The number of real values of ` x` for which `(a/b) = x - 2x^2 - 4 , ` where ` a, b>0 `

The number of values of the pair (a, b) for which a(x+1)^2 + b(-x^2 – 3x - 2) + x + 1 = 0 is an identity in x, is

The number of real solutions of |2x-x^2-3|=1 is (a) 0 (b) 2 (c) 3 (d) 4

The number of integral values of b for which the equation (3sin x-4cos x)^(2)-(b^(2)+b-5)|3sin x-4cos x| + b^(3)+3b^(2)+2b+6=0 ,has real solution is

Let f(x)=2x+1. Then the number of real number of real values of x for which the three unequal numbers f(x),f(2x),f(4x) are in G.P.is 1 b.2 c.0 d.none of these

Let f(x)=2x+1. Then the number of real number of real values of x for which the three unequal numbers f(x),f(2x),f(4x) are in G.P. is 1 b. 2 c. 0 d. none of these

Let f(x)=2x+1. Then the number of real number of real values of x for which the three unequal numbers f(x),f(2x),f(4x) are in G.P. is 1 b. 2 c. 0 d. none of these

Let f(x)=2x+1. Then the number of real number of real values of x for which the three unequal numbers f(x),f(2x),f(4x) are in G.P. is 1 b. 2 c. 0 d. none of these

Number of integral values of 'b' for which inequality (a^2 + 1)x^2 + 4(a+b)x +2 < 0 is true for atleast one 'x' and for all Real a, is (A)0 (B) 1 (C) 2 (D)3

The number of values of the triple (a,b,c) for which a coss 2x+bsin^2 x+c =0 is satisfied by all real x, is

The number of real roots of the equation |[a, a,x],[b, x, b], [x,x,x]|=0 where a and b are distinct non-zero real numbers, is