List of top Questions asked in AP EAPCET

Identify the functions of diencephalon in frog’s brain among the following
Assertion (A): The placenta is connected to the embryo through an umbilical cord.
Reason (R): Somatomammotropin released from placenta has anti-insulin effect on mother.
Slowest and most primitive type of locomotion in protozoan is

Match the following

The integral form of the exponential growth equation is
The chylomicrons are broken down to fatty acids and glycerol by the action of the enzyme
Example of anadromous migration is
Evaluate \( \left[ 1 + \sec 2\theta \right] \left[ 1 + \sec 40^\circ \right] \):
Let \( \vec{a} = 3\vec{i} + \vec{j} - 2\vec{k} \), \( \vec{b} = -5\vec{i} + 7\vec{j} \), and \( \vec{c} = 3\vec{i} + y\vec{j} \) be three vectors such that \( |\vec{a} - \vec{b} + \vec{c}| = \sqrt{141} \). If \( y_1 \) and \( y_2 \) are the values of \( y \) satisfying the given condition, then \( |y_1 - y_2| = \)
The area (in square units) of the triangle formed by the lines \( x = 0 \), \( y = 0 \), and \( 3x + 4y = 12 \) is:
A function \( f(x) \) is defined as: \[ f(x) = \begin{cases} ax^2 + bx + c, & x \leq -1
2x^2 + 4x + 1, & -1<x<1
cx^2 + bx + a, & x \geq 1 \end{cases} \] If \( f(x) \) is continuous on \( \mathbb{R} \) and \( \lim_{x \to -\frac{3}{2}} f(x) = 14 \), then \( \lim_{x \to 2} f(x) = \):
Let \( c_1, c_2, c_3, c_4 \) be arbitrary constants. The order of the differential equation corresponding to \[ y = c_1 e^x + c_2 e^{\log_e x} + c_3 \sin^2 x - c_4 (\cos^5 x - 1) \] is:
\(A(-2, 9)\) and \(B(1, 6)\) are two points on the curve \(y = x^2 + 5\). The coordinates of the point \(C\) on the curve such that the tangent drawn at \(A\) is parallel to the chord \(BC\) is:
Let the curve \(x^2 + 2y^2 = 2\) intersect the line \(x + y = 1\) at two points \(P\) and \(Q\) and \(O\) be the origin. If \(\theta\) is the acute angle between the lines \(OP\) and \(OQ\), then \(\tan \theta =\)
Assertion (A): The function \( f(x) = \begin{cases} 1 - \cos x, & x<0 \\ \sin x, & x \geq 0 \end{cases} \) is continuous at \(x = 0\). Reason (R): \(\lim_{x \to 0} \sin x = 0\)
The function \( f(x) = x^2 + \dfrac{54}{x} \)
In a game, a pair of dice is rolled 24 times. If a person wins the game by not getting 6 on both the dice in any one of the 24 rolls, then the probability that a person wins the game is:
Tangents are drawn from point $ (1, 1) $ to the ellipse $ x^2 + y^2 + 10x + 8y - 23 = 0 $. If $ m_1, m_2 $ (with $ m_1>m_2 $) are the slopes of these tangents, then with respect to the given ellipse, the point $ P(m_1, m_2) $ lies:
Let $ [t] $ represent the greatest integer not exceeding $ t $. The number of discontinuous points of $ [10^t] $ in $ (0, 10) $ is:
The particular solution of the differential equation \[ \frac{dx}{dy} = \frac{\sin y(1 + y \cot y)}{x \log(x^2 e)}, \quad y(1) = 0 \] Options:
The point of intersection of the tangents drawn at the points where the line \[ 2x - y + 3 = 0 \] meets the circle \[ x^2 + y^2 - 4x - 6y + 4 = 0 \] is:
If \( 5f(x) + 3f\left( \frac{1}{x} \right) = 2 - \frac{1}{x}, x \ne 0 \), then \( \int_1^2 f\left( \frac{1}{x} \right) dx = \)
If the points \( (k, 1, 5), (1, 0, 3), (7, -2, m) \) are collinear, then \( (k, m) = \)
If the acute angle between the pair of tangents drawn from the origin to the circle \( x^2 + y^2 - 4x - 8y + 4 = 0 \) is \( \alpha \), then \( \tan \alpha = \)
The area bounded by \( y - 1 = -|x| \) and \( y + 1 = |x| \) is: