TS ICET 19th August 2021 Shift-2
For the following questions answer them individually
The coefficient of $$x^{-7}$$ in the binomial expansion of $$\left(3x^{\frac{1}{5}} + \frac{4}{\sqrt{x}}\right)^{21}$$
If a, b, c, are distinct real numbers and
$$\begin{vmatrix}a &a^2 & a^3 - 1 \\b & b^2 & b^3 - 1\\c & c^2 & c^3 - 1\end{vmatrix} = 0$$, then
$$A= \begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\ 0 & 0 & 1 \end{bmatrix}$$ and
$$B= \begin{bmatrix}0 & 0 & 1\\ 0 & 1 & 0\\ 1 & 0 & 0 \end{bmatrix}$$ then $$A^{25}B^{37} + A^{24}B^{36}= $$
In the diagram below, the lines $$l_{1}, l_{2}$$ are parallel to each other, then $$\theta$$ =
In the adjacent figure $$\angle BAT = 130^{\circ}$$ and $$\angle T= 25^{\circ}$$, then $$\angle TCA =$$
If $$(x_{1},y_{1})$$ and $$(x_{2},y_{2})$$ are the points of trisection of the line segment joining the points (-7, 5) and (2, -4), then $$\frac{x_{1}+x_{2}}{y_{1}+y_{2}}$$
