List of top Mathematics Questions asked in TS EAMCET

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

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 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 = $

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 $5K$:

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 $a$:

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 = $:

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 $.

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

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

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

For $ n \in \mathbb{N} $, the largest positive integer that divides $ 81^n + 20n - 1 $ is $ k $. If $ S $ is the sum of all positive divisors of $ k $, then find $ S - k $.

If $1\cdot3\cdot5 + 3\cdot5\cdot7 + 5\cdot7\cdot9 + \ldots$ to $n$ terms is $n(n+1)f(n)$, then $f(2) =$

$\frac{1}{3.6} + \frac{1}{6.9} + \frac{1}{9.12} + \dots$ up to 9 terms $=$

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

(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:

The equation $ 16x^4 + 16x^3 - 4x - 1 = 0 $ has a multiple root. If $ \alpha, \beta, \gamma, \delta $ are the roots of this equation, then $ \frac{1}{\alpha^4} + \frac{1}{\beta^4} + \frac{1}{\gamma^4} + \frac{1}{\delta^4} = $

If the probability that a randomly selected student from a college is good at mathematics is 0.6, then the probability of having exactly two students who are good at mathematics in a group of 8 students standing in front of the college is:

Among the 4-digit numbers that can be formed using the digits $\{1,2,3,4,5,6\}$ without repeating any digit, the number of such numbers which are divisible by 6 is \;?