List of practice Questions

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 ?

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

Match the following:

A metal target with atomic number \( Z = 46 \) is bombarded with a high-energy electron beam. The emission of X-rays from the target is analyzed. The ratio \( r \) of the wavelengths of the \( K_\alpha \)-line and the cutoff is found to be \( r = 2 \). If the same electron beam bombards another metal target with \( Z = 41 \), the value of \( r \) will be:

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 \( 3^a + b^2 \)?

An object is placed at a distance of 18 cm in front of a mirror. If the image is formed at a distance of 4 cm on the other side, then the focal length, nature of the mirror and nature of the image are respectively:

∫ √(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 ?

Atomicity of Phosphorus is:
Isotones are the atoms of different elements having:
Atomicity is given by:
Atomicity of an element is:
Avogadro’s hypothesis relates volume of gases and:
The compound which does not show a simple ratio of atoms is:
The Principle of Uncertainty was introduced by:
In the beginning of the 20th century, the matter wave concept was introduced by:
Atomicity of primary gases is:
Atoms of different elements with the same number of neutrons are called:
Atoms of different elements possessing the same atomic mass are called:
C\(^ {126}\) and C\(^ {14}\) are:
Isotopes are the atoms of the same element, with the same atomic number, but with different:
The Greek term ‘atomos’ means:
When sunlight passes through the window of your house, the dust particles scatter the light making the path of the light visible. This phenomenon is called as:
Which law relates solubility of solvents with pressure?
On increasing the temperature, the solubility of the solute in the solvent: