Question

If the $p^{th},q^{th}$ and $r^{th}$ term of a G.P. are a,b,c respectively , then $a^{q-r}\cdot b^{r-p}\cdot c^{p-q}$ is equal to

• A. 0
• B. 1
• C. abc
• D. pqr

Answer 1

The correct option is B 1

$n^{th}$ term of $GP=A{P}^{n-1}$

$p^{th}$ term of $GP=a$

$Ap=a$

$A{R}^{p-1}=a$

$a=A{R}^{p-1}$

$a^{q-r}= (AR^{p-1})^{q-r}

$=a^{q-r}.b^{r-p}.c^{p-q}$

$=$ by solving $=A^o{R}^o=1$

$q^{th}$ term

$Aq=b$

$A{R}^{q-1}=b$

$b=A{R}^{q-1}$

$b=(A{R}^{q-1}{)}^{r-p}$

$r^{th}$ term

$Ar=c$

$A{R}^{r-1}=c$

$c=A{R}^{r-1}$

$c^{p-q}=(A{R}^{r-1}{)}^{p-2}$

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$MHT-CET=35$ Students

$AIEEE=40$

$IIT=40$

$MHE-CET-AIEE=20$

$AIEEE$ & $IIT=17$

$MHT-CET$ & $IIT=15$

All $3=5$

$\left(1\right)200-68=132$

$\left(2\right)$ fail-lid un $AIEEE8IIT=12$