List of top Questions asked in AP EAPCET- 2022

Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the 10 pages selected at random have no print mistakes is:
Which of the following solids is not a molecular solid?
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
The pair of elements that form both oxides and nitrides, when burnt in air are
If \( x^3 - 2x^2y + 5x + y - 5 = 0 \), then at (1,1), \( y'(1) = \)
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 $f(x) = \sqrt{2 - x^2}$ and $g(x) = \log(1 - x)$ are two real-valued functions, then the domain of the function $(f+g)(x)$ is:
The standard deviation of first 10 multiples of 4 is
In a triangle \( ABC \), the identity holds: \[ s \left( \frac{r_1 - r}{a} + \frac{r_2 - r}{b} + \frac{r_3 - r}{c} \right) = ? \]
A large tank open to the atmosphere at the top and filled with water develops a small hole in the side at a point 20 m below the water level. If the rate of flow of water from the hole is \(3 \times 10^{-3}\,\text{m}^3/\text{min}\), then the area of the hole is: (Take \( g = 10\,\text{m/s}^2 \))
In a U-tube with radii 2 mm and 4 mm, surface tension = 0.03 N/m, density = 1500 kg/m\(^3\), contact angle = 0. Height difference in limbs 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: $[Ne] 3s^2$
If $\cosech\,x = \dfrac{4}{5}$, then $\sinh x = $ ?
The condition that \( f(x) = ax^3 + bx^2 + cx + d \) has no extreme value is
\( \lim_{x \to 0} x^3 (\sqrt{x^2+\sqrt{x^4+1}} - \sqrt{2}x) = \)
The equation of the circle passing through the origin and cutting orthogonally the circles \( x^2 + y^2 + 6x - 15 = 0 \) and \( x^2 + y^2 - 8y - 10 = 0 \) is:
If \( y = \tan(3\tan^{-1} x) \), then: \[ (1 - 3x^2)\frac{d^2y}{dx^2} - 12x \frac{dy}{dx} = \]
Find the locus of midpoints of points of intersection of the line $$ x \cos \theta + y \sin \theta = 1 $$ with the coordinate axes.
Identify the correct statements about the anomalous behavior of Boron.
Simplify: $\dfrac{\cos\theta}{1 - \tan\theta} + \dfrac{\sin\theta}{1 - \cot\theta}$
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.
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 \( \frac{d}{dt} \int_{g(t)}^{h(t)} f(x)\,dx = \)
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: