Relations and F...

Let $$\displaystyle f\left ( x \right ) = x^{3} + 2x^{2} + 3x + 4$$, then the equation $$\displaystyle \frac{1}{x - f\left ( 1 \right )} + \frac{2}{x - f\left ( 2 \right )} + \frac{3}{x - f\left ( 3 \right )} = 0$$, has

If ,$$(x-1, y+2)= (7, 5)$$ then values of $$x$$ and $$y$$ are

Ordered pairs (a, 3) and (5, x) are equal ,the values of $$a$$ and $$x$$ are

If $$(x, y) = (3, 5)$$ ; then values of $$x$$  and $$y $$ are 

Given $$M = (0, 1, 2)$$ and $$N = (1, 2, 3)$$. Find $$(N - M) \times (N \cap M)$$

If $$A = \{5, 7\}, B= \{7, 9\}$$ and $$C = \{7, 9, 11\},$$ find $$(A \times B) \cup (A \times C)$$

If $$n(A) = 4$$ and $$n(B) = 5$$, then $$n(A \times  B) = $$

If $$R$$ be a relation defined from $$\displaystyle A=\left \{ 1,2,3,4 \right \}$$ to $$\displaystyle B=\left \{ 1,3,5 \right \},i.e.\left ( a,b \right )\in R$$ iff $$a<b$$ then $$\displaystyle R o R^{-1}$$ is

A relation $$R$$ is defined on the set $$Z$$ of integers as follows: R=$$(x,y)$$ $$\displaystyle \in {R}:x^{2}+y^{2}= 25$$. Express $$R$$ and $$\displaystyle R^{-1}$$ as the sets of ordered pairs and hence find their respective domains.

The value of $$b$$ and $$c$$ for which the identify $$f (x + 1) - f (x) = 8x + 3$$ is satisfied, where $$f (x)\, =\, bx^{2}\, +\, cx\, +\, d$$, are -