TS ICET 2018 Shift 2

A person walking towards the foot of the mountain observes the angle of elevation of its peak to the $$30^\circ$$ and $$60^\circ$$ respectively. If the distance between two points A, B of observation is $$\sqrt{3}$$ km then the height of the mountain in meters is

$$x + \frac{1}{x} = 5 \Rightarrow x^4 + \frac{1}{x^4} =$$

For two polynomials p(x) and q(x) the highest commonfactor is (x - 2) and the least common multiple is $$x^3 - 9x^2 + 26x - 24$$. If $$P(x) = x^2 - 6x + 8$$ then q(x) =

If the polynomial $$x^3 + 10x^2 + ax + b$$ is exactly divisible by (x - 1) and (x + 2) then a - b =

If a polynomial p(x) leaves remainders 6 and 4 respectively when divided by (x - 2) and (x - 3) then the remainders when p(x) is divided by $$(x^2 - 5x + 6)$$ will be

The sumof a two digit number and the numberobtained by reversing the order of its digits is 121 and the digits differ by 3. The largest of such numbers is

If $$\frac{3}{x + y} + \frac{2}{x - y} = 2$$ and $$\frac{9}{x + y} - \frac{4}{x - y} = 1$$ then x : y =

The $$r^{th}$$ term of an arithmetic progression whose sum of first n terms is $$2n + 3n^2$$ is

If the $$6^{th}$$ and $$13^{th}$$ terms of a geometric progression are 24 and $$\frac{3}{16}$$ respectively, then its $$25^{th}$$ term is

The coefficient of $$x^{n - 1}$$ in the product $$(x + 1)(x + 2)(x + 3).....(x + n)$$ is