to a circle with centre \(O(-5, 3)\). If coordinates of P and Q are \((3, 1)\) and \((0, 6)\) respectively, then using distance formula, show that \(PQ \perp OQ\).

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