AP ICET 26th April 2019 Shift-1

The numerically greatest term in the expansion of $$(2 + 3x)^5$$ when $$x = \frac{5}{4}$$ is

If $$A = \begin{bmatrix}3 & -4 \\1 & -1 \end{bmatrix}$$ then $$A^4 - A^3 + A^2 - A =$$

The value of x for which the matrix $$\begin{bmatrix}x-2 & 2x-3 & 3x-4 \\x-4 & 2x-9 & 3x-16 \\x-8 & 2x-27 & 3x-64 \end{bmatrix}$$ does not possess inverse, is

$$\lim_{x \rightarrow 0}\frac{e^x - 1}{\sqrt{1 + x} - 1} =$$

$$\lim_{x \rightarrow 3}\frac{x^4 - 81}{2x^2 - 5x - 3} =$$

In the adjoining figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If $$\angle DBC = 55^\circ$$ and $$\angle BAC = 45^\circ$$, then $$\angle BCD =$$

A and B are the end points of the longest line drawn in the circle with centre x. If C is a point on the circle such that AC = Ax = 3. Then the perimeter of $$\triangle ABC$$ is

A, B and C are three points on the circumference of a circle with centre O. If in $$\triangle ABC \angle B = 60^\circ$$ and $$\angle C = 70^\circ$$ then $$\angle BOC = $$

If A(3, 10), B (-3, 4) and C (5, 8) are the vertices of a $$\triangle ABC$$ and AD and CF are its medians. then the ratio of the length of AD to the length of CF is

If (-2, -1), (1, 0) and (4, 3) are three consecutive vertices of a parallelogram, then the sum of the lengths of the diagonals of that parallelogram is