Mathematics Tes...

If |z + 1 – i| = 1 and arg  then minimum value of |z – ω| is

If (1 + x + x²)ⁿ = a₀ + a₁ x + ... + a₂ x² + ... + a_2n x²ⁿ, then the value of a₀ + a₃ + a₆ + ... is

Let f : [0, 1) → [0, ∞) be a function such that 

If the equation x² + 2 (k + 1) x + 9k – 5 = 0 has only negative roots, then

 then the number of ways of selecting two numbers from the set {1, 2, 3, ....., 12} whose sum is divisible by 3 is

If n is a natural number ≥ 2, then roots of equation zⁿ = (1 + z)ⁿ lie on

The number of integral values of x satisfying the equation 2^x (4 – x) = 2x + 4

Let f : [– 10, 10] → R, where f(x) = sin x + [x²/a] and [.] denotes the greatest integer function be an odd function. Then set of values of parameter ‘a’ is/are

Consider the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, .... Then 1025th term will be

The set of values of a, such that the equation  has two distinct real roots is given by