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 0 (b) 1 (c) 3 (d) infinite

find all the possible triplets (a_(1), a_(2), a_(3)) such that a_(1)+a_(2) cos (2x)+a_(3) sin^(2) (x)=0 for all real x.

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

Find the number of all three elements subsets of the set {a_1, a_2, a_3, a_n} which contain a_3dot

Find the set of all possible real value of a such that the inequality (x-(a-1))(x-(a^2+2))<0 holds for all x in (-1,3)dot

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 common ratio of G.P can be

The number of solutions of the equation sin^3xcosx+sin^2xcos^2x+sinxcos^3x=1 in the interval [0,2pi] is/are 0 (b) 2 (c) 3 (d) infinite

The number of values of a for which the lines 2x+y-1=0 , a x+3y-3=0, and 3x+2y-2=0 are concurrent is 0 (b) 1 (c) 2 (d) infinite

Find the number of ways of arranging 15 students A_1,A_2,........A_15 in a row such that (i) A_2 , must be seated after A_1 and A_3 , must come after A_2 (ii) neither A_2 nor A_3 seated brfore A_1

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 length sqrt(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)

Find the sum of first 24 terms of the A.P. a_1, a_2, a_3, , if it is know that a_1+a_5+a_(10)+a_(15)+a_(20)+a_(24)=225.