List of top Mathematics for Economy Questions asked in Indian Institute Of Technology Joint Admission Test for MSc

Consider a linear programming problem (𝑃) min 𝑧 = 4𝑥₁ + 6𝑥₂ + 6𝑥₃ subject to
𝑥₁+3𝑥₂≥3
𝑥₁+2𝑥₃ ≥5 
𝑥₁, 𝑥₂, 𝑥₃ ≥ 0 
If \(𝑥^∗ = (𝑥^∗_1 , 𝑥^∗_2 , 𝑥^∗_3 )\) is an optimal solution and 𝑧^∗ is an optimal value of (𝑃) and 𝑤^∗ =\((𝑤^∗_1 , 𝑤^∗_2 )\) is an optimal solution of the dual of (𝑃) then

For K∈R, let 𝑓(𝑥)=𝑥⁴+2𝑥³+𝑘𝑥²−𝑘, X∈R. If 𝑥=\(\frac{3}{2}\) is a point of local minima of 𝑓 and 𝑚 is the global minimum value of 𝑓 then 𝑓(0) − 𝑚 is equal to _______ (in integer).

If (𝑥^∗ , 𝑦^∗) is the optimal solution of the problem
maximize 𝑓(𝑥, 𝑦) = 100−𝑒^−𝑥−𝑒 ^−𝑦 
subject to 𝑒𝑥+𝑦=\(\frac{𝑒}{𝑒−1},\) 𝑥 ≥ 0, 𝑦 ≥ 0. 
Then \(\sqrt{\frac{y^*}{x^*}}\) is equal to ________ (round off to 2 decimal places).

Let \(x^3+3y^2=4\) for all \(x,y\isin\R,\) \(y'=\frac{dy}{dx}\) and \(y''=\frac{d^2y}{dx^2}\). Then

Let a second order difference equation be
\(y_{n+2} + 4y_n = 4y_{n+1}, \, n=2,3,4,......, \,\, y_0=1, y_1=4\)
Then the general solution is

Let the function \(f: R^2⇢R\)  be \(f(x, y) = \frac{xy^2}{ x^3+  2xy + y^3}\,\,  f(0, 0) = 0.\) Then

Let ƒ be defined by $f(x) = |x| + |cos({\frac{\pi }{2} - x }), x \, \, \epsilon \, \,(-\frac{\pi }{2},\frac{\pi }{2}).$ Then

Let the system of equations be αu+w=0, u+αν =0, v+αw=0, where a ∈ ℜ. Then the system has infinite solutions if a =_____ (in integer).

Let f: [0,∞) → \(\R\) be a function defined by \(f(x)=\frac{x+1}{x+2}\) for all \(x\isin\R\). Then f is

Let a,b $\epsilon$ R. If f(x)= ax+bis such that
a+b=4 and f(x + y) = f(x)+f(y)-2 for all x, y $\epsilon$ R,
then  $ \sum_{n=1} ^{50} f(n)$ =__________  (in integer).

Choose the option that represents the original linear programming problem based on the initial simplex tableau given below, where \(S_i\) represents slack/surplus variables and \(A_i\) represents the artificial variables corresponding to the \(i^{th}\)constraint: 

Which of the following statements is CORRECT for Game A and Game B?

Game A: Mary wants to watch a movie and John is interested in watching a football match. Both wish to be together. The payoff matrix is:

Game B: The Prisoner's dilemma problem is shown below:

The sum of the eigen values of the square matrix $ \begin{pmatrix} {1} & {1} & {3}\\ {1} & {5} & {1}\\ {3} & {1} & {1} \end{pmatrix}$ (in integer).

Let the linear programming problem be
Maximize Z = - 0.2x₁ + x₂
subject to 2x₁ + 5x₂ ≤ 70,
x₁ + x₂ ≤ 20,
x₁, x₂ ≥ 0.
If x₁ = a and x₂ = b is the optimal solution, then a+b=______ (in integer).

Which of the following functions is/are homogeneous?

If \(\int t\log(1+\frac{2}{t})dt=g(t)(\frac{t^2}{2}-2)+f(t)\frac{t^2}{2}+Kt+C\), where C is an arbitrary constant, then 2K is ______ (in integer).