Mathematics Tes...

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is α and the number of persons who speak only Hindi is β, then the eccentricity of the ellipse 25(β²x² + α²y²) = α²β² is

Let D be the domain of the function f(x) = sin^–1   if If the range of the function  defined by g(x) = x − ⌊x⌋ (where ⌊x⌋ is the greatest integer function is (α ,β) 

 represents a circle, whose centre and radius, respectively, are

If a ∈ R and the equation −3(x−[x])² + 2(x−[x]) + a² = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution but has real solutions, then all possible values of a lie in the interval:

then A¹⁰⁰ = A × A × ..... (100 times) is equal to

If x, y, z are not all simultaneously equal to zero, satisfying the system of equations sin(3θ)x – y + z = 0; cos(2θ)x + 4y + 3z = 0; 2x + 7y + 7z = 0, then the sum of all possible values of θ (0 ≤ θ ≤ 2π) is

If two positive numbers are in the ratio  then the ratio between their A.M (arithmetic mean) and G.M (geometric mean) is

The area of the region enclosed by the curve {(x,y) : 4x² + 25y² = 100} is