List of top Questions asked in AP EAPCET

The area bounded by \( y - 1 = -|x| \) and \( y + 1 = |x| \) is:
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 the points \( (k, 1, 5), (1, 0, 3), (7, -2, m) \) are collinear, then \( (k, m) = \)
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 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 \( \tan \alpha = \)
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 degree of the differential equation $\log \left( \frac{dy}{dx} \right) = \left( 2x + 3 \frac{dy}{dx} \right)^2$ 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 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:
If $I_n = \int \tan^n x \, dx \quad (n>1)$, then $I_4 + I_6 =$
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:
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 \( \left| \frac{z - 2}{z} \right| = 2 \), then the greatest value of \( |z| \) is:
A team of 5 students is to be selected from 12 students. If two particular students are to be included in that team, then the number of ways that such team can be selected is:
The least value of \( n \) such that \( {}^{n-1}C_6 + {}^{n-1}C_7<{}^nC_8 \) is
In \( \triangle ABC \), if \( \sin B = \sin C \) and \( 3 \cos B = 2 \cos C \), then \( \triangle ABC \) is:
\(f(x)\) is a continuous function on \(\mathbb{R}\) and \(y = f(x)\) is a curve. If \((\alpha, \beta)\) is a point such that \(\beta = f(\alpha)\) and \(p\alpha + m\beta + n = 0\ (p \ne 0, m \ne 0)\), then which one of the following is True?
If the roots of the equation \( 16x^3 - 44x^2 + 36x - 9 = 0 \) are in harmonic progression, then its greatest root is
Let \( A(-1, 1, 2), B(1, 2, 3), C(1, 1, 6) \) be three points. If \( l_1, m_1, n_1 \) are the direction cosines of \( AB \) and \( l_2, m_2, n_2 \) are the direction cosines of \( AC \), then \( |l_1 l_2 + m_1 m_2 + n_1 n_2| = \)
If \( Q \) is the inverse point of the point \( P(2, 3) \) with respect to the circle \( x^2 + y^2 - 2x - 2y + 1 = 0 \), then the circle with \( PQ \) as diameter is
If a real valued function \( f \) is defined by \( f(x) = \frac{ax + \sqrt{a^2 - x^2}}{bx} \), then \( f \) is:
If $ \cos A + \cos B + \cos C = 0 $ and $ \sin A + \sin B + \sin C = 0 $, then $ \cos(A - B) = $
If \( \csc\theta \) and \( \cot\theta \) are the roots of \( cx^2 + bx + a = 0 \) where \( bc \neq 0 \), then evaluate \( b^2(b^2 - 4ac) \):