List of top Questions asked in AP EAPCET- 2023

The area (in square units) of the triangle formed by the lines \( x = 0 \), \( y = 0 \), and \( 3x + 4y = 12 \) is:
A function \( f(x) \) is defined as: \[ f(x) = \begin{cases} ax^2 + bx + c, & x \leq -1
2x^2 + 4x + 1, & -1<x<1
cx^2 + bx + a, & x \geq 1 \end{cases} \] If \( f(x) \) is continuous on \( \mathbb{R} \) and \( \lim_{x \to -\frac{3}{2}} f(x) = 14 \), then \( \lim_{x \to 2} f(x) = \):
Let \( c_1, c_2, c_3, c_4 \) be arbitrary constants. The order of the differential equation corresponding to \[ y = c_1 e^x + c_2 e^{\log_e x} + c_3 \sin^2 x - c_4 (\cos^5 x - 1) \] is:
\(A(-2, 9)\) and \(B(1, 6)\) are two points on the curve \(y = x^2 + 5\). The coordinates of the point \(C\) on the curve such that the tangent drawn at \(A\) is parallel to the chord \(BC\) is:
Let the curve \(x^2 + 2y^2 = 2\) intersect the line \(x + y = 1\) at two points \(P\) and \(Q\) and \(O\) be the origin. If \(\theta\) is the acute angle between the lines \(OP\) and \(OQ\), then \(\tan \theta =\)
Assertion (A): The function \( f(x) = \begin{cases} 1 - \cos x, & x<0 \\ \sin x, & x \geq 0 \end{cases} \) is continuous at \(x = 0\). Reason (R): \(\lim_{x \to 0} \sin x = 0\)
The function \( f(x) = x^2 + \dfrac{54}{x} \)
In a game, a pair of dice is rolled 24 times. If a person wins the game by not getting 6 on both the dice in any one of the 24 rolls, then the probability that a person wins the game is:
Tangents are drawn from point $ (1, 1) $ to the ellipse $ x^2 + y^2 + 10x + 8y - 23 = 0 $. If $ m_1, m_2 $ (with $ m_1>m_2 $) are the slopes of these tangents, then with respect to the given ellipse, the point $ P(m_1, m_2) $ lies:
Let $ [t] $ represent the greatest integer not exceeding $ t $. The number of discontinuous points of $ [10^t] $ in $ (0, 10) $ is:
The particular solution of the differential equation \[ \frac{dx}{dy} = \frac{\sin y(1 + y \cot y)}{x \log(x^2 e)}, \quad y(1) = 0 \] Options:
The point of intersection of the tangents drawn at the points where the line \[ 2x - y + 3 = 0 \] meets the circle \[ x^2 + y^2 - 4x - 6y + 4 = 0 \] is:
If \( 5f(x) + 3f\left( \frac{1}{x} \right) = 2 - \frac{1}{x}, x \ne 0 \), then \( \int_1^2 f\left( \frac{1}{x} \right) dx = \)
If the points \( (k, 1, 5), (1, 0, 3), (7, -2, m) \) are collinear, then \( (k, m) = \)
If the acute angle between the pair of tangents drawn from the origin to the circle \( x^2 + y^2 - 4x - 8y + 4 = 0 \) is \( \alpha \), then \( \tan \alpha = \)
The area bounded by \( y - 1 = -|x| \) and \( y + 1 = |x| \) is:
The degree of the differential equation $\log \left( \frac{dy}{dx} \right) = \left( 2x + 3 \frac{dy}{dx} \right)^2$ is
If the equation \(x^4 + 7x^3 + 18x^2 + 20x + 8 = 0\) has a repeated root, then that repeated root is:
If the equation \(2x^3 + 5x^2 - 4x - 12 = 0\) has a repeated root, then the constant term of the quadratic equation whose roots are the distinct roots of the given equation is:
The range of a random variable \( X \) is \( \{0, 1, 2\} \). If \( P(X=0) = 3C^3 \), \( P(X=1) = 4C-10C^2 \), and \( P(X=2) = 5C-1 \), then the value of \( C \) is:
If \( \left| \frac{z - 2}{z} \right| = 2 \), then the greatest value of \( |z| \) is:
If $I_n = \int \tan^n x \, dx \quad (n>1)$, then $I_4 + I_6 =$
If $X=x+h, Y=y+k$ transforms $\frac{dy}{dx} = \frac{2x+3y-7}{3x+2y-8}$ to a homogeneous differential equation, then $(h,k)=$
If $ \cos A + \cos B + \cos C = 0 $ and $ \sin A + \sin B + \sin C = 0 $, then $ \cos(A - B) = $
If the lines joining the origin to the points of intersection of $ 2x + 3y = k $ and $ 3x^2 - xy + 3y^2 + 2x - 3y - 4 = 0 $ are at right angles, then: