JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q69

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MathematicsSingle correct+4 / -1Question 69 of 90

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is :

2-\sqrt3

2+\sqrt3

\sqrt2+\sqrt3

3+\sqrt2

Answer and worked solution

Official answer: B

The G.P. is $a,ar,ar^2$ . If $a,2ar,ar^2$ are in A.P., then $4ar=a+ar^2$ , so $r^2-4r+1=0$ and $r=2\pm\sqrt3$ . The G.P. is increasing, so $r=2+\sqrt3$ .

Topics:Geometric progression Arithmetic progression

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JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 69