List of top Questions asked in AP EAPCET

The area bounded by the curves \( y - 1 = \cos x \), \( y = \sin x \) and the X-axis between \( x = 0 \) and \( x = \pi \) is
If \( f(x) = \begin{cases} ax^2 - bx + 2, & x<3 \\ bx - 3, & x \geq 3 \end{cases} \) is differentiable at every \( x \in \mathbb{R} \), then the area (in sq units) of the triangle formed by the line \(\frac{x}{a} + \frac{y}{b} = 1\) with the coordinate axes is:
If \( (2, a) \) and \( (b, 19) \) are two stationary points of the curve \( y = 2x^3 - 15x^2 + 36x + c \), then \( a + b + c = \dots \)
If \( \vec{p} = 4\vec{i} - \vec{j} + \vec{k} \) is a point and \( \vec{q} = 9\vec{i} - 2\vec{j} + 6\vec{k} \) is a vector, then the perpendicular distance of origin from the plane passing through \( \vec{p} \) and perpendicular to \( \vec{q} \) is:
If \( A = \{ (a, b) : 4a = 5b, a \in \{1, 2, 3, \dots, 30\} \}, \) then the number of such ordered pairs \( (a, b) \) is:
a, b, c, d are arbitrary constants. Then the corresponding differential equation to \( y = ae^x + be^{-x} + c \cos x + d \sin x \) is
If the graph of the anti derivative \( g(x) \) of \( f(x) = \log(\log x) + (\log x)^{-2} \) passes through \( (e, 2023 - e) \) and the term independent of \( x \) in \( g(x) \) is \( k \), then the sum of all the digits of \( k \) is
The multiplicative inverse of $ z $ is:
If $ \int_{n}^{n+1} g(x) \, dx = n^2 $, $ \forall n \in Z $, then the value of $ \int_{-3}^{3} g(x) \, dx $ is
If \( P(X = x) = k \left( \frac{3}{8} \right)^x \), where \( x = 1, 2, 3, \dots \) is the probability distribution function of a discrete random variable X, then \( k = \)
The probability that a person chosen at random is left handed is 0.1. Then the probability that in a group of 10 people there is exactly one left-handed person is
An equation of a plane parallel to the plane \( x - 2y + 2z - 5 = 0 \) and which is at one unit distance from the origin is:
If the sum of the cubes of the roots of the equation \( x^3 - ax^2 + bx - c = 0 \) is zero, then \( a^3 + 3c = \):
In \( \triangle ABC \), if \( r_1 : r_2 = 7:8 \) and \( r_1 : r_3 = 3:4 \), then \( a : b : c = \)
In \( \triangle ABC \), if \[ a \cos^2 \frac{C}{2} + \cos^2 \frac{A}{2} = \frac{3b}{2}, \] then \( a + c : b \) is:
If \( f(x) = px^3 + qx^2 + rx + t \) attains local minimum and local maximum values at \( x = -2 \) and \( x = 2 \) respectively and \( p \) is a root of \( 9x^2 - 1 = 0 \), then \( p + q + r = \)
Let \( P(h, k) \) be the point of contact of the tangent to the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) which is parallel to the line \( \sqrt{3}x - y + 1 = 0 \). If \( P \) lies in the fourth quadrant then \( 3h^2 - 2k = \)
If the focal chord drawn through the point $ P(5, 5) $ to the parabola $ y^2 = 5x $ meets the parabola again at the point $ Q $, then the tangent drawn to this parabola at $ Q $ meets the axis of the parabola at the point:
Let the length of the latus rectum of an ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) be equal to the length of its semi-major axis. If the radius of its director circle is \( \sqrt{3} \) and \( e \) is its eccentricity, then the length of its latus rectum is:
In \( \triangle ABC \), if \( \frac{1}{r_1}, \frac{1}{r_2}, \frac{1}{r_3} \) are in arithmetic progression, then \( r_1 : r_2 : r_3 = \)?
If \( \cosh \alpha + \sinh \alpha = e^x \) and \( \sinh x = \frac{\alpha}{\alpha + 1} \), then \( \tanh x = \)
If \[ \left| 1 - \cos \left( \frac{\pi}{2} - \alpha \right) + \sin \left( \frac{3\pi}{2} - \alpha \right) \right| \left[ 1 - \sin \left( \frac{3\pi}{2} - \alpha \right) - \cos \left( \frac{\pi}{2} - \alpha \right) \right] = a + b \sin \left( \frac{\pi}{4} + \alpha \right) \] then \( a^2 + b^2 = \)
Let \(Z\) be the point of intersection of the axis and the directrix of the parabola \(4x^2 - 12x + 4y + 5 = 0\). If \(S\) is its focus, then the point which divides \(SZ\) in the ratio \(2:1\) is:
If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( |\vec{a}| = \sqrt{14} \), \( |\vec{b}| = \sqrt{14} \), and \( \vec{a} \cdot \vec{b} = -7 \), then \[ \frac{|\vec{a} \times \vec{b}|}{|\vec{a} \cdot \vec{b}|} \] is:
If \( z_1, z_2, z_3 \) are the vertices of an equilateral triangle and \( z \) is its circumcentre, then