Mathematics Test - 1

Let S={x ∊ R : x ≥ 0 and 2∣√ x −3∣+ √x ( √x −6)+6=0}. Then S:

The sum of the co-efficients of all odd degree terms in the expansion of (x+√x³-1)⁵+(x-√x³-1)⁵ ,(x>1) in:

The area (in square units) bounded by the curves y = √x, 2y - x + 3 = 0, x-axis, and lying in the first quadrant is

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

Given : A circle, 2x² + 2y² = 5 and a parabola, y² = 4√5x.

Statement−I : An equation of a common tangent to these curves is y = x + √5.

Statement−II : If the line, y=mx + √5/m (m!=0) is either common tangent, then m satisfies m⁴ - 3m² + 2 = 0

ABCD is a trapezium such that AB and CD are parallel and BC⊥CD. If ∠ADB = θ, BC = p and CD = q, then AB is equal to

If x, y, z are in A.P. and tan^-1x, tan^-1y and tan^-1z are also in A.P., then

If the equations x² + 2x + 3 = 0 and ax² + bx + c = 0, a, b, c ∈ R, have a common root, then a : b : c is

"For each t ∊ R, let [t] be the greatest integer less than or equal to t. Then