List of top Questions asked in TS EAMCET

The number of real solutions of $\tan^{-1}x + \tan^{-1}(2x) = \frac{\pi}{4}$ is

If a, b are real numbers and $\alpha$ is a real root of $x^2+12+3\sin(a+bx)+6x=0$ then the value of $\cos(a+b\alpha)$ for the least positive value of $a+b\alpha$ is

If $\cos\alpha = \frac{l\cos\beta+m}{l+m\cos\beta}$, then $\frac{\tan^2(\alpha/2)}{\tan^2(\beta/2)} =$

If $P = \sin\frac{2\pi}{7} + \sin\frac{4\pi}{7} + \sin\frac{8\pi}{7}$ and $Q = \cos\frac{2\pi}{7} + \cos\frac{4\pi}{7} + \cos\frac{8\pi}{7}$, then the point (P,Q) lies on the circle of radius

If $\tan(\frac{\pi}{4}+\frac{\alpha}{2}) = \tan^3(\frac{\pi}{4}+\frac{\beta}{2})$, then $\frac{3+\sin^2\beta}{1+3\sin^2\beta}=$

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 $2(A-C+B+D)=$

Let K be the number of rational terms in the expansion of $(\sqrt{2}+\sqrt[6]{3})^{6144}$. If the coefficient of $x^P (P \in N)$ in the expansion of $\frac{1}{(1+x)(1+x^2)(1+x^4)(1+x^8)(1+x^{16})}$ is $a_P$, then $a_K - a_{K+1} - a_{K-1} =$

Numerically greatest term in the expansion of $(3x-4y)^{23}$ when $x=\frac{1}{6}$ and $y=\frac{1}{8}$ is

The number of positive integral solutions of $xyz = 60$ 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 $1+2i$ is a root of the equation $x^4 - 3x^3 + 8x^2 - 7x + 5 = 0$, then sum of the squares of the other roots is

If local maximum of $f(x) = \frac{ax+b}{(x-1)(x-4)}$ exists at $(2,-1)$, then $a+b=$

If $\omega \neq 1$ is a cube root of unity, then one root among the $7^{th}$ roots of $(1+\omega)$ 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 $|Z_1 - 3 - 4i| = 5$ 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 $2^{4n+3} + 3^{3n+1}$ is divisible by P for all natural numbers $n$, then P is

The ratio of \(\sigma\) bonds to \(\pi\) bonds in Q is

The reaction of benzene with CO and HCl in the presence of anhydrous AlCl\(_3\) gives a compound X. X can also be obtained from which of the following reaction?

Cumene on oxidation in air gives a compound, X. This on reaction with dilute acid gives Y and Z. Y reacts with sodium metal and not Z. What is Z?

Chlorobenzene when subjected to Fittig reaction gives a compound 'X'. The sum of \(\sigma\) and \(\pi\)-bonds in X is

Consider the following
Assertion (A): Aspirin is useful in the prevention of heart attacks
Reason (R): Aspirin acts as anti-blood clotting agent
The correct answer is

The general structure of alpha amino acid can be represented as

. Which amino acid is not correctly matched with R-given?

Polymer X is an example of polyester and Y is an example of polyamide. X and Y are respectively

Which one of the following complex ions is diamagnetic in nature?