List of top Mathematics Questions asked in AP EAPCET

Let \( A(2, 3) \), \( B(3, -1) \), and \( C(-3, 2) \) be three points. If the centre of the circle passing through A, B, and C is \( (h, k) \), then \( 2k - 4 = \):
If a straight line \( L \) perpendicular to the line \( 3x - 4y = 6 \) forms a triangle of area 6 square units with coordinate axes, then the minimum perpendicular distance from the point \( (1,1) \) to the line \( L \) is:
If \( \frac{6x^3 + 7x^2 - 14x + 11}{6x^3 + x^2 - 10x + 3} = \frac{a}{x + p} + \frac{b}{qx + 3} + \frac{c}{3x + p} \), then \( a + b \) is:
If $\log y$ is an integrating factor of $\frac{dx}{dy}+P(y)x=Q(y)$, then $P(y)=$
If a set \( A \) has \( n \) elements, then the number of functions defined from \( A \) to \( A \) that are not one-one is:
The probability that a non-leap year contains 53 Sundays is
Which one of the following is a homogeneous differential equation?
If \( f(x) = \begin{vmatrix} 1 & 6 + x & 36 + x^2 \\ 0 & x - 3 & 3x^2 - 27 \\ 0 & 2x - 4 & 8x^2 - 32 \end{vmatrix} \), then \( \lim\limits_{x \to 1} \frac{f(x)}{f(-x)} \) is:
The value of the following expression is: \[ \cos \left( \frac{\pi}{2^2} \right) \cdot \cos \left( \frac{\pi}{2^3} \right) \cdot \cos \left( \frac{\pi}{2^4} \right) ... \cdot \cos \left( \frac{\pi}{2^{10}} \right) \]
If \( \alpha \in \mathbb{R} \setminus \{-1\} \) and \[ f(x) = |x| + \alpha |x|(|x| - 1), \] then the number of points at which \( f(x) \) is not differentiable is:
If \( f(x) = \begin{cases} x \left( 1 + \frac{1}{2} \sin(\log x^2) \right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then \( \lim_{x \to 0} \frac{f(x) - f(0)}{x} \)
The lengths of the intercepts made by a circle \(S\) on the \(X\) and \(Y\)-axes are \(\frac{2\sqrt{13}}{3}\) and \(\frac{2\sqrt{17}}{3}\) respectively. Then the equation of the circle is:
If a circle \(S\) passing through the points \(A(1, 2)\) and \(B(2, 1)\) has its centre \(C\) located in the third quadrant at a distance of \(\frac{7}{\sqrt{2}}\) units from \(AB\), then the point \(P(1, -2)\)
If the line passing through the points \( (5,1,a) \) and \( (3,b,1) \) crosses the YZ plane at the point \( \left( 0, \frac{17}{2}, \frac{-13}{2} \right) \), then \( a + b = \):
The greatest term in the expansion of $ (1+x)^{15} $, when $ x = \frac{1}{2} $ is
If p and q are the x and y intercepts respectively of the line passing through the points \( (a \cos \alpha, b \sin \alpha) \) and \( (a \cos \beta, b \sin \beta) \), then:
The substitution \( x = vy \) converts which one of the following differential equations to an equation solvable by the variable separable method?
\( \int_{-4\pi}^{4\pi} \tan^9 x \sin^6 x \cos^3 x \, dx = \)
If $ a = 2n $ and $ b = 2m+1 $ for all $ m, n \in \mathbb{N} $, then \[ \int_{-\pi}^{\pi} e^{\sin^2 x} \cot^{b}(2n+1) x \, dx = \]
Let \( (a, b) \) denote the angle between vectors \( \mathbf{a} \) and \( \mathbf{b} \). If \( \mathbf{a} = 2i + 3j + 6k \), \( |\mathbf{a}| = 4 \), and \( (\mathbf{a}, \mathbf{b}) = \cos^{-1} \left( \frac{4}{21} \right) \), then \( \mathbf{a} + \mathbf{b} = \)
If \((l_1, m_1, n_1), (l_2, m_2, n_2)\) are the direction cosines of two lines, then \[ (l_2m_1 - l_1m_2)^2 + (m_1n_2 - m_2n_1)^2 + (n_1l_2 - n_2l_1)^2 + (l_1l_2 + m_1m_2 + n_1n_2)^2 = \]
Evaluate the integral: \[ \int \frac{dx}{4 + 5 \cos x} \]
The value of the constant \( c \), so that \( P(x) = c\left(\dfrac{2}{3}\right)^x,\, x = 1,2,3,\ldots \) is the probability distribution function of a discrete random variable \( X \), is:
If \( A(3, -1, 1), B(0, 2, 3), C(4, 8, 11) \) are three points, then the coordinates of the foot of the perpendicular drawn from the point A to the line joining the points B and C is:
Let \( B = \begin{bmatrix} 2 & 6 & 4 \\ 1 & 0 & 1 \\ -1 & -1 & -1 \end{bmatrix} \), \( C = \begin{bmatrix} -1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2 \end{bmatrix} \), and if a matrix \( A \) is such that \( BAC = I \), then \( A^{-1} = \)