List of top Mathematics Questions asked in AP EAPCET

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
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
The number of integers between 10 and 10,000 such that in every integer every digit is greater than its immediate preceding digit, is
If $\alpha$, $\beta$, and $\gamma$ are the roots of the equation $2x^3 + 3x^2 - 5x - 7 = 0$, then $\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2} =$
The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \ge 1$ is
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 equation of the curve passing through the point \( (0, \pi) \) and satisfying the differential equation \( ydx = (x + y^3 \cos y)dy \) is
Evaluate the integral \( \displaystyle \int_{1/5}^{1/2} \frac{\sqrt{x - x^2}}{x^3} \, dx \):
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 \( m \) 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:
Evaluate the limit: \[ \lim_{x \to 0} \frac{(\csc x - \cot x)(e^x - e^{-x})}{\sqrt{3} - \sqrt{2 + \cos x}} \]
If a real valued function \( f(x) = \begin{cases} (1 + \sin x)^{\csc x} & , -\frac{\pi}{2} < x < 0 \\ a & , x = 0 \\ \frac{e^{2/x} + e^{3/x}}{ae^{2/x} + be^{3/x}} & , 0 < x < \frac{\pi}{2} \end{cases} \) is continuous at \(x = 0\), then \(ab = \)
If the direction cosines of two lines satisfy the equations $ l - 2m + n = 0 $ and $ lm + 10mn - 2nl = 0 $, and $ \theta $ is the angle between the lines, then $ \cos \theta = $
If \(3x+2\sqrt{2}y+k=0\) is a normal to the hyperbola \(4x^2-9y^2-36=0\) making positive intercepts on both the axes, then \(k=\) Options :
If (1, a), (b, 2) are conjugate points with respect to the circle \(x^2 + y^2 = 25\), then \(4a + 2b =\)
If the combined equation of the lines joining the origin to the points of intersection of the curve $ x^2 + y^2 - 2x - 4y + 2 = 0 $ and the line $ x + y - 2 = 0 $ is $ (l_1x + m_1y)(l_2x + m_2y) = 0 $, then $ l_1 + l_2 + m_1 + m_2 = $
If the equation of the pair of lines passing through (1, 1) and perpendicular to the pair of lines \(2x^2 + xy - y^2 - x + 2y - 1 = 0\) is \(ax^2 + 2hxy + by^2 + 2gx + 3y = 0\). then \(\frac{b}{a} =\)
After the coordinate axes are rotated through an angle \(\frac{\pi}{4}\) in the anticlockwise direction without shifting the origin, if the equation \(x^2 + y^2 - 2x - 4y - 20 = 0\) transforms to \(ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0\) in the new coordinate system, then
\[ \begin{vmatrix} a & h & g \\ h & b & f \\ g & f & c \end{vmatrix} \]