- Home
- Standard 11
- Mathematics
7.Binomial Theorem
normal
$(1+x)^{15}$ ના વિસ્તરણમાં છેલ્લા આઠ ક્રમિક પદોના સહગુણકનો સરવાળો મેળવો
A
$2^{15}$
B
$2^{14}$
C
$2^{16}$
D
$2^8$
Solution
Sum of last eight coefficient are
${\rm{S}} = {15_{{C_8}}} + {15_{{{\rm{C}}_9}}} + {15_{{{\rm{C}}_{10}}}} + \ldots \ldots + {15_{{{\rm{C}}_{15}}}}$ …….$(i)$
${\rm{S}} = {15_{{C_7}}} + {15_{{C_6}}} + {15_{{C_5}}}, + \ldots \ldots + {15_{{{\rm{C}}_0}}}$ ……..$(ii)$
(We know that ${{{15}_{{{\rm{C}}_8}}} = {{15}_{{{\rm{C}}_7}}}}$)
equation $(i) + (ii)$
$2{\rm{S}} = {15_{{C_0}}} + {15_{{C_1}}} + {15_{{C_2}}} + \ldots \ldots + {15_{{C_{15}}}}$
$\Rightarrow 2 \mathrm{S}=2^{15} \Rightarrow \mathrm{S}=2^{14}$
Standard 11
Mathematics
