NIMCET 2022 — Mathematics PYQ

Correct option (B) 1

Let a be the first term and d be the common difference of the corresponding AP. Then

$p^{\text{th}}$ term of AP ($T_p$) = $a+(p-1)d=\frac{1}{q}$ ... (1)

$q^{\text{th}}$ term of AP ($T_q$) = $a+(q-1)d=\frac{1}{p}$

From Eqs. (1) and (2),

$(p-q)d=\frac{1}{q}-\frac{1}{p}=\frac{p-q}{pq}\Rightarrow d=\frac{1}{pq}$

From Eq. (1),

$a+(p-1)\frac{1}{pq}=\frac{1}{q}\Rightarrow a=\frac{1}{pq}$

Therefore,

$T_{pq}=a+(pq-1)d$

$=\frac{1}{pq}+(pq-1)\frac{1}{pq}=1$

So, $p{q}^{\text{th}}$ term is 1.