If `[x^2]+x-a=0` has a solution where `a in NN` and `a le 20.` then total number of different values of `'a'` can be

Consider the equation x^(2) + 2x - n = 0 m where n in N and n in [5, 100] . The total number of different values of n so that the given equation has integral roots is

If the equation x^(2)+ax+a=0 and x^(2)+2x+a=0 where a in R has atleast one common root,then number of different values of 'a' is

consider the equation x^(2)+x-n=0 where a is an integer lying between 1 to 100. Total number of different values of n so that the equation has integral roots,is

If a. 3^(tanx) + a. 3^(-tanx) - 2 = 0 has real solutions, x != pi/2 , 0 le x le pi, then find the set of all possible values of parameter 'a'.

IF [x^(2) - 2x + a]=0 has no solution, then find the values of a (where [*] represents the greatest integer).

IF [x^(2) - 2x + a]=0 has no solution, then find the values of a (where [*] represents the greatest integer).

IF [x^(2) - 2x + a]=0 has no solution, then find the values of a (where [*] represents the greatest integer).

If f(x) = cos x,0 le x le ( pi )/( 2) , then the real number 'c' of the mean value theorem is