જો $\sum\limits_{r = 0}^{25} {\left\{ {^{50}{C_r}.{\,^{50 - r}}{C_{25 - r}}} \right\} = K\left( {^{50}{C_{25}}} \right)} $ હોય તો $K$ ની કિમત મેળવો.
$(25)^2$
$2^{25} -1$
$2^{24}$
$2^{25}$
સંખ્યા $111......1$ ($91$ વખત) એ . . .
$\sum \limits_{ r =0}^{22}{ }^{22} C _{ r }{ }^{23} C _{ r }$ નું મૂલ્ય $.......$ છે.
$\sum\limits_{k = 0}^{10} {^{20}{C_k} = } $
જો $\sum_{r=1}^{10} r !\left( r ^{3}+6 r ^{2}+2 r +5\right)=\alpha(11 !),$ તો $\alpha$ ની કિમંત મેળવો.
ધારો કે $\mathrm{a}=1+\frac{{ }^2 \mathrm{C}_2}{3!}+\frac{{ }^3 \mathrm{C}_2}{4!}+\frac{{ }^4 \mathrm{C}_2}{5!}+\ldots$, $\mathrm{b}=1+\frac{{ }^1 \mathrm{C}_0+{ }^1 \mathrm{C}_1}{1!}+\frac{{ }^2 \mathrm{C}_0+{ }^2 \mathrm{C}_1+{ }^2 \mathrm{C}_2}{2!}+\frac{{ }^3 \mathrm{C}_0+{ }^3 \mathrm{C}_1+{ }^3 \mathrm{C}_2+{ }^3 \mathrm{C}_3}{3!}+\ldots .$ તો $\frac{2 b}{a^2}=$...........