If the determinant `|[b-c,c-a, a-b],[b^(prime)-c ', c^(prime)-a ', a^(prime)-b '],[ b' ' -c ' ' ,c' ' -a ' ', a' ' -b ' ']|=m|[a, b, c],[ a ', b ', c '],[ a ' ', b ' ' ,c ' ']|` , then the value of `m` is a. `0` b. `2` c. `1` d. `-1`

If |(b +c,c +a,a +b),(a +b,b +c,c +a),(c +a,a +b,b +c)| = k |(a,b,c),(c,a,b),(b,c,a)| , then the value of k, is 1 b. 2 c. 3 d. 4

If a+c , a+b , b+c are in G.P and a,c,b are in H.P. where a , b , c gt 0 , then the value of (a+b)/(c ) is

|{:(1+a," "b," "c),(" "a,1+b," "c),(" "a," "b,1+c):}|

The determinant |[y^2,-x y, x^2],[a, b, c],[ a ', b ', c ']| is equal to a. |[b x+a y, c x+b y],[ b^(prime)x+a ' y, c^(prime)x+b ' y]| b. |[a x+b y, b x+c y],[ a^(prime)x+b ' y, b ' x+c ' y]| c. |[b x+c y, a x+b y],[ b^(prime)x+c ' y, a^(prime)x+b ' y]| d. |[a x+b y, b x+c y],[ a^(prime)x+b ' y, b^(prime)x+c ' y]|

Let D_1=|[a, b, a+b], [c, d, c+d], [a, b, a-b]| and D_2=|[a, c, a+c], [b, d, b+d], [a, c, a+b+c]| then the value of |(D_1)/(D_2)| , where b!=0 and a d!=b c , is _____.

If (a + b + c + d) (a - b - c + d) = (a + b - c - d) (a - b + c - d) , then prove that a : b = c : d

If the value of the determinant |(a,1, 1) (1,b,1) (1,1,c)| is positive then a. a b c >1 b. a b c> -8 c. a b c -2

|{:(a-b, b-c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c):}|=

If a, b, c be in Arithmetic progression, then, then value of (a+2b-c)(2b+c-a)(a+2b+c) is

If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],[ q c ,r a, p b],[ r b, p c, q a]|i s (a) 0 (b) p a+q b+r c (c) 1 (d) none of these