List of top Questions asked in TS EAMCET- 2025

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 expression for K is given as a sum of terms up to infinity. Find the value of K.

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

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

If one of the roots of the equation \(6x^3 - 25x^2 + 2x + 8 = 0\) is an integer and \(\alpha>0\), \(\beta<0\) are the other two roots, then \( \frac{4}{\alpha} + \frac{1}{\beta} = \)

If f(x) is a second degree polynomial such that \(f(x) \ge 0 \forall x \in \mathbb{R}>\), \(f(-3) = 0\) and \(f(0) = 18\) then \(f(3) = \)

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 \(C_0, C_1, C_2, ..., C_{10}\) represent the binomial coefficients in the expansion of \((1+x)^{10}\), then \(C_0C_6 + C_1C_7 + C_2C_8 + C_3C_9 + C_4C_{10} = \)

If the coefficient of \(3^{\text{rd}}\) term from the beginning in the expansion of \( \left(ax^2 - \frac{8}{bx}\right)^9 \) is equal to the coefficient of \(3^{\text{rd}}\) term from the end in the expansion of \( \left(ax - \frac{2}{bx^2}\right)^9 \) then the relation between \( a \) and \( b \) is

If \( f(x)=\tan \left(\frac{\pi}{\sqrt{x+1}+4}\right) \) is a real valued function then the range of \( f \) is

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

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

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 $\alpha$ 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 $|Z_1 - 3 - 4i| = 5$ and $|Z_2| = 15$ then the sum of the maximum and minimum values of $|Z_1 - Z_2|$ 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 $\cos\alpha+\cos\beta+\cos\gamma = 0 = \sin\alpha+\sin\beta+\sin\gamma$, then $\sin 2\alpha + \sin 2\beta + \sin 2\gamma =$

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

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

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

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

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