TS ICET 2017
For the following questions answer them individually
If the coefficients of $$x^7$$ and $$x^8$$ are equal in the binomial expansion of $$\left(3 + \frac{x}{2}\right)^n$$, then n =
Let $$ A = \begin{bmatrix}0 & \alpha \\\beta & 0 \end{bmatrix}, \alpha \neq 0, \beta \neq 0$$. If $$A^3 + A = 0$$, then $$\alpha \beta =$$
$$f(\theta) = \begin{bmatrix}\sin \theta & -\cos \theta \\\cos \theta & \sin \theta \end{bmatrix} \Rightarrow f^{-1}(\theta) = $$
$$\lim_{x \rightarrow \infty} \frac{(1 + x)^{10} + (2 + x)^{10} + ........ + (5 + x)^{10}}{100 + x^{10}} =$$
$$y = \tan^{-1}\left(\frac{\cos x + \sin x}{\cos x - \sin x}\right) \Rightarrow \frac{dy}{dx} =$$
In the adjacent diagram ABCD is a quadrilateral; E and F are the foot of the perpendiculars drawn from B and Don AC. If AC = 8, EC = 3, BC = and area of ABCD = 20, then DF =
P, A, B are three points on a circle and PT is a tangent to the circle. If $$\angle APB = 45^\circ$$ and $$\angle TPB = 60^\circ$$, then $$\angle ABP =$$
The radius of the circumcircle of the triangle with vertices (0, 0); (4, 4) and (0, 8) is
The coordinates of the point on the y-axis which is equidistant from the points (7, 6) and (-3, 4) is
