The correct options are
C m=3
D m=−3
The general term in the given expansion is given by
Tr+1=(−1)r× 10Cr×(√x)10−r×(mx2)r
=(−1)r× 10Cr×x(5−r2)×mrx2r
=(−1)r× 10Cr×x(5−r2−2r)×mr
=(−1)r× 10Cr×x(5−5r2)×mr.
Let Tr+1 be free from x.
Then, the power of x in Tr+1 must be 0.
∴5−5r2=0⇒5r2=5⇒r=2⇒r+1=3.
So, T3 will be free from x.
Now, T3=T(2+1)
=(−1)2× 10C2×x0×m2
=(10×92×m2)=45m2.
But, it is given that the term independent of x is 405.
∴45m2=405⇒m2=9⇒m=±3.
Hence, m=±3.