List of top Mathematics Questions asked in TS EAMCET

Evaluate the integral: \[ I = \int_{-\frac{\pi}{15}}^{\frac{\pi}{15}} \frac{\cos 5x}{1 + e^{5x}} \, dx \]

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his own wife is ?

If $ A(1, 2, -3) $, $ B(2, 3, -1) $, and $ C(3, 1, 1) $ are the vertices of triangle $ \Delta ABC $, then find $ \left| \frac{\cos A}{\cos B} \right|.$

The equation of the circle passing through the origin and cutting the circles $x^2 + y^2 + 6x - 15 = 0$ and $x^2 + y^2 - 8y - 10 = 0$ orthogonally is:

Define $ f: \mathbb{R} \to \mathbb{R} $ by \[ f(x) = \begin{cases} \frac{1 - \cos 4x}{x^2}, & x < 0 \\ a, & x = 0 \\ \frac{\sqrt{x}}{\sqrt{16 + \sqrt{x}} - 4}, & x > 0 \end{cases} \] Find the value of $ a $ such that $ f $ is continuous at $ x = 0 $.

If $ x $ and $ y $ are two positive real numbers such that $ x + iy = \frac{13\sqrt{5} + 12i}{(2 - 3i)(3 + 2i)} $, then $ 13y - 26x = $:

Given a square matrix $A$ where $A^2 + I = 2A$, find $A^9$.

In a triangle ABC, if $ r_1 = 6 $, $ r_2 = 9 $, $ r_3 = 18 $, then $ \cos A $ is:

The mean of a binomial variate $ X \sim B(n, p) $ is 1. If $ n>2 $ and $ P(X = 2) = \frac{27}{128} $, then the variance of the distribution is:}

If the function

\[ f(x) = \begin{cases} \frac{(e^x - 1) \sin kx}{4 \tan x}, & x \neq 0 \\ P, & x = 0 \end{cases} \]

is differentiable at $ x = 0 $, then:

The equations \[ 7x + y - 24 = 0 \quad \text{and} \quad x + 7y - 24 = 0 \] represent the equal sides of an isosceles triangle. If the third side passes through $ (-1,1) $, then a possible equation for the third side is: \

Evaluate the integral: \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{dx}{\sec^2 x + (\tan^{2022} x - 1)(\sec^2 x - 1)} \]

All the letters of the word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without meaning) thus formed are arranged in the dictionary order. Then the rank of the word 'COLLEGE' is:

If $ m $ and $ M $ are respectively the absolute minimum and absolute maximum values of a function $ f(x) = 2x^3 + 9x^2 + 12x + 1 $ defined on $[-3,0]$, then $ m + M $ is:

If the normal drawn at the point $(2, -1)$ to the ellipse $x^2 + 4y^2 = 8$ meets the ellipse again at $(a, b)$, then $17a$ is:

The foot of the perpendicular drawn from the point $(-2, -1, 3)$ to a plane is $(1, 0, -2)$. If $a, b, c$ are the intercepts made by the plane $\pi$ on $X, Y, Z$-axes respectively, then $3a+b+5c =$

If $ \sin^{-1}(4x) - \cos^{-1}(3x) = \frac{\pi}{6} $, then $ x = $:

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 $5K$:

\[ \lim_{n\to\infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\right)\cdots\left(1+\frac{n^2}{n^2}\right)\right]^{\frac{1}{n}} = \]

Evaluate the integral: \[ \int 4\cos^2 x - 5\sin^2 x \cos x \, dx. \]

If $ x = \cos 2t + \log (\tan t) $ and $ y = 2t + \cot 2t $, then $ \frac{dy}{dx} $ is:

If $6x-5y-20=0$ is a normal to the ellipse $x^2 + 3y^2 = k$, then $k =$

The maximum value of the function \[ f(x) = 3\sin^{12}x + 4\cos^{16}x \] is ?

If $2\,\tan^{-1}x = 3\,\sin^{-1}x$ and $x \neq 0$, then $8x^2 +1 =\;?$

If \[ \int e^x (x^3 + x^2 - x + 4) \, dx = e^x f(x) + C, \] then $ f(1) $ is: