Let `f(x)=-x^2 sin^2 theta-2x cos theta + 1, theta !=npi`, .Then locus of vertex of parabola `y=f(x)` is :
(A) `x^2/y^2 - 1/y = 1`
(B) `x^2/y^2 + 1/y = 1`
(C) `y^2/x^2 + 1/y = 1`
(D) none of these

Let f(x)=-x^2 sin^2 theta-2x cos theta + 1, theta !=npi, nepsilonZ The parabola y=f(x) cuts x-axis at : (A) no point (B) at exactly one point (C) at two points (D) None of these

If y=sin(m\ sin^(-1)x) , then (1-x^2)y_2-x y_1 is equal to m^2y (b) m y (c) -m^2y (d) none of these

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Let f'(x) = sin(x^2) and y = f(x^2 +1) then dy/dx at x=1 is

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