The number of all the possible triplets `(a_1,a_2,a_3)` such that `a_1+a_2cos(2x)+a_2sin^2(x)=0` for all `x` is 0 (b) 1 (c) 3 (d) infinite

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

If p(x),q(x) and r(x) be polynomials of degree one and a_1,a_2,a_3 be real numbers then |(p(a_1), p(a_2),p(a_3)),(q(a_1), q(a_2),q(a_3)),(r(a_1), r(a_2),r(a_3))|= (A) 0 (B) 1 (C) -1 (D) none of these

Three rectangles A_1, A_2 and A_3 have the same area. Their lengths a_1, a_2 and a_3 respectively are such that a_1

If a_1,a_2,a_3 are in G.P. having common ratio r such that sum_(k=1)^n a_(2k-1)= sum_(k=1)^na_(2k+2)!=0 then number of possible value of r is (A) 1 (B) 2 (C) 3 (D) none of these

a_1, a_2, a_3, in R-{0} and a_1+a_2cos2x+a_3sin^2x=0fora l lx in R , then (a)vector vec a=a_1 hat i+a_2 hat j+a_3 hat ka n d vec b=4 hat i+2 hat j+ hat k are perpendicular to each other (b)vector vec a=a_1 hat i+a_2 hat j+a_3 hat ka n d vec b=- hat i+ hat j+2 hat k are parallel to each other (c)vector vec a=a_1 hat i+a_2 hat j+a_3 hat k is of lengthsqrt(6) units, then one of the ordered triple (a_1, a_2, a_3)=(1,-1,-2) (d)are perpendicular to each other if 2a_1+3a_2+6a_3=26 ,t h e n|a_1 hat i+a_2 hat j+a_3 hat k|i s2sqrt(6)