Mathematics Tes...

The area (in sq. units) of the region {(x, y) : y² ≥ 2x and x² + y² ≤ 4x, x ≥ 0, y ≥ 0} is :-

A line y = mx + 1 intersects the circle (x – 3)² + (y + 2)² = 25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate -3/5, then which one of the following options is correct?

The axis of parabola is along the line y = x and the distance of vertex from origin is √2 and that of origin from its focus is 2√2. If vertex and focus both lie in the 1^st quadrant, then the equation of the parabola is :

The common tangents to the circle x² + y² = 2 and the parabola y² = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is :

If chords of the hyperbola x² – y² = a² touch the parabola y² = 4ax then the locus of the middle points of these chords is the curve :

L₁ and L₂ are two lines whose vector equations are

where λ and μ are scalars. If 'α' is the acute angle between L₁ and L₂, which is independent of 'θ', then α =

Then the range of a, so that f(x) has maximum at x = –2, is :-

exists and is equal to 0, then

Let g : R → R be a differentiable function satisfying g(x) = g(y) g(x – y) x, y ∈ R and g'(0) = a and g'(3) = b then g'(–3) is :-