List of top Mathematics Questions asked in AP EAPCET

For all \( n \in \mathbb{N} \), which of the following is less than or equal to \( \frac{3^n - 1}{2} \)?
If a real-valued function \( f : [-1, 2] \to B \) is defined by: \[ f(x) = \begin{cases} 1 - x, & \text{when } -1 \leq x \leq 1 \\ x - 1, & \text{when } 1 < x \leq 2 \end{cases} \] and if \( f \) is a surjection, then \( B = ? \)
Let \( f : \mathbb{N} \to \mathbb{N} \) be a function such that \( f(x + y) = f(x) + f(y) + xy \) for every \( x, y \in \mathbb{N} \). If \( f(1) = 2 \), then \( \sum\limits_{k=0}^{10} f(k) \) is equal to:
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2x^2 - xy - y^2}{x^2 - y^2} \]
Evaluate the integral: \[ \int \frac{\sin x + \cos x}{\sin x - \cos x} \, dx =\ ? \]
Evaluate the integral: \[ \int_0^{\pi} \frac{x \sin x}{\sin^2 x + 2\cos^2 x} \, dx \]
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{1^2 + n^2} + \frac{2}{2^2 + n^2} + \frac{3}{3^2 + n^2} + \cdots + \frac{n}{n^2 + n^2} \right) \]
If \[ \int \frac{1}{\cot \frac{x}{2} \cot \frac{x}{3} \cot \frac{x}{6}} \, dx = A \log \left| \cos \frac{x}{2} \right| + B \log \left| \cos \frac{x}{3} \right| + C \log \left| \cos \frac{x}{6} \right| + k, \] then \(A + B + C =\)
If \( \cosh 2x = 199 \), then \( \cot hx = \)
In a \( \triangle ABC \), \( A - B = 120^\circ \), \( R = 8r \), then \[ \frac{1 + \cos C}{1 - \cos C} =\ ? \]
If \( z = x + iy \) and if the point \( P \) in the Argand diagram represents \( z \), then the locus of the point \( P \) satisfying the equation \( 2|z - 2 - 3i| = 3|z + i - 2| \) is a circle with centre:
The minimum value of \( |z - 1| + |z - 5| \) is:
From the top of a tower 50 meters high, the angle of depression to a point on the ground is 30°. What is the distance from the base of the tower to that point on the ground? (Assume the ground is horizontal)
In \(\triangle ABC\), if \(a = 2\), \(b = 3\), and \(\angle C = 60^\circ\), then the value of \(c^{2}\) is:
Evaluate the integral: $$ \int_0^1 \frac{\ln (1+x)}{1+x^2} \, dx $$
The general solution of the differential equation \( \frac{dy}{dx} + 2y = e^{-x} \) is:
The general solution of the equation \( \cos(2x) = \frac{1}{2} \) is:
A bag contains 4 red and 6 blue balls. Two balls are drawn one after the other without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn was blue?
If vectors \( \vec{a} = 2\hat{i} + 3\hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} - \hat{j} + 2\hat{k} \), then the magnitude of the projection of \( \vec{a} \) on \( \vec{b} \) is:
A bag contains 5 red, 4 blue, and 3 green balls. Three balls are drawn at random. What is the probability that at least two balls are of the same color?
If \( f(x) = \lfloor x \rfloor + \lfloor -x \rfloor \), where \( \lfloor \cdot \rfloor \) is the greatest integer function, then the value of \( f(2.5) \) is:
A circle touches the x-axis at point \( (4,0) \) and its center lies on the line \( x + y = 6 \). What is the equation of the circle?
If \( (x - 2) \) is a factor of \( x^3 - 4x^2 + ax + 8 \), find the value of \( a \):
The radius of a sphere is increased by 20%. What is the percentage increase in its volume?
The 10th term of an arithmetic progression is 35 and the 20th term is 65. What is the first term?