131. Given
exp. (1 -1/2) + (1/2 – 1/2) + (1/3 – 1/4)
+ (1/4 – 1/5) +…..+ (1/11 – 1/12 ) = (1 – 1/12 ) = 11/12.
132. Clearly,
sum of first 6 terms is zero, so, sum of first 30 terms -0.
Required sum = (1/2 + 1/3 – 1/4 – 1/2 - 1/3) = -1/4.
133. Given
exp.= (1000 – 4/999) x 999 =9990000- 4 = 9989996.
134. Given
exp.
=(1000 -6/7 ) + (1000 – 5/7 ) + (1000 – 4/7) + (1000 – 3/7 ) + (1000 – 2/7
) + (1000 -1/7)
= ( 6000 – (6/7 + 5/7 + 4/7 + 3 /& +2/7 + 1/7) = 6000 – 3 = 5997.
135. Given
exp. 4 x 3³
+ 3²
+ 3 + 1/ 4 x 3³ = 108 + 9 + 3 + 1 / 108 = 121 / 108.
136. Given
exp. = (4.5.6 + 5.6 + 2.6 + 2.3 / 1.2.3.4.5.6 = 120 + 30 + 12 + 6 / 720 = 7/30.
137. Given
exp. = (1/1²
- 1/2²)
+ (1/2²
- 1/3²
) +(1/3²
-1/4²
) +(1/4²
- 1/5²)
+….+ (1/9²
- 1/10²)
= (1/1²
- 1/10²
) = ( 1- 1/100) = 99/100.
138. Number
of pieces = (42.5x 100 / 85) = 4250/85 = 50.
139. Income
after 1 year = Rs. (4 x 2¹) lakhs.
Income
after 2 years = Rs. (4 x 2 x 2) lakhs = Rs.(4 x 2²) lakhs
Income after 5 years = Rs. (4 x 2 )⁵
lakhs. = Rs. 128 lakhs =Rs.1.28 crores.
140. Total
number of children = (30 x 16) = 480.
Number
of columns of 24 children each = (480 / 24) 20.
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