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.

Find the locus of midpoints of points of intersection of the line $$ x \cos \theta + y \sin \theta = 1 $$ with the coordinate axes.

Find the locus of the point of intersection of tangents drawn at the ends of a **normal chord** of the hyperbola: $$ x^2 - y^2 = a^2 $$

The wavelength associated with the electron moving in the first orbit of hydrogen atom with velocity $ 2.2 \times 10^6\, \text{m/s} $ is (in nm):
(Given: $ m_e = 9.0 \times 10^{-31}\, \text{kg},\ h = 6.6 \times 10^{-34}\, \text{Js} $)

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: $[Ne] 3s^2$

Let z and w be two distinct non-zero complex numbers if $|z|^2w - |w|^2z = z - w$, then

$\tanh(\log x) = $ (Assuming $\log x$ is natural logarithm $\ln x$)

The standard deviation of first 10 multiples of 4 is

From a well shuffled pack of 52 cards, two cards are drawn at random. Then, the probability of both the cards being kings is

$ \lim_{x \to 0} x^3 (\sqrt{x^2+\sqrt{x^4+1}} - \sqrt{2}x) = $

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 $ ^{2n}C_3 : ^nC_3 = 12 : 1 $, then $ n = $ ?

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:

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:

If $ \int f(x) dx = F(x) + C $, then $ \frac{d}{dt} \int_{g(t)}^{h(t)} f(x)\,dx = $

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 $A + B + C = \pi$, $\cos B = \cos A \cos C$, then $\tan A \tan C =$

In a triangle $ABC$, $2(bc \cos A + ac \cos B + ab \cos C) =$

Evaluate: $$ \int \frac{e^{\tan^{-1}x}}{1+x^2} \left[\left(\sec^{-1}(\sqrt{1+x^2})\right)^2 + \cos^{-1} \left( \frac{1 - x^2}{1 + x^2} \right)\right] dx $$

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

The number of real values of $ m $ such that the equation \[ x^2 + (2m + 1)x + m = 0 \] has equal roots is:

The number of positive real roots of the equation \[ 3^{x+1} + 3^{-x+1} = 10 \] is:

In a triangle ABC, $r_1 \cot \dfrac{A}{2} + r_2 \cot \dfrac{B}{2} + r_3 \cot \dfrac{C}{2} = $ ?

If the solution of $ \frac{dy}{dx} = y \log_e 0.5 = 0 $, $ y(0) = 1 $, and $ y(x) \to k $ as $ x \to \infty $, then $ k = $