List of top Mathematics Questions asked in TS EAMCET

A circle C touches the X-axis and makes an intercept of length 2 units on the Y-axis. If the centre of this circle lies on the line $y=x+1$, then a circle passing through the centre of the circle C is
If the normal drawn at the point P on the curve $y^2 = x^2-x+1$ makes equal intercepts on the coordinate axes, then the equation of the tangent drawn to the curve at P is
For $a\neq0$ and $b\neq0$, if the real valued function $f(x) = \frac{\sqrt[4]{625+4x}-5}{\sqrt[4]{625+5bx}-5}$ is continuous at $x=0$, then $f(0) =$
The value of the integral \( \int_0^1 x^2 \, dx \) is:
If $f(x) = \log_{(x-1)^2}(x^2-3x+2)$, $x \in \mathbb{R}-[1,2]$ and $x\neq0$, then $f'(3)=$
If \( g \circ f \) is a bijective function, then:
$\int \frac{\log x}{(1+x)^2}dx = $
Number of all possible words (with or without meaning) that can be formed using all the letters of the word CABINET in which neither the word CAB nor the word NET appear is
Find the value of \( k \) such that \( 5 \cdot 2^n - 48n + k \) is divisible by 24.
If \(m\cos(\alpha + \beta) - n\cos(\alpha - \beta) = m\cos(\alpha - \beta) + n\cos(\alpha + \beta)\), then \(\tan \alpha \tan \beta\) is:
The number of solutions of the equation \[ \sin 7\theta - \sin 3\theta = \sin 4\theta \] that lie in the interval \( (0, \pi) \) is:
Evaluate the expression: \[ \cos^{-1} \frac{3}{5} + \sin^{-1} \frac{5}{13} + \tan^{-1} \frac{16}{63} \]

If

\[ \cosh^{-1}\left(\frac{5}{3}\right) + \sinh^{-1}\left(\frac{3}{4}\right) = k, \]

then \( e^k \) is:

If \( \theta \) is an acute angle and \( 2\sin^2 \theta = \cos^4 \frac{\pi}{8} + \sin^4 \frac{3\pi}{8} + \cos^4 \frac{5\pi}{8} + \sin^4 \frac{7\pi}{8} \), then \( \theta \) is:
If \(2 \tan^2 \theta - 4 \sec \theta + 3 = 0\), then \(2 \sec \theta\) is:

\[ \sin^{-1} x - \cos^{-1} 2x = \sin^{-1} \left(\frac{\sqrt{3}}{2}\right) - \cos^{-1} \left(\frac{\sqrt{3}}{2}\right) \]

Then, \[ \tan^{-1} x + \tan^{-1} \left(\frac{x}{x+1}\right) = ? \]

\[ \text{sech}^{-1}\left(\frac{3}{5}\right) - \text{tanh}^{-1}\left(\frac{3}{5}\right) = ? \]

In a triangle ABC, if \( a = 5 \), \( b = 3 \), and \( c = 7 \), then the ratio:

\[ \sqrt{\frac{\sin(A - B)}{\sin(A + B)}} \]

The system of equations \[ x + 3by + bz = 0, \quad x + 2ay + az = 0, \quad x + 4cy + cz = 0 \] has:
If the homogeneous system of linear equations \(x - 2y + 3z = 0\), \(2x + 4y - 5z = 0\), \(3x + \lambda y + \mu z = 0\) has a non-trivial solution, then \(8\mu + 11\lambda =\)

The system of simultaneous linear equations : 

 

\[ \begin{array}{rcl} x - 2y + 3z &=& 4 \\ 2x + 3y + z &=& 6 \\ 3x + y - 2z &=& 7 \end{array} \]

The system of equations \( x + 3y + 7 = 0 \), \( 3x + 10y - 3z + 18 = 0 \), and \( 3y - 9z + 2 = 0 \) has:
If \(AX = D\) represents the system of linear equations \[ 3x - 4y + 7z + 6=0,\quad 5x + 2y - 4z + 9=0,\quad 8x - 6y - z + 5=0, \] then AX = D ?

Evaluate the integral: \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{dx}{\sec^2 x + (\tan^{2022} x - 1)(\sec^2 x - 1)} \]

If \[ \int e^x (x^3 + x^2 - x + 4) \, dx = e^x f(x) + C, \] then \( f(1) \) is: