The value of k for which the system, of equations has infinite number of solutions, is

Solution:

The given system of equations are

$2 x+3 y=5$

$4 x+k y=10$

For the equations to have infinite number of solutions, $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

Here, $a_{1}=2, a_{2}=4, b_{1}=3, b_{2}=k$

Therefore $\frac{2}{4}=\frac{3}{k}=\frac{5}{10}$

By cross multiplication of $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}$ we get,

$\frac{2}{4}=\frac{3}{k}$

$2 k=12$

$k=\frac{12}{2}$

$k=6$

And

$\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\frac{3}{k}=\frac{5}{10}$

$30=5 k$

$\frac{30}{5}=k$

$6=k$

Therefore the value of k is 6

Hence, the correct choice is $c$