List of top Questions asked in TS EAMCET

Matrix Inverse Sum Calculation

Given the matrix:

    A =    | 1  2  2 |    | 3  2  3 |    | 1  1  2 |    

The inverse matrix is represented as:

    A-1 =    | a11  a12  a13 |    | a21  a22  a23 |    | a31  a32  a33 |    

The sum of all elements in A-1 is:

∑ aij = 3

The temperature at which the rms speed of oxygen molecules is 75\% of the rms speed of nitrogen molecules at a temperature of \( 287^\circ C \) is: 

Match the following:

At 300 K, 3.0 moles of an ideal gas at 3.0 atm pressure is compressed isothermally to one half of its volume by an external pressure of 6.0 atm. The work done (in kJ) is:

If the real-valued function

\[ f(x) = \sin^{-1}(x^2 - 1) - 3\log_3(3^x - 2) \]

is not defined for all \( x \in (-\infty, a] \cup (b, \infty) \), then what is \( 3^a + b^2 \)?

∫ √(2x2 - 5x + 2) dx = ∫ (41/60) dx,

and

-1/2 > α > 0, then α = ?

The number of common roots among the 12th and 30th roots of unity is ?

Calculate the determinant of the matrix:
 


 

S = (-1,1) is the focus, \( 2x - 3y + 1 = 0 \) is the directrix corresponding to S and \( \frac{1}{2} \) is the eccentricity of an ellipse. If \( (a,b) \) is the centre of the ellipse, then \( 3a + 2b \) is:

Calculate the variance of the data set: 1, 2, 3, 5, 8, 13, 17.

Match the following:
 


The correct answer is:
 

Evaluate the integral: \[ \int e^{-2x} \left( \tan 2x - 2\sec^2 2x \tan 2x \right) dx. \]
If \( Z_1, Z_2, Z_3 \) are three complex numbers with unit modulus such that \[ |Z_1 - Z_2|^2 + |Z_1 - Z_3|^2 = 4 \] then \[ Z_1 Z_2 + \overline{Z_1} Z_2 + Z_1 Z_3 + \overline{Z_1} Z_3 = \]
If the ratio of the radii of nuclei \( \mathbf{^{52}X_A} \) and \( \mathbf{^{13}Al^{27}} \) is 5:3, then the number of neutrons in the nucleus \( X \) is:
Choose the correct answer from the options given below:

\[ \textbf{If } | \text{Adj} \ A | = x \text{ and } | \text{Adj} \ B | = y, \text{ then } \left( | \text{Adj}(AB) | \right)^{-1} \text{ is } \]

Let \( A = [a_{ij}] \) be a \( 3 \times 3 \) matrix with positive integers as its elements. The elements of \( A \) are such that the sum of all the elements of each row is equal to 6, and \( a_{22} = 2 \). 
 

The voltage gain of a transistor in common emitter configuration is 160. The resistances in base and collector sides of the circuit are 1k\( \Omega \) and 4k\( \Omega \), respectively. If the change in base current is 100\( \mu \)A, then the change in output current is
The direction cosines of two lines are connected by the relations \[ l - m + n = 0, \quad 2lm - 3mn + nl = 0. \] If \( \theta \) is the angle between these two lines, then \( \cos \theta \) is:

The mean deviation about the mean for the following data is:
 


 

The position vectors of the vertices \( A, B, C \) of a triangle are given as: \[ \vec{A} = \hat{i} - 2\hat{j} + k, \quad \vec{B} = 2\hat{i} + \hat{j} - k, \quad \vec{C} = \hat{i} - \hat{j} - 2k \] If \( D \) and \( E \) are the midpoints of \( BC \) and \( CA \) respectively, then the unit vector along \( \overrightarrow{DE} \) is:
If \(\tan A<0\) and \(\tan 2A = -\frac{4}{3}\), then \(\cos 6A\) is:

A student has to write the words ABILITY, PROBABILITY, FACILITY, MOBILITY. He wrote one word and erased all the letters in it except two consecutive letters. If 'LI' is left after erasing then the probability that the boy wrote the word PROBABILITY is: \

One of the roots of the equation \( x^{14} + x^9 - x^5 - 1 = 0 \) is:
x and y are two complex numbers such that \(|x| = |y| = 1\). If \( \text{Arg}(x) = 2\alpha \), \( \text{Arg}(y) = 3\beta \) and \( \alpha + \beta = \frac{\pi}{36} \), then \( x^6 y^4 + \frac{1}{x^6 y^4} \) is:
The point P denotes the complex number \(z = x + iy\) in the Argand plane. If \( \frac{2z - i}{z - 2} \) is purely real number, then the equation of the locus of P is.