A line segment A B is divided internally and externally in the same ratio (1) at P and Q respectively and M is mid point of A B. Statement-1: MP, MB, MQ are in G.P. Statement-2 AP , AB and AQ are in HP.

Question

A line segment A B is divided internally and externally in the same ratio (>1) at P and Q respectively and M is mid point of A B. Statement-1: MP, MB, MQ are in G.P. Statement-2 AP , AB and AQ are in HP. (A) STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is correct explanation for STATEMENT-1 (B) STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is not correct explanation for STATEMENT-1Pro (C) STATEMENT-1 is true, STATEMENT-2 is false (D) STATEMENT-1 is false, STATEMENT-2 is true

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/06adb5933d7901fd49d5654d17442481-.png" /> AP , AB , AQ are in H.P. A P-(A B/2), A B-(A B/2), A Q-(A B/2) are in G.P. M P, M B, M Q are in G.P.

Q. A line segment $A B$ is divided internally and externally in the same ratio $(> 1)$ at $P$ and $Q$ respectively and $M$ is mid point of $A B$ .
Statement-1 : MP, MB, MQ are in G.P.
Statement-2 $A P, A B$ and $A Q$ are in $H P$ .

STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is correct explanation for STATEMENT-1

STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is not correct explanation for STATEMENT-1Pro

STATEMENT-1 is true, STATEMENT-2 is false

STATEMENT-1 is false, STATEMENT-2 is true

$A P, A B, A Q$ are in H.P.
$A P - \frac{A B}{2}, A B - \frac{A B}{2}, A Q - \frac{A B}{2}$ are in G.P.
$MP, MB, MQ$ are in G.P.

Q. A line segment AB is divided internally and externally in the same ratio (>1) at P and Q respectively and M is mid point of AB. Statement-1 : MP, MB, MQ are in G.P. Statement-2 AP,AB and AQ are in HP.