Which of the following is correct option
`[(-6a^3b^5)(2a^2b^3)]/(-18a^4b^8c^3)=`

`A.(-2a^2b)/(3c^3)`
`B.(2a)/(3c^3)`
`C.(2a^2b)/(3bc^3)`
`D.(-2ab)/(3c^3)`

Simplify the following: (6) (i) (a^(3)b^(2)c-ab^(3)c)-(3abc^(3)-a^(3)b^(2)c)-(4ab^(3)c+2abc^(3))

If a+b+c=0, then which of the following are correct? 1. a^(3) + b^(3) + c^(3) = 3abc 2. a^(2) + b^(2) + c^(2) = -2(ab + bc + ca) 3. a^(3) + b^(3) + c^(3) = -3ab(a+b) Select the correct answer using the code given below

The value of x satisfying the equation (6x+2a+3b+c)/(6x+2a-3b-c)=(2x+6a+b+3c)/(2x+6a-b-3c)quad is(ab)/(c)(b)(2ab)/(c)(c)(ab)/(3c) (d) (ab)/(2c)

Factorize the following 3,a+b+c,a^(3)+b^(3)+c^(3)a+b+c,a^(2)+b^(2)+c^(2),a^(4)+b^(4)+c^(4)a^(2)+b^(2)+c^(2),a^(3)+b^(3)+c^(3),a^(5)+b^(5)+c^(5)]|

|(1,a^(2)+bc,a^(3)),(1,b^(2)+ac,b^(3)),(1,c^(2)+ab,c^(3))|=-(a-b)(b-c)(c-a)(a^(2)+b^(2)+c^(2))

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

If a, b, c and d are in proportion, then show that (a^(3)+3ab^(2))/(3a^(2)b+b^(3))=(c^(3)+3cd^(2))/(3c^(2)d+d^(3))

A library has a copies of one book, b copies each of two books, c copies each of three books, a single copy of d books. The total number of ways in which these books can be arranged in a shelf is equal to a. ((a+2b+3c+d)!)/(a !(b !)^2(c !)^3) b. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^3) c. ((a+b+3c+d)!)/((c !)^3) d. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^)