ⁿC_r x^n-r . y^r

x^n-r . y^r

nC0 xn + nC1 xn-1 . y + nC2 xn-2 . y2 + … + nCn yn

ⁿC₀ xⁿ - ⁿC₁ x^n-1 . y + ⁿC₂ x^n-2. y² + … + ⁿC_n yⁿ

$n_{c_{n+\frac{1}{2}}}\$ when n is odd

$n_{c_{\frac{n+1}{2\ }}}\$ when n is even

$n_{c_{\frac{n}{2}}}\$ when n is even

$\frac{n+1}{2}\$ when n is odd

$\frac{n+3}{2}\$ when n is even

$\frac{n+3}{2\ }\$ when n is odd

both 1 & 3

$n_{c_{\frac{n}{2}}}$ when n is odd

$n_{c_{\frac{n+1}{2}}}$ when n is odd

$n_{c_{\frac{n-1}{2}}}$ when n is even

$n_{c_{\frac{n-1}{2}}}$ when n is odd

Both 2 & 4

 $t_p$  

 $t_{p-1}$  

 $T_{\frac{p+1}{ }}$  

both 1 & 3

 $t_p$  

 $t_{p-1}$  

 $T_{\frac{p+1}{ }}$  

both 1 & 3

 $n_{c_{r+1}}-\ n_{c_r}$  

 $n_{c_r-}n_{c_{r-1}}$  

 $n_{c_{r_{ }}}+n_{c_{r-1}}$  

none of these

 $n.\ n+1_{c_{r-1}}$  

 $\ n.\ \ n-1_{c_{r-1}}$  

both 1 & 2

none of these

a+b = n

a = b

both 1 & 2

none of these

 $2^0$  

 $2^n$  

both 1 & 2

 $n_{c_r}$  

 $0$  

 $2^n$  

both 1 & 2

 $n_{c_r}$  

 $c_1+c_2+c_3+c_{4\ }+............$  

 $c_1+c_3+c_5+c_{7\ }+c_9+.........$  

Both 1 & 2

0

 $\left(-1\right)^{\frac{n}{2}\ }\ .\ n_{c_{\frac{n}{2}}}$  

 $2n_{c_n}$  

0

both 1 & 3

 $\left(-1\right)^{\frac{n}{2}\ }\ .\ n_{c_{\frac{n}{2}}}$  if n is odd

 $2n_{c_n}$  

0 if n is even

both 1 & 3

none of these

$\left(-1\right)^{\frac{n}{2}\ }\ .\ n_{c_{\frac{n}{2}}}$ if n is even

$2n_{c_n}$

0 if n is odd

both 1 & 3

none of these