Write `3\ x\ a\ x\ a\ x\ 2\ x\ b\ x\ b\ x\ b\ x\ c\ x\ c\ x\ c\ x\ c` in the exponential form.

If f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2|,t h e n prove that f^(prime)(x)=3x^2+2x(a^2+b^2+c^2)dot

The determinant |y^2-x y x^2a 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|

Find x in terms of a , b and c : (a)/(x - a) + (b)/(x - b) = (2 c)/(x - c) , x - a , b , c

(x-a) (x-b) (a-b) +(x-b) (x-c) (b-c) +(x -c) (x -a) (c-a) is equal to which of the following?

The following steps are involved in finding the value of ((x^a)/(x^b))((x^b)/(x^c))((x^c)/(x^a)) . Arrange them in sequential order. (A) x^0=1 (B) x^(a-b+b-c+c-a) (C) ((x^a)/(x^b))((x^b)/(x^c))((x^c)/(x^a))=x^(a-b).x^(b-c).x^(c-a)

Let a,b,c be even natural numbers, then /_\=|(a-x, a, a+x),(b-x, b, b+x),(c-x, c, c+x)| is a multiple of (A) 2 (B) 5 (C) 3 (D) none of these