List of top Questions asked in TS EAMCET- 2024

\[ \begin{array}{c|c} X = x & P(X = x) \\ \hline 1 & 3K^2 \\ 3 & K \\ 5 & K^2 \\ 2 & 2K \end{array} \]

If water is poured into a cylindrical tank of radius 3.5 ft at the rate of 1 cubic ft/min, then the rate at which the level of the water in the tank increases (in ft/min) is:

The numerically greatest term in the expansion of (3x - 16y)¹⁵ when x = ²⁄₃ and y = ³⁄₂ is ?

The end of a latus rectum of the ellipse $3x^2 + 4y^2 = 12$ is lying in the third quadrant. If the normal drawn at $L_1$ to this ellipse intersects the ellipse again at the point $P(a,b)$, then find the value of $a$:

Evaluate the integral: \[ I = \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \,dx \]

Among the following four statements, the statement which is not true, for all $ n \in N $ is:

If $ p $ and $ q $ are the real numbers such that the 7th term in the expansion of $ \left( \frac{5}{p^3} \cdot \frac{3q}{7} \right)^8 $ is 700, then $ 49p^2 = $:

If the tangents $ x + y + k = 0 $ and $ x + ay + b = 0 $ drawn to the circle $ S : x^2 + y^2 + 2x - 2y + 1 = 0 $ are perpendicular to each other and $ k, b $ are both greater than 1, then find $ b - k $.

The equation of the normal drawn to the curve $ y^3 = 4x^5 $ at the point $ (4,16) $ is:

If $\tan A<0$ and $\tan 2A = -\frac{4}{3}$, then $\cos 6A$ is:

If on average 4 customers visit a shop in an hour, then the probability that more than 2 customers visit the shop in a specific hour is:

$\lim_{x \to 0}$ $\frac{3^{\sin x} - 2^{\tan x}}{\sin x}$ =

Let $ A = [a_{ij}] $ be a $ 3 \times 3 $ matrix with positive integers as its elements. The elements of $ A $ are such that the sum of all the elements of each row is equal to 6, and $ a_{22} = 2 $.