TS ICET 19th August 2021 Shift-1

For $$0 \leq r \leq 10$$, if $$C_r = 10_{c_{r}}$$ then $$1.c_1 + 2.c_2 + 3.c_3 + ...... + 10.c_{10} = $$

If the matrix $$\begin{bmatrix}7 & 1 & -3 \\4 & 2 & x\\1 & -1 & 5 \end{bmatrix}$$ is singular, then x =

If $$x_2, x_1 < x_2$$ are the pair of values of x satisfying the matrix equation
$$\begin{bmatrix}1 & x & 1 \end{bmatrix} \begin{bmatrix}1 & 3 & 2 \\2 & 5 & 1\\15 & 3 & 2 \end{bmatrix} \begin{bmatrix}1 \\ 2 \\ x \end{bmatrix} = \begin{bmatrix}0 \\ 0 \\ 0 \end{bmatrix}$$, then $$\frac{x_1}{x_2} =$$

$$\lim_{x \rightarrow 0}\frac{1 - \cos 5x}{4x^2} =$$

If $$y = \sqrt{x} + \frac{1}{\sqrt{x}}$$, then $$\frac{dy}{dx}$$ at $$x = 1$$ is equal to

The equation of the line passing through the point (1, 2) and perpendicular to the line $$x + y + 1 = 0$$ is

ABCD is a trapezium with AB and CD as its parallel sides. If the diagonals AC and BD intersect in E and CE : EA = 3 : 2, then AB : CD =

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

If A(3, -7), B(-2, 5) and the point C(x, y) is on the line segment AB between A and B such that AC = 8, then 3x + 2y =

If a line makes unequal intercepts on x, y axis with the sum 12 and if it passes through the point (2, 4), then the perpendicular distance from origin to the line is