List of top Questions asked in AP EAPCET- 2026

If \(f(x)=\sqrt{-(1+x)}\sec^{-1}x\) is a real valued function, then \(f'(x)=\)

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

If \[ y=\sec^{-1}\left(\frac{1+x^2}{2x}\right) \quad \text{and} \quad x>1, \] then \[ \frac{dy}{dx}= \]

If $f(x)=\begin{cases}\frac{1-\sin^{3}x}{3\cos^{2}x}, & x\ne\frac{\pi}{2} \\ \frac{1}{2}, & x=\frac{\pi}{2}\end{cases}$, then $f^{\prime}\left(\frac{\pi}{2}\right)=$

If $y = \tan^{-1}\left(\frac{\sin x + \cos x}{\cos x - \sin x}\right)$, then $\frac{dy}{dx} = $

If \(x \in [-1,1]\) and \(y=(\cot^{-1}x)^{\cot^{-1}x}\), then \(\left(\frac{dy}{dx}\right)_{x=0}=\)

If $x = a \cos^3 t$ and $y = a \sin^3 t$, then the value of $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$ is:

If \( x^{2}y - xy^{2} + x^{3} - y^{3} = 0 \), then \( \frac{dy}{dx} \) at the point (1, 1) is

The value of \[ \lim_{x\to0}\frac{\sin5x-5\sin x}{x^3} \] is:

If \[ f(x)= \begin{vmatrix} 2+\dfrac{\sin x}{x} & 1 & 3
[4pt] 2 & 1+\dfrac{\sin x}{x} & 3
[4pt] 2 & 1 & 3+\dfrac{\sin x}{x} \end{vmatrix}, \] then \[ \lim_{x\to 0} f(x)= \]

If \[ \lim_{x\to\infty} \left(\frac{ax^2+bx+c}{lx^2+mx+n}\right) \left(\frac{lx-1}{lx+a}\right)^{\frac{x}{2}} = \frac{3}{\sqrt{16e}}, \] then \[ \lim_{x\to0} \frac{l+mx+cx^2}{a+bx+nx^2} = \]

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

Consider the quadratic expression \( f(x) = x^2 + (10-a)x - 10a \). The sum of all values of 'a', such that the roots of \( f(x)=3 \) are integers is:

The expression \( \frac{n(n + 1)^2(n+2)}{12} \) for all \( n \in \mathbb{N} \) is always:

If $\alpha,\beta$ are the roots of the equation \[ x^2-p(x+1)-c=0, \] then \[ \frac{\alpha^2+2\alpha+1}{\alpha^2+2\alpha+c} + \frac{\beta^2+2\beta+1}{\beta^2+2\beta+c} = \]

If $\alpha, \beta$ are the roots of the quadratic equation $x^2 - 2x + 4 = 0$, then the value of $\alpha^n + \beta^n$ is:

If the roots of the equation \[ x^3-px^2+qx-s=0 \] are in geometric progression, then

If the sum of two roots of the cubic equation $x^3 - 5x^2 - 2x + 24 = 0$ is $2$, then the roots of the equation are:

The quadratic expression having zero's equal to the non-integral roots of \( ||3x-4|-6|=5 \) is:

If $\alpha,\beta$ $(\alpha<\beta)$ are the roots of \[ 2x^2-x-6=0 \] and \[ \alpha x^2+kx-\beta\leq0 \quad \forall x\in\mathbb{R}, \] then the number of integral values $k$ takes is

If the roots of the quadratic equation $x^2 - 2px + q^2 = 0$ are real and distinct, then:

A positive root of the equation \[ 18x^3-9x^2-5x+2=0 \] is twice another root of it. If among its three roots, the least value is \(a\) and the greatest value is \(b\), then \(2a+3b=\)

If the roots of the equation $x^3 - 7x^2 + 14x - 8 = 0$ are in geometric progression, then the common ratio can be:

If \( a, b, c \in \mathbb{R} \) and \( -a^{2}x^{2}+bx+c>0 \quad \forall x \in \left(\frac{3-\sqrt{14}}{2},\frac{3+\sqrt{14}}{2}\right) \), then \( c^{2}-\left(\frac{b}{4}\right)^{2} = \)

If $\alpha,\beta,\gamma$ are the roots of \[ x^3-10x^2+7x+8=0, \] match List-I with List-II and choose the correct option.