Veto q&a 7 Month22 (1)

@hang out
Speed of downstream = (a+b) km/hr
Speed of upstream
= (a-b) km/hr
• If the speed of downstream is ‘x km/hr’ and that
of upstream is ‘y km/hr’, then
x + y
Speed of Boat in still water = km/hr
2
x − y
Speed of stream = km/hr
2
PRoGReSSion
arithmatic Progression (a.P)
• Common difference, d = second term (t 2
) - first
term (t 1
)
• If the first term of an A.P be ‘a’ and common
difference be ‘d’ then, n th term t n
= a + (n-1)d
• If the first term and last term of an A.P are t 1
and
t n
respectively and the common difference be ‘d’,
and ‘n’, the number of terms , then the number of
tn
− t1 terms in the A.P, n = + 1
d
n
• Sum of an A.P, S = (t 1
+t n
)
2
• If ‘a’ is the first term, ‘d’ is the common difference
n
and ‘n’ be the total number of terms in an A,P, then
2
the sum of terms, S = [2a+(n-1)d]
2018
May
GeomeTRic PRoGReSSion (G.P)
• Common ratio, r =
• If ‘a’ be the first term, ‘r’ the common ratio, and ‘n’
the number of terms of a G.P then, the n th
term, t n
= ar n-1
• Sum of G.P, S n
=
PeRmuTaTionS anD
comBinaTionS
• Let ‘n’ be a positive integer then,
factorial n, n! = n(n-1) (n-2) ..............3 x 2 x 1
• Number of permutations : Number of all permutations
of ‘n’ things taken ‘r’ at a time is given by
n
P r
=
• Number of Combinations : Number of all combinations
of ‘n’ things taken ‘r’ at a time is given by,
n
c r
=
n
P
r
Second term
First term
n
a
1(1-r ) , #1
1-r
= n!
( n−
r )!
n!
r!( n−
r)!
r
n
c n
= 1
n
c 0
= 1
n
• a = a
n
( a)
n
( a)
Q&A Bonus
SuRDS
eXPonenTS
n n n
• ab = a × b
a
• n =
b
n
• = a
m n
• a =
m
n
n
1
n
mn
• =
a
b
n
a
a
m
a 0 =1
m
( a ) =
a 1 −m
1
=a
a
m
a
a m x a n = a m + n
m
ab
m
⎛ a⎞
a
a m ÷a n = a m - n ⎜ ⎟ =
⎝b⎠
b
−m
⎛ a⎞ ⎛b⎞
⎜ ⎟ = ⎜ ⎟
⎝b⎠ ⎝ a⎠
m
n
a
mn
( ) = a m xb
m
Radio broadcasting was started in India in - 1923
m
m
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