List of top Mathematics Questions asked in TS EAMCET

The numerically greatest term in the expansion of (3x - 16y)15 when x = 2⁄3 and y = 3⁄2 is ?

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

The approximate value of \( \sec 59^\circ \) obtained by taking \( 1^\circ = 0.0174 \) and \( \sqrt{3} = 1.732 \) is:

The maximum value of the function \[ f(x) = 3\sin^{12}x + 4\cos^{16}x \] is ?

The equation of the normal drawn to the curve \( y^3 = 4x^5 \) at the point \( (4,16) \) is:
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:
If \(A + B + C = 2S\), then \[ \sin(S - A)\,\cos(S - B)\;-\;\sin(S - C)\,\cos S \;=\;? \]
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 \( \log y = y^{\log x} \), then \( \frac{dy}{dx} \) is:
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:
The general solution of the differential equation \[ \frac{dy}{dx} + \frac{\sin(2x + y)}{\cos x} + 2 = 0 \] is:

∫ √(2x2 - 5x + 2) dx = ∫ (41/60) dx,

and

-1/2 > α > 0, then α = ?

If the function \( f(x) \) is given by \[ f(x) = \begin{cases} \frac{\tan(a(x-1))}{\frac{x-1}{x}}, & tif0<x<1 
\frac{x^3-125}{x^2 - 25} , & \text{if } 1 \leq x \leq 4 
\frac{b^x - 1}{x}, & \text{if } x>4 \end{cases} \] is continuous in its domain, then find \( 6a + 9b^4 \).

Evaluate the integral: \[ \int 4\cos^2 x - 5\sin^2 x \cos x \, dx. \]
Evaluate the integral: \[ \int \frac{4\tan^4 x + 3 \tan^2 x - 1}{\tan^2 x + 4} \, dx. \]
Evaluate the integral: \[ \int \frac{(\sin^4x + 2\cos^2x - 1) \cos x}{(1 + \sin x)^6} \, dx \]
Evaluate the integral: \[ \int (\log x)^3 \, dx \]
Evaluate the integral: \[ \int \left( \sin^3 x + \cos^2 x \right)^2 \, dx \]
Evaluate the integral: \[ I = \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \]
The area of the region enclosed by the curves \( y^2 = 4(x+1) \) and \( y^2 = 5(x-4) \) is:
If \(\cos x + \cos y = \tfrac{2}{3}\) and \(\sin x - \sin y = \tfrac{3}{4}\), then \[ \sin(x - y) \;+\; \cos(x - y) \;=\;? \]
If \(\theta\) is the angle between the vectors \(4\mathbf{i} - \mathbf{j} + 2\mathbf{k}\) and \( \mathbf{i} + 3\mathbf{j} - 2\mathbf{k}\), then \(\sin 2\theta\) is:
If the inverse point of the point \(P(3,3)\) with respect to the circle \(x^2 + y^2 - 4x + 4y + 4 = 0\) is \(Q(a,b)\), then \(a + 5b =\)
If the line \( 4x - 3y + p = 0 \) (where \( p + 3>0 \)) touches the circle \( x^2 + y^2 - 4x + 6y + 4 = 0 \) at the point \( (h,k) \), then the value of \( h - 2k \) is: