`a_1, a_2, a_3, in R-{0}` and `a_1+a_2cos2x+a_3sin^2x=0` for all `x in R ,` then

a_(1), a_(2),a_(3) in R - {0} and a_(1)+ a_(2)cos2x+ a_(3)sin^(2)x=0 " for all " x in R then

The number of all possible triplets (a_1,a_2,a_3) such that : a_1 + a_2cos2x + a_3sin^2x = 0 for all x is :

The number of all the possible triplets (a_1,a_2,a_3) such that a_1+a_2cos(2x)+a_3sin^2(x)=0 for all x is (a) 0 (b) 1 (c) 3 (d) infinite

Suppose a_1, a_2, are real numbers, with a_1!=0. If a_1, a_2,a_3, are in A.P., then (a) A=[(a_1,a_2,a_3),(a_4,a_5,a_6),(a_5,a_6,a_7)] is singular (where i=sqrt(-1) ) (b)The system of equations a_1x+a_2y+a_3z=0,a_4x+a_5y+a_6z=0,a_7x+a_8y+a_9z=0 has infinite number of solutions. (c) B=[(a_1,i a_2),(ia_2,a_1)] is non-singular (d)none of these

For an increasing A.P. a_1, a_2, a_n ifa_1+a_3+a_5=-12 and a_1a_3a_5=80 , then which of the following is/are true? a. a_1=-10 b. a_2=-1 c. a_3=-4 d. a_5=+2

A sequence of no. a_1,a_2,a_3 ..... satisfies the relation a_n=a_(n-1)+a_(n-2) for nge2 . Find a_4 if a_1=a_2=1 .

Let a_1,a_2,a_3…… ,a_n be in G.P such that 3a_1+7a_2 +3a_3-4a_5=0 Then find common ratio of G.P.

Let a_1, a_2, a_3.......... be in A.P. and h_1,h_2,h_3..... ,in H.P. If a_1=2 = h_1, and a_30=25=h_30 then a_7h_24+ a_14 + a_17=

If cos4x=a_0+a_1cos^2x+a^2cos^4x is true for all values of x in R , then the value of 5a_0+a_1+a_2 is_______

For all real values of a_0.a_1,a_2,a_3 satisfying a_0x+a_1x^2/2+a_2x^3/3+a_3x^4/4=0 , the equation a_0+a_1x+a_2x^2+a_3x^3=0 has a real root in the interval