CTET 2 Math and Science Dec 2019 Paper

Given, $21168=2^{\mathit{a}}\times 3^{\mathit{b}}\times 7^{\mathit{c}}$...(i)
Here, 21168 = 42 × 504
⇒ 21168 = 2 × 3 × 7 × 8 × 9 × 7
$=2\times 3\times 7\times 2^3\times 3^2\times 7$
$=2^4\times 3^3\times 7^2$...(ii)
From (i) and (ii), we get
$2^{\mathit{a}}\times 3^{\mathit{b}}\times 7^{\mathit{c}}$ $=2^4\times 3^3\times 7^2$
∴ a = 4, b = 3, c = 2
where, a, b and c are rational numbers
∴ 4a – 5b + c = 4 × 4 – 5 × 3 + 2
= 16 – 15 + 2 = 18 – 15 = 3
Hence, the value of (4a – 5b + c) = 3.