List of top Mathematics Questions asked in TS EAMCET

If the tangent and the normal drawn to the curve $xy^2 + x^2y = 12$ at the point (1,3) meet the X-axis in T and N respectively, then TN =

(a,b) are the new coordinates of the point (2,3) after shifting the origin to the point (3,2) by translation of axes. If (c,d) are the new coordinates of the point (a,b) after rotating the axes through an angle \( \frac{\pi}{4} \) about the origin in the anti-clockwise direction, then d-c =

If \( f(x) = x^{2}+bx+c \) and \( f(1+k) = f(1-k) \) \( \forall K \in \mathbb{R} \), for two real numbers b and c, then

Let $\vec{a}=\hat{i}-\hat{j}+\hat{k}$, $\vec{b}=\hat{i}-2\hat{j}-2\hat{k}$, $\vec{c}=6\hat{i}+3\hat{j}-2\hat{k}$ be three vectors. If $\vec{d}$ is a vector perpendicular to both $\vec{a}$, $\vec{b}$ and $|\vec{d}\times\vec{c}|=14$, then $|\vec{d}\cdot\vec{c}|=$

If \( x = \alpha, y = \beta, z = \gamma \) is the solution of the system of equations \( 2x+3y+z=-1 \), \( 3x+y+z=4 \), \( x-3y-2z=1 \), then the value of \( \beta \) is

If \( f: \mathbb{R}-\{0\} \to \mathbb{R} \) is defined by \( 3f(x) + 4f\left(\frac{1}{x}\right) = \frac{2-x}{x} \), then \( f(3) = \)

\( (\frac{1+i}{1-i})^{228}\)

Functions are formed from the set $A = \{a_1, a_2, a_3\}$ to another set $B = \{b_1, b_2, b_3, b_4, b_5\}$. If a function is selected at random, the probability that it is a one-one function is

The domain and range of $f(x) = \frac{1}{\sqrt{|x|-x^2}}$ are A and B respectively. Then $A \cup B = $ ?

If $A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 1 & 1 \\ 1 & 3 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 3 & 4 \\ 3 & 2 & 2 \\ 2 & 4 & 2 \end{pmatrix}$, then $\sqrt{|\text{Adj}(AB)|} =$

\( ^{20}P_3 - ^{19}P_3 = \)

If the domain of the real valued function $f(x) = \frac{1}{\sqrt{\log_{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a,b)$, then $2b =$

The positive value of 'a' for which the system of linear homogeneous equations \( x+ay+z=0 \), \( ax+2y-z=0 \), \( 2x+3y+z=0 \) has non-trivial solutions is

The domain of the real valued function \( f(x) = \log_{5}(\sqrt{x^2+x} + \sqrt{x^2-x}) \) is

There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at at least two consecutive stations, then the number of ways in which the train can be stopped is

The domain of the derivative of the function \( f(x) = \cos^{-1}(2x-5) - \sin^{-1}(x-2) \) is

An urn contains 7 red, 5 white and 3 black balls. Three balls are drawn randomly one after the other without replacement. If it is known that first ball drawn is red and the second ball drawn is white, then the probability that the third ball drawn is not red is

If $\frac{3x+1}{(x-1)^2(x^2+1)} = \frac{A}{x-1} + \frac{B}{(x-1)^2} + \frac{Cx+D}{x^2+1}$, then $2(A-C+B+D)=$

If the differential equation having $y = Ae^x + B\sin x$ as its general solution is $f(x)\frac{d^2y}{dx^2}+g(x)\frac{dy}{dx}+h(x)y=0$, then $f(x)+g(x)+h(x) =$

The inverse of the function \( y = \frac{10^x - 10^{-x}}{10^x + 10^{-x}} + 1 \) is \( x = \)

If $2^{4n+3} + 3^{3n+1}$ is divisible by P for all natural numbers $n$, then P is

The number of integers lying between 1000 and 10000 such that the sum of all the digits in each of those numbers becomes 30 is

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + \frac{a}{2}x + b = 0$ and $(\alpha-\beta)(\alpha-\gamma)$, $(\beta-\alpha)(\beta-\gamma)$, $(\gamma-\alpha)(\gamma-\beta)$ are the roots of the equation $(y+a)^3 + K(y+a)^2 + L = 0$, then $\frac{L}{K}= $

If $x = \sin 2\theta \cos 3\theta$, $y = \sin 3\theta \cos 2\theta$, then $\frac{dy}{dx} =$

If y=f(x) is the solution of the differential equation \( (1+\cos^2 x)f'(x) - 4\sin(2x) - f(x)\sin(2x) = 0 \) when f(0)=0, then \( f(\pi/3) = \)