List of top Questions asked in AP EAPCET

The general solution of the differential equation \(\frac{dy}{dx} + xy = 4x - 2y + 8\) is
\( \int \frac{x}{(1-x^2)\sqrt{2 - x^2} dx = \)}
Evaluate the integral $\displaystyle \int_0^{\frac{\pi{2}} \log(\tan x + \cot x)\, dx$}
If \( \int x^2 \cos^3 x\, dx = \frac{1}{6}f(x) + g(x) \sin 2x + h(x) \cos 2x + c \), then \( f(1) + g(2) + h\left(\frac{1}{2}\right) = \)
Evaluate the integral \[ \int_{0}^{\pi} x \cdot \sin x \cdot \int_{x}^{5} \frac{\cos x}{x} \cdot dx = \]
\( \int \frac{1 + x + \sqrt{x + x^2}}{\sqrt{x + \sqrt{1 + x}}} dx = \)
If \( \int \frac{dx}{(x-1)^2(x-3)^2 = \sqrt{f(x)} + c \), then \( f(-1) - f(0) = \)}
If \(y = (ax + b)\cos x\), then \(y_2 + y_1 \sin 2x + y(1 + \sin^2 x) = \)
If \(x^2 + y^2 = \dfrac{1}{t} \text{ and } x^4 + y^4 = t^2 + \dfrac{1}{t^2},\) then \(\dfrac{dy}{dx} =\)
If the normal drawn at the point P on the curve \(y = x \log x\) is parallel to the line \(2x - 2y = 3\), then P =
If the function \(y = \sin(x)(1 - \cos x)\) is defined in the interval \([-\pi, \pi]\), then y is strictly increasing in the interval
If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration is
If the curves \(y^2 = 16x \text{ and } 9x^2 + \alpha y^2 = 25\) intersect at right angles, then \(\alpha =\)
If the angles between the sides of triangle ABC formed by A(2,3,5), B(-1,2,3), and C(3,5,-2) are \(\alpha, \beta, \gamma\), then \(\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma =\)
Evaluate \(\lim\limits_{x \to \infty} \dfrac{5x^3 - x^2 \sin 5x}{x^3 \cos 4x + 7|x|^3 - 4|x| + 3}\)
If \( y = \tanh^{-1} \left( \dfrac{1 - x}{1 + x} \right) \), then \( \dfrac{dy}{dx} = \)
If \(O(0,0,0), A(1,2,1), B(2,1,3)\), and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(OAB\) and edge \(BC\) is
If a function defined by \[ f(x) = \begin{cases} \dfrac{1 - \cos 4x}{x^2}, & x<0
a, & x = 0
\dfrac{\sqrt{x}}{\sqrt{16 + \sqrt{x} - 4}}, & x>0 \end{cases} \] is continuous at \(x = 0\), then \(a =\)
If the four points (6,2,4), (1,3,5), (1,-2,3), and (6,k,2) are coplanar, then \(k =\)
If \(\lim\limits_{x \to a^-} f(x) = p\), \(\lim\limits_{x \to a^+} f(x) = m\), and \(f(a) = k\), then which one of the following is true?
The angle between the tangents drawn from the point (2, 2) to the circle \(x^2 + y^2 + 4x + 4y + c = 0\) is \(\cos^{-1} \left( \frac{7}{16} \right)\). If two such circles exist, then the sum of values of \(c\) is
The tangents drawn to the hyperbola \(5x^2 - 9y^2 = 90\) through a variable point \(P\) make angles \(\alpha\) and \(\beta\) with its transverse axis. If \(\alpha\) and \(\beta\) are complementary angles, then the locus of \(P\) is
If \(\theta\) is the acute angle between the asymptotes of a hyperbola \(7x^2 - 9y^2 = 63\), then \(\cos \theta =\)
The square of the slope of a common tangent to the circle \(4x^2 + 4y^2 = 25\) and ellipse \(4x^2 + 9y^2 = 36\) is
The angle between the tangents drawn from point (1, 4) to parabola \(y^2 = 4x\) is