List of top Questions asked in AP EAPCET- 2026

If the quadratic equations \[ x^2+2x-4k=0 \] and \[ x^2+9x+3k=0 \] have exactly one common root and \(k\neq 0\), then the equation having \(k\) as a root is

All possible 3 digit numbers are formed using all the digits \(2,3,5,7,9\) without using any digit more than once. Among these 3 digit numbers, the number of numbers which are divisible by \(3\) but not divisible by \(5\) is

The area (in sq. units) of the region bounded by \[ x=0,\quad x=\frac{\pi}{2}, \] \[ y=0,\quad y=\cos x,\quad \text{and}\quad y=\tan x \] is

Evaluate \[ \int x^2(\log x)^2\,dx. \]

If \[ \int \frac{x^2-x+1}{x^2+1}\,e^{\cot^{-1}x}\,dx = A(x)e^{\cot^{-1}x}+C, \] then \(A(x)=\)

If \[ \tan^{-1}\left(\frac{1}{2\sqrt2}\right) - \cos^{-1}\left(\frac{1}{\sqrt3}\right) + \sin^{-1}(x) = 0, \] then \(x=\)

Assertion (A): If \[ 2+6+16+40+\cdots \text{ to } k \text{ terms}=4608, \] then \(k=9\). Reason (R): \[ 2+3\cdot2+4\cdot2^2+\cdots+n\cdot2^{\,n-1}=n\cdot2^n, \qquad \forall n\in\mathbb N \] Which one of the following options is correct?

Find the sum of the infinite series \[ -1+\frac{7}{10}\cdot 2^2-\frac{7\cdot 9}{10\cdot 15}\cdot 2^3+\frac{7\cdot 9\cdot 11}{10\cdot 15\cdot 20}\cdot 2^4-\cdots\infty \]

If \(\vec c\) and \[ (\vec b\times \vec c)\times(\vec c\times \vec a) \] are parallel vectors, then \[ \left[\vec c\times\vec a\;\;\; \vec a\times\vec b\;\;\; \vec b\times\vec c\right] = \]

At any point on the curve \[ by^2=(x+a)^3, \] if the length of the sub-tangent (ST) and the length of the sub-normal (SN) are such that \[ p(\text{SN})=q(\text{ST})^2, \] then \[ \frac{p}{q}= \]

There are 15 identical balls for sale among which 4 are red, 5 are black and 6 are white. If a person buys at least one ball out of these 15 balls, then the total number of ways in which that person can buy the balls is

There are 10 cards numbered \(1\) to \(10\). The number of ways in which at least 3 cards can be chosen from these 10 cards is

If standard deviation of the data \[ 1,15,35,53,72,64 \] is \(x\), then the variance of the data \[ 62,70,51,33,13,-1 \] is

Consider the lines \[ L_1: 2x+3y+1=0 \] and \[ L_2: 3x-2y+1=0. \] The locus of a variable point that is equidistant from the two lines \(L_1=0\) and \(L_2=0\) is

The lines \[ L_1:2x+y+1=0 \] and \[ L_2:x-2y+4=0 \] intersect at \(A\). Let \(P\) be a point at a distance \(5\) units from \(L_1=0\) and \(\alpha\) units from \(L_2=0\). If \(M\) and \(N\) are the feet of the perpendiculars from \(P\) on the lines \(L_1=0\) and \(L_2=0\) respectively, and the area of the quadrilateral \(AMPN\) is \(25\) sq. units, then the point \(P\) lies on the line

If \(P(\alpha,\alpha+1)\) is the foot of the perpendicular drawn from the origin to the line \(L\) and the \(x\)-intercept of \(L\) is \[ \left(-\frac52,0\right), \] then the sum of the squares of the distances from the origin to all such possible points \(P\) is

If the slope of one of the lines is twice the slope of the other in the pair of straight lines \[ 6x^2+2hxy+y^2=0, \] then \[ |h|= \]

If the equation \[ \lambda x^2-5xy+6y^2+x-3y=0 \] represents a pair of straight lines, then the point of intersection of these straight lines is

If \[ u=\sqrt{a^2\cos^2\theta+b^2\sin^2\theta} + \sqrt{a^2\sin^2\theta+b^2\cos^2\theta}, \] then the difference between the maximum and minimum values of \(u^2\) is

If \[ \sinh x=-\frac12,\qquad \cosh y=2, \] and \[ x+y=\log p, \] then \(p=\)

If \(f(x)\) is defined by \[ f(x)= \begin{cases} \dfrac{1-\tan x}{4x-\pi}, & x\ne \dfrac{\pi}{4},\; x\in\left[0,\dfrac{\pi}{2}\right] \\[6pt] k, & x=\dfrac{\pi}{4} \end{cases} \] and \(f(x)\) is continuous in \[ \left[0,\frac{\pi}{2}\right], \] then \(k=\)

If \[ \lim_{x\to\infty}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2x}=e^2, \] then \(a=\)

A \(=(-2,2,3)\), \(B=(13,-3,13)\) are two points and \(P\) is a variable point such that \[ PA:PB=2:3. \] If \(P\) lies on the sphere \[ x^2+y^2+z^2+ux+vy+wz-247=0, \] then \[ u+v+w= \]

The general solution of the differential equation \[ y(2x+y)\,dx=x(x+y)\,dy \] is

The maximum volume (in cu. m) of a right circular cone having slant height \(3\) m is