B.TECH - Semester 5 advanced mathematics and queuing models Question Paper 2019 (feb)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- Write down the various steps in solving an LPP by graphical method. Give its limitations.
- How would you resolve the complications (i) equalities in constraints and (ii) tie for the leaving basic variables in an LPP ?
- Explain the terms (i) optimistic (ii) most likely and (iii) pessimistic time estimates associated with PERT. How do you compute expected duration of an activity by using these ?
- Define subspace. Do the solution vectors of a consistent nonhomogeneous system of $m$ linear equations in $n$ unknowns form a subspace of $R^{n}$ ? Justify your answer.
- What do you mean by column space of a matrix ? Give an example of a $3 \times 3$ matrix whose column space is a plane through the origin in 3 -space.
- Define orthogonal complement of a subspace of an inner product space. If A is an $m \times n$ matrix, show that the null space of $A$ and the row space of $A$ are orthogonal complements in $\mathrm{R}^{\mathrm{n}}$ with respect to the Euclidean Inner...
- How do you find the least squares straight line fit to a given set of finitely many data points ? Explain.
- Describe some of the performance measures used in analysing queues.
- What are the main characteristics of a queueing model ? Explain.
- Explain how the inflow and outflow rates related to M/M/1:N/FIFO model are different from those related to M / M / c : $\infty$ / FIFO model. ( $\mathbf{1 0} \boldsymbol{\times} \mathbf{4} \boldsymbol{=} \mathbf{4 0}$ Marks)
- Max. $Z=4 \mathrm{x}_{1}+10 \mathrm{x}_{2}$ subject to $2 x_{1}+x_{2} \leq 10$ $2 x_{1}+5 x_{2} \leq 20$ $2 x_{1}+3 x_{2} \leq 18$ $\mathrm{x}_{1}, \mathrm{x}_{2} \geq 0$ Also find out two optimal solutions for the problem. | Activity | $1-2$ | $1-3...
- Min. $Z=2 \mathrm{x}_{1}+4 \mathrm{x}_{2}$ subject to $2 \mathrm{x}_{1}-3 \mathrm{x}_{2} \geq 2$ $-x_{1}+x_{2} \geq 3$ $\mathrm{x}_{1}, \mathrm{x}_{2} \geq 0$ | Activity | $1-2$ | $1-3$ | $1-4$ | $2-5$ | $3-5$ | $4-6$ | $5-6$ | | :--- | :---: | :---...
- $$ A=\left[\begin{array}{rr} 1 & 1 \\ -1 & 1 \\ -1 & 2 \end{array}\right] \text { and } b=\left[\begin{array}{r} 7 \\ 0 \\ -7 \end{array}\right] $$ $$ A=\left[\begin{array}{rrr} 3 & 1 & 1 \\ -1 & 3 & 1 \end{array}\right] $$
- $$ A=\left[\begin{array}{rrrrr} 2 & 2 & -1 & 0 & 1 \\ -1 & -1 & 2 & -3 & 1 \\ 1 & 1 & -2 & 0 & -1 \\ 0 & 0 & 1 & 1 & 1 \end{array}\right] $$ $A=\left[\begin{array}{rrr}3 & -6 & -3 \\ 2 & 0 & 6 \\ -4 & 7 & 4\end{array}\right]$ Use this to solve the s...
- i) What is the repairman's expected idle time on each day ? ii) How many jobs are ahead on the average set just brought in ?