List of top Questions asked in AP EAPCET- 2025

The moment of inertia of a solid cylinder of mass 2.5 kg and radius 10 cm about its axis is

Let \( f(x) = \frac{1+x{1-x} \). Find the value of \( f(x) + f(-x) \):}

Let $[x]$ represent the greatest integer less than or equal to $x$, $\{x\} = x - [x]$. Given \[ \sqrt{2} = 1.414
\text{and}
\sqrt{3} = 1.732. \] If \[ f(x) = x + \frac{x}{1 + x^2} \] is a real valued function, then find \[ f(\sqrt{2}) + f(-\sqrt{3}). \]

If \( \sinh^{-1}(2) + \sinh^{-1}(3) = \alpha \), then \( \sinh\alpha = \) ?

For which reaction \( \Delta H \neq \Delta U \)?

If \( k \in N \) then \( \lim_{n\to\infty} \left[ \frac{1}{n+1} + \frac{1}{n+2} + \frac{1}{n+3} + \dots + \frac{1}{kn} \right] = \) (Note: The last term should be \( \frac{1}{n+ (k-1)n} = \frac{1}{kn} \) or sum up to \(n+(k-1)n\). The given form \(1/kn\) as the endpoint of the sum means sum from \(r=1\) to \((k-1)n\). The sum is usually \( \sum_{r=1}^{(k-1)n} \frac{1}{n+r} \). If the last term is \( \frac{1}{kn} \), it means \( n+r = kn \implies r = (k-1)n \). So it's \( \sum_{r=1}^{(k-1)n} \frac{1}{n+r} \).) Let's assume the sum goes up to \( \frac{1}{n+(k-1)n} = \frac{1}{kn} \). So the sum is \( \sum_{r=1}^{(k-1)n} \frac{1}{n+r} \). No, this seems to be \( \frac{1}{n+1} + \dots + \frac{1}{n+(kn-n)} \). The sum should be written as \( \sum_{i=1}^{(k-1)n} \frac{1}{n+i} \). The dots imply the denominator goes up. The last term is \( \frac{1}{kn} \). This means the sum is actually \( \frac{1}{n+1} + \frac{1}{n+2} + \dots + \frac{1}{n+(k-1)n} \). The number of terms is \( (k-1)n \).

If a complex number $ z = x + iy $ represents a point $ P $ on the Argand plane and $$ \text{Arg} \left( \frac{z - 3 + 2i}{z + 2 - 3i} \right) = \frac{\pi}{4} $$ then the locus of $ P $ is

The numerically greatest term in the expansion of $ (x + 3y)^{13} $, when $ x = \frac{1}{2},\ y = \frac{1}{3} $, is

The radius of fourth orbit in \( He^+ \) ion is \( R_1 \) pm and radius of third orbit in \( Li^{2+} \) ion is \( R_2 \) pm. The value of \( (R_1 - R_2) \) in pm is:

The angle made by a line \(L\) with positive X-axis measured in the positive direction is \(\frac{\pi}{6}\) and the intercept made by \(L\) on Y-axis is negative. If \(L\) is at a distance 5 units from the origin, then the perpendicular distance from the point \(\left(1,-\sqrt{3}\right)\) to the line \(L\) is?

The equation of the circle touching the lines \(|x-2| + |y-3| = 4\) is?

What are X and Y respectively in the following reaction sequence? (\(anhy = \text{anhydrous}\)) \[ \text{C}_6\text{H}_5\text{N}_2^+\text{X}^- \xrightarrow{\text{C}_2\text{H}_5\text{OH}} \text{X} \xrightarrow{\text{CO, HCl, anhy. AlCl}_3} \text{Y} \] % The question implies the first X is an anion, the second X is an organic product. Let's call the organic product P1 to avoid confusion. % So, C6H5N2+Anion- → P1 → Y

If \( y = \operatorname{Sin}^{-1} \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \) and \( -\frac{3\pi}{2}<x<-\frac{\pi}{2} \), then \( \frac{dy}{dx} \) is:

A person of mass 45 kg having leg bones each of length 50 cm and area of cross-section of 5 cm$^2$ jumps safely from a height of 2 m. If his leg bones can withstand a stress of $0.9 \times 10^8$ N m$^{-2}$, then the Young’s modulus of the leg bones is
(Acceleration due to gravity $g = 10$ m s$^{-2}$)