List of top Questions asked in AP EAMCET- 2024

In a nuclear reactor, the fuel is consumed at the rate of \( 1 \times 10^{-3} \) gs\(^{-1}\). The power generated in kW is:
In the diodes shown in the diagrams, which one is reverse biased?
The moment of inertia of a solid sphere about its diameter is 20 kg m². The moment of inertia of a thin spherical shell having the same mass and radius about its diameter is:
An alternating current is given by \( i = (3 \sin \omega t + 4 \cos \omega t) \) A. The rms current will be:
Among the 4-digit numbers formed using the digits \( 0, 1, 2, 3, 4 \) when repetition of digits is allowed, the number of numbers which are divisible by 4 is:
The independent term in the expansion of \( (1 + x + 2x^2) \left( \frac{3x^2}{2} - \frac{1}{3x} \right)^9 \) is:
The equations of the perpendicular bisectors of the sides AB and AC of \( \triangle ABC \) are \( x - y + 5 = 0 \) and \( x + 2y = 0 \) respectively. If the coordinates of \( A \) are \( (1, -2) \), then the equation of the line BC is:
A unit vector perpendicular to the vectors \( \bar{a} = 2\bar{i} + 3\bar{j} + 4\bar{k} \) and \( \bar{b} = 3\bar{j} + 2\bar{k} \) is:
Given the equation: \[ y = (\tan^{-1} 2x)^2 + (\cot^{-1} 2x)^2, \] find the expression: \[ (1+4x^2)^2 y'' - 16. \]
In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange’s Mean Value Theorem is not applicable.
In a Binomial distribution \( B(n,p) \), the sum and product of the mean and the variance are 5 and 6 respectively, then \( 6(n + p - q) = \):
If \(f(x) = \begin{cases} ax^2 + bx - \frac{13}{8}, & x \le 1 \\ 3x - 3, & 1<x \le 2 \\ bx^3 + 1, & x>2 \end{cases}\)is differentiable \(\forall x \in \mathbb{R}\), then \( a - b = \)
If the mean of the data 7, 8, 9, 7, 8, 7, \(\lambda\), 8 is 8, then the variance of the data:
A pair of lines drawn through the origin forms a right-angled isosceles triangle with right angle at the origin with the line \( 2x + 3y = 6 \). The area (in square units) of the triangle thus formed is:
The circumference of a circle passing through the point \( (4, 6) \) with two normals represented by \( 2x - 3y + 4 = 0 \) and \( x + y - 3 = 0 \) is:
If \( A \subseteq \mathbb{Z} \) and the function \( f: A \to \mathbb{R} \) is defined by \[ f(x) = \frac{1}{\sqrt{64 - (0.5)^{24+x- x^2} }} \] then the sum of all absolute values of elements of \( A \) is:
The set of all real values of \(x\) satisfying the inequality \(\frac{7x^2 - 5x - 18}{2x^2 + x - 6}<2\) is
The set of all values of \(k\) for which the inequality \(x^2 - (3k+1)x + 4k^2 + 3k - 3>0\) is true for all real values of \(x\) is
Which of the following functions are odd? 
\[ \begin{aligned} \text{I. } & f(x) = x \left( \frac{e^x -1}{e^x +1} \right) \\[8pt] \text{II. } & f(x) = k^x + k^{-x} + \cos x \\[8pt] \text{III. } & f(x) = \log \left( x + \sqrt{x^2 +1} \right) \end{aligned} \]
If the probability distribution of a random variable \( X \) is given as follows, then find \( k \):
probability distribution of a random variable X
The number of ways of arranging 2 red, 3 white, and 5 yellow roses of different sizes into a garland such that no two yellow roses come together is:
The \( n^{th} \) term of the series \[ 1 + (3+5+7) + (9+11+13+15+17) + \dots \] is:
The general solution of \( \cot \frac{x}{2} - \cot x = \csc \frac{x}{2} \) is:
Let \( T_1 \) be the tangent drawn at a point \( P(\sqrt{2}, \sqrt{3}) \) on the ellipse \( \frac{x^2}{4} + \frac{y^2}{6} = 1 \). If \( (a, \beta) \) is the point where \( T_1 \) intersects another tangent \( T_2 \) to the ellipse perpendicularly, then \( a^2 + \beta^2 = \):
If \( P \) is a point which divides the line segment joining the focus of the parabola \( y^2 = 12x \) and a point on the parabola in the ratio 1:2, then the locus of \( P \) is: