List of top Mathematics Questions asked in AP EAPCET

The coefficient of \( x^r \) in the expansion of \( \frac{1}{\sqrt{(1 - 2x)^3}} \) is
\(\displaystyle \int e^x \left( \log x + \frac{1}{x^2} \right) dx =\)

If $ N(n) = n \prod_{r=1}^{2023} (n^2 - r^2) $ where $ n > 2023 $, then the value of $ {}^{n}C_{N-1} $ when $ n = 2024 $ is:

The equation of a plane passing through \( (-1, 2, 3) \) and whose normal makes equal angles with the coordinate axes is:
For \( x \in \mathbb{R} \), if \( f(x) = \sqrt{\log_{10} \left( \frac{3-x}{x} \right)} \), then the domain of \( f \) is:
Let origin be the centroid of an equilateral triangle ABC and one of its sides is along the straight line \( x + y = 3 \). If \( R \) and \( r \) are its circumradius and inradius respectively, then \( R + r = \):
Let $ \bar{a}, \bar{b}, \bar{c} $ be three non-coplanar vectors. Then the point of intersection of the line joining the points $ \mathbf{a} + \bar{b} + \bar{c} $, $ \bar{a} - \bar{b} + 3\bar{c} $ and the line joining the points $ 2\bar{a} - \bar{b} + \bar{c} $, $ \bar{a} - 2\bar{b} + 4\bar{c} $ is
If one ticket is selected at random from 30 tickets each with a distinct number from 1 to 30, then the probability that the number on the selected ticket is a multiple of 3 or 5 is
If A and B are among 20 persons who sit at random along a round table, then the probability that there are exactly six persons between A and B is:
The point $ P(2, 1) $ is translated to a point $ Q $ parallel to the line $ L: x - y - 4 = 0 $ by $ 2\sqrt{5} $ units. If the point $ Q $ lies in the third quadrant, then the equation of the line passing through $ Q $ and perpendicular to $ L $ is:
The order and degree of the differential equation \[ 3x^2 \frac{d^2 y}{dx^2} - \sin\left( \frac{d^3 y}{dx^3} \right) + \cos(xy) = 0 \] are:
The length of the chord of contact from point $(2,1)$ to the circle $x^2+y^2+4x+2y+1=0$ is
If the angle between the pair of lines \( x^2 + 2\sqrt{2} xy + ky^2 = 0, k>0 \) is \( 45^\circ \), then the area (in square units) of the triangle formed by the pair of bisectors of the angles between these lines and the line \( x + 2y + 1 = 0 \) is
The coordinates of the point \( (3, -5) \) in the new system, when the origin is shifted to the point \( (-1, -1) \) by the translation of axes, is
The curve represented by $x = t^5 + 5t^3 + 20t + 7$ and $y = 4t^3 - 3t^2 - 18t + 3$ is decreasing in the interval
If \( S \) is the sample space of a random experiment \( \xi \) and \( P \) is a probability function defined on the power set \( P(S) \) of \( S \), then which one of the following is not satisfied by \( P \)?
If A and B are any two events of a sample space, then set-theoretic description for the event "Exactly one of the events A, B to occur" is:
In \( \Delta ABC \), if \( \sin 2A + \sin 2B + \sin 2C = \frac{\cos A + \cos B + \cos C - 1}{\cos A + \cos B + \cos C - 1} \), then:
From out of 100 enrolled students, two sections of strength 40 and 60 are formed. If you and your friend are among those 100 students, then the probability that both of you are placed in the same section is
Let \([t]\) represent the greatest integer not exceeding \( t \) and \( C = 1 - 2e^2 \).
If the function \[ f(x) = \begin{cases} [e^x], & x < 0 \\ ae^x + [x - 2], & 0 \leq x < 2 \\ [e^x] - C, & x \geq 2 \end{cases} \] is continuous at \(x = 2\), then \(f(x)\) is discontinuous at:
The absolute value of the tangent of the difference of the angles made by the lines \( 4x^2 - 24xy + 11y^2 = 0 \) with the X-axis is:
The range of the expression: \[ \frac{1}{\sin^2x + 3\sin x \cos x + 5\cos^2x} \] is:

If $ \frac{k}{kx + 3} + \frac{3}{3x-k}= \frac{12x + 5}{(kx + 3)(3x - k)} $, then both the roots of the equation $ kx^2 - 7x + 3 = 0 $ are:

The number of six-digit natural numbers that can be formed with the digits 2, 3, 4, 0, 5, 6, 7, 8 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 $y\left(\frac{1}{2}\right) =$