List of top Questions asked in AP EAPCET- 2023

If \( \cos\alpha + \cos\beta = \frac{1}{3} \) and \( \sin\alpha + \sin\beta = \frac{1}{4} \), then \( \cos(\alpha + \beta) = \)
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 $y = y(x)$ 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 six-digit natural numbers that can be formed with the digits 2, 3, 4, 0, 5, 6, 7, 8 is:
The multiplicative inverse of $ z $ is:
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
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
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
The area bounded by the curves \( y - 1 = \cos x \), \( y = \sin x \) and the X-axis between \( x = 0 \) and \( x = \pi \) 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 \( A = \{ (a, b) : 4a = 5b, a \in \{1, 2, 3, \dots, 30\} \}, \) then the number of such ordered pairs \( (a, b) \) is:
If \( \vec{p} = 4\vec{i} - \vec{j} + \vec{k} \) is a point and \( \vec{q} = 9\vec{i} - 2\vec{j} + 6\vec{k} \) is a vector, then the perpendicular distance of origin from the plane passing through \( \vec{p} \) and perpendicular to \( \vec{q} \) is:
In \( \triangle ABC \), if \( r_1 : r_2 = 7:8 \) and \( r_1 : r_3 = 3:4 \), then \( a : b : c = \)
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:
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 \(A = (2, 3, 4)\) and \(B = (-2, 3, 4)\), then the locus of a point \(P\) such that \(PA + PB = 4\) 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 the sum of the cubes of the roots of the equation \( x^3 - ax^2 + bx - c = 0 \) is zero, then \( a^3 + 3c = \):
If \( (2 - 5x)^{\frac{-1}{5}} = a_0 + a_1 x + a_2 x^2 + ... \), then \( \frac{a_1}{a_2} = \)
In \( \triangle ABC \), if \[ a \cos^2 \frac{C}{2} + \cos^2 \frac{A}{2} = \frac{3b}{2}, \] then \( a + c : b \) 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 \( k = \)
If \( (2, a) \) and \( (b, 19) \) are two stationary points of the curve \( y = 2x^3 - 15x^2 + 36x + c \), then \( a + b + c = \dots \)
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 focal chord drawn through the point $ P(5, 5) $ to the parabola $ y^2 = 5x $ meets the parabola again at the point $ Q $, then the tangent drawn to this parabola at $ Q $ meets the axis of the parabola at the point:
If \( \cosh \alpha + \sinh \alpha = e^x \) and \( \sinh x = \frac{\alpha}{\alpha + 1} \), then \( \tanh x = \)