Properties of Inequalities
Q. If n is a positive integer, then 2n>1+n√(2n−1).
Q. a, b, c are in H.P. and n does not lie between 0 and 1 then an+cn>2bn
Q. The area of an arbitrary triangle is less than one-fourth the square of its semi-perimeter.
Q. If log1√2sin x>0, xϵ[0, 4π] then the number of values of x which are integral multiples of π4 is
- None of these
Q. The sum of the hypotenuse and the altitude of a right angled triangle dropped on the hypotenuse exceeds the half-perimeter of the triangle.
Q. If a, b, c be three real numbers of the same sign then the value of ab+bc+ca lies in the interval
- [2, ∞)
- [3, ∞)
- (3, ∞)
- (−∞, 3)
Q. If a and b are two positive quantities whose sum is λ, then the minimum value of √(1+1a)(1+1b) is
All possible values of expression x2−4x+9 is