List of top Mathematics Questions asked in TS EAMCET

Let z = x+iy represent a point P(x, y) in the Argand plane. If z satisfies the condition that amplitude of \( \frac{z-3}{z-2i} = \frac{\pi}{2} \), then the locus of P is

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

If \( \begin{vmatrix} 9 & 25 & 16 \\ 16 & 36 & 25 \\ 25 & 49 & 36 \end{vmatrix} = K \), then \( K, K+1 \) are the roots of the equation

If the augmented matrix corresponding to the system of equations \( x+y-z=1 \), \( 2x+4y-z=0 \) and \( 3x+4y+5z=18 \) is transformed to \( \begin{bmatrix} 1 & a & 0 & -1 \\ 0 & 2 & 1 & b \\ 0 & 0 & c & 32 \end{bmatrix} \), then

The product of all the values of \( (\sqrt{3}-i)^{\frac{3}{7}} \) is

The range of the real valued function \( f(x)=\sin ^{-1}\left(\sqrt{x^{2}+x+1}\right) \) is

If $\cos\alpha+\cos\beta+\cos\gamma = 0 = \sin\alpha+\sin\beta+\sin\gamma$, then $\sin 2\alpha + \sin 2\beta + \sin 2\gamma =$

If $\alpha$ is a root of the equation $x^2-x+1=0$ then $(\alpha + \frac{1}{\alpha}) + (\alpha^2 + \frac{1}{\alpha^2}) + (\alpha^3 + \frac{1}{\alpha^3}) + \dots$ to 12 terms =

\( \omega \) is a complex cube root of unity and \( Z \) is a complex number satisfying \( |Z-1| \le 2 \). The possible values of \( r \) such that \( |Z-1| \le 2 \) and \( |\omega Z - 1 - \omega^2| = r \) have no common solution are

If \( n, K \in \mathbb{N} \) such that \( n \neq 3K \), then \( (\sqrt{3}+i)^{2n} + (\sqrt{3}-i)^{2n} = \)

The amplitude of the complex number is:
\[\frac{(\sqrt{3}+i)(1-\sqrt{3}i)}{(-1+i)(-1-i)}\]

Number of real values of $(-1-\sqrt{3}i)^{3/4}$ is

If the eight vertices of a regular octagon are given by the complex numbers $\frac{1}{x_j-2i}$ ($j=1,2,3,4,5,6,7,8$), then the radius of the circumcircle of the octagon is

If $|Z_1 - 3 - 4i| = 5$ and $|Z_2| = 15$ then the sum of the maximum and minimum values of $|Z_1 - Z_2|$ is

One of the values of $\sqrt{24-70i} + \sqrt{-24+70i}$ is

The set of all values of $\theta$ such that $\frac{1-i\cos\theta}{1+2i\sin\theta}$ is purely imaginary is

In Argand plane, no value of \( \sqrt[3]{1-i\sqrt{3}} \) lie in

If a complex number $z = x+iy$ represents a point $P(x, y)$ in the Argand plane and z satisfies the condition that the imaginary part of $\frac{z-3}{z+3i}$ is zero, then the locus of the point P is

$(\sqrt{3}+i)^{10} + (\sqrt{3}-i)^{10} =$

If $Z=r(\cos\theta+i\sin\theta)$, $(\theta \neq -\pi/2)$ is a solution of $x^3 = i$, then $r^9(\cos(9\theta)+i\sin(9\theta)) =$

If $\omega \neq 1$ is a cube root of unity, then one root among the $7^{th}$ roots of $(1+\omega)$ 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

Number of all possible ways of distributing eight identical apples among three persons is

The number of non negative integral solutions of the equation \( x+y+z+t=10 \) when \( x \ge 2, z \ge 5 \) is

The constant term in the expansion of \( \left(1+\frac{1}{x}\right)^{20} \left(30x(1+x)^{29} + (1+x)^{30}\right) \) is