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Question

Assertion :If y,x,z are in AP, then 2x+y,2y+z and 2x+z are in G.P Reason: Three numbers a,b,c are in GP if b2=ac

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

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
y,x,z are in A.P.
y+(x+y+z),x+(x+y+z),z+(x+y+z) are in A.P.
x+z,y+z,x+y are in A.P.
2(y+z)=x+z+x+y
22(y+z)=2x+z2x+y
(2(y+z))2=2x+z2x+y
Assertion is correct.
Reason is correct and Reason is the correct explaination for Assertion.

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