? N = (875)16
? log N = log (875)16
? log N = 16 log (875)
= 16 x (2.942)
= 47.072
? No.of digits = 47 + 1 = 48
We have r = Rate of increase
= 52/1000 x 100
= 5.2, n = 5, P0 = 265000
? P = 265000(1 + 5.2 / 100)5
? log P = log 265000 + 5(log 105.2 - log 100)
= 5.4232 + 5(2.0220 - 2)
= 5.4232 + 0.1100
= 5.5332
? P = antilog(5.5332) = 341400
? 3000 = 2000(1 + r/200)6
? 3/2 = (1 + r/200)6
? 1 + r/200 = (3/2)1/6
? log(1 + r/200)= 1/6(log 3 - log 2 )
? log(1 + r/200)= 1/6(0.4771-.3010)
= 0.02935
? (1 + r/200) = antilog(.02935)
? 1 + r/200 = 1.070 = 1 + 7/100
? r = 14%
P (getting a prize ) = 20 / (20 + 15 ) = 20 / 35 = 4/7
? Total no. of favourable cases i,e., (5, 10, 15, 20, 25, 30, ....., 105, 110, 115, 120) = 24.
? Reqd . Prob = 24/120 = 1/5
Total number of letters = n(S) = 11
whereas, number of vowels = n(E) = 4
? Required probability = n(E)/n(s) = 4/11
Clearly, n(S) = 20 and E = { 3, 6, 9, 12, 15, 18, 7, 14 } i.e., n(E) = 8
? P(E) = n(E)/ n(S) = 8/20 = 2/5
Number of cases favourable of E = 4
Total Number of cases = (5 + 4 ) = 9
? P(E) = 4/9
n(S) = Number of ways of drawing 2 balls out of 13 = 13C2 = 13 x 12 / 2= 78
n(E) = No. of ways of drawing 2 balls out of 5 = 5C2 = 5 x 4 / 2 = 10
? P(E) = n(E)/n(S) = 10/78 = 5/39
? n(S) = (2)3 = 8
E = Event of getting 0, or 1 or 2 heads
= {TTT, TTH, THT, HTT, HHT, HTH, THH}
? n(E) = 7
? P(E) = n(E)/n(S) = 7/8
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