List of top Questions asked in AP EAPCET- 2026

Rain is falling vertically with a speed of \(2\,\text{ms}^{-1}\). A boy from rest starts moving with a constant acceleration of \(2\,\text{ms}^{-2}\) along a straight road holding an umbrella. For the rain to be always parallel to the axis of umbrella, the rate at which the angle of axis of umbrella with the vertical should be changing at time \(t\) is

If the percentage error in the measurement of radius is \(2\%\), then the error in measurement of volume of a sphere is

Consider the random experiment of throwing a die and tossing a coin. Let \[ \{(a,b)\mid a\in\{H,T\},\ b\in\{1,2,\ldots,6\}\} \] denote the outcomes of the experiment. If $X$ is a random variable defined by \[ X(a,b)=b, \] then the variance of $X$ is

Assertion (A): If each of the angles $A,B,C$ is not a multiple of $\pi$, then the vectors \[ \vec r_1=(\sec^2A)\hat i+\hat j+\hat k, \] \[ \vec r_2=\hat i+(\sec^2B)\hat j+\hat k, \] \[ \vec r_3=\hat i+\hat j+(\sec^2C)\hat k \] are coplanar. Reason (R): The three vectors \[ \vec a=a_1\hat i+a_2\hat j+a_3\hat k, \] \[ \vec b=b_1\hat i+b_2\hat j+b_3\hat k, \] \[ \vec c=c_1\hat i+c_2\hat j+c_3\hat k \] are coplanar if and only if \[ \begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix}=0. \] Which of the following is true?

If the function $f(x)=\begin{cases}\frac{2h(x)-g(x)}{(h(x)+7)^{2/3}}, & x\ne0 \\ \frac{7}{4}, & x=0\end{cases}$ is continuous at $x=0$ and $\lim_{x\rightarrow0}h(x)=1$, then $\lim_{x\rightarrow0}g(x)=$

Let $f:\mathbb{R}^{+}\rightarrow\mathbb{R}$ be such that $f(e)=\frac{7}{4}$ and $f^{\prime}(x^{2})=\frac{3\log x}{x^{2}}$, then $f(e^{2})=$

If the point P which divides the line segment joining $A(1,1,1)$ and $B(2,2,2)$ in the ratio 1: m lies on the plane $x+2y+3z-1=0$, then $m=$

The area of the region bounded by the curve $y=x^{2}+x$, the lines $y=x$, $x=1$ and $y=2$ is

If \[ \frac34+\frac{15}{16}+\frac{63}{64}+\cdots+n \text{ terms} =\frac{939}{256}, \] then $5n=$

If $I_{n}=\int\sin^{n}x dx$, then $I_{6}-\frac{5}{6}I_{4}=$

When the origin is shifted to the point \[ \left(\frac74,-\frac14\right) \] by translation of axes, the transformed equation of \[ x^2-2xy+3y^2+2gx+2fy-6=0 \] is \[ 8X^2-16XY+24Y^2+k=0. \] Then \[ -27(2f+g)= \]

If $\int\frac{1}{x^{2}+4x+\alpha}dx=\frac{1}{2\sqrt{2}}\tan^{-1}\left(\frac{x+2}{2\sqrt{2}}\right)+c$, then $\int\frac{1}{x^{2}+4x-\alpha}dx=$

If $(h, k)$ is the pole of the line $2x-3y+4=0$ with respect to the circle $x^{2}+y^{2}-4x+6y-3=0$, then $10h+k=$

If the acute angle between the parabolas $y=8x-x^{2}$ and $y=x^{2}-4x$ is $\theta$, then $\tan\theta=$

The shortest distance between the two lines \[ \vec r=(\hat i-\hat j)+s(\hat j+2\hat k) \] and \[ \vec r=(2\hat i+\hat k)+t(\hat i-\hat j+\hat k) \] is

A $\subseteq \mathbb{R}$ and $f:A \to \mathbb{R}$ is a function defined by $f(x)=\dfrac{x-1}{x+1}$. If the domain of the function $f(2x)$ is $B$, then $A \cap B =$

If \[ \frac{x}{(x^2+1)^2(x-1)} = \frac{Ax+B}{x^2+1} + \frac{Cx+D}{(x^2+1)^2} + \frac{E}{x-1}, \] then \[ A+B-C+2D= \]

Let $[y]$ represent the greatest integer less than or equal to $y$. Then the set of all $x$ at which $f(x)=\cos^{-1}[4x+3]$ is differentiable is

$\lim_{x\rightarrow1}\frac{(9x-1)(\sqrt{x}-1)}{3x^{2}+2x-5}=$

If $X\sim B(n,p)$ is a binomial variate, $8p^2+15p-2=0$ and the product of the mean and variance of $X$ is $\dfrac78$, then $P(X=4)=$

If $\lim_{n\rightarrow5}(\frac{[n]}{2})^{3}-(\frac{[n]^{3}}{2^{4}})=k$, then $\lim_{n\rightarrow k^{+}}(\frac{[n]}{2})^{3}-(\frac{[n]^{3}}{2^{4}})=$

The mean deviation about the mean for the following data is \[ \begin{array}{c|cccc} x_i & 1 & 2 & 4 & 7\\ \hline f_i & 3 & 2 & 4 & 1 \end{array} \]

If \(f(x)=\frac{\cos^{4}x-1}{x^{2}}\), \(x\ne0\) and \(f(0)=2\) is a real valued function, then:

The origin is shifted to (2, 3) and axes are rotated through angle \(\theta\). If \(3x^2+2xy+3y^2-18x-22y+50=0\) transforms to \(4x^2+2y^2-1=0\), then \(\theta =\)

If one of the lines \(my^2 + (1-m^2)xy - mx^2 = 0\) is a bisector of the angle between the lines \(xy = 0\), find \(m\).