NCERT Solutions for Class 10 Maths Chapter 14 Statistics Exercise 14.1

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CBSE X Related Questions

1.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them

Monthly consumption 
(in units)

 Number of consumers

65 - 85 

4

85 - 105

5

105 - 125

13

125 - 145

20

145 - 165

14

165 - 185

8

185 - 205

4

      2.
      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) \(1^2 , 5^2, 7^2, 7^3\), . . . .

          3.

          Solve the following pair of linear equations by the substitution method. 
          (i) x + y = 14 
              x – y = 4   

          (ii) s – t = 3 
              \(\frac{s}{3} + \frac{t}{2}\) =6 

          (iii) 3x – y = 3 
                9x – 3y = 9

          (iv) 0.2x + 0.3y = 1.3 
               0.4x + 0.5y = 2.3 

          (v)\(\sqrt2x\) + \(\sqrt3y\)=0
              \(\sqrt3x\) - \(\sqrt8y\) = 0

          (vi) \(\frac{3x}{2} - \frac{5y}{3}\) =-2,
              \(\frac{ x}{3} + \frac{y}{2}\) = \(\frac{ 13}{6}\)

              4.

              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.

                  5.
                  Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (i) \(x + y = 5\),\( 2x + 2y = 10\) (ii)\( x – y = 8 , 3x – 3y = 16\) (iii) \(2x + y – 6 = 0\) , \(4x – 2y – 4 = 0\) (iv) \(2x – 2y – 2 = 0,\) \( 4x – 4y – 5 = 0\)

                      6.
                      Find the sums given below :
                      1. \(7 + 10\frac 12+ 14 + ....... + 84\)
                      2. \(34 + 32 + 30 + ....... + 10\)
                      3. \(–5 + (–8) + (–11) + ....... + (–230)\)

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