List of top Questions asked in TS EAMCET- 2024

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 $a$:

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 $.

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

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

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

The common solution set of the inequalities \[ x^2 - 4x \leq 12 \quad \text{and} \quad x^2 - 2x \geq 15 \] taken together is:

If $ \alpha, \beta, \gamma $ are the roots of the equation $ 4x^3 - 3x^2 + 2x - 1 = 0 $, then $ \alpha^3 + \beta^3 + \gamma^3 = $

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

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

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

$$ \begin{vmatrix} x-2 & 3x-3 & 5x-5 \\ x-4 & 3x-9 & 5x-25 \\ x-8 & 3x-27 & 5x-125 \end{vmatrix} = 0 $$

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:

The mean and variance of a binomial variate $X$ are $\frac{16}{5}$ and $\frac{48}{25}$ respectively. Given that $P(X \geq 1) = 1 - K \left(\frac{3}{5}\right)^7$, find $5K$:

(a,b) is the point of concurrency of the lines $x-3y+3=0$, $Kx+y+k=0$ and $2x+y-8=0$. If the perpendicular distance from the origin to the line $L: ax-by+2k=0$ is $p$, then the perpendicular distance from the point $(2,3)$ to $L=0$ is:

A rhombus is inscribed in the region common to the two circles \[ x^2 + y^2 - 4x - 12 = 0 \] and \[ x^2 + y^2 + 4x - 12 = 0. \] If the line joining the centres of these circles and the common chord of them are the diagonals of this rhombus, then the area (in Sq. units) of the rhombus is:

The range of the real valued function $ f(x) = \log_3 (5 + 4x - x^2) $ is

If \[ \int \sqrt{\csc x + 1} \, dx = k \tan^{-1} (f(x)) + c, \] then \[ \frac{1}{k} f\left(\frac{\pi}{6}\right) = ? \]

If the expression $ 7 + 6x - 3x^2 $ attains its extreme value $ \beta $ at $ x = \alpha $, then the sum of the squares of the roots of the equation $ x^2 + ax - \beta = 0 $ is:

The equations of the directrices of the ellipse $9x^2 + 4y^2 - 18x - 16y - 11 = 0$ are:

If $ 3^{2n+2} - 8n - 9 $ is divisible by $ 2^p $ $\forall n \in \mathbb{N}$, then the maximum value of $ p $ is

\[ \textbf{If } | \text{Adj} \ A | = x \text{ and } | \text{Adj} \ B | = y, \text{ then } \left( | \text{Adj}(AB) | \right)^{-1} \text{ is } \]

\[ D = \begin{vmatrix} -\frac{bc}{a^2} & \frac{c}{a} & \frac{b}{a} \\ \frac{c}{b} & -\frac{ac}{b^2} & \frac{a}{b} \\ \frac{b}{c} & \frac{a}{c} & -\frac{ab}{c^2} \end{vmatrix} \]

The point $(p, q)$ is the point of intersection of a latus rectum and an asymptote of the hyperbola $9x^2 - 16y^2 = 144$. If $p>0$ and $q>0$, then $q = \ldots$

If \[ f(x) = 3x^{15} - 5x^{10} + 7x^5 + 50\cos(x - 1), \] then \[ \lim_{h \to 0} \frac{f(1 - h) - f(1)}{h^2 + 3h} \] is: