Assertion :If y,x,z are in AP, then 2x+y,2y+zand2x+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.