List of top Mathematics Questions asked in AP EAPCET

The number of integers between 10 and 10,000 such that in every integer every digit is greater than its immediate preceding digit, is
The number of ways in which a cricket team of 11 members can be formed out of 6 batsmen, 6 bowlers, 4 all-rounders, and 4 wicket-keepers by selecting at least 4 batsmen, at least 3 bowlers, at least 2 all-rounders, and only one wicket-keeper is
All letters of the word `AGAIN' are permuted in all possible ways, and the words so formed (with or without meaning) are written as in a dictionary. Then the $50^{th}$ word is
If $y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + ... \infty$, then
Sum of the coefficients of $x^4$ and $x^6$ in the expansion of $(1 + x - x^2)^6$ is
The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \ge 1$ is
If $\alpha$, $\beta$, and $\gamma$ are the roots of the equation $2x^3 + 3x^2 - 5x - 7 = 0$, then $\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2} =$
If the order and degree of the differential equation \(x \frac{d^2 y}{dx^2} = \left(1 + \left(\frac{d^2 y}{dx^2}\right)^2\right)^{-1/2}\) are \(k\) and \(l\) respectively, then \(k, l\) are the roots of
The general solution of the differential equation \( \left(x - (x + y)\log(x + y)\right) dx + x\,dy = 0 \) is:
The equation of the curve passing through the point \( (0, \pi) \) and satisfying the differential equation \( ydx = (x + y^3 \cos y)dy \) is
Area of the region (in sq. units) bounded by the curve $ y = x^2 - 5x + 4 $, $ x = 0 $, $ x = 2 $, and the X-axis is
Evaluate the integral \( \displaystyle \int_{1/5}^{1/2} \frac{\sqrt{x - x^2}}{x^3} \, dx \):
\( \int_{-\pi/2}^{\pi/2} \sin^2 x \cos^2 x (\sin x + \cos x) \, dx = \)
If \(\int \frac{1}{((x+4)^3 (x+1)^5)^{1/4}} \, dx = A \cdot \left(\frac{x+4}{x+1}\right)^n + c\), then
If \( \int e^{\sin x}(1 + \sec x \tan x)\, dx = e^{\sin x}f(x) + c \), then in \( 0 \leq x \leq 2\pi \), the number of solutions of \( f(x) = 1 \) is
Evaluate: \[ \int \frac{dx}{(x+1)\sqrt{x^2+1}} \]
If \( \int \left( x^6 + x^4 + x^2 \right) \sqrt{2x^4 + 3x^2 + 6} \, dx = f(x) + c \), then \( f(3) = \)
If \( m \) and \( M \) are the absolute minimum and absolute maximum values of the function \( f(x) = 2\sqrt{2 \sin x - \tan x} \) in the interval \( \left[0, \frac{\pi}{3} \right] \), then \( m + M = \)
The function \( f(x) = xe^{-x} \) for all \( x \in \mathbb{R} \) attains a maximum value at \( x = k \), then \( k = \)
The slope of a tangent drawn at the point \( P(\alpha, \beta) \) lying on the curve \( y = \frac{1}{2x - 5} \) is \( -2 \). If \( P \) lies in the fourth quadrant, then \( \alpha - \beta = \)
The interval in which the function \( f(x) = \tan^{-1}(\sin x + \cos x) \) is an increasing function, is:
If \( y = (\log x)^{1/x} + x^{\log x} \), then at \( x = e \), \( \frac{dy}{dx} \) equals:
If \( y = \tan^{-1} \sqrt{x^2 - 1} + \sinh^{-1} \sqrt{x^2 - 1} \), \( x > 1 \), then \( \frac{dy}{dx} = \)
Evaluate the limit: \[ \lim_{x \to 0} \frac{(\csc x - \cot x)(e^x - e^{-x})}{\sqrt{3} - \sqrt{2 + \cos x}} \]
If \((2, -1, 3)\) is the foot of the perpendicular drawn from the origin \((0, 0, 0)\) to a plane then the equation of that plane is