Jee Main 2024 01 02 2024 Shift 1 - Question1
Question 1
If $3, a, b, c$ are in A.P. and $3, a-1, b+1$ are in G.P. Then arithmetic mean of $a, b$ and $c$ is
(1) 11
(2) 10
(3) 9
(4) 13
Show Answer
Answer: (1)
Solution:
3, a, $b, c$ are in A.P. $a-3=b-a$ (common diff.) $2 a=b+3$
and $3, a-1, b+1$ are in G.P.
$\frac{a-1}{3}=\frac{b+1}{a-1}$
$a^{2}+1-2 a=3 b+3$
$a^{2}-8 a+7=0$
$[\because 2 a=b+3]$
$(a-7)(a-1)=0$
If $a=7, b=2(7)-3=11, \quad b=11$
and $c-b=a-3$
$c-11=4$
$c=15$
$\therefore$ A.M of $7,11,15=\frac{7+11+15}{3}$
$=\frac{33}{3}=11$
BETA
