List of top Questions asked in AP EAPCET- 2026

The complete range of the function \( f(x) = [x]^2 + 5[x] + 6 \), where \([x]\) is the greatest integer function, is:

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 \(m\).

If the sum of the slopes of the lines given by \(x^2-2cxy-7y^2=0\) is four times their product, find the value of \(c\).

If a real valued function \( f:(1, 2] \rightarrow B \) defined by \( f(x) = \log_{10}(x-1) \) is a bijection, then \( B = \)

Points \((h,k)\), \((1,2)\), \((-3,4)\) lie on \(L_1\). Line \(L_2\) through \((h,k)\) and \((4,3)\) is perpendicular to \(L_1\). Find \(\frac{k}{h}\).

The mean of 5 observations is 5. If three of the observations are 1, 2, 6 and the other two observations are such that each is greater than 5, then the mean deviation from the mean of the observations is

In a binomial distribution with 5 trials, the probabilities of 1 success and 2 successes are 0.4096 and 0.2048 respectively. Find the variance of the distribution.

A circle passes through the ends of the latus rectum of parabola \( y^2=12x \) and has its centre at the vertex. The area inside the circle and outside the parabola in the \( 1^{st} \) quadrant is:

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 \(\theta =\)

Evaluate \(\lim_{x\rightarrow2}(x^{2}-3x+3)^{\frac{1}{x^{2}-4}}\).

If \[ f(x)= \begin{cases} \dfrac{x^{2}-4}{\sqrt{2-x}}, & x<2\\ a, & x=2\\ \log(x-2), & x>2 \end{cases} \] is a real valued function, then:

If \[ \frac{3x^2+x+2} {(3x^2+x+4)(3x^2+x+1)} = \frac{Ax+B}{3x^2+x+4} + \frac{Cx+D}{3x^2+x+1}, \] then \((A+B)+(C+D)\) is:

If the two systems of equations \( x+y-2z=0, 4x+4y-8z=0, 3x+3y-6z=0 \) and \( x+y+z=3, 2x+2y-z=\lambda, x+y-\mu z=1 \) have the same set of solutions, then \( \lambda+\mu = \)

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

If the equation of the plane containing the line \[ \vec r=\hat i+2\hat j+\hat k+t(\hat i-\hat j+2\hat k) \] and parallel to the line \[ \vec r=-\hat i+2\hat j+s(-\hat i+2\hat j+\hat k) \] in Cartesian coordinates is \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1, \] then \(a+3b+c=\)

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

The sum of all the values of \(\theta\in(0,2\pi)\) satisfying the equation \[ \sin\theta+3\cos2\theta+\sin3\theta = \cos\theta+3\sin2\theta+\cos3\theta \] is

Two balls are drawn at random from a box containing 4 white and 6 black balls one after the other without replacement. If it is known that the second ball drawn is black, then the probability that the first ball drawn is also black is

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

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

If \[ A= \begin{bmatrix} 3 & x & 2\\ 2x & 3 & -1\\ 1 & 2 & 3x \end{bmatrix} \] is a singular matrix and \(x\gt 0\), then \(\sqrt{3}\,x=\)

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

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

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

If \[ \int \frac{\tan x}{1+\tan x+\tan^2x}\,dx = x-\frac{K}{\sqrt A} \tan^{-1} \left( \frac{K\tan x+1}{\sqrt A} \right) +C, \] then the ordered pair \((K,A)\) is