Mathematics Tes...

If x is real, the expression  takes all values in the interval

If the coefficients of x³ and x⁴ in the expansion of (1 + ax + bx²) (1 – 2x)¹⁸ in powers of x are both zero, then (a, b) is equal to

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, then all possible values of a lie in the interval:

The letters of word ‘SOCIETY’ are placed at random in a row. The probability that three vowels come together, is

If a, b and c are all different form zero such that  then which is not true for the matrix 

The value of sin  is equal to

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is

If α, β ≠ 0, and f(n) = αⁿ + βⁿ and  = K(1 - α)²(1 - β)²(α - β)², then K is equal to

The function f(x) satisfying {f(x)}² + 4f(x)f'(x) + {f'(x)}² = 0 is given by