List of top Questions asked in TS EAMCET

The IUPAC names of the compounds A and B respectively are

 

0.1435 g of silver chloride was obtained from 0.0945 g of an organic compound by Carius method. The percentage of chlorine by weight in the compound is (molar mass of AgCl = 143.5 g mol\(^{-1}\))

In the following reaction sequence X and Y respectively are

The concentration of 1 L of CaCO\(_3\) solution is \(10^{-5}\) M. Its concentration in ppm is. (Ca=40u; C=12u; O=16u)

The following graph is obtained for KCl solution at 300 K. What is \( \Lambda_m^0 \) (in S cm² mol\(^{-1}\)) of KCl? 

Identify the correct statements from the following:
I. The order of reaction is determined from experiment only
II.The order of reaction can be zero , positive integer or a fraction
III.In a multistep reaction, the slow step determines the rate
If \(1\cdot3\cdot5 + 3\cdot5\cdot7 + 5\cdot7\cdot9 + \ldots\) to \(n\) terms is \(n(n+1)f(n)\), then \(f(2) =\)
If \(A\) is a non singular matrix, then \(\text{Adj}(A^{-1}) =\)
If the homogeneous system of linear equations \(x - 2y + 3z = 0\), \(2x + 4y - 5z = 0\), \(3x + \lambda y + \mu z = 0\) has a non-trivial solution, then \(8\mu + 11\lambda =\)
If \( \alpha \) is a root of the equation \( x^2 - x + 1 = 0 \), then \(\left(\alpha + \frac{1}{\alpha}\right)^3 + \left(\alpha^2 + \frac{1}{\alpha^2}\right)^3 + \left(\alpha^3 + \frac{1}{\alpha^3}\right)^3 + \left(\alpha^4 + \frac{1}{\alpha^4}\right)^3 =\)

If \[ z = \frac{(2-i)(1+i)^3}{(1-i)^2} \] then \[ \text{Arg}(z) = ? \]

The solution set of the inequality \( \sqrt{x^2 + x - 2}>(1 - x) \) is:
If \( \alpha, \beta, \gamma \) are the roots of the equation \( 4x^3 - 3x^2 + 2x - 1 = 0 \), then \( \alpha^3 + \beta^3 + \gamma^3 = \)
The number of ways in which 6 distinct things can be distributed into 2 boxes so that no box is empty is:
If \(\frac{x^2}{2x^2 + 7x + 6} = \frac{Ax + B}{x^2 + a} + \frac{Cx + D}{ax^2 + 3}\), then \(A + B + C - 2D =\)
Given \((\sin \theta - \csc \theta)^2 + (\cos \theta + \sec \theta)^2 = 5\) and \(\theta\) lies in the third quadrant, find \((\sin \theta + \cos \theta)^3\).
If \( \theta \) is an acute angle and \( 2\sin^2 \theta = \cos^4 \frac{\pi}{8} + \sin^4 \frac{3\pi}{8} + \cos^4 \frac{5\pi}{8} + \sin^4 \frac{7\pi}{8} \), then \( \theta \) is:

\[ \sin^{-1} x - \cos^{-1} 2x = \sin^{-1} \left(\frac{\sqrt{3}}{2}\right) - \cos^{-1} \left(\frac{\sqrt{3}}{2}\right) \]

Then, \[ \tan^{-1} x + \tan^{-1} \left(\frac{x}{x+1}\right) = ? \]

\[ \text{sech}^{-1}\left(\frac{3}{5}\right) - \text{tanh}^{-1}\left(\frac{3}{5}\right) = ? \]

In a triangle ABC, if \( a = 5 \), \( b = 3 \), and \( c = 7 \), then the ratio:

\[ \sqrt{\frac{\sin(A - B)}{\sin(A + B)}} \]

Given the position vectors of points \(A\) and \(B\) as \( \mathbf{A} = 2\mathbf{i} - 3\mathbf{j} + \mathbf{k} \) and \( \mathbf{B} = \mathbf{i} + 2\mathbf{j} - 3\mathbf{k} \), and \(C\) divides \(AB\) in the ratio 3:2. If \( \mathbf{D} = 3\mathbf{i} - \mathbf{j} + 2\mathbf{k} \) is the position vector of point \(D\), find the unit vector in the direction of \( \mathbf{CD} \):
Given vectors \( \mathbf{a} = \mathbf{i} + \mathbf{j} - 2\mathbf{k} \), \( \mathbf{b} = \mathbf{i} - 2\mathbf{j} + \mathbf{k} \), and \( \mathbf{c} = 2\mathbf{i} + \mathbf{j} - \mathbf{k} \). If \( \mathbf{d} \) is a normal to the plane of \( \mathbf{a} \) and \( \mathbf{b} \) and satisfies \( \mathbf{d} \cdot \mathbf{c} = 2 \), find the magnitude of \( \mathbf{d} \):
The numbers 2, 3, 5, 7, 11, 13 are written on six distinct paper chits. If 3 of them are chosen at random, calculate the probability that the sum of the numbers on the obtained chits is divisible by 3.
If two dice are rolled, determine the probability that the sum of the numbers on the top faces is a multiple of 3, given that their sum is an odd number.

\[ \begin{array}{c|c} X = x & P(X = x) \\ \hline 1 & 3K^2 \\ 3 & K \\ 5 & K^2 \\ 2 & 2K \end{array} \]