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.

a x a x 3 x b x b x 2 x c x c= .............

Write down each of the following in exponential form: (i) 4a^3\ x\ \ 6a b^2\ x\ \ c^2 (ii) 5x y\ x\ 3x^2y\ x\ 7y^2 (iii) a^3x\ 3a b^2x\ 2a^2b^2

Let A = { x: x is a multiple of 2, x B = {x:x is a multiple of 3,x C = { x : x is a prime x Write each one of the sets A ,B ,C in Roster 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

If a , b , c are real numbers, then find the intervals in which f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2| is increasing or decreasing.

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|

If f(x)=|(0, x-a, x-b), (x+a, 0, x-c),(x+b, x+c, 0)| , then

If f(x)=|[x+a^2 , a b , a c],[a b, x+b^2,b c],[ ac,b c, x+c^2]| . then f^(prime)(x)

If A={x in C : x^2=1}\ a n d\ B={x in C : x^4=1} , then write A-B\ a n d\ B-Adot

If x ^(2) +bx+b is a factor of x ^(3) +2x ^(2)+2x + c (c ne 0), then b+c is :