AP ICET 10th September 2020 Shift-1

The top of a tower makes angles of elevation $$30^\circ$$ and $$45^\circ$$ at the two points A, B which are collinear with the foot of the tower on the level ground. If AB = 100 m, then the height of the tower, (in meters) is

If $$x + y + z = 8, x^3 + y^3 + z^3 - 3xyz = 128$$ then $$x^2 + y^2 + z^2 =$$

A polynomial of degree 4, with leading coefficient one and with rational coefficients for which $$2 - \sqrt{3} - \sqrt{5}$$ is a zero is

If $$px + q$$ is the remainder when $$x^4 + 7x^3 + 13x^2 + 4x - 3$$ is divided by $$x^2 + 2x + 5$$, then $$q - p =$$

A polynomial in $$x$$ leaves remainders -1 and 7 when it is divided by $$x + 1$$ and $$x - 3$$ respectively. If the same polynomial is divided by $$x^2 - 2x - 3$$ then the remainder will be

The present age of a father is 4 times that of his son. After 10 years father's age is twice that of his son. Then the difference of their present ages is

If $$\frac{24}{x + y} + \frac{30}{x - y} = 7$$ and $$\frac{30}{x + y} - \frac{9}{x - y} = 1$$, then $$2x + 4y =$$

If the sum to 2n terms of the arithmetic progression 2, 5, 8, ... . .. is equal to the sum to n terms of the arithmetic progression 57, 59, 61. ... ... then n =

In a geometric progression with positive common ratio, the ratio of $$13^{th}$$ term to the $$7^{th}$$ term is 27 : 1 then the ratio of its $$9^{th}$$ term to $$16^{th}$$ term is

If the constant term in the binomial expansion of $$\left(2x^2 - \frac{1}{3x}\right)^9$$ is $$\frac{p}{q}$$ where GCD of (p, q) = 1, then q - p =