Correct option is (d) \(\frac{35}2\)
The given linear equation is
4x + 7y − 10 = 0
10x + ky − 25 = 0
Here a1 = 4, b1 = 7, c1 = −10
and a2 = 10, b2 = k, c2 = −25
\(\therefore \frac{a_1}{a_2} = \frac 4{10} = \frac 25\)
\(\frac{b_1}{b_2} = \frac 7k\)
\(\frac{c_1}{c_2} = \frac{-10}{-25} = \frac 25\)
If a linear equation represents a coincident lines then
\(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
Then \(\frac 7k = \frac 25\)
\(\therefore k = \frac{35}2\)