Q.

If u=x2+y2 and x=s+3t,y=2s−t where t__ does not depend on s, then d2uds2 is

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a

12

b

32

c

10

d

0

answer is C.

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Detailed Solution

dxds=1,  dyds=2  .......(1)d2xds2=0,  d2yds2=0  .......(2)u=x2+y2duds=2xdxds+2ydydsd2uds2=2dxds2+2xd2xds2+2dyds2+2yd2yds2 From 1 and 2d2uds2=2×1+0+2×4+0=2+8=10
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