List of top Mathematics Questions asked in AP EAPCET

If a polygon of $n$ sides has 560 diagonals, then $n$ = ?
The range of the real valued function \( f(x) = \frac{x^2 + x + 1}{x} \) is
If the equation of the plane passing through the point $A(-2, 1, 3)$ and perpendicular to the vector $3\vec{i} + \vec{j} + 5\vec{k}$ is $ax + by + cz + d = 0$, then $\dfrac{a + b}{c + d} =$
Let \( x \in \mathbb{R} \) and \( |x|<1 \). Then \( \tanh^{-1} x = \) ?
If \( \cos\theta - \sin\theta = \sqrt{5} \sin\theta \), then the value of \( \cos\theta + 4\sin\theta \) is:
Let the slopes $ m_1 $ and $ m_2 $ of the lines represented by: $$ ax^2 + 2hxy + by^2 = 0 $$ satisfy: $$ 3(m_1 - m_2) - 7 = 0 \quad \text{and} \quad m_1 m_2 - 2 = 0 $$ Then find the correct relation among $ a, b, h $.
If the pair of straight lines $9x^2 + axy + 4y^2 + 6x + by - 3 = 0$ represents two parallel lines then
If the angle between the lines joining the foci and the ends of the minor axis of the ellipse $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $$ is $ 90^\circ $, then its **eccentricity** is:
If the slope of the line through \( (0, 0) \) which is tangent to the curve \( y = x^2 + x + 16 \) is \( m \), then find the value of \( m - 4 \).
Which of the following is \textbf{not} a property of a Binomial distribution?
A line passing through $P(2, 3)$ and making an angle of $30^\circ$ with the positive direction of $x$-axis meets $x^2 - 2xy - y^2 = 0$ at $A$ and $B$. Then the value of $PA \cdot PB$ is
Three points $ A, B, C $ in the plane have: - x-coordinates in G.P. - y-coordinates in the same G.P. Then, the points $ A, B, C $ lie on:
Find the radius of the circle that has the lines: $$ 3x - 4y + 4 = 0 \quad \text{and} \quad 6x - 8y - 7 = 0 $$ as its tangents.
Let point $ P $ divide the line segment joining $ A(1, 2, -1) $ and $ B(-1, 0, 1) $ externally in the ratio $ 1:2 $. Given point $ Q = (1, 3, -1) $, find $ PQ $.
If \( a^2+b^2+c^2=1, a,b,c \in R \), then the set of extreme values of \(ab+bc+ca\) is
\( \lim_{n \to \infty} \left( \frac{1}{1 + n^5} + \frac{2^4}{2^5 + n^5} + \frac{3^4}{3^5 + n^5} + \ldots + \frac{n^4}{n^5 + n^5} \right) = \)
Given \[ \frac{d}{dx} \left( \frac{(x+1)^2 \sqrt{x-1}}{(x+4)^3 e^x} \right) = f(x) \left[ \frac{2}{x+1} + \frac{1}{2(x-1)} - \frac{3}{x+4} - 1 \right] \] Then find \( f(5) \).
If \( \int \frac{\sin(x-\pi/4)}{2+\sin 2x} dx = -\frac{1}{\sqrt{2}} \tan^{-1}(f(x)) + C \), then \(f(x) = \)
Given 5 different green toys, 4 different blue toys, and 3 different red toys, how many combinations of toys can be chosen taking at least one green and one blue toy?
Evaluate the integral: \[ \int_{-\pi}^{\pi} \frac{2x(1 + \sin x)}{1 + \cos^2 x}\, dx \]
Let $\vec{a} = xi + yj + zk$ and $x = 2y$. If $|\vec{a}| = 5\sqrt{2}$ and $\vec{a}$ makes an angle of $135^\circ$ with the z-axis then $\vec{a} =$
The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(16, 0.25)$ and $Y \sim P(2)$. Then the sum of the variances of $X$ and $Y$ is
If \( A \) and \( B \) are two independent events such that \( P(A) = 0.3 \), \( P(B) = x \), and \( P(A \cup B) = 0.44 \), then \( x = \):
During the winter months, in a certain village in Scotland, the probability of a day having severe fog is 0.6. The probability that in a given week there will be exactly two days with severe fog is
For any two nonzero real numbers $a$ and $b$, if the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ is a tangent to the circle $x^2 + y^2 = 1$, then which of the following is true?