TS ICET 28th July 2022 Shift-1

A local train arrives at station A for every 45 minutes when Mr X came to station A, an announcement says that a local train has departed from station A, 18 minutes back and the next train will come at 11:41 AM. Then the time of the arrival of Mr.X to station A is

Five persons A, B, C, D, E are sitting around a table facing the centre. A sits to the left of E and C sits to the right of B. D is between A and C then the person on the right of E is

For real numbers a and b define $$a \triangle b = a^{2} - b^{2} + ab$$. Then the number of real values of a such that $$a \triangle a = 4$$ is

For the natural numbers $$x$$ and y, define
$$x * y = \sqrt{xy} + \frac{1}{\sqrt{xy}}$$ and $$x \odot y = \sqrt{xy} - \frac{1}{\sqrt{xy}}$$, then $$\frac{(3*4)*(3 \odot 4)}{(3*4)\odot(3 \odot 4)}$$ =

If $$x \oplus y = (x + y + 1)^{2}$$ and $$x \ominus y = (x - y + 2)^{2}$$, then $$(1 \oplus 4) \ominus (2 \oplus 5)$$ =

$$(25x^{2})^{\frac{1}{5}}.(5x^{4})^{\frac{2}{5}}.\left(125x^{\frac{27}{5}}\right)^{-\frac{1}{3}}$$=

$$\frac{\left(a+\frac{1}{b}\right)^{x}\left(a-\frac{1}{b}\right)^{y}}{\left(b +\frac{1}{a}\right)^{x}\left(b -\frac{1}{a}\right)^{y}}$$=

If $$x:y = 3:4$$, then $$(4x + 5y): (5x - 2y)$$ =

The sum of the cubes of three positive integers is 8072. If the ratio of the first and the second as also of the second and the third is as 3 : 2. Then the sum of the three numbers is

$$\frac{4+3\sqrt{3}}{7+3\sqrt{3}} = a + \sqrt{b}$$, then $$a - \sqrt{b} =$$