List of top Questions asked in AP EAPCET- 2026

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 \(k=\)

Evaluate \[ \lim_{x\to 0}\frac{x\cdot 2^x-x}{1-\cos x}. \]

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

If \[ f(x)=\cot^{-1}\!\left(\sqrt{\cos 2x}\right), \] then \[ f'\!\left(\frac{\pi}{6}\right)= \]

If \(f\) is a differentiable function such that \[ f(1)=8 \] and \[ f'(1)=\frac18. \] If \(f\) is invertible and \(g=f^{-1}\), then

An angle between the plane \[ x+y+z=5 \] and the line \[ \frac{x-16}{0} = \frac{y-0}{-1} = \frac{z+47}{4} \] is

Area of the quadrilateral formed by joining the extremities of the major axis and minor axis of the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] is \(8\sqrt3\). If the distance between its foci is \(4\sqrt2\), then the eccentricity of the ellipse is

The direction ratios of a line \(L\) are \((ab,b,b)\) \((b\gt 0)\) and the line \(L\) passes through \[ P(b,b,b). \] If \(Q(x,y,z)\) is a point on the line at a distance of \(b\) units from \(P\), then \[ x+y+z= \]

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 normal drawn to the parabola \[ y^2=8x \] at \((2,4)\) meets the parabola again at the point

If \(C\) is the centre of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] and the tangent drawn at any point \(P\) on the hyperbola meets the lines \[ bx-ay=0 \] and \[ bx+ay=0 \] at \(Q\) and \(R\) respectively, then \[ CQ\cdot CR= \]

If the centre of a circle \(S\) is \((2,4)\) and the length of the chord made by the secant \[ x+y+2=0 \] on \(S\) is \(6\) units, then the equation of the circle \(S\) is

If the points \[ (2,0),\ (0,1),\ (4,0),\ (0,k) \] are concyclic, then \(k=\)

If \(a\neq 0\) and the line \[ 2bx+3cy+4d=0 \] passes through the points of intersection of the parabolas \[ y^2=4ax \] and \[ x^2=4ay, \] then

For all real values of \(\lambda\), the point that lies on the polar of \[ (2\lambda,\lambda-4) \] with respect to the circle \[ x^2+y^2-4x-6y+1=0 \] is

The equation of the circle passing through the points of intersection of the circles \[ x^2+y^2-2x-4y+1=0, \] \[ x^2+y^2-4x-2y+4=0 \] and having its centre on the line \[ x-2y-3=0 \] is

The equation of the line that is a tangent to the circle \[ x^2+y^2-6x+4y+12=0 \] is

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 \[ |h|= \]

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

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

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 the coordinate axes are rotated about the origin through an angle \[ \frac{\pi}{8} \] in the positive direction to remove the \(xy\)-term from the equation \[ ax^2+bxy+y^2=0, \] then

Let \(S\) be the set of all words formed by arranging all the letters of the word HOMOGENEOUS. If a word is randomly chosen from the set \(S\), then the probability that the word selected has all the consonants together is

The following is the probability distribution of a discrete random variable. If its mean is \(2.81\), then \(\alpha\beta=\) \[ \begin{array}{|c|c|c|c|c|c|} \hline X=x & -1 & -2 & 1 & \alpha & 3\\ \hline P(X=x) & \frac{1}{25} & \beta & \frac14 & \frac{9}{25} & \frac{3}{10}\\ \hline \end{array} \]