Question

Assertion: If $a,b,c$ are in A.P., then $b+c,c+a,a+b$ are in A.P.
Reason: If $a,b,c$ are in A.P., then $10^a,10^b,10^c$ are in G.P.

• A. Assertion is correct, reason is correct; reason is a correct explanation for assertion.
• B. Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• C. Assertion is correct, reason is incorrect
• D. Assertion is incorrect, reason is correct

Answer 1

Answer: (B)

Assertion: $b+c,c+a,a+b$ will be in A.P.
if $(c+a)-(b+c)=(a+b)-(c+a)$
i.e. if $2b=a+c$ i.e. if $a,b,c$ are in A.P.
Reason: $10^a,10^b,10^c$ are in G.P. if $\frac{10^b}{10^a}=\frac{10^c}{10^b}$
i.e. if $10^{b-a}=10^{c-b}$
i.e. if $b-a=c-b$
$\Rightarrow 2b=a+c$ which is true.