149
157
Percentage
(d) 8
Tot 12
7
of
vawe
by
%
5oooo
ofror 2 years a.
decreases . mually
Ron value of the
be. its population
20 atouts what will
Answers
Answer:
Sports are an essential part of Maharashtrian culture. In Maharashtra, cricket is considered the most popular sport, but Kabaddi, field hockey, Kho Kho, badminton, and table tennis are also widely played. In the state's rural regions, wrestling championships such as Hind Kesari and Maharashtra Kesari regularly take place. Among youths in the state, games like Viti-Dandu and Pakada-pakadi (tag) are also popular.
The state is home to various domestic level franchise-based leagues for hockey, chess, tennis, and badminton, all of which are governed by the Directorate of Sports and Youth Services located in Pune. Maharashtra has produced many popular athletes, such as cricketers Sachin Tendulkar and Sunil Gavaskar.
Answer:
Coefficient of x⁶y³ is 672.
Step-by-step explanation:
General term of expansion (a+b)ⁿ is
\bf \: T_{r+1} = \: \: ^nC_r \: \: \large \frak{ a ^{n−r} b ^r}T
r+1
=
n
C
r
a
n−r
b
r
For (x+2y)⁹,
Putting n =9, a=x, b=2y
\begin{gathered} \bf \: T_{r+1} = \: \: ^{9} C_r (x) ^{9−r} (2y) ^r \\ \\ \bf \: T _{r+1} = \: \: ^{9} C_r (x) ^{9−r} .(y) ^r .(2) ^r\end{gathered}
T
r+1
=
9
C
r
(x)
9−r
(2y)
r
T
r+1
=
9
C
r
(x)
9−r
.(y)
r
.(2)
r
Comparing with x⁶ y³ , we get, r = 3
Therefore,
\begin{gathered} \bf \: T _{r+1} \\ \: \tt ^9C_3 (x)^9−3 .y³ .2³ \\ \tt\: \: 9! (2)³× x⁶ × y³) / (3!.6!) \\ \: \tt 672x⁶ y³\end{gathered}
T
r+1
9
C
3
(x)
9
−3.y³.2³
9!(2)³×x⁶×y³)/(3!.6!)
672x⁶y³