List of top Mathematics Questions asked in AP EAPCET

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:
\[ \text{Assertion (A): If } y = f(x) = (|x| - |x - 1|)^2, \text{ then } \left.\frac{dy}{dx}\right|_{x = 1} = 1 \] \[ \text{Reason (R): If } \lim_{x \to a} \frac{f(x) - f(a)}{x - a} \text{ exists, then it is called the derivative of } f(x) \text{ at } x = a. \] Then:
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
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
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
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
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

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

Which one of the following functions is monotonically increasing in its domain?
Problem: From a point \( P \) on the circle \( x^2 + y^2 = 4 \), two tangents are drawn to the circle \( x^2 + y^2 - 6x - 6y + 14 = 0 \). If \( A \) and \( B \) are the points of contact of those lines, then the locus of the center of the circle passing through the points \( P \), \( A \), and \( B \) is: Identify the correct option from the following:
Evaluate the integral: \[ \int_0^1 x^{5/2} (1 - x)^{3/2} \, dx = \]
A manufacturing company has 3 units A, B, and C which produce 25%, 35%, 40% of bulbs respectively. 5%, 4%, and 2% of their production is defective. If a bulb is found defective, the probability it came from B is
If the sum of the roots of the quadratic equation $ x^2 - 5x + k = 0 $ is 5, find the value of $ k $.
Find the slope of the line perpendicular to the line $ 3x + 4y - 12 = 0 $.
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:
If \( \left(\frac{2}{3},0\right) \) is the centroid of the triangle formed by the lines \( 4x^2 - y^2 = 0 \) and \( lx + my + n = 0 \), then \( l+m+n= \):
Let \(P(a \sec \theta, b \tan \theta)\) and \(Q(a \sec \phi, b \tan \phi)\) where \(\theta + \phi = \frac{\pi}{2}\) be two points on the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\). If \((h,k)\) is the point of intersection of the normals drawn at \(P\) and \(Q\), then find \(k\).
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
If \( \theta \) is the acute angle between the tangents drawn from the point \( (1,1) \) to the hyperbola \( 4x^2-5y^2-20=0 \), then \( \tan\theta \) is:
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 $\cot(\cos^{-1} x) = \sec\left(\tan^{-1}\left(\frac{a}{\sqrt{b^2 - a^2}}\right)\right)$, $b>a$, then $x =$
If the difference of the roots of the equation $x^2 - 7x + 10 = 0$ is same as the difference of the roots of the equation $x^2 - 17x + k = 0$, then a divisor of $k$ is
Evaluate the integral: \[ \int \left[\frac{1}{\cos x} - \frac{1}{\sin x} - \frac{1}{\sin x + 3\cos x}\right] dx \]
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 \( A + B = \frac{\pi}{4} \), then \( \dfrac{\cos B - \sin B}{\cos B + \sin B} \) is equal to: