List of top Mathematics Questions asked in AP EAPCET

If \( A = \left\{ \frac{x}{9x^2 + 20} \right\} \) and \( f: A \to \mathbb{R} \) is defined by \( f(x) = 2x^3 - 15x^2 + 36x - 48 \), then the maximum value of \( f(x) \) is
The function \( f(x) = \frac{\sqrt{3x^2 - 5x - 2}}{2x^2 - 7x + 5} \) has discontinuous points at \( x = \dots \)
If the points of contact of the tangents drawn from \( (0,0) \) to the curve \( y = x^2 + 3x + 4 \) are \( (\alpha, \beta) \) and \( (\gamma, \delta) \), then \( \beta + \delta = \):
Evaluate the integral \( \int x^3 (\log x)^2 dx \):
If \[ \frac{2x^2 + 5x + 6}{(x + 2)^3} = \frac{a}{x + 2} + \frac{b}{(x + 2)^2} + \frac{c}{(x + 2)^3}, \] then \( a \cdot b + b \cdot c + c \cdot a = \)?
If the solution for the system of equations \[ x + 2y - z = 3, \ 3x - y + 2z = 1, \ 2x - 2y + 3z = 2 \] is \( ( \alpha, \beta, \gamma ) \), then find the value of \( \alpha^2 + \beta^2 + \gamma^2 \).
If \[ \begin{vmatrix} x & 4 & -1 \\ 2 & 1 & 0 \\ 0 & 2 & 4 \end{vmatrix} = 0, \text{ then find the value of } x. \]
If \( \frac{17x - 2}{12x^2 - x - 20} = \frac{A}{ax + 5} + \frac{B}{3x + b} \), then \( a \cdot A + b \cdot B \) is:
If the mean and variance of a binomial variable X are 2.4 and 1.44 respectively, then the parameters \( n \) and \( p \) are respectively:
The maximum value of \( x^4 y^4 \) when \( a^2 x^4 + b^2 y^4 = c^6 \) is:
If the slope of the tangent on a curve at any point \((x, y)\) is equal to \[ \frac{y^2 - x^2}{2xy} \] then the equation of the normal at the point \(\left(1, \frac{\sqrt{3}}{2}\right)\) is
A point on the plane passing through the points \((\sqrt{2},1,4), (0,-1,0)\) and \((0,0,1)\) is:
A box contains 5 white balls and 7 black balls. In how many ways can 3 balls be drawn from the box such that at least one black ball is included?}
If \[ \vec{a} = -2\hat{i} + 9\hat{j} - 6\hat{k}, \quad \vec{b} = t\hat{i} - 2\hat{j} + 6\hat{k} \] are vectors such that \(|\vec{a} + \vec{b}| = 25\), then the sum of the values of \(t =\ ?\)
If \( \alpha \) is the modulus of \( z_1 = 4 + 3i \), then a point that does not lie in the region represented by } \[ |z - z_1| \leq \alpha \] is
Let \( n \in (0, \infty) \). If for all the curves \( y = x^n \log x \) for distinct values of \( n \), we have \( y = x - 1 \) as the tangent at a fixed point \((\alpha, \beta)\), then \(\alpha + \beta = \):
If \( A = \begin{bmatrix} 2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2 \end{bmatrix} \) is expressed as a sum of a symmetric matrix \( P \) and a skew-symmetric matrix \( Q \), then \( P^T - Q^T \) equals:
In \( \triangle ABC \), if the midpoints of the sides \( AB, BC, CA \) are respectively \( (l, 0, 0), (0, m, 0), (0, 0, n) \), then: \[ \frac{AB^2 + BC^2 + CA^2}{l^2 + m^2 + n^2} = ? \]
If \( f(0) = 0, f(1) = 1, f(2) = 2 \) and \( f(x) = f(x-2) + f(x-3) \) for \( x = 3, 4, 5, \dots \), then find \( f(10) \).
Let \( f(x) = |x - 3| + |x + 5| \) and \( A = \left\{ a \in \mathbb{R} / \lim_{x \to a} \frac{f(x) - f(a)}{x - a} \text{ exists} \right\} \). Then the number of real numbers which are in \( [-8, 3] \cup [5, \infty) \) but not in \( A \) is
In a city it is found that 10 accidents took place in a span of 50 days. Assuming that the number of accidents follow the Poisson distribution, the probability that there will be 3 or more accidents in a day in that city, is
If \( A = (2, 3) \) and \( B = (-4, 5) \) are two fixed points, then the locus of a point \( P \) such that the area of \( \triangle PAB \) is 12 square units is
Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be a function defined by \( f(x) = \frac{2x+1}{3} \). If \( \alpha \) is an element in the domain of \( f \) whose image is \( \frac{1}{\alpha} \), then the sum of all possible values of such \( \alpha \) is
Assertion (A): If $ f(x) $ is not continuous at $ x = a $, then it is not differentiable at $ x = a $. Reason (R): If $ f(x) $ is differentiable at a point, then it is continuous at that point.
If the planes $ 2x + 3y + 4z + 7 = 0 $ and $ 4x + ky + 8z + 1 = 0 $ are parallel, then the equation of the plane passing through the point $ (k, k, k) $ and having the direction ratios of its normal as $ (k-1, k, k+1) $ is