List of top Mathematics Questions asked in AP EAPCET

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
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 \(ab = \)
Evaluate the limit: \[ \lim_{x \to 0} \frac{x^2 \sin^2(3x) + \sin^4(6x)}{(1 - \cos(3x))^2} \]
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 a hyperbola has asymptotes \(3x-4y-1=0\) and \(4x-3y-6=0\), then the transverse and conjugate axes of that hyperbola are
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 the tangents of the parabola $ y^2 = 8x $ passing through the point $ P(1, 3) $ touch the parabola at points $ A $ and $ B $, then the area (in sq. units) of $ \triangle ABC $ is
If P(\(\alpha, \beta\)) is the radical centre of the circles \(S=x^2+y^2+4x+7=0\), \(S'=2x^2+2y^2+3x+5y+9=0\) and \(S''=x^2+y^2+y=0\), then the length of the tangent drawn from P to S' = 0 is
If the pole of the line \(x + 2by - 5 = 0\) with respect to the circle \(S = x^2 + y^2 - 4x - 6y + 4 = 0\) lies on the line \(x + by + 1 = 0\), then the polar of the point \((b, -b)\) with respect to the circle \(S = 0\) is
If (1, a), (b, 2) are conjugate points with respect to the circle \(x^2 + y^2 = 25\), then \(4a + 2b =\)
The slope of one of the direct common tangents drawn to the circles \(x^2 + y^2 - 2x + 4y + 1 = 0\) and \(x^2 + y^2 - 4x - 2y + 4 = 0\) is