List of top Questions asked in AP EAPCET

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 = $ ?
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 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 $ABC$, $2(bc \cos A + ac \cos B + ab \cos C) =$
Simplify: \( \sin(x + y) \sec x \sec y = \)
The number of real values of \( m \) such that the equation \[ x^2 + (2m + 1)x + m = 0 \] has equal roots is:
For the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), if the length of the transverse axis is 8 and the distance between the foci is \( 2\sqrt{41} \), then the length of its latus rectum is:
The number of positive real roots of the equation \[ 3^{x+1} + 3^{-x+1} = 10 \] is:
Let \( z \) and \( w \) be two complex numbers such that \( \bar{z} + i\bar{w} = 0 \) and \( \text{Arg}(zw) = \pi \). Then \( \text{Arg}(z) = \)
In a triangle ABC, $r_1 \cot \dfrac{A}{2} + r_2 \cot \dfrac{B}{2} + r_3 \cot \dfrac{C}{2} = $ ?
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