List of top Questions asked in TS EAMCET

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

\( \omega \) 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 $\alpha$ 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 =

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

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

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

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

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

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

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

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

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

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

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

All the letters of the word MOTHER are arranged in all possible ways and the resulting words (may or may not have meaning) are arranged as in the dictionary. The number of words that appear after the word MOTHER is

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

The number of all possible three letter words that can be formed by choosing three letters from the letters of the word FEBRUARY so that a vowel always occupies the middle place is

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

When \( |x|>3 \), the coefficient of \( \frac{1}{x^n} \) in the expansion of \( x^{3/2} (3+x)^{1/2} \) 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

If all the letters of the word ACADEMICIAN are permuted in all possible ways then the number of permutations in which no two A's are together and all the consonants are together is

If all the letters of the word MOST are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order then the rank of the word STOM when counted from the rank of the word MOST, is