List of top Questions asked in AP EAPCET- 2026

The area (in square units) of the region bounded by the parabola $y^2 = 4x$ and the line $y = 2x$ is:

If \[ A= \begin{bmatrix} 1&2\\ 3&4 \end{bmatrix}, \] then \(\det(A)\) is equal to:

The area (in square units) of the region bounded by the parabola $y^2 = 4x$ and the line $y = 2x$ is:

If the axes are rotated about the origin in positive direction through an angle of \(30^\circ\), then the transformed equation of \[ x^2+2\sqrt{3}xy-y^2=2a^2 \] is

The determinant \[ \det \begin{bmatrix} \frac{a^2 + b^2}{c} & c & c a & \frac{b^2 + c^2}{a} & a b & b & \frac{c^2 + a^2}{b} \end{bmatrix} \] is equal to:

If the tangent drawn at \((\sqrt2,1)\) on the circle \[ x^2+y^2=3 \] is also a tangent to the two circles of equal radius \(2\sqrt3\) with centres at \[ (0,\beta_1) \quad \text{and} \quad (0,\beta_2), \] then \[ |\beta_1-\beta_2|= \]

The domain of the function $f(x) = \sqrt{\log_{10} \left(\frac{5x - x^2}{4}\right)}$ is:

If \(f\) is a derivable function and \[ 2f(\sin x)+f(\cos x)=x \qquad \forall x\in \mathbb{R}, \] then \[ f'(x)= \]

If the straight lines $x + 2y - 9 = 0$, $3x + 5y - 5 = 0$ and $ax + by - 1 = 0$ are concurrent, then the straight line $22x - 35y = 1$ passes through the point:

If $f : [1, \infty) \to [1, \infty)$ is defined by $f(x) = 2^{x(x-1)}$, then $f^{-1}(x) =$

If the straight lines $x + 2y - 9 = 0$, $3x + 5y - 5 = 0$ and $ax + by - 1 = 0$ are concurrent, then the straight line $22x - 35y = 1$ passes through the point:

The equation of the tangent to the ellipse \[ \frac{x^2}{16}+\frac{y^2}{9}=1 \] which is parallel to the line \[ 3x+4y+5=0 \] is

Let \[ \overrightarrow{OA}=\hat{i}+2\hat{j}-4\hat{k} \] and \[ \overrightarrow{OB}=3\hat{i}-4\hat{j}-2\hat{k} \] be the position vectors of points \(A\) and \(B\). If a point \(C\) divides the line segment \(AB\) in the ratio \(1:3\) externally, then the position vector of a point which divides \(OC\) in the ratio \(4:1\) internally is

A particle is moving on a straight line so that its distance \(s\) from a fixed point at any time \(t\) is proportional to \(t^n\). If \(v\) is the velocity and \(a\) is the acceleration of the particle at any time \(t\), then \[ \frac{nas}{n-1} = \]

If a vector \(3\hat i-6\hat j+2\hat k\) makes angles \(\alpha,\beta,\gamma\) with the positive \(x,y,z\)-axes respectively, then \(\cos\alpha+\cos^2\beta+7\cos^3\gamma=\)

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

If M is the foot of the perpendicular drawn from \( P(1,2,-1) \) to the plane passing through the point \( A(3,-2,1) \) and perpendicular to the vector \( 4\overline{i}+7\overline{j}-4\overline{k} \) then the length of PM is

If the arithmetic mean of the numbers \[ 2,4,6,\ldots,2n \] is \(\frac{7}{4}\), then \(n\) is equal to:

The number of points of discontinuity of the function \[ f(x)=[x]+|x-2|, \qquad -3<x<3 \] is

If it is known that a woman has two children and she has at least one girl child, then the probability that both children are girls is

If the distance between the foci of an ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] is \(6\) and the distance between its directrices is \(10\), then the equation of one of the tangents of the ellipse drawn parallel to the line \[ y=\sqrt2\,x+5 \] is

Evaluate \[ \tan^{-1}\left(\frac12\right) +\tan^{-1}\left(\frac18\right) +\tan^{-1}\left(\frac1{18}\right) +\tan^{-1}\left(\frac1{32}\right). \]

If \[ \vec a=2\hat i+\hat j-\hat k \] and \[ \vec b=\hat i-2\hat j+3\hat k, \] then the value of \[ \vec a+\vec b \] is:

The value of the definite integral $\int_{-\pi/2}^{\pi/2} (x^3 + x\cos x + \tan^5 x + 1) \, dx$ is:

If the point \(P\) represents a complex number \(z\) in the Argand diagram and \[ \frac{z-i}{z-1} \] is always purely imaginary, then the locus of \(P\) is