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^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 2sec^2A-sec^4A-2cos e c^2A+cos e c^4A=(15)/4,t h e n tan A is equal 1//sqrt(2) (b) 1/2 (c) 1/2sqrt(2) (d) -1/(sqrt(2))

If A=[0 1 2 1 2 3 3a1]a n d A_1=[1//2 12//12//-4 3c5//2-3//2 1//2] , then the values of a anti c are equal to 1,1 b. 1,-1 c. 1,2 d. -1,1

If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0 are in the ratio a. 1/2(-1+sqrt(3)) b. 1/2(1-isqrt(3)) cdot1/2(-1-isqrt(3)) d. 1/2(1+isqrt(3))

If A=[[a+i b, c+i d],[-c+i d, a-i b]]a n da^2+b^2+c^2+d^2=1,t h e nA^(-1) is equal to a. [[a+i b,-c+i d],[-c+i d, a-i b]] b. [[a-i b,-c-i d],[-c-i d, a+i b]] c. [[a+i b,-c-i d],[-c+i d, a-i b]] d. none of these

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_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 roots common, 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

If a, b, c are the sides of a scalene triangle such that |[a , a^2 , a^(3)-1 ],[b , b^2 , b^(3)-1],[ c, c^2 , c^(3)-1]|=0 , then the geometric mean of a, b c is

If y^2=4b(x-c) and y^2 =8ax having common normal then (a,b,c) is (a) (1/2,2,0) (b) (1,1,3) (c) (1,1,1) (d) (1,3,2)

If a^(2) + b^(2) + c^(3) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to