List of top Questions asked in AP EAPCET- 2025

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 \( y = \tan^{-1}\left(\frac{x}{1+2x^2}\right) + \tan^{-1}\left(\frac{x}{1+6x^2}\right) \), then \( \frac{dy}{dx} = \)
\([x]\) 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 \( \sin\theta + \cos\theta = \)
If \( \text{sech}^{-1}x = \log 2 \) and \( \text{cosech}^{-1}y = -\log 3 \), then \( (x+y) = \)
The transformed equation of \( 3x^2 - 4xy = r^2 \) when the coordinate axes are rotated about the origin through an angle of \( \tan^{-1}(2) \) in positive direction is
If \(k\) is a positive integer and \(10^k\) is a divisor of the number \(9^{11} + 11^9\), then the greatest value of \(k\) is:
The general solution of the differential equation \[ y + \cos x \left( \frac{dy}{dx} \right) - \cos^2 x = 0 \] is
All the letters of the word LETTER are arranged in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order. Then the rank of the word TETLER is:
5-digit numbers are formed by using the digits 0, 1, 2, 3, 5, 7 without repetition and all of them are arranged in ascending order. Then the rank of the number 70513 is:
Points \( P \) and \( Q \) are given by \( \vec{OP} = \vec{i} - \vec{j} - \vec{k} \) and \( \vec{OQ} = -\vec{i} + \vec{j} + \vec{k} \). A line along the vector \( \vec{a} = \vec{i} + \vec{j} \) passes through point \( P \), and another line along the vector \( \vec{b} = \vec{j} - \vec{k} \) passes through point \( Q \). If a line along the vector \( \vec{c} = \vec{i} - \vec{j} + \vec{k} \) intersects both the lines along \( \vec{a} \) and \( \vec{b} \) at \( L \) and \( M \) respectively, then \( \vec{PM} = \) ?
For \( a \in \mathbb{R} \), if the vectors \( \vec{p} = (a+1)\hat{i} + a\hat{j} + a\hat{k} \), \( \vec{q} = a\hat{i} + (a+1)\hat{j} + a\hat{k} \) and \( \vec{r} = a\hat{i} + a\hat{j} + (a+1)\hat{k} \) are coplanar and \( 3\left(\vec{p} \cdot \vec{q} \right)^2 - \lambda \left|\vec{r} \times \vec{q} \right|^2 = 0 \), then the value of \( \lambda \) is:
If the angle between the lines joining the origin to the points of intersection of \( x + 2y + \lambda = 0 \) and \( 2x^2 - 2xy + 3y^2 + 2x - y - 1 = 0 \) is \( \dfrac{\pi}{2} \), then a value of \( \lambda \) is:
Let \( \theta \) be the angle between the circles \( S = x^2 + y^2 + 2x - 2y + c = 0 \) and \( S' = x^2 + y^2 - 6x - 8y + 9 = 0 \). If \( c \) is an integer and \( \cos\theta = \dfrac{5}{16} \), then the radius of the circle \( S = 0 \) is:
The values of \( p \) and \( q \) so that the system of equations \[ \begin{aligned} 2x + py + 6z &= 8, \\ x + 2y + qz &= 5, \\ x + y + 3z &= 4 \end{aligned} \] may have no solution are:
A is the set of all matrices of order 3 with entries 0 or 1 only. Let \( B \subset A \) be the subset consisting of all matrices with determinant value 1. Let \( C \subset A \) be the subset consisting of all matrices with determinant value -1. Then, which of the following is true?
Evaluate the integral: \[ \int \frac{1}{9\cos^2 x - 24 \sin x \cos x + 16 \sin^2 x} \, dx = \]
If \[ \int \frac{1}{\cot \frac{x}{2} \cot \frac{x}{3} \cot \frac{x}{6}} \, dx = A \log \left| \cos \frac{x}{2} \right| + B \log \left| \cos \frac{x}{3} \right| + C \log \left| \cos \frac{x}{6} \right| + k, \] then \(A + B + C =\)
Consider the following.
Statement-I: Gold sol is prepared by Bredig’s arc method.
Statement-II: Bredig’s arc method involves only dispersion but not condensation.
Which of the following does not involve in Friedel-Crafts reaction?
The oxides of nitrogen obtained by the reaction of nitric acid with
Consider the following statements:
Statement-I: CH$_3$NH$_2$ is more basic than NH$_3$, but C$_6$H$_5$NH$_2$ is less basic than NH$_3$.
Statement-II: The order of basic strength of amines in aqueous phase follows
(C$_2$H$_5$)$_2$NH > C$_2$H$_5$NH$_2$ > C$_6$H$_5$NH$_2$

Which of the following is the correct statement for an ideal gas (constant =\( \textit{energy}\) )?
 

The ion with 4f$^7$ configuration is:
Which of the following statements are correct? (only correct)
I) The energy of hydrogen atom in its ground state is -13.6 eV.
II) On the basis of Bohr's model, the radius of the 3$^{rd}$ orbit of hydrogen atom is 158.7 pm.
III) The order of radius of the first orbit of H, He$^+$, Li$^{2+}$ and Be$^{3+}$ is H > He$^+$ > Li$^{2+}$ > Be$^{3+}$
Observe the following reactions
I) Sucrose (aq) + H2O →[x] glucose + fructose
II) Glucose (aq) →[y] ethanol + CO2
What are $x$ and $y$ respectively? Identify the correct option from the following: