Question

11. The value of (1003)1/3 according to binomial theorem is
(1) 10.01
(2) 10.00
(3) 10.3
(4) 10.03


12. The value of (997)1/3 according to binomial theorem is
(1) 9.00
(2) 9.99
(3) 10.90
(4) 9.33
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Answer 1

HOPE IT HELPS UH.........

Answer 2

(1003)^(1/3) = [(1000)×1.003]^(1/3) = (1000)^(1/3)×(1+0.003)^(1/3)

=10[1+(1/3)×0.003 +(1/2!)(1/3)(-2/3)×(0.003)^2+…..] ~ 10..001 up to 3 places of decimal, where we have neglected the subsequent terms of the Binomial expansion (valid as 0.003 < 1), as they are very small in comparison because of the higher powers of 0.003.

Out of the given choices (all of which are approximate) 10.001 is nearest to 10.00.