List of top Applied Mathematics Questions on System of Linear Equations asked in CBSE CLASS XII

Tabulate the trend values of the years and compute the expected sales trend for the year 2002.
If \( R_2 \) is the feasible region, then what are the other two non-trivial constraints?
If \( R_1 \) is the feasible region, then what are the other two non-trivial constraints?
Find the inverse of matrix \( A \).
Write the system of linear equations in \( x \) and \( y \) formed from the given situation.
Determine the probability that the student studied for at least 2 hours.
A cistern has three pipes A, B, and C. Pipes A and B are inlet pipes, whereas C is an outlet pipe. Pipes A and B can fill the cistern separately in 3 hours and 4 hours respectively, while pipe C can empty the completely filled cistern in 1 hour. If the pipes A, B, and C are opened in order at 5, 6, and 7 a.m. respectively, at what time will the cistern be empty?
Give a linear equation that describes the computer system's book value at the end of \( t \)th year, where \( 0 \leq t \leq 3 \).
The mean weekly sales of a 4-wheeler was 50 units per agency in 20 agencies. After an advertising campaign, the mean weekly sales increased to 55 units per agency with a standard deviation of 10 units. Test whether the advertising campaign was successful.
[Given \( \sqrt{5} = 2.24 \), \( t_{19}(0.05) = 1.729 \)]
Evaluate \( \int_{0}^{1} \frac{e^{-x}}{1 + e^x} \, dx \).

A man bought an item for ₹ 12,000. At the end of the year, he decided to sell it for ₹ 15,000. If the inflation rate was 6%, find the nominal and real rate of return.

Given matrix equation: \[ \begin{bmatrix} x - y & 2x + z \\ 2x - y & 3z + w \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 13 \end{bmatrix} \] Find the values of \( x, y, z, \) and \( w \).
In an LPP, if the objective function \( Z = ax + by \) has the same maximum value on two corner points of the feasible region, then the number of points at which the maximum value of \( Z \) occurs is: