AP ICET 2022 Question Paper Shift-1 (25th July)

The contradiction, among the following when p, q are two statements is

Let N and Z denote the set of all natural numbers and the set of all integers respectively. The function $$f : N \rightarrow Z$$ defined by $$f(n) = \frac{n}{2}$$ or $$-\left(\frac{n - 1}{2}\right)$$, according as n is even or odd, is

The equation of the line wi1ich is perpendicular to the line L, and passing through the point (1, 1) where L is the line making intercepts $$\frac{1}{4}$$ and $$\frac{1}{5}$$ respectively on the x - axis and y- axis, is

$$\frac{\cos \theta}{\sec \theta - 1}+\frac{\cos \theta}{\sec \theta + 1} =$$

The ordered pair $$(\alpha, \beta)$$ such that the polynomial $$x^4 + \alpha x^3 + \beta x^2 - 12x + 16$$ bas the quadratic expression $$x^2 + x - 2$$ as a factor is

The angles of elevation of the top of a tower and the top of a flagstaff on it are observed to be $$30^\circ$$ and $$60^\circ$$ respectively from a point P on the level ground 200 meters away from the foot of the tower. Then the length of the flagstaff (in meters) is

If $$a_1 < a_2 < a_3 < ....... < a_9$$ are nine arithmetic means between 5 and 65 then $$a_7 =$$

$$(\sqrt{3} - 1)^6 + (\sqrt{3} + 1)^6 =$$

$$\lim_{x \rightarrow 0}\frac{1 - \cos \alpha}{x^2} =$$

Given that A (2, 2), B (6, 1) and C (7, 3) are the vertices of a triangle, the length of the median through A is