NCERT Solutions for Class 10 Maths Chapter 14 Statistics Exercise 14.3

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CBSE X Related Questions

1.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

      2.

      A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

          3.
          Which of the following are APs? If they form an AP, find the common difference d and write three more terms.
          (i) 2, 4, 8, 16, . . . .
          (ii) \(2, \frac{5}{2},3,\frac{7}{2}\), . . . .
          (iii) – 1.2, – 3.2, – 5.2, – 7.2, . . . .
          (iv) – 10, – 6, – 2, 2, . . .
          (v) 3, \(3 + \sqrt{2} , 3 + 3\sqrt{2} , 3 + 3 \sqrt{2}\) . . . .
          (vi) 0.2, 0.22, 0.222, 0.2222, . . . .
          (vii) 0, – 4, – 8, –12, . . . .
          (viii) \(\frac{-1}{2}, \frac{-1}{2}, \frac{-1}{2}, \frac{-1}{2}\), . . . .
          (ix) 1, 3, 9, 27, . . . .
          (x) a, 2a, 3a, 4a, . . . .
          (xi) a, \(a^2, a^3, a^4,\)  . . . .
          (xii) \(\sqrt{2}, \sqrt{8} , \sqrt{18} , \sqrt {32}\) . . . .
          (xiii) \(\sqrt {3}, \sqrt {6}, \sqrt {9} , \sqrt {12}\) . . . . .
          (xiv) \(1^2 , 3^2 , 5^2 , 7^2\), . . . .
          (xv) \(1^2 , 5^2, 7^2, 7^3\), . . . .

              4.

              Form the pair of linear equations for the following problems and find their solution by substitution method.

              (i) The difference between two numbers is 26 and one number is three times the other. Find them.

              (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

              (iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.

              (iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km.

              (v) A fraction becomes\(\frac{ 9}{11}\), if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes \(\frac{5}{6}\). Find the fraction.

              (vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

                  5.
                  Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).

                      6.
                      A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

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