TS ICET 28th July 2022 Shift-1

If A, B, C are three subsets of a set X, then
{(A - B) - C} - {A - (B - C)} =
(Here A' = X - A)

Let U = {x $$\mid$$ x is a natural number $$\leq$$ 20}. Define
A = {x $$\mid$$ x $$\in$$ U and x is a prime number},
B = {x $$\mid$$ x $$\in$$ U and x is an even number},
and C = {x $$\mid$$ x $$\in$$ U and x is a multiple of 3 }. Then $$(A \cup B) \cap C$$ =

If the roots of the equation $$x^{4} - 10x^{3} + 35x^{2} - 50x + 24 =0$$ are 1, 2, 3 and 4, then the roots of the equation $$24x^{4} - 50x^{3} + 35x^{2} - 10x + 1 = 0$$ are

How much is to be added to the polynomial $$(x + 2)(x + 4)(x + 6)(x + 8)$$ to make it a perfect square?

If $$(x - 1)$$ and $$(x - 2)$$ are the factors of $$x^{4} - 5x^{3} + 4x^{2} + ax + b$$ then, $$\frac{a}{b}$$ =

If$$(x^{2} - 3x + 2)$$ is a factor of $$x^{3} - 6x^{2} + ax+ b$$ then $$a^{2} + b^{2} =$$

The digits of a 3 digit number are in strict descending order. Then the largest prime that always, divides the difference of the given 3-diigit number and the 3 digit number obtained by reversing the digits of the given number is

If length and breadth are reduced by 2 units each, area of rectangle reduces by 22 sq. units, then the perimeter of the rectangle is

If the solution of the system of equations
$$\frac{x}{4} + 2y = 7; \frac{19}{x+\frac{y}{4}} = 4$$ is $$x=\alpha$$ and $$y=\beta$$, then $$\alpha^{2} + \beta^{2}$$

The third term of Geometric Progression is 4; then the product of its first 5 terms in that Geometric Progression is