Mathematics Tes...

If A² - A + I = 0, then inverse of A is

The equation x³ – 3x + [a] = 0, will have three real and distinct roots if –

(where [ ] denotes the greatest integer function)

If the progressions 3, 10, 17, ....... and 63, 65, 67, ....... are such that their nth terms are equal, then n is equal to

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

The tangent to the circle x² + y² = 5 at (1, − 2) also touches the circle x² + y² − 8x + 6y + 20 = 0. Then the point of contact is

If f : R → R is defined by

f (x) = x² – 3x; if x > 2

= x + 2; if x < 2,

then f(4) =

If f : [1,∞) [2,∞) is given by f(x) = x +1/x , then f –1(x) is equal to

Suppose f(x) = (x + 1)² for x - 1. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to line y = x, then g(x) is equal to

Let function f : R → R be defined by f(x) = cos x for x∈ R. Then f is

If f(x) = x/1+x is defined as [0,∞) → [0, ∞), then f(x) is

∞

Find the range of f(x) = x² + x + 2/x² + x + 1.

Cos^-1 (cos7π/6) =

If tan^-1 (x - 1) + tan^-1 x + tan^-1 (x + 1) = tan^-1 3x, then x is equal to

If |x| > 1, then which one of the following is different from the other three?