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Correct
The gradient of the curve y + px + qy = 0 at (1, 1) is 1/2. (1, 1) is on the curve, so satisfy the equation of the curve.
∴ 1 + p + q = 0 -------(1)
Differeniate the equation of the curve .r.t.x we get
dy /dx + p +qdy/dx = 0
substituting the vaue of x = 1 , y = 1 and dy/dx = 1/2 we get
1/2 + p +q(1/2) = 0
1 + 2p + q = 0 -------(2)
Substracting (1) from (2) we get,
p = 0
substituting p = 0 in equation (1) we get,
1 + 0 + q = 0
q = -1.
(p , q) = (0,-1)
Answer : (d)