Question

Assertion :If $y,x,z$ are in $AP$, then $2^{x+y},2^{y+z}and{2}^{x+z}$ are in $G.P$ Reason: Three numbers $a,b,c$ are in $GP$ if $b^2=ac$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$y,x,z$ are in AP
$\Rightarrow -y,-x,-z$ are in A.P.
$\Rightarrow -y+(x+y+z),-x+(x+y+z),-z+(x+y+z)$ are in A.P.
$\Rightarrow x+z,y+z,x+y$ are in A.P.
$\Rightarrow 2(y+z)=x+z+x+y$
$\Rightarrow 2^{2(y+z)}=2^{x+z}{2}^{x+y}$
$\Rightarrow (2^{(y+z)}{)}^2=2^{x+z}{2}^{x+y}$
Assertion is correct.
Reason is correct and Reason is the correct explaination for Assertion.