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Question

If the slope of the curve y=axbx at the point (1, 1) is 2 then values of a and b respectively


A

1, -2

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B

-1, 2

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C

1, 2

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D

2,7

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Solution

The correct option is C

1, 2


We have, y=axbx
=dydx=(bx)aax(1)(bx2)=ab(bx)2
[dydx](1,1)=ab(b1)2(given)....(1)
Since the curve passes through the point (1,1), therefore,
1=ab1a=b1
On putting a=b-1 in equation (1), we get
(b1)b(b1)2=2b=2.1=21=1.
Hence a =1, b=2
Hence (c) is the correct answer.

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