List of top Questions asked in AP EAMCET- 2024

If \( y = \frac{ax + \beta}{\gamma x + \delta} \), then \( 2y_1 y_3 = \) ?
The point which lies on the tangent drawn to the curve \( x^4 e^y + 2 \sqrt{y} + 1 = 3 \) at the point \( (1,0) \) is:
Evaluate the limit: $$ \lim_{n \to \infty} \frac{17^7 + 27^7 + \dots + n^{77}}{n^{78}}. $$ 
The equation of the normal drawn to the parabola \( y^2 = 6x \) at the point \( (24,12) \) is:
If \( z = x+iy \), \( x^2+y^2 = 1 \) and \( z_1 = e^{i\theta} \), then the expression \( \frac{z_1^{2n-1} - 1}{z_1^{2^n-1} + 1} \) simplifies to:
If five-digit numbers are formed from the digits 0, 1, 2, 3, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 is
If the mean deviation about the mean is \(m\) and the variance is \(\sigma^2\) for the following data, then \(m + \sigma^2 =\) % Data table \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline f & 4 & 24 & 28 & 16 & 8 \\ \hline \end{array} \]
Two natural numbers are chosen at random from 1 to 100 and are multiplied. If \(A\) is the event that the product is an even number and \(B\) is the event that the product is divisible by 4, then \(P(A \cap \bar B) = \)
A test containing 3 objective type of questions is conducted in a class. Each question has 4 options and only one option is the correct answer. No two students of the class have answered identically and no student has written all correct answers. If every student has attempted all the questions, then the maximum possible number of students who have written the test is:
A box \( P \) contains one white ball, three red balls and two black balls. Another box \( Q \) contains two white balls, three red balls and four black balls. If one ball is drawn at random from each one of the two boxes, then the probability that the balls drawn are of different color is
Let \( A(2, 3), B(1, -1) \) be two points. If \( P \) is a variable point such that \( \angle APB = 90^\circ \), then the locus of \( P \) is
If the origin is shifted to remove the first degree terms from the equation \(2x^2 - 3y^2 + 4xy + 4x + 4y - 14 = 0\), then with respect to this new co-ordinate system, the transformed equation of \(x^2 + y^2 - 3xy + 4y + 3 = 0\) is
The angle between the line with the direction ratios \( (2, 5, 1) \) and the plane \( 8x + 2y - z = 4 \) is given by
The equation of the straight line passing through the point of intersection of the lines represented by \(x^2 + 4xy + 3y^2 - 4x - 10y + 3 = 0\) and the point \((2,2)\) is:
Equation of a tangent line of the parabola \(y^2 = 8x\), which passes through the point \((1, 3)\) is:
If \( L_1 \) and \( L_2 \) are two lines which pass through origin and have direction ratios \( (3, 1, -5) \) and \( (2, 3, -1) \) respectively, then the equation of the plane containing \( L_1 \) and \( L_2 \) is:
The general solution of the equation \( \sin^2 \theta + 3 \cos^2 \theta = 5 \sin \theta \) is:
In \(\triangle ABC\), if \(4r_1 = 5r_2 = 6r_3\), then \(\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} =\)
In \(\triangle ABC\), \(r r_1 \cot^ \frac{A}{2} + r r_2 \cot^ \frac{B}{2} + r r_3 \cot^ \frac{C}{2} = \)
If \( O(0, 0, 0), A(3, 0, 0), B(0, 4, 0) \) form a triangle then the incenter of triangle OAB is:
In the interval \([0, 3]\), the function \(f(x) = |x - 1| + |x - 2|\) is:
Evaluate the integral \( \int_0^{\frac{\pi}{2}} \frac{1}{1 + \sqrt{\tan x}} \, dx \):
The largest among the distances from the point \(P(15,9)\) to the points on the circle \(x^2 + y^2 - 6x - 8y - 11 = 0\) is:
The solution of the differential equation \[ x dy - y dx = \sqrt{x^2 + y^2} dx \] when \( y(\sqrt{3}) = 1 \) is:
If a complex number \( z \) is such that \( \frac{z-2i}{z-2} \) and the locus of \( z \) is a closed curve, then the area of the region bounded by that closed curve and lying in the first quadrant is: