Mathematics Tes...

Let A and B be two events such that  where A̅ stands for the complement of the event A. Then the events A and B are:

The value of : tan{sin^–1(cos(sin^–1 x))}. tan{cos^-1(sin(cos^–1 x))} ; x ∈ (0, 1) is equal to ;

The area of the region described by A ={(x, y) : x² + y² ≤ 1 and y² ≤ 1 - x} is:

One of the bisectors of the angle between the lines a(x – 1)² + 2h(x – 1)(y – 2) + b(y – 2)² = 0 is x + 2y – 5 = 0. The other bisector is

The locus of the foot of perpendicular drawn from the centre of the ellipse x² + 3y² = 6 on any tangent to it is

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is

If the median of 21 observations is 40 and if the observations greater than the median are increased by 5 then the median of the new data will be

Two dice are thrown simultaneously to get the coordinates of a point on x – y plane. Then, the probability that this point lies on or inside the region bounded by |x| + |y| = 3 is

If x̅ & y̅ are two non-collinear vectors and a, b, c represent the sides of a ΔABC satisfying (a – b)x̅ + (b – c)y̅ + (c – a)(x̅ × y̅) = 0, then ΔABC is