List of top Questions asked in AP EAPCET

If A(1, 2, 3), B(2, 3, -1), C(3, -1, -2) are the vertices of a triangle ABC, then the direction ratios of the bisector of $\angle$ABC are
Variance of the following discrete frequency distribution is \begin{tabular}{|l|c|c|c|c|c|} \hline Class Interval & 0-2 & 2-4 & 4-6 & 6-8 & 8-10
\hline Frequency (\(f_i\)) & 2 & 3 & 5 & 3 & 2
\hline \end{tabular}
Which one of the following functions is monotonically increasing in its domain?
The lengths of the two focal chords of the parabola \( y^2 = 16x \) is 25 units each. If these two chords cut the parabola at \( A, B, C, D \), then the area (in sq. units) of the quadrilateral formed by \( A, B, C, D \) is:
Evaluate the integral: \[ I = \int_0^x \frac{t^2}{\sqrt{a^2 + t^2}} dt \]
The general solution of the differential equation \( \sec(x - y + 1) dy = dx \) is:
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2xy-4x+y-2}{2xy+x-4y-2} \] is:
A line \(L_1\) passing through the point of intersection of the lines \(x-2y+3=0\) and \(2x-y=0\) is parallel to the Line \(L_2\). If \(L_2\) passes through origin and also through the point of intersection of the lines \(3x-y+2=0\) and \(x-3y-2=0\), then the distance between the lines \(L_1\) and \(L_2\) is
If the distance between the foci of a hyperbola H is 26 and distance between its directrices is \( \frac{50}{13} \), then the eccentricity of the conjugate hyperbola of the hyperbola H is
If the tangent drawn at the point \( (x_1,y_1) \), \(x_1,y_1 \in N \) on the curve \( y = x^4 - 2x^3 + x^2 + 5x \) passes through origin, then \( x_1+y_1 = \)

If

\[ \cos x + \sin x = \frac{1}{2} \]

and

\[ 0 < x < \pi, \text{ then } \tan x = \ ? \]

A straight line passing through the origin \( O \) meets the parallel lines \( 4x + 2y = 9 \) and \( 2x + y + 6 = 0 \) at the points \( P \) and \( Q \) respectively. Then the point \( O \) divides the line segment \( PQ \) in the ratio
Evaluate the integral: \[ \int_0^1 x^{5/2} (1 - x)^{3/2} \, dx = \]
The number of ways of arranging 3 red, 2 white, and 4 blue flowers of different sizes into a garland such that no two blue flowers come together is:
Find the slope of the line perpendicular to the line $ 3x + 4y - 12 = 0 $.
If the sum of the roots of the quadratic equation $ x^2 - 5x + k = 0 $ is 5, find the value of $ k $.
If \( A + B = \frac{\pi}{4} \), then \( \dfrac{\cos B - \sin B}{\cos B + \sin B} \) is equal to:
If \( A = (0, 4, -3),\ B = (5, 0, 12),\ C = (7, 24, 0) \), then \( \angle BAC = \)
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2x^2 - xy - y^2}{x^2 - y^2} \]
By taking $ \sqrt{a \pm ib} = x + iy, x>0 $, if we get $$ \frac{\sqrt{21} + 12\sqrt{2}i}{\sqrt{21} - 12\sqrt{2}i} = a + ib, $$ then $ \frac{b}{a} = $ ?
If the median AD of the triangle ABC is bisected at E and BE meets AC in F, then AF : AC =
If $ A(0, 1, 2) $, $ B(2, -1, 3) $, and $ C(1, -3, 1) $ are the vertices of a triangle, then the distance between its circumcentre and orthocentre 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
If $\cot(\cos^{-1} x) = \sec\left(\tan^{-1}\left(\frac{a}{\sqrt{b^2 - a^2}}\right)\right)$, $b>a$, then $x =$
If $2x - 3y + 1 = 0$ is the equation of the polar of a point $P(x_1, y_1)$ with respect to the circle $x^2 + y^2 - 2x + 4y + 3 = 0$, then $3x_1 - y_1 =$