List of top Questions asked in AP EAPCET

If \( x^3 - 2x^2y + 5x + y - 5 = 0 \), then at (1,1), \( y'(1) = \)
The condition that \( f(x) = ax^3 + bx^2 + cx + d \) has no extreme value is
If \( y = \tan(3\tan^{-1} x) \), then: \[ (1 - 3x^2)\frac{d^2y}{dx^2} - 12x \frac{dy}{dx} = \]
\(\tanh(\log x) = \) (Assuming \(\log x\) is natural logarithm \(\ln x\))
\( \lim_{x \to 0} x^3 (\sqrt{x^2+\sqrt{x^4+1}} - \sqrt{2}x) = \)
In an exam:
- Three subjects have maximum marks = $ n $ each
- Fourth subject has max marks = $ 2n $
- Find the number of ways to score total $ 3n $ marks.
If $f(x) = \sqrt{2 - x^2}$ and $g(x) = \log(1 - x)$ are two real-valued functions, then the domain of the function $(f+g)(x)$ is:
Let z and w be two distinct non-zero complex numbers if \(|z|^2w - |w|^2z = z - w\), then
If the general solution of \( \frac{dy}{dx} = \frac{-y^2}{xy-y^2-x^2} \) is \( \tan^{-1}\left(\frac{x}{y}\right) = f(y) + C \), then \( f(e^3) = \)
If $\cosech\,x = \dfrac{4}{5}$, then $\sinh x = $ ?
Identify the correct statements about the anomalous behavior of Boron.
Which of the following solids is not a molecular solid?
Simplify: $\dfrac{\cos\theta}{1 - \tan\theta} + \dfrac{\sin\theta}{1 - \cot\theta}$
In which of the following, oxides of three elements X, Y, and Z are arranged in increasing order of acidic nature? Their electronic configurations are:
X: $[Ne] 3s^2 3p^1$, \quad Y: $[Ne] 3s^2 3p^3$, \quad Z: $[Ne] 3s^2$
For the parabola represented parametrically by \( x = t^2 + t + 1 \) and \( y = t^2 - t + 1 \), the length of the latus rectum is:
If the product of the perpendicular distances from any point on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) to its asymptotes is 6, and the eccentricity of the hyperbola is \( \sqrt{3} \), then the length of the conjugate axis is:
For what values of $a \in \mathbb{Z}$, the quadratic expression $(x + a)(x + 1991) + 1$ can be factorised as $(x + b)(x + c)$, where $b, c \in \mathbb{Z}$?
If a number is chosen at random from the set \( \{1, 2, 3, \dots, 100\} \), then the probability that it is a perfect cube is:
The straight line touching the circle \(x^2+y^2-2x-3=0\) and remaining normal to the circle \(x^2+y^2-4y-6=0\) is
If \( \int f(x) dx = F(x) + C \), then \( \frac{d}{dt} \int_{g(t)}^{h(t)} f(x)\,dx = \)
If \( ^{2n}C_3 : ^nC_3 = 12 : 1 \), then \( n = \) ?
Evaluate: $$ \int \frac{e^{\tan^{-1}x}}{1+x^2} \left[\left(\sec^{-1}(\sqrt{1+x^2})\right)^2 + \cos^{-1} \left( \frac{1 - x^2}{1 + x^2} \right)\right] dx $$
In a triangle $ABC$, $2(bc \cos A + ac \cos B + ab \cos C) =$
If $A + B + C = \pi$, $\cos B = \cos A \cos C$, then $\tan A \tan C =$
The number of real values of \( m \) such that the equation \[ x^2 + (2m + 1)x + m = 0 \] has equal roots is: