List of top Questions asked in AP EAMCET

If \( \theta \) is the angle between \( \vec{f} = i + 2j - 3k \) and \( \vec{g} = 2i - 3j + ak \) and \( \sin \theta = \frac{\sqrt{24}}{28} \), then \( 7a^2 + 24a = \) ?
For a dataset, if the coefficient of variation is 25 and the mean is 44, find the variance.
If \( x_1, x_2, x_3, \dots, x_n \) are \( n \) observations such that \( \sum (x_i + 2)^2 = 28n \) and \( \sum (x_i - 2)^2 = 12n \), then the variance is:
Based on the following statements, choose the correct option: Statement-I: The variance of the first \( n \) even natural numbers is \[ \frac{n^2 - 1}{4} \] Statement-II: The difference between the variance of the first 20 even natural numbers and their arithmetic mean is 112.
If m and M denote the mean deviations about mean and about median respectively of the data 20, 5, 15, 2, 7, 3, 11, then the mean deviation about the mean of m and M is:

Evaluate the integral \( \int \frac{dx}{\sqrt{\sin^3 x \cdot \cos (x - \alpha)}} \):

Evaluate the integral \( \int \frac{2 - \sin x}{2 \cos x + 3} \, dx \):
If \(2.4^{2n+1} + 3^{3n+1}\) is divisible by \(k\) for all \(n \in \mathbb{N}\), then \(k\) is:
In \(\triangle ABC\), \(bc - r_2 r_3 = \)
If \(\sec \theta + \tan \theta = \frac{1}{3}\), then the quadrant in which \(2\theta\) lies is:
The probability that a man failing to hit a target is \(\frac{1}{3}\). If he fires 4 times, then the probability that he hits the target at least thrice is
Evaluate the integral \( \int \frac{\sin^{-1} \left(\frac{x}{\sqrt{a + x}}\right) \sqrt{a + x}}{dx} \):
Evaluate the integral \( \int \frac{e^{2x}}{\sqrt{e^x + 1}} \, dx \):
Evaluate the limit: \[ \lim_{x \to 0} \frac{e^{x} - a - \log(1+x)}{\sin x} = 0, { then find } a. \]
If 7 and 8 are the lengths of two sides of a triangle and \( a \) is the length of its smallest side. The angles of the triangle are in AP and \( a \) has two values \( a_1 \) and \( a_2 \) satisfying this condition. If \( a_1<a_2 \), then \( 2a_1 + 3a_2 = \):
In a triangle ABC, if \( BC = 5 \), \( CA = 6 \), \( AB = 7 \), then the length of the median drawn from \( B \) onto \( AC \) is:
Evaluate the integral \( \int \frac{dx}{x(x^4 + 1)} \):
If \(f(x) = \begin{cases} 2x + 3, & \text{if } x \leq 1 \\ 2ax + bx, & \text{if } x > 1 \end{cases}\) is differentiable \(\forall x \in \mathbb{R}\), then \(f(2) =\)
Evaluate the integral \( \int_0^{\pi} \frac{x \sin x}{1 + \cos^2 x} \, dx \):
If \( A, B, C \) are the angles of a triangle, then \[ \sin 2A - \sin 2B + \sin 2C = \]
If \([x]\) is the greatest integer function, then evaluate the integral \( \int_{0}^{5} [x] \, dx \):
In \( \triangle ABC \), if \( a = 13 \), \( b = 14 \), and \( \cos \frac{C}{2} = \frac{3}{\sqrt{13}} \), then \( 2r_1 = \):
In \( \triangle ABC \), \( (r_2 + r_3) \csc^2 \frac{A}{2} =\)
If \( \frac{3 - 2i \sin \theta}{1 + 2i \sin \theta}\) is a purely imaginary number, then \( \theta \) is:
Evaluate the limit: \[ \lim_{x \to \frac{\pi}{4}} \frac{4\sqrt{2} - (\cos x + \sin x)^5}{1 - \sin 2x} = \]