List of top Mathematics Questions asked in TS EAMCET

If \[ \frac{x^4}{(x^2+1)(x-2)} = f(x) + \frac{Ax+B}{x^2+1} + \frac{C}{x-2} \] then \( f(14) + 2A - B = \) ?
If \( y = a \cos 3x + b e^{-x} \), then \( y'(3\sin 3x - \cos 3x) = \):
If A and B are arbitrary constants, then the differential equation having \[ y = Ae^{-x} + B \cos x \] as its general solution 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:
The vertical angle of a right circular cone is \( 60^\circ \). If water is being poured into the cone at the rate of \( \frac{1}{\sqrt{3}} \) m\(^3\)/min, then the rate (m/min) at which the radius of the water level is increasing when the height of the water level is 3m is:
If \( \theta \) is the acute angle between the curves \( y^2 = x \) and \( x^2 + y^2 = 2 \), then \( \tan \theta \) is:
The equations of the directrices of the ellipse \(9x^2 + 4y^2 - 18x - 16y - 11 = 0\) are:
If \(\tan A<0\) and \(\tan 2A = -\frac{4}{3}\), then \(\cos 6A\) is:
If \( \log y = y^{\log x} \), then \( \frac{dy}{dx} \) is:
If \( \alpha, \beta \) are the roots of the equation \( x + \frac{4}{x} = 2\sqrt{3} \), then \( \frac{2}{\sqrt{3}}\left| \alpha^{2024} - \beta^{2024} \right| \) is:
If \( \omega \) is the complex cube root of unity and \[ \left( \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2} \right)^k + \left( \frac{a + b\omega + c\omega^2}{b + a\omega^2 + c\omega} \right)^2 = 2, \] then \( 2k + 1 \) is always:

Match the functions in List--I with their corresponding properties in List--II:

If the normal drawn at the point \( P(9, 9) \) on the parabola \( y^2 = 9x \) meets the parabola again at \( Q(a, b) \), then \( 2a + b = \text{?} \)

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

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


 

The equation of the normal drawn to the curve \( y^3 = 4x^5 \) at the point \( (4,16) \) is:
The general solution of the differential equation $$ \frac{dy}{dx} = \frac{2y^2 + 1}{2y^3 - 4xy + y}. $$ 
If \(A + B + C = 2S\), then \[ \sin(S - A)\,\cos(S - B)\;-\;\sin(S - C)\,\cos S \;=\;? \]
The equation that is satisfied by the general solution of the equation \( 4 - 3 \cos \theta = 5 \sin \theta \cos \theta \) is:
One of the values of \( (-64i)^{5/6} \) is:}
If \( \sinh^{-1}(-\sqrt{3}) + \cosh^{-1}(2) = K \), then \( \cosh K = \):

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

If \( m_1 \) and \( m_2 \) are the slopes of the direct common tangents drawn to the circles \[ x^2 + y^2 - 2x - 8y + 8 = 0 \quad \text{and} \quad x^2 + y^2 - 8x + 15 = 0 \] then \( m_1 + m_2 \) 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 \( y (\cos x)^{\sin x} = (\sin x)^{\sin x} \), then the value of \( \frac{dy}{dx} \) at \( x = \frac{\pi}{4} \) is: