Put n = 1, now the sum of the series = 1.2.4 = 8
Put n = 1, in the options
(a) 1(1 + 1) (1 + 2) = 6
(b) 1(1 + 1)/12 x (3 + 19 + 26) = 8
(c) (1 + 1) (1 + 2) (1 + 3)/4 = 6
(d) 1(1 + 1) (1 + 2) (1 + 3 )/3 = 8
As, the sum of series = 8
Hence, option (a) and (c) can be rejected.
Now, put n = 2
Sum 1. 2. 4 + 2 . 3 . 5 = 38
Put n = 2, in option (b)
2(2 + 1)/12 (3 x 4 + 19 x 2 + 26)38
Hence, (b) is the correct option.
Given that, 30 % of A = 20 % of B
? A/B = 20/30 = 2/3
? A : B = 2 : 3
Let initial quantity be Q, and final quantity be F
F = Q(1 - 8/Q)
=> Q = 20
? log5[(x2 + x ) / x] = 2
? log10(x + 1) = 2
? x + 1 = 25
? x = 24
∴ Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
We know that speed is inversely proportional to time.
Given that, (Speed of A ) : (speed of B ) = 2 : 7
?(Time taken by A ) : (Time taken by B ) = 1/2 : 1/7 = 7 : 2
Let th distance = D
and usual speed = V
According to the question,
D/(3V/4) - D/V = 2
? D/V = 3 x 2 = 6
Time taken to cover the distance with usual speed = 6 h
?2n = 64
? 2n/2 = 26
? n/2 = 6
? n = 12
Distance = 160 km
Relative Speed = 8 + 2 = 10
Time = Distance/Relative speed = 160/10 = 16 h
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