List of top Mathematics Questions asked in AP EAPCET

In $ \triangle ABC $, the expression $ \frac{a}{s-a} + \frac{b}{s-b} + \frac{c}{s-c} $ is equivalent to:
If \( \cos\alpha + \cos\beta = \frac{1}{3} \) and \( \sin\alpha + \sin\beta = \frac{1}{4} \), then \( \cos(\alpha + \beta) = \)
If $y = y(x)$ is a particular solution of $\sqrt{1 - x^2} \frac{dy}{dx} + \frac{2x}{\sqrt{1 - x^2}} y = x$, $y(0) = 1$, then $y\left(\frac{1}{2}\right) =$
The number of positive even divisors of 6300 is:
If \( X \) is a random variable such that \[ P(X = -2) = P(X = -1) = P(X = 2) = P(X = 1) = \frac{1}{6}, \quad P(X = 0) = \frac{1}{3}, \] then the mean of \( X \) is:
Let \( \vec{a}, \vec{b}, \vec{c} \) be coinitial vectors and \( \vec{a} = 2\hat{i} - \hat{j} + 5\hat{k}, \vec{b} = 3\hat{i} + 7\hat{j} - \hat{k} \). If \( \cos(\theta) = 0 \), where \( \theta \) is the angle between \( \vec{a} \) and \( \vec{b} \), and \( \vec{c} \) is the vector along the bisector of the angle \( \angle ABC \), then the vector \( \mathbf{c} \) is:
If \( m \in \mathbb{Z}^+, n = 2m \) and \[ \int_0^{\frac{\pi}{2}} \sin^n x \cos^m x \, dx = K(m) \int_0^{\frac{\pi}{2}} \sin^m x \, dx, \text{ then } \frac{2^{n-1}(m - 1)!}{(2m - 1)!} \cdot K(m) = \]
Given that the solid obtained by rotating a rectangle about one of its sides is a cylinder. If the perimeter of a rectangle is 48 cm and the volume of the cylinder formed by rotating it is maximum, then the dimensions of that rectangle is
The area bounded by the curves \( y - 1 = \cos x \), \( y = \sin x \) and the X-axis between \( x = 0 \) and \( x = \pi \) is
If \( f(x) = \begin{cases} ax^2 - bx + 2, & x<3 \\ bx - 3, & x \geq 3 \end{cases} \) is differentiable at every \( x \in \mathbb{R} \), then the area (in sq units) of the triangle formed by the line \(\frac{x}{a} + \frac{y}{b} = 1\) with the coordinate axes is:
If the graph of the anti derivative \( g(x) \) of \( f(x) = \log(\log x) + (\log x)^{-2} \) passes through \( (e, 2023 - e) \) and the term independent of \( x \) in \( g(x) \) is \( k \), then the sum of all the digits of \( k \) is
An equation of a plane parallel to the plane \( x - 2y + 2z - 5 = 0 \) and which is at one unit distance from the origin is:
If \( (2 - 5x)^{\frac{-1}{5}} = a_0 + a_1 x + a_2 x^2 + ... \), then \( \frac{a_1}{a_2} = \)
If \(A = (2, 3, 4)\) and \(B = (-2, 3, 4)\), then the locus of a point \(P\) such that \(PA + PB = 4\) is:
The multiplicative inverse of $ z $ is:
Let \( A \subseteq \mathbb{R}, B \subseteq \mathbb{R} \) and \( f : A \to B \) be defined by \( f(x) = x^2 - 3x + 2 \). If \( f \) is a bijection, then
If \( A = \{ (a, b) : 4a = 5b, a \in \{1, 2, 3, \dots, 30\} \}, \) then the number of such ordered pairs \( (a, b) \) is:
a, b, c, d are arbitrary constants. Then the corresponding differential equation to \( y = ae^x + be^{-x} + c \cos x + d \sin x \) is
If \( (2, a) \) and \( (b, 19) \) are two stationary points of the curve \( y = 2x^3 - 15x^2 + 36x + c \), then \( a + b + c = \dots \)
If $ \int_{n}^{n+1} g(x) \, dx = n^2 $, $ \forall n \in Z $, then the value of $ \int_{-3}^{3} g(x) \, dx $ is
If \( P(X = x) = k \left( \frac{3}{8} \right)^x \), where \( x = 1, 2, 3, \dots \) is the probability distribution function of a discrete random variable X, then \( k = \)
The probability that a person chosen at random is left handed is 0.1. Then the probability that in a group of 10 people there is exactly one left-handed person is
If the sum of the cubes of the roots of the equation \( x^3 - ax^2 + bx - c = 0 \) is zero, then \( a^3 + 3c = \):
In \( \triangle ABC \), if \( r_1 : r_2 = 7:8 \) and \( r_1 : r_3 = 3:4 \), then \( a : b : c = \)
In \( \triangle ABC \), if \[ a \cos^2 \frac{C}{2} + \cos^2 \frac{A}{2} = \frac{3b}{2}, \] then \( a + c : b \) is: