If `A=[(n,0 ,0),( 0,n,0),( 0, 0,n)]` and `B=[(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3)]` , then `A B` is equal to (A) `B` (B) `n B` (C) `B^n` (D) `A+B`

if D_1=|{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}| and D_2=|{:(a_1+2a_2+3a_3,2a_3,5a_2),(b_1+2b_2+3b_3,2b_3, 5b_2),(c_1+2c_2 + 3c_3 , 2c_3 , 5c_2):}| then D_2/D_1 is equal to :

If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3)|=0 and vectors (1,a,a^2),(1,b,b^2) and (1,c,c^2) are non coplanar then the product abc equals (A) 2 (B) -1 (C) 1 (D) 0

If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^2)|=0 and vectors (1,a,a^2),(1,b,b^2) and (1,c,c^2) are hon coplanar then the product abc equals (A) 2 (B) -1 (C) 1 (D) 0

If a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0 and |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 , then the given system has, 1) more than two solutions 2) one trivial and one non trivial solutions 3) no solution 4) only trivial solution (0, 0, 0)

If A=[(1,2),(0,1)], then A^n= (A) [(1,2n),(0,1)] (B) [(2,n),(0,1)] (C) [(1,2n),(0,-1)] (D) [(1,n),(0,1)]

|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 then the system of equations a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0 has

Let A = [(1,0),(2,3)] and A^(n) = [(a, b),(c,d)] then lim_(n to oo) (b + c)/(a + d) =

If A-B=pi//4 , then (1+t a n A)(1-t a n B) is equal to 2 b. 1 c. 0 d. 3

If x,a_1,a_2,a_3,…..a_n epsilon R and (x-a_1+a_2)^2+(x-a_2+a_3)^2+…….+(x-a_(n-1)+a_n)^2le0 , then a_1,a_2,a_3………a_n are in (A) AP (B) GP (C) HP (D) none of these

If (1+x)^n=a_0+a_1x+a_2x^2+....+a_nx^n , then (a_0-a_2+.....)^2+(a_1-a_3+.....)^2 is equal to (A) 3^n (B) 2^n (C) ((1-2^n)/(1+2^n)) (D) none of these