If `a^2+b^2+c^2=1,t h e na b+b c+c a` lie in the interval `[1/3,2]` b. `[-1,2]` c. `[-1/2,1]` d. `[-1,1/2,]`

If A=2sin^2theta-cos2theta,t h e nA lies in the interval (a) [-1,3] (b) [1,2] (c) [-2,4] (d) none of these

If a^2+b^2=1 t h e n (1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+i b

If a+b+c=0a n da^2+b^2+c^2=1, then the value of a^4+b^4+c^4 is 1 b. 4 c. 1/2 d. 1/4

Suppose a ,b, and c are in A.P. and a^2, b^2 and c^2 are in G.P. If a

If a+b+c=2,a^(2)+b^(2)+c^(2)=1 and abc = 3 then 1/a+1/b+1/c is equal to

If a+b+c=0 and a^2+b^2+c^2=1, then (a) a b+b c+c a=1/2 (b) a b+b c+c a=-1/2 (c) a^4+b^4+c^4=1/2 (d) a^4+b^4+c^4=3/2

If 4a^2+b^2+2c^2+4a b-6a c-3b c=0, then the family of lines a x+b y+c=0 may be concurrent at point(s) (-1,-1/2) (b) (-1,-1) (-2,-1) (d) (-1,2)

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a ,b ,c and a^prime ,b^(prime),c ' from the origin, then a. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0 b. 1/(a^2)-1/(b^2)-1/(c^2)+1/(a^('2))-1/(b^('2))-1/(c^('2))=0 c. 1/(a^2)+1/(b^2)+1/(c^2)-1/(a^('2))-1/(b^('2))-1/(c^('2))=0 d. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0

If a ,b and c are in A.P. and b-a ,c-b and a are in G.P., then a : b : c is (a). 1:2:3 (b). 1:3:5 (c). 2:3:4 (d). 1:2:4

If a_1x^3 + b_1x² + c_1x + d_1 = 0 and a_2x^3 + b_2x^2+ c_2x + d_2 = 0 have a pair of repeated common roots, then prove that |[3a_1,2b_1,c_1],[3a_2,2b_2,c_2],[a_2b_1-a_1b_2,c_1a_2-c_2a_1,d_1a_2-d_2a_1]|=0