TS ICET 30th Sep 2020 Shift-2

A straight high way leads to the foot of a tower. Anil standing at the top of the tower observes a car at an angle of depression 30°. Six seconds later, the angle of depression of the car is found to be $$60^{\circ}$$. If the car is approaching the foot of tower with a uniform speed, the time taken by the car to reach the foot of that tower from this, the later point (in seconds) is

If $$a + b + c = 15$$ and $$a^{2} + b^{2} + c^{2} = 77$$ then $$ab + bc + ca =$$

If $$x^{4} + 6x^{3} + ax^{2} + 12x + b$$ is a perfect square, then 3a - 2b =

If the remainder when a certain integer $$x$$ is divided by 5 is 2, then each one of the following could also be an integer, except

The remainder if $$73 \times 74 \times 5 \times 76$$ is divided by 14 is

If $$\frac{4}{x + y} + \frac{3}{x - y} = 2, \frac{8}{x + y} - \frac{1}{x - y} = \frac{1}{2}$$, then ($$x$$, y) =

If the difference of $$\frac{7}{12}$$th of a positive integer and $$\frac{8}{15}$$ of the same positive integer is 6, then the number of distinct primes that divide that positive integer is

The sum of the infinite G.P. is

$$5, \frac{20}{7}, \frac{80}{49}, \frac{320}{343}$$, ...

The sum to infinite terms of a G.P, is 15 and the sum of their squares is 150. If r is the common ratio of the G .P. , then $$100 r^{2}$$ =

The numerically greatest term in the expansion of $$(2x - 3y)^{12}$$,
when $$x = 1, y = \frac{5}{3}$$ is