Q98 / 150 · MHT CET 2019 (Shift 1) · Mathematics

If A, B, C are $p^{t h}, q^{t h}$ and $r^{t h}$ terms of a GP respectively then $A^{q - r} . B^{r - p} . C^{p - q} =$ ….

Solution

Let first term and common ratio of a GP are m and n respectively. Then,

A = m (n^{p - 1}) \dots

(i)

B = m (n^{q - 1}) \dots

(ii)
and

C = m (n^{r - 1}) \dots

(iii)
Now,

A^{q - r} . B^{r - p} . C^{p - q}

= m^{(q - r)} . n^{(q - r) (p - 1)} . m^{(r - p)} . n^{(r - p) (q - 1)} . m^{(p - q)} . n^{(p - q) (r - 1)}

= m^{q - r + r - p + p - q} . n^{q p - q - r p + r + r q - r - r - p q + p + p r - p - q r + q}

= m^{0} . n^{0} = 1 \times 1 = 1

Hence, the correct answer is option: 'B'.