KVPY Government Jobs Exams

A circle touches the parabola y^2 = 4x at (1, 2) and also touches its directrix. The y-coordinates of the point of
contact of the circle and the directrix is-

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KVPY Other Question

Let I, ω and ω2 be the cube roots of unity. The least possible degree of a polynomial, with real coefficients,
having 2ω^2, 3 + 4ω, 3 + 4ω^2 and 5 – ω – ω^2 as roots is- Let ABC be an equilateral triangle, let KLMN be a rectangle with K, L on BC, M on AC and N on AB.
Suppose AN/NB = 2 and the area of triangle BKN is 6. The area of the triangle ABC is-
(A) 54 (B) 108
(C) 48 (D) not determinable with the above data