List of top Questions asked in AP EAPCET- 2025

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 \( A_1 : A_2 = \)
The angle between the tangents drawn from the point (2, 2) to the circle \(x^2 + y^2 + 4x + 4y + c = 0\) is \(\cos^{-1} \left( \frac{7}{16} \right)\). If two such circles exist, then the sum of values of \(c\) is
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 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$_2$
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 number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word INCONVENIENCE is:
If vectors \( \vec{a} = 2\hat{i} + 3\hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} - \hat{j} + 2\hat{k} \), then the magnitude of the projection of \( \vec{a} \) on \( \vec{b} \) 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$^{-2}$)
\( \sum_{k=1}^{n} k(k+1)(k+2)...(k+r-1) = \)
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
At $T(K)$, the vapor pressure of water is $x$ kPa. What is the vapor pressure (in kPa) of 1 molal solution containing non-volatile solute?
The numerically greatest term in the expansion of $ (x + 3y)^{13} $, when $ x = \frac{1}{2},\ y = \frac{1}{3} $, is
A ray of light incidents at an angle of \(60^\circ\) on the first face of a prism. The angle of the prism is \(30^\circ\) and its second face is silvered. If the light ray inside the prism retraces its path after reflection from the second face, then the refractive index of the material of the prism is
A and B are playing chess game with each other. The probability that A wins the game is 0.6, the probability that he loses is 0.3 and the probability it is draw is 0.1. If they played three games, then the probability that A wins at least two games is
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:
Among \( \text{B}_2\text{O}_3 \), \( \text{Al}_2\text{O}_3 \), and \( \text{In}_2\text{O}_3 \), the oxides which react with alkalies are:
In which of the following intramolecular H-bonding is absent?
Options:
- Salicylic acid
- Salicylaldehyde
- Quinol
- Catechol
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
If the polynomial \( f(x) = x^4 + ax^3 + bx^2 + cx + d \) is divided by \( x - 1 \) and \( x + 1 \), the remainders are 5 and 3 respectively. If \( f(x) \) is divided by \( x^2 - 1 \), then the remainder is
Electrolysis of aqueous solution of potassium acetate gives an alkane (x) and \({CO}_2\) (y) at anode. The volume ratio of these two gases \(x\) and \(y\) at STP is respectively:
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 \( (\overline{a} \times \overline{b}) \cdot (\overline{c} \times \overline{d}) = \)
If $\sin x - \sin y = \frac{27{65}$ and $\cos x - \cos y = -\frac{21}{65}$, then $\sin(x+y)= $}
For a first-order reaction, the rate constant \( k \) is \( 1.386 \times 10^{-3} \, \text{s}^{-1} \). What is the half-life \( t_{1/2} \) of the reaction? (Use \( \ln 2 = 0.693 \))
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:
The radii of inner and outer spheres of a spherical capacitor are $8~\text{cm$ and $9~\text{cm}$ respectively. The outer sphere is earthed and the inner sphere is charged. If the space is filled with a dielectric constant $K = 5$, the capacitance is}