List of top Mathematics Questions asked in TS EAMCET

The domain of the real valued function: \[ f(x) \;=\; \sqrt[3]{\frac{x \,-\, 2}{2x^2 \,-\, 7x \,+\,5}} \;+\; \log\bigl(x^2 \,-\, x \,-\, 2\bigr). \]

If \( Z_1 = \sqrt{3} + i\sqrt{3} \) and \( Z_2 = \sqrt{3} + i \), and \[ \left( \frac{Z_1}{Z_2} \right)^{50} = x + iy, \] then the point \( (x,y) \) lies in:

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:

If \( f \) is a real valued function from \( A \) onto \( B \) defined by \( f(x) = \frac{1}{\sqrt{|x| - |x|}} \), then \( A \cap B \) 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 \( \alpha,\,\beta,\,\gamma \) are the roots of the equation \[ \begin{vmatrix} x & 2 & 2\\ 2 & x & 2\\ 2 & 2 & x \end{vmatrix} = 0 \]

A, B, C, D are square matrices such that A + B is symmetric, A - B is skew-symmetric, and D is the transpose of C.

If

\[ A = \begin{bmatrix} -1 & 2 & 3 \\ 4 & 3 & -2 \\ 3 & -4 & 5 \end{bmatrix} \]

and

\[ C = \begin{bmatrix} 0 & 1 & -2 \\ 2 & -1 & 0 \\ 0 & 2 & 1 \end{bmatrix} \]

then the matrix \( B + D \) is:

The number of ways of arranging all the letters of the word "COMBINATIONS" around a circle so that no two vowels come together is

If \(4+3x-7x^2\) attains its maximum value \(M\) at \(x=\alpha\) and \(5x^2-2x+1\) attains its minimum value at \(x=\beta\), then \[ \frac{28\,(M - \alpha)}{5\,(m + \beta)} =\,? \] \textit{(Assume \(m\) is that minimum value of \(5x^2 -2x +1\) at \(x=\beta\))}

If the coefficient of \( x^r \) in the expansion of \( (1 + x + x^2)^{100} \) is \( a_r \), and \( S = \sum\limits_{r=0}^{300} a_r \), then

\[ \sum\limits_{r=0}^{300} r a_r = \]

\[ \begin{array}{c|c} X = x & P(X = x) \\ \hline 1 & 3K^2 \\ 3 & K \\ 5 & K^2 \\ 2 & 2K \end{array} \]

If \( A = \begin{pmatrix} 9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2 \end{pmatrix} \) and

\[ A^T A^{-2} = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \]

then

\[ \sum_{1 \leq i \leq 3} \sum_{1 \leq j \leq 3} a_{ij} \]

is:

If \( x \) and \( y \) are two positive integers such that \( x + y = 24 \) and \( x^3 y^5 \) is maximum, then \( x^2 + y^2 \) is:

Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]

Evaluate the integral: \[ \int \left( \sin^3 x + \cos^2 x \right)^2 \, dx \]

If the period of the function \[ f(x) = 2\cos(3x+4) - 3\tan(2x-3) + 5\sin(5x) - 7 \] is \( k \), then \( f(x) \) is periodic with fundamental period \( k \). Find \( k \).

If \( \triangle ABC \) is an isosceles triangle with base \( BC \), then \( r_1 = ? \)

Given \( \cos B - \sin A = \frac{\sqrt{3}+1}{4\sqrt{2}} \) and \( 2 \cos A \cos B = \frac{1+\sqrt{2}+\sqrt{3}}{2\sqrt{2}} \), calculate \( \cos^2 \frac{4B}{3} - \sin^2 \frac{4A}{5} \):

All the letters of the word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without meaning) thus formed are arranged in the dictionary order. Then the rank of the word 'COLLEGE' is:

If \( M_1 \) is the mean deviation from the mean of the discrete data \( 44, 5, 27, 20, 8, 54, 9, 14, 35 \) and \( M_2 \) is the mean deviation from the median of the same data, then \( M_1 - M_2 = \):

A point \( P \) is moving on the curve \( x^3 y^4 = 27 \). The x-coordinate of \( P \) is decreasing at the rate of 8 units per second. When the point \( P \) is at \( (2, 2) \), the y-coordinate of \( P \) is:

A particle moving from a fixed point on a straight line travels a distance \(S\) meters in \(t\) sec. If \(S = t^3 - t^2 + t + 3\), then the distance (in mts) travelled by the particle when it comes to rest is: