List of top Questions asked in TS EAMCET- 2024

The mean deviation about the mean for the following data is:
 


 

The point of intersection of two tangents drawn to the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{4} = 1 \] lie on the circle \[ x^2 + y^2 = 5. \] If these tangents are perpendicular to each other, then \( a \) is:
If all the numbers which are greater than 6000 and less than 10000 are formed with the digits \( 3,5,6,7,8 \) without repetition of the digits, then the difference between the number of odd numbers and the number of even numbers among them is:
If \[ \frac{1}{x^4 + x^2 + 1} = \frac{Ax + B}{x^2 + ax + 1} + \frac{Cx + D}{x^2 - ax + 1} \] then \( A + B - C + D = ? \)

If \( 0 \leq x \leq \frac{\pi}{2} \), then \[ \lim\limits_{x \to a} \frac{2\cos x - 1}{2\cos x - 1} \] Options: 

If the function

\[ f(x) = \begin{cases} \frac{(e^x - 1) \sin kx}{4 \tan x}, & x \neq 0 \\ P, & x = 0 \end{cases} \]

is differentiable at \( x = 0 \), then:

Given the position vectors of points \(A\) and \(B\) as \( \mathbf{A} = 2\mathbf{i} - 3\mathbf{j} + \mathbf{k} \) and \( \mathbf{B} = \mathbf{i} + 2\mathbf{j} - 3\mathbf{k} \), and \(C\) divides \(AB\) in the ratio 3:2. If \( \mathbf{D} = 3\mathbf{i} - \mathbf{j} + 2\mathbf{k} \) is the position vector of point \(D\), find the unit vector in the direction of \( \mathbf{CD} \):
Calculate the variance of the data set: 1, 2, 3, 5, 8, 13, 17.
A circle \( S \) passes through the points of intersection of the circles \( x^2 + y^2 - 2x - 3 = 0 \) and \( x^2 + y^2 - 2y = 0 \). If \( x + y + 1 = 0 \) is a tangent to the circle \( S \), then the equation of \( S \) is:
If \( (1,1) \) is the vertex and \( x + y + 1 = 0 \) is the directrix of a parabola. If \( (a, b) \) is its focus and \( (c, d) \) is the point of intersection of the directrix and the axis of the parabola, then \( a + b + c + d \) is:
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 \( \alpha,\,\beta,\,\gamma \) are the roots of the equation \[ \begin{vmatrix} x & 2 & 2\\ 2 & x & 2\\ 2 & 2 & x \end{vmatrix} = 0 \]
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 \(x=\beta\))}
Evaluate the integral: \[ \int e^{-2x} \left( \tan 2x - 2\sec^2 2x \tan 2x \right) dx. \]
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 \( A = \begin{pmatrix} x & y & y \\ y & x & y \\ y & y & x \end{pmatrix} \) and \( 5A^{-1} = \begin{pmatrix} -3 & 2 & 2 \\ 2 & -3 & 2 \\ 2 & 2 & -3 \end{pmatrix} \), then \( A^2 - 4A \) is:

If \( a \neq b \neq c \), then

\[ \Delta_1 = \begin{vmatrix} 1 & a^2 & bc \\ 1 & b^2 & ca \\ 1 & c^2 & ab \end{vmatrix}, \quad \Delta_2 = \begin{vmatrix} 1 & 1 & 1 \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3 \end{vmatrix} \]

and

\[ \frac{\Delta_1}{\Delta_2} = \frac{6}{11} \]

then what is \( 11(a + b + c) \)?

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 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:
The domain of the real-valued function $$ f(x) = \sin^{-1} \left( \log_2 \left( \frac{x^2}{2} \right) \right) $$ is:
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 roots of the equation \( x^3 - 3x^2 + 3x + 7 = 0 \) are \( \alpha, \beta, \gamma \) and \( w, w^2 \) are complex cube roots of unity. If the terms containing \( x^2 \) and \( x \) are missing in the transformed equation when each one of these roots is decreased by \( h \), then 

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 \( \sinh x = \frac{12}{5} \), then \( \sinh 3x + \cosh 3x \) = ?
The variance of the first 10 natural numbers which are multiples of 3 is: