List of top Questions asked in AP EAPCET- 2025

G(1,0) is the centroid of the triangle ABC. If A = (1, -4, 2) and B = (3, 1, 0), then AG$^2$ + CG$^2$ =
Identify the correct option from the following:

If all letters of the word COMBINATION are arranged to form 11-letter words with $ C $ and $ N $ at the ends and no vowel in the middle position, find the number of such words.

$ \int \frac{x}{(1-x^2)\sqrt{2 - x^2} dx = $}

A steel sphere of radius $1.2~\text{cm}$ collides with another steel sphere at rest.
If the collision is elastic and the first sphere moves with $\dfrac{7}{9}$ of its initial velocity after collision,
then the radius of the second sphere is

A transistor works as an amplifier when

Which of the following orders is not correct about the property shown against it?

If the roots of the equation $x^2 + 2ax + b = 0$ are real, distinct and differ utmost by $2m$, then b lies in the interval

If $\cos\theta = -\frac{3}{5}$ and $\theta$ does not lie in second quadrant, then $\tan\frac{\theta}{2} =$

$ \int_{-\pi/2}^{\pi/2} \sin^2 x \cos^2 x (\sin x + \cos x) \, dx = $

The ratio of the wavelengths of the spectral lines emitted due to transitions $ 3 \rightarrow 2 $ and $ 2 \rightarrow 1 $ orbits in the hydrogen atom is

Consider the following sequence of reactions.
\[ \mathrm{C}_6\mathrm{H}_5\mathrm{COONa} \xrightarrow{\text{NaOH/CaO}, \Delta} \text{X} \xrightarrow{\text{CO} + \text{HCl}, \text{Anhyd. AlCl}_3} \text{Y} \xrightarrow{\text{NaOH}} \text{A} + \text{B} \]
If A is the reduction product of Y, what is B?

Which of the following represents the wavelength of spectral line of Balmer series of He$^+$ ion? (R = Rydberg constant, n $>$ 2)

If $ A = \begin{pmatrix} 1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6 \end{pmatrix} $ and $ |adj(adj(A))|(adj A)^{-1} = kA $, then k =

$[x]$ denotes the greatest integer less than or equal to x. If $\{x\}=x-[x]$ and $ \lim_{x\to 0} \frac{\sin^{-1}(x+[x])}{2-\{x\}} = \theta $, then $ \sin\theta + \cos\theta = $

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat utilised to increase the internal energy of the gas is

One mole of $ \text{C}_2\text{H}_5\text{OH(l)} $ was completely burnt in oxygen to form $ \text{CO}_2\text{(g)} $ and $ \text{H}_2\text{O(l)} $. The standard enthalpy of formation ($ \Delta_f H^\ominus $) of $ \text{C}_2\text{H}_5\text{OH(l)} $, $ \text{CO}_2\text{(g)} $ and $ \text{H}_2\text{O(l)} $ is x, y, z kJ mol$^{-1}$ respectively. What is $ \Delta_r H^\ominus $ (in kJ mol$^{-1}$) for this reaction?