MHT CET 2017 Math Solved Paper

(c) Suppose that slope of the curve y =√x−1 is m1
∴ m1=

dy

dx

=

d

dx

√x−1

1

2√x−1

slope of the line 2x+y−5=0 is m2
∴ m2=

dy

dx

=

d

dx

(5−2x)=−2
As, lines are perpendicular if m1m2=−1
So,

1

2√x−1

⋅(−2)=−1 ⇒ √x−1=1
⇒ x−1=1⇒x=2
After substituting x=2 in y=√x−1, we get y=1
Hence, required point is (2,1) .