RRB NTPC Mains or Stage 2 Model Paper 10 with solutions

(a) x = a (1 + cos θ cos ϕ) =$\frac{\mathit{x}}{\mathit{a}}\mathit{–}1$ = cos θ cos ϕ...(i)
y = b (1 + cos θ sin ϕ) =y/b – 1 = cos θ sin ϕ...(ii)
and $\mathit{z}=\mathit{c}\left(1+\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }\right)=\frac{\mathit{z}}{\mathit{c}}-1$ sinθ ...(iii)
On squaring and adding Eqs. (i), (ii) and(iii), we get
${\left[\frac{\mathit{x}-\mathit{a}}{\mathit{a}}\right]}^2+{\left[\frac{\mathit{y}-\mathit{b}}{\mathit{b}}\right]}^2+{\left[\frac{\mathit{z}-\mathit{c}}{\mathit{c}}\right]}^2$
$=\mathit{c}\mathit{o}{\mathit{s}}^2\mathit{\theta }\left(\mathit{c}\mathit{o}{\mathit{s}}^2\mathit{\varphi }+\mathit{s}\mathit{i}{\mathit{n}}^2\mathit{\varphi }\right)+\mathit{s}\mathit{i}{\mathit{n}}^2\mathit{\theta }=1$