TS ICET 30th September 2020 Shift-1

An express train departs from station X at 5.00 am with maximum allocated speed 120 kmph. The train is scheduled to arrive station Z and return to station Y to halt at night. At what time the train will reach station Y, if the total waiting time between the stations of boarding is 45 minutes?

Eight persons A,B,C,D,E,F,G and H are sitting in a straight line facing North but not necessarily in the same order. F sits fifth to the right of A. D sits fifth to the right of E. E sits to the immediate right of A. H sits towards the left of D. B sits third to the right of G. G is an immediate neighbour of A . Which of the following is definitely true?

Let $$\& x \& = 5x - 7$$ and $$*y*z* = \frac{3y}{z}$$. If $$P = *7*15*$$, then $$\& P \& =$$

If $$a*b = (a + b) + (a - b)^{2}$$ and $$a \triangle b = (a + b)^{2} - (a - b)$$ then $$(3 \triangle 5):(3 * 5) =$$

For real numbers $$x$$, y, define two binary operations $$\odot$$ and $$\ominus$$ by

$$x \odot y = x^{2} + y^{2} + 3xy - 5$$
$$x \ominus y = 3x + 4y + 5xy + 6$$ then
$$(1 \odot 2) \ominus (2 \odot 3) = $$

The value of $$\frac{(37 \times 37 \times 37) + (8 \times 8 \times 8)}{37 \times 37 - 296 + 64}$$

$$\left[3 \times 2^{x} + 2^{x+2} + 2^{x+3}\right]$$ is always divisible by

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

Three persons A, B and C invested their annual savings in a bank at 20% rate of simple interest per annum. If each of them gets an equal amount after 10, 15 and 20 years, respectively. Then the ratio of their initial investments is

If $$x = \sqrt[4]{21}, y = \sqrt[5]{23}$$, then which of the following is correct?