AP ICET 10th September 2020 Shift-2

A flagstaff of 5 mts high stands on a building of 25 mts high. For an observer at a height of 30 mts, the flagstaff and the building subtend equal angles. Then the distance of the observer (in mts) from the top of the flag staff is

Number of positive integers $$x$$ for which $$f(x) = x^3 - 8x^2 + 20x - 13$$ is a prime number is

If $$x + \frac{1}{x} = 5$$, then $$x^4 + \frac{1}{x^4} =$$

The value of $$a + b$$ for which the polynomial $$3x^3 - ax^2 - 74x + b$$ is a multiple of $$x^2 + 2x - 24$$ is

If $$f(x) = x^2 + 5x + p$$ and $$g(x) = x^2 + 3x + q$$ have a common factor $$Q(x)$$, then $$Q(x$$) =

Atal's age 3 years ago was three times the present age of Amit. At present Anil's age is twice the age of Amit. Anil is 11 years younger than Atal. Then the present age of Anil (in years) is

A shopkeeper sells an item at a profit of 15%. If he reduces the price of that item by Rs. 200, he makes a loss of 10% on it. Then the cost price of that item (in Rs.) is

A manufacturer of TV sets produced 600 sets in third year and 700 sets in the seventh year. If the production of sets increases uniformly by a fixed number every year, the total production in first seven years is

A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are $$2 \frac{1}{2}$$ m apart, the length of the wood (in cms) required for the rungs is

If the coefficients of $$x^7$$ and $$x^8$$ in the expansion of $$\left(3 + \frac{x}{2}\right)^n$$ are equal, then n =