AP ICET 17th September 2021 Shift-2

If 'p', 'q', 'r' are statements, then the contrapositive of $$p \rightarrow(q \rightarrow r)$$ is equivalent to

If $$f : ℝ \rightarrow ℝ$$ and $$g : ℝ \rightarrow ℝ$$ be defined by $$f(x) = 6x + 8$$ and $$g(x) = \frac{x - 2}{3}$$, then $$f o  g(\frac{1}{2}) =$$

The equation of a line parallel to the line $$2x - 3y = 1$$ and passing through the mid-point of the line segment joining the points (1 , 3) and (1 , -7) is

From the top of a building 60 meters high if the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of that tower, then the height (in meters) of that tower is

If $$x + 1$$ and $$x - 1$$ are factors of $$x^{3} + 2x^{2} + ax + b$$ , then (a , b) =

If the sum of the four consecutive odd numbers is 72, then the ratio of the smallest and the largest of these numbers is

If the first term of an infinite geometric progression is 2 and sum of all its terms is 6, then the $$5^{th}$$ term of that progression is

If the sum of the first 21 terms of an arithmetic progression is 357, then the $$11^{th}$$ term of that progression is

If $$A = \begin{bmatrix} 1 & -1 \\ 2 &  -1 \end{bmatrix}, B = \begin{bmatrix} a &  1 \\ b & -1 \end{bmatrix}$$ and $$(A+B)^{2} = A^{2} + B^{2}$$ , then a + b =

D , E , F are respectively the mid points of the sides BC , CA , AB of a $$\triangle$$ ABC. If the area of the quadrilateral AFDE formed is 14 square units, then area of $$\triangle$$ ABC, in square units, is