The number of integral triplets (a, b, c) such thet `a+b cos 2x+c sin^(2)x=0` for all x, is

The number of all triplets (a_1,a_2,a_3) such that a_1 + a_2 cos 2x + a_3 sin^2 x = 0 for all x is : (A) 0 (B) 1 (C) 3 (D) Infinite

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

The number of all the possible triplets (a_(1),a_(2),a_(3)) such that a_(1)+a_(2)cos(2x)+a_(2)sin^(2)(x)=0 for all x is 0 (b) 1(c)3(d) infinite

integral of 1/(a sin x+b cos x+c)

Statement-1: If a, b, c are distinct real numbers, then a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x for each real x. Statement-2: If a, b, c in R such that ax^(2) + bx + c = 0 for three distinct real values of x, then a = b = c = 0 i.e. ax^(2) + bx + c = 0 for all x in R .

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

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

integral of 1/(a sin x+b cos x)

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

Integral of form (a sin x+b cos x+c)/(p cosx+q sin x+r)