Mathematics Tes...

Let O be the vertex and Q be any point on the parabola, x²=8y . If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is:

If the angles of elevation of the top of a tower from three collinear points A, B and C on a line leading to the foot of the tower, are 30^∘,45^∘ and 60^∘ respectively, then the ratio AB : BC, is:

The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is:

The equation of the plane containing the line  2x−5y + z=3; x + y + 4z = 5, and parallel to the plane x + 3 y + 6 z = 1, is:

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is:

Locus of the image of the point (2, 3) in the line (2x − 3y + 3) + k (x−2y+3) = 0, k ∈ R, is a:

The sum of coefficients of integral powers of x in the binomial expansion of  (1−2 √x)⁵⁰ is: