List of top Questions asked in AP EAPCET- 2026

If \[ {}^{n}P_{4}=5040 \] and \[ {}^{15}P_{r}=2730, \] then the value of \(n+r\) is:

A bag \(P\) contains \(5\) white and \(4\) blue balls. Another bag \(Q\) contains \(4\) white and \(5\) blue balls. One ball is drawn at random from bag \(P\) and transferred to another bag. Then one ball is drawn from bag \(Q\). Find the probability that the ball drawn from bag \(Q\) has the same colour as the ball transferred from bag \(P\).

If the circle $x^2 + y^2 - 4x - 6y + \lambda = 0$ touches the x-axis, then the value of $\lambda$ is:

The minimum value of the function $f(x) = x^2 + \frac{250}{x}$ for $x > 0$ is:

If \(\sin\theta\neq 0\) and \[ \frac{1}{2}\sin\theta,\quad \cos\theta,\quad \cot\theta \] are in geometric progression, then the number of values of \(\theta\) lying in the interval \((-2\pi,2\pi)\) is

If \[ a_n= \sqrt{7+\sqrt{7+\sqrt{7+\cdots}}} \] (\(n\) radicals), then which of the following is true?

The maximum value of $y = x(\log x)^2$ is:

If the mean deviation of the numbers $1, 1+d, 1+2d, \dots, 1+100d$ from their mean is 255, then $d =$

The value of the integral \( \int_{0}^{\pi/2} \sin^6 x \cos^4 x \, dx \) is equal to:

If \[ f(x)= \begin{cases} \dfrac{\sqrt{2+\cos x}-1}{(\pi-x)^2}, & x\neq \pi\\ k, & x=\pi \end{cases} \] is continuous at \(x=\pi\), then \(k=\)

The equations of the pairs of opposite sides of a parallelogram are \[ x^2-5x+6=0 \] and \[ y^2-6y+5=0. \] Then the equations of its diagonals are

If \(O\) is the origin and \(H\) is the orthocenter of a triangle formed by the lines \[ x+y=1, \] \[ 6x^2-13xy+6y^2=0, \] then \[ OH= \]

The value of the integral \( \int_{-2\pi}^{2\pi} \sin^4 x \cos^6 x \, dx \) is equal to:

In \(\triangle ABC\), if \[ \overrightarrow{AB}=2\hat{i}-\hat{j}+2\hat{k} \] and \[ \overrightarrow{AC}=3\hat{i}-3\hat{j}+4\hat{k}, \] then the triangle \(ABC\) is

The value of the definite integral $\int_0^{\pi/2} \ln(\tan x) \, dx$ is:

If the unit vector which is perpendicular to the normals drawn to the planes \[ \vec r\cdot(2\hat{i}+\hat{j}-\hat{k})=3 \] and \[ \vec r\cdot(6\hat{i}+3\hat{j}+2\hat{k})=4 \] is \[ x\hat{i}+y\hat{j}+z\hat{k}, \] then \(x+y+z=\)

If \( A(1,0,1) \), \( B(0,1,-1) \), \( C(-1,1,0) \) are the vertices of a triangle ABC, then \( \cos^{2}A+\cos^{2}B = \)

If the equation \[ x^4-10x^3+37x^2-60x+36=0 \] has two distinct real roots, where each one of them is a repeated root, then the sum of squares of all the roots of the given equation is

If \[ A(0,1,-2),\quad B(-1,2,-3),\quad C(2,-3,4) \] and \[ D(3,4,5) \] are the vertices of a tetrahedron \(ABCD\), then the volume of the tetrahedron is

A dice is thrown twice. If getting a number greater than four is considered a success, the variance of the probability distribution of the number of successes is

Let \[ A= \begin{bmatrix} 1 & 2\\ 2 & 1 \end{bmatrix}. \] Then the determinant of \(A^2\) is:

For \(n\in\mathbb{N}\), \[ 1^2+2^2+3^2+\cdots+n^2 > \]

When the origin is shifted to $(2, 3)$ by translation of axes, the coordinates of a point $P$ become $(1, -2)$. The original coordinates of $P$ are:

The area (in square units) of the region bounded by the parabola $y^2 = 4x$ and the line $y = 2x$ is: