If the equation `cot^4x-2cos e c^2x+a^2=0` has at least one solution, then the sum of all possible integral values of `a` is equal to 4 (b) 3 (c) 2 (d) 0

The equation tan^4x-2sec^2x+a=0 will have at least one solution if A) 1 < a ≤ 4 B) a ≥ 2 C) a ≤ 3 D) None of these

The equations x^2 +3x+5=0 and ax^2+bx+c=0 have a common root. If a,b,c in N then the least possible values of a+b+c is equal to

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

Let the quadratic equation (c-5)x^2 -2cx+c-4=0 has one root in (0,2) and other root in (2,3) then find the number of intergral values of c in solution set (a) 18 (b) 12 (c) 11 (d) 10

The number of positive integral solutions of x^4-y^4=3789108 is a. 0 b. 1 c. 2 d. 4

Show that the equation x^9 - 5x^5 + 4x^4 + 2x^2 + 1 =0 has at least 6 imaginary solutions.

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

The minimum value of e^(2x^2-2x+1)sin^2x is e (b) 1/e (c) 1 (d) 0

If cos(x+pi/3)+cos x=a has real solutions, then (a) number of integral values of a are 3 (b) sum of number of integral values of a is 0 (c) when a=1 , number of solutions for x in [0,2pi] are 3 (d) when a=1, number of solutions for x in [0,2pi] are 2

If the equation 4y^(3) - 8a^(2)yx^(2) - 3ay^(2)x +8x^(3) = 0 represents three straight lines, two of them are perpendicular, then sum of all possible values of a is equal to