KVPY Government Jobs Exams

All the points (x, y) in the plane satisfying the equation x^2 + 2x sin (xy) + 1 = 0 lie on -
(A) a pair of straight lines (B) a family of hyperbolas
(C) a parabola (D) an ellipse

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KVPY Other Question

Consider the cubic equation x^3 + ax^2 + bx + c = 0, where a, b, c are real numbers. Which of the following
statements is correct ?
(A) If a^2 – 2b < 0, then the equation has one real and two imaginary roots
(B) If a^2 – 2b ≥ 0, then the equation has all real roots
(C) If a^2 – 2b > 0, then the equation has all real and distinct roots
(D) If 4a^3 – 27b^2 > 0, then the equation has real and distinct roots Let A = (4, 0), B = (0, 12) be two points in the plane. The locus of a point C such that the area of triangle
ABC is 18 sq. units is