List of top Questions asked in AP EAPCET- 2023

The equation of a plane passing through \( (-1, 2, 3) \) and whose normal makes equal angles with the coordinate axes is:
The equation of the normal to the curve \( y = \cosh x \) drawn at the point nearest to the origin is:
If $[\cdot]$ denotes the greatest integer function, then $\int_{0}^{1000} e^{x - \lfloor x \rfloor} dx =$
Let \([t]\) represent the greatest integer not more than \(t\). Then the number of discontinuous points of \(f(x) = \left[\frac{1}{x}\right]\) in \((0, \infty)\) is
\(\displaystyle \int e^x \left( \log x + \frac{1}{x^2} \right) dx =\)
For \( x \in \mathbb{R} \), if \( f(x) = \sqrt{\log_{10} \left( \frac{3-x}{x} \right)} \), then the domain of \( f \) 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:
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
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 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:
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:
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:
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:
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:
The range of the expression: \[ \frac{1}{\sin^2x + 3\sin x \cos x + 5\cos^2x} \] is:
The length of the chord of contact from point $(2,1)$ to the circle $x^2+y^2+4x+2y+1=0$ 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
In $ \triangle ABC $, the expression $ \frac{a}{s-a} + \frac{b}{s-b} + \frac{c}{s-c} $ is equivalent to:

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:

A point on the straight line \( 3x + 5y = 15 \) which is equidistant from the coordinate axes will lie in
If \( X \) is a random variable such that \[ P(X = -2) = P(X = -1) = P(X = 2) = P(X = 1) = \frac{1}{6}, \quad P(X = 0) = \frac{1}{3}, \] then the mean of \( X \) is:
If \( m \in \mathbb{Z}^+, n = 2m \) and \[ \int_0^{\frac{\pi}{2}} \sin^n x \cos^m x \, dx = K(m) \int_0^{\frac{\pi}{2}} \sin^m x \, dx, \text{ then } \frac{2^{n-1}(m - 1)!}{(2m - 1)!} \cdot K(m) = \]
The number of positive even divisors of 6300 is: