List of top Questions asked in AP EAPCET- 2026

The variance of the first $n$ even natural numbers is:

If $y = e^{a \sin^{-1} x}$, then $(1 - x^2) y_2 - x y_1 =$

If $f(x) = \frac{k \cos x}{\pi - 2x}$ for $x \neq \frac{\pi}{2}$ and $f\left(\frac{\pi}{2}\right) = 3$ is continuous at $x = \frac{\pi}{2}$, then the value of $k$ is:

In a triangle \(ABC\), if \(a=6,\ b=5,\ c=9\), then the sum of the squares of the reciprocals of the altitudes of the triangle is

If $\vec{a} = 2\vec{i} + 3\vec{j} - \vec{k}$, $\vec{b} = -\vec{i} + 2\vec{j} - 4\vec{k}$ and $\vec{c} = \vec{i} + \vec{j} + \vec{k}$, then $(\vec{a} \times \vec{b}) \cdot (\vec{a} \times \vec{c}) =$

From the set \[ \{2,3,5,7\} \] two numbers are selected one after the other with replacement. If \(X\) is the random variable representing the absolute difference of the two numbers selected, then the mean of \(X\) is

If the probability that a person suffers a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ will suffer a bad reaction is:

The value of the integral \[ \int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec(2023x)}{1 + (2023)^{2023x}} \, dx \] is equal to:

If a real valued function \(f : A \to B\) defined by \(f(x)=|x|-[x]\) is a bijection, then \(A\) and \(B\) are respectively:

Evaluate \[ \lim_{n\to\infty} \frac{1+2^4+3^4+\cdots+n^4}{n^5} - \lim_{n\to\infty} \frac{1+2^3+3^3+\cdots+n^3}{n^5}. \]

If \(A(1,1,1)\), \(B(2,3,4)\) and \(C(2,5,7)\) are the vertices of \(\triangle ABC\), then the length of the altitude drawn through the vertex \(A\) is:

A vector \( \vec{a} \) has components \( 2p \) and \( 1 \) with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the positive direction. If with respect to the new system, \( \vec{a} \) has components \( p+1 \) and \( 1 \), then the values of \( p \) are:

The integral \[ \int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}} \, dx \] is equal to:

The equation of the normal to the curve \( y = \log_e x \) at the point \( P(1,0) \) is ____.

Let \(f,g,h\) be differentiable functions such that \[ \begin{vmatrix} f(x) & g(x) & h(x)\\ f'(x) & g'(x) & h'(x)\\ f''(x) & g''(x) & h''(x) \end{vmatrix} =0. \] Then which of the following statements is correct?

The variance of the data \[ 4,\;7,\;8,\;10,\;13,\;16,\;19 \] is

The maximum area of a rectangle inscribed in a circle of radius $r$ is:

If the ends of the major axis \(A'\) and \(A\) of the ellipse \[ \frac{(x-2)^2}{a^2}+\frac{(y-3)^2}{b^2}=1 \] are respectively at distances \(9\) and \(3\) units from a directrix \(L\), then the foci of the ellipse are:

If \[ z=\frac{(1-i)^3}{(\sqrt{3}-i)^2}, \] then the complex conjugate of \(z\) is:

If \[ z=\cos\theta+i\sin\theta, \] then \(|z|\) is equal to:

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

If $a_n = \sum_{r=0}^n \frac{1}{^{n}C_r}$ and $b_n = \sum_{r=0}^n \frac{r}{^{n}C_r}$, then $\frac{b_n}{a_n} =$

The value of the integral \( \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \, dx \) is equal to:

In a binomial distribution, the mean is 4 and the variance is 3. Then the number of trials $n$ is:

Consider the system of linear equations \[ x+y+z=6, \] \[ x+2y+3z=10, \] \[ 3x+2y+\lambda z=\mu. \] If the system has infinitely many solutions, then the value of \(\mu+\lambda\) is: