List of top Questions asked in AP EAPCET

The ratio of the areas of the greatest and the smallest circles touching \((x \pm 1)^2 + (y \pm 1)^2 = 1\) is (The equation \((x \pm 1)^2 + (y \pm 1)^2 = 1\) represents four circles with radius 1, centered at (1,1), (1,-1), (-1,1), (-1,-1).)

The locus of the point of intersection on the line \( \sqrt{3}x - y - 4\sqrt{3}k = 0 \) and \( \sqrt{3}kx + ky - 4\sqrt{3} = 0 \) for different real values of k is a hyperbola H. If e is the eccentricity of H then \(4e^2 = \)

\( \int \sqrt{x+\sqrt{x^2+2}} \ dx = \)

3.1 g of a compound, 'X' (molar mass = 62 g mol$^{-1}$) is dissolved in 19.5 g of other compound, Y (molar mass = 78 g mol$^{-1}$). The ratio of mole fractions of X and Y in the solution is

Find the false statement for ideal gases:

The function $ y = x^3 - ax^2 + 48x + 7 $ is increasing for all real values of $ x $. Find the interval in which $ a $ lies:

Find the distance between the point \( (6, 4\sqrt{3}) \) and the focus of the parabola \( y^2 = 8x \)

The relative basic strength of the compounds is correctly shown in the option:

If $\displaystyle \lim_{x \to 0} \dfrac{|x|}{\sqrt{x^4 + 4x^2 + 5}} = k$, $\displaystyle \lim_{x \to 0} x^4 \sin\left(\dfrac{1}{3\sqrt{x}}\right) = l$, Then $k + l = $

Match the following: List - I \quad (Type of hydride) \quad List - II \quad (Example) A) Electron precise \quad i) SiH$_4$ B) Saline \quad ii) H$_2$O C) Electron deficient \quad iii) MgH$_2$ D) Electron rich \quad iv) B$_2$H$_6$

If \( A = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 8 & 0 \\7 & 1 \end{bmatrix} \), and \( A^3 = B \), then \( x = \) ?

Given that $ \vec{a}, \vec{b}, \vec{c} $ are non-coplanar vectors and: $$ \vec{a} + 3\vec{b} + 4\vec{c} = x(\vec{a} - 2\vec{b} + 3\vec{c}) + y(\vec{a} + 5\vec{b} - 2\vec{c}) + z(6\vec{a} + 14\vec{b} + 4\vec{c}) $$ Find $ x + y + z $

A ray makes angles \( \alpha, 2\alpha, 3\alpha \) with the coordinate axes OX, OY, OZ respectively. Then possible values of \( \alpha \) are:

The value of $\dfrac{1 + \tanh x}{1 - \tanh x} =$ ?

For a Poisson distribution:
- Mean $ = \ell $
- Variance $ = m $
- $ \ell + m = 8 $
Then evaluate: $$ e^4 \cdot \left[1 - P(X>2)\right] $$