While A runs 1000 m, B runs 1000 - 80 = 920 m and
While B runs 1000 m, C runs 1000 - 60 =940 m.
? While B runs 920 m; C runs
940 / 1000 × 920 = 4324 / 5 m
? While B runs 920 m; C runs 940 × 920 / 1000 = 4324 / 5 m
? While A runs 1000 m, C runs 4324 / 5 m
? A can beat C by 1000 - 4324 / 5 = 676 / 5 = 1351?5 m.
176 = 2 x 2 x 2 x 2 x 11
So, in order to make it a perfect square, it must be multiplied by 11.
Number of members = ?2209
= 47
?256 / ?x = 2
? 16 = 2?x
? ?x = 8
? x = 64.
N = 25/16
? ?N = ?25/16
= 5/4
= 11/4
(x + 1)/(x - 1) - (x - 1)/(x + 1) = {(x + 1)2 - (x - 1)2} / {(x - 1) (x + 1)}
= (x2 + 1 + 2x) - (x2 + 1 - 2x) / (x2 - 1)
= 4x / (x2 - 1) = 4(?3 + ?2) / {(?3 + ?2)2 - 1}
= 4(?3 + ?2) / (3 + 2 + 2?6 - 1) = 4(?3 + ?2) / (4 + 2 ?6)
= 4(?3 + ?2) / 2 ?2 (?3 + ?2)
= ?2
?8 and ?1000 = 81/3 and 10001/3
Since 1000 > 8
? ?1000 > ?8
?81 and ?1 = 811/2 and 11/2
Since, 1 < 81
? ?1 < ?81
Let the number be x.
According to the question,
x2 + (14)3 = 4425
? x2 = 4425 - (14)3
? x2 = 4425 - 2744
? x2 = 1681
? x = ?1681 = 41
?10 and ?8 = 101/4 and 81/3
Since, LCM of 4 and 3 is 12.
? 101/4 = 103/12 = (103)1/12 = (1000)1/12 = 12?1000
and 81/3 = 84/12 = (84)1/12 (4096)1/2 = 12?4096
? 4096 > 1000
Hence, 81/3 >101/4
? ?8 > ?10
74088 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 7
= (2 x 2) x (3 x 3) x (7 x 7) x ( 2 x 3 x 7)
? Least number which should be multiplied to 74088 to make it a perfect suqare = 2 x 3 x 7 = 42
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