TS ICET 20th August 2021 Shift-1

Seen from the top of a tower 100 meters tall the angles of depression of two points A and B on the ground which are on the opposite sides of the tower are $$30^{\circ}$$ and $$60^{\circ}$$ respectively. The distance AB in meters is:

If a polynominal in $$x$$ leaves remainder -2 and 19 when divided by $$(x + 3)$$ and $$(x - 4)$$ then the remainder it leaves when it is divided by $$x^{2} - x -12$$ is

The roots of the equation $$\sqrt{6} x^{2} - 5x + \sqrt{6} = 0$$ are

If $$(x - 5)$$ is a factor of the polynominal $$p(x)$$, then a factor of the polynomial $$p(x^{3} - 3)$$ is

A number when divided by 5, leaves 3 as remainder. When the square of that number is divided by 5, then the remainder will be

Three pens and four pencils cost Rs.18. Four pens and three pencils cost Rs.17. Then, the cost of 14 pens and 14 pencils (in rupees) is

If $$\mid x - 2\mid + \mid x - 3\mid < 4$$, then the range of $$x$$ is

The sum of n terms of a progression is $$S_{n} = 5n^{2} + 2n$$. Then, the $$n^{th}$$ term $$t_{n}$$?

If the $$5^{th}$$ and $$9^{th}$$ terms of a Geometric Progression are $$\frac{1}{9}$$ and $$\frac{1}{729}$$, then the first term of that Geometric Progression is

The coefficient of $$x^{7}$$ in the binomial expansion of $$\left(x^{3} - \frac{2}{x^{2}}\right)^{5}$$ is