List of top Mathematics Questions asked in TS EAMCET

The equation of the pair of transverse common tangents drawn to the circles $ x^2 + y^2 + 2x + 2y + 1 = 0 $ and $ x^2 + y^2 - 2x - 2y + 1 = 0 $ is:

The sum of two roots of the equation $x^4 - x^3 - 16x^2 + 4x + 48 = 0$ is zero. If $\alpha, \beta, \gamma, \delta$ are the roots of this equation, then $\alpha^4 + \beta^4 + \gamma^4 + \delta^4$ is:

Given the function:

\[ f(x) = \frac{2x - 3}{3x - 2} \]

and if $ f_n(x) = (f \circ f \circ \ldots \circ f)(x) $ is applied $ n $ times, find $ f_{32}(x) $.

If $\tan A<0$ and $\tan 2A = -\frac{4}{3}$, then $\cos 6A$ is:

If $z = 1 - \sqrt{3}\,i$, then $z^3 - 3z^2 + 3z = \;?$

If $\alpha, \beta, \gamma$ are the roots of the equation $2x^3 - 3x^2 + 5x - 7 = 0$, then $\Sigma \alpha^2 \beta^2$ is:

Given a square matrix $A$ where $A^2 + I = 2A$, find $A^9$.

The general solution of the differential equation \[ (9x - 3y + 5) dy = (3x - y + 1) dx. \]

Find the domain of the real valued function: \[ f(x) \;=\; \sqrt{\cos(\sin x)} + \cos^{-1}\left(\frac{1+x^2}{2x}\right). \]

For $ n \in \mathbb{N} $, the largest positive integer that divides $ 81^n + 20n - 1 $ is $ k $. If $ S $ is the sum of all positive divisors of $ k $, then find $ S - k $.

The sum of all the 4-digit numbers formed by taking all the digits from $2, 3, 5, 7$ without repetition is

If $ \mathbf{a} = 4\hat{i} + 5\hat{j} - 3\hat{k} $ and $ \mathbf{b} = 6\hat{i} - 2\hat{j} - 2\hat{k} $ are two vectors, then the magnitude of the component of $ \mathbf{b} $ parallel to $ \mathbf{a} $ is:

If $ (2, -1) $ is the point of intersection of the pair of lines \[ 2x^2 + axy + 3y^2 + bx + cy - 3 = 0 \quad \text{then} \quad 3a + 2b + c = \]

P and Q are the points of trisection of the line segment joining the points $ (3, -7) $ and $ (-5,3) $. If line PQ subtends a right angle at a variable point R, then the locus of R is:

{If $f(x)$ is a quadratic function such that $f\left(\frac{1}{x}\right) = f(x) + f\left(\frac{1}{1-x}\right)$, then $\sqrt{f\left(\frac{2}{3}\right) + f\left(\frac{3}{2}\right)} =$}

If $ f(x) = ax^2 + bx + c $ is an even function and $ g(x) = px^3 + qx^2 + rx $ is an odd function, and if $ h(x) = f(x) + g(x) $ and $ h(-2) = 0 $, then $ 8p + 4q + 2r = $?

If $1\cdot3\cdot5 + 3\cdot5\cdot7 + 5\cdot7\cdot9 + \ldots$ to $n$ terms is $n(n+1)f(n)$, then $f(2) =$

Given matrices $ A $ and $ B $ where:

\[ A = \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} x & y \\ 1 & 2 \end{bmatrix} \]

and the condition:

\[ (A + B)(A - B) = A^2 - B^2 \]

If matrix $ C $ is defined as:

\[ C = \begin{bmatrix} x & 2 \\ 1 & y \end{bmatrix} \]

then the trace of $ C $ is:

\[ \text{Tr}(C) = x + y \]

$$ \begin{vmatrix} x-2 & 3x-3 & 5x-5 \\ x-4 & 3x-9 & 5x-25 \\ x-8 & 3x-27 & 5x-125 \end{vmatrix} = 0 $$

If $A$ is a non singular matrix, then $\text{Adj}(A^{-1}) =$