List of top Questions asked in AP EAPCET- 2025

If \( \overline{a} = \overline{i} - 2\overline{j} - 3\overline{k} \), \( \overline{b} = -2\overline{i} + 3\overline{j} + 4\overline{k} \), \( \overline{c} = 5\overline{i} - 4\overline{j} + 3\overline{k} \), and \( \overline{d} = 3\overline{i} + \overline{j} + 5\overline{k} \) are four vectors, then \( (\overline{a} \times \overline{b}) \cdot (\overline{c} \times \overline{d}) = \)
The general solution of the differential equation \( \left(x - (x + y)\log(x + y)\right) dx + x\,dy = 0 \) is:
If the slope of the tangent drawn at any point \((x, y)\) on a curve is \(x + y\), then the equation of that curve is
If \(\int \left( \frac{x^{49} \tan^{-1}(x^{50})}{1 + x^{100}} + \frac{x^{50}}{1 + x^{100}} \right) dx = k f(x) + c\) where \(k\) is a constant, then \(f(x) - f\left( \frac{1}{x^{49}} \right) =\)
The ratio of the focal lengths of a convex lens when kept in air and when it is immersed in a liquid is 1:2. If the refractive index of the material of the lens is 1.5, then the refractive index of the liquid is
The number of molecules having lone pair of electrons on central atom in the following is: BF$_3$, SF$_4$, SiCl$_4$, XeF$_4$, NCl$_3$, XeF$_6$, PCl$_5$, HgCl$_2$, SnCl$_2$
If the number of diagonals of a regular polygon is 35, then the number of sides of the polygon is
Let \( A_1 \) be the area of the given ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \). Let \( A_2 \) be the area of the region bounded by the curve which is the locus of mid point of the line segment joining the focus of the ellipse and a point P on the given ellipse, then \( A_1 : A_2 = \)
If \( \sqrt{x-xy} + \sqrt{y-xy} = 1 \), then \( \frac{dy}{dx} = \)
A solid sphere of mass 4 kg and radius 28 cm is on an inclined plane. If the acceleration of the sphere when it rolls down without sliding is \( 3.5 \, \text{m s}^{-2} \), then the acceleration of the sphere when it slides down without rolling is
Match the following List-I (Type of reaction) \hspace{1cm List-II (Final product)
Reimer-Tiemann reaction
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 $\sin x - \sin y = \frac{27{65}$ and $\cos x - \cos y = -\frac{21}{65}$, then $\sin(x+y)= $}
Let \( A(5,4) \) and \( B(5,-4) \) be two points. If \( P \) is a point in the coordinate plane such that \( |APB| = \frac{\pi}{4} \), then the point \( P \) lies on the curve:
If a proton and an alpha particle are accelerated through the same potential difference, then the ratio of their de Broglie wavelengths is:
\( \sum_{k=1}^{n} k(k+1)(k+2)...(k+r-1) = \)
For a positive real number p, if the perpendicular distance from a point \( -\vec{i} + p\vec{j} - 3\vec{k} \) to the plane \( \vec{r} \cdot (2\vec{i} - 3\vec{j} + 6\vec{k}) = 7 \) is 6 units, then p =
If the lines \(x+y-2=0\), \(3x-4y+1=0\) and \(5x+ky-7=0\) are concurrent at \((\alpha, \beta)\), then equation of the line concurrent with the given lines and perpendicular to \(kx+y-k=0\) is
The synthetic detergents of the following are
synthetic detergents of the following are
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:
If \( x = \sqrt{2}e^t(\sin t - \cos t) \) and \( y = \sqrt{2}e^t(\sin t + \cos t) \), then \( \left[ \frac{d^2y}{dx^2} \right]_{t=\frac{\pi}{4}} \) 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:
Let \(\mathbf{a} = \mathbf{i} + 2\mathbf{j} - \mathbf{k}\) and \(\mathbf{b} = 6\mathbf{i} - \mathbf{j} + 2\mathbf{k}\) be two vectors. If \[ |\mathbf{a} \times \mathbf{b}|^2 + |\mathbf{a} . \mathbf{b}|^2 = f(x,y)(x+y) - 46 = 0, \] then what does this represent?
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?