TS ICET 19th August 2021 Shift-1

A person comes for an interview at 10.10 am which was 30 minutes before scheduled time, which in fact was already delayed by 35 minutes. Then the time at which the interviews started is

Four bells A, B, C & D ring regularly at intervals of 25 minutes, 35 minutes, 40 minutes and 80 minutes respectively. If all the bells rang together at 10 am on Sunday when will they ring again simultaneously?

For the integers m, n define
$$m \alpha n = m + 2n, m \beta n= 2m + n$$ and $$m \gamma n = m^2 + n^2$$ then $$\left((-5)\alpha 6\right)\left((-2)\gamma (-3)\right) = $$

For $$a, b, \in N$$ and $$b > 1$$ define * by $$a * b = a \left(1 + \frac{1}{b} + \frac{1}{b^2} + ....\right)$$. Then $$(2 * 3)* 2 =$$

If $$a \otimes b = (a - b - 1)^2$$, and $$a \oplus b = \frac{ab}{3}$$ then $$(2 \otimes 5) \oplus 9 = $$

If $$\left(\sqrt[3]{\frac{3}{2}}\right)^x = \left(\frac{9}{4}\right)^{2x - 7}$$, then x =

$$\left\{4 - \left\{x^2 + \left(3 - \frac{1}{x^2}\right)^{-1}\right\}^{-1}\right\}^{-1} = $$

28 litres of a mixture contains milk and water in the ratio of 3 : 4. If 8 litres of pure milk is added to this mixh1re, then the ratio of water to milk in the resulting mixnire is

At a certain party the ratio of gents to ladies was 4 : 3. After some time 6 men and 4 women left the party and the ratio of men to women was 21 : 16. How many people were present in the patty initially?

The smallest number among
$$x = 3\sqrt{7} - \sqrt{61}, y = 6 - \sqrt{34}, z = 5 - \sqrt{23}$$ and $$w = 2\sqrt{3} - \sqrt{10}$$ is