List of top Questions asked in AP EAPCET

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 \( f(e^3) = \)
Identify the correct statements about the anomalous behavior of Boron.
Simplify: $\dfrac{\cos\theta}{1 - \tan\theta} + \dfrac{\sin\theta}{1 - \cot\theta}$
Which of the following solids is not a molecular solid?
If the lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ intersect on the x-axis, which of the following is in general incorrect
Find the locus of the point of intersection of tangents drawn at the ends of a **normal chord** of the hyperbola: $$ x^2 - y^2 = a^2 $$
When a ball is dropped from a height $h$ it takes $t$ sec to reach the ground. If the same experiment is done on a different planet having the mass 100 times the earth’s mass and radius 10 times the earth’s radius, then the time it will take to cover the same height $h$ is
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: $[Ne] 3s^2$
The standard deviation of first 10 multiples of 4 is
Two planets, A and B, orbit around a star such that the time period of A is 8 times the time period of B. The ratio of orbital velocities of the planets A and B is
In a triangle \( ABC \), the identity holds: \[ s \left( \frac{r_1 - r}{a} + \frac{r_2 - r}{b} + \frac{r_3 - r}{c} \right) = ? \]
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
In a triangle $ABC$, $2(bc \cos A + ac \cos B + ab \cos C) =$
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: $$ \int \frac{e^{\tan^{-1}x}}{1+x^2} \left[\left(\sec^{-1}(\sqrt{1+x^2})\right)^2 + \cos^{-1} \left( \frac{1 - x^2}{1 + x^2} \right)\right] dx $$
If $A + B + C = \pi$, $\cos B = \cos A \cos C$, then $\tan A \tan C =$
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 the points of intersection of the coordinate axes and $|x + y| = 2$ form a rhombus, then its area is
Find the length of the intercept made by the line $ x + 1 = 0 $ between the lines: $$ 3x + 2y = 5 \quad \text{and} \quad 3x + 2y = 3 $$
Evaluate \( \int \frac{\cos(\sec^2 x) - 2022}{\cos^{2022} x} dx = f(x) + C \Rightarrow f\left( \frac{\pi}{4} \right) = \)
The values of \(\theta\), for which \( \frac{3+2i\sin\theta}{1-2i\sin\theta} \) is real are