List of top Questions asked in TS EAMCET

Find out mismatched pair from the following:
Final acceptor of electrons in light reaction:
The length of DNA is 510 Å. It has 20% of 6-aminopurines. Find out the total number of nucleotides and total hydrogen bonds in that DNA:
Transduction was discovered by 'X' in 'Y'. Identify 'X' and 'Y' respectively:
Crop varieties bred by hybridization, selection for disease resistance to fungi, bacteria and viral disease are given below. Identify mismatch:
Find the value of \( k \) such that \( 5 \cdot 2^n - 48n + k \) is divisible by 24.
The molecular weight of a gas is 32. If 0.5 moles of the gas occupy 22.4 liters at standard temperature and pressure (STP), what is the density of the gas?

Match the following: 

A ball is projected vertically up with speed \( V_0 \) from a certain height H. When the ball reaches the ground the speed is \( 3V_0 \). The time taken by the ball to reach the ground and height H respectively are (g = acceleration due to gravity)
If \(m\cos(\alpha + \beta) - n\cos(\alpha - \beta) = m\cos(\alpha - \beta) + n\cos(\alpha + \beta)\), then \(\tan \alpha \tan \beta\) is:
The number of solutions of the equation \[ \sin 7\theta - \sin 3\theta = \sin 4\theta \] that lie in the interval \( (0, \pi) \) is:
Evaluate the expression: \[ \cos^{-1} \frac{3}{5} + \sin^{-1} \frac{5}{13} + \tan^{-1} \frac{16}{63} \]

If

\[ \cosh^{-1}\left(\frac{5}{3}\right) + \sinh^{-1}\left(\frac{3}{4}\right) = k, \]

then \( e^k \) is:

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:
If \(2 \tan^2 \theta - 4 \sec \theta + 3 = 0\), then \(2 \sec \theta\) 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:

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

If \(AX = D\) represents the system of linear equations \[ 3x - 4y + 7z + 6=0,\quad 5x + 2y - 4z + 9=0,\quad 8x - 6y - z + 5=0, \] then AX = D ?
The system of equations \( x + 3y + 7 = 0 \), \( 3x + 10y - 3z + 18 = 0 \), and \( 3y - 9z + 2 = 0 \) has:

The system of simultaneous linear equations : 

 

\[ \begin{array}{rcl} x - 2y + 3z &=& 4 \\ 2x + 3y + z &=& 6 \\ 3x + y - 2z &=& 7 \end{array} \]

The system of equations \[ x + 3by + bz = 0, \quad x + 2ay + az = 0, \quad x + 4cy + cz = 0 \] has:
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 \(8\mu + 11\lambda =\)
\[ \lim_{n\to\infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\right)\cdots\left(1+\frac{n^2}{n^2}\right)\right]^{\frac{1}{n}} = \]

Evaluate the integral: \[ \int \frac{dx}{4 + 3\cot x} \]