List of top Mathematics for Economy Questions

The linear system of equations
𝑥 + 𝑦 = 3,
$𝑥 + (𝑘^2 − 8)𝑦 = 𝑘, 𝑘 ∈ 𝑅$
has no solution for 𝑘 = _____ (in integer).

Let $f ∶ R^2 → R$ be a function defined as
$f(x,y) =\begin{cases}\frac{x^2y}{x^4 + Y^2} & if (x, y) \neq (0, 0)\\ 0 & if (x, y) = (0, 0)\end{cases} $ Then, which of the following is/are CORRECT?

Let $M =\begin{bmatrix} \alpha & − 6 \\-1 & -1 \end{bmatrix}, \alpha\, \epsilon\, R $ be a 2 × 2 matrix. If the eigenvalues of $M$ are $\beta$ and 4, then which of the following is/are CORRECT?

The differential equation satisfied by circles with radius 3 and center lying on the Y-axis is

In a two-player game, player 1 can choose either U or D as strategies. Player 2 can choose either L or R as strategies. Let 𝑐 be a real number such that $0 < 𝑐 < 1$. If the payoff matrix is

	L	R
U	0, 0	0, −c
D	−c, 0	1 − c, 1 − c

then the number of pure strategy Nash Equilibria in the game equals

To study the effect of $X_1$ and $X_2$ on Y, the following regression model is estimated using a large sample:
$ Y = a + \beta_1 X_1 + \beta_2X_2 + ∈ $
The OLS estimates and standard errors are presented below:

	$a$	$\beta_1$	$\beta_2$
Estimates	2.3	0.39	1.8
Standard errors	1.15	0.13	1

Given the above information, which of the following is CORRECT?

In a two-player game, player 1 can choose either M or N as strategies. Player 2 can choose either X, Y, or Z as strategies. The payoff matrix is as follows:

a	X	Y	Z
M	3, 1	0, 0	−1, 2
N	0, 0	1, 3	0.5, 1

Which set of strategy profiles survives iterated elimination of strictly dominated strategies?

The solution of the differential equation
$ xy 𝑑𝑥 − (x^2 + y^2) 𝑑y = 0, y(0) = 1$ is

The optimal value of the linear programming problem
Maximise $z = 2x + 3y$
subject to
$5x + 4y ≤ 20,$
$ 3𝑥 + 5𝑦 ≤ 15,$
$ 2𝑥 + 𝑦 ≤ 4,$
$ 𝑥, 𝑦 ≥ 0,$
is

$ \lim_{𝑥→\infty}(1+\frac{1}{x})$ is equal to

Let $S_1 = {(x, y) ∈ R^2 ∶ x + y ≥ 1, x + y ≤ 2, y ≥ x^2, x, y ≥ 0}$ and $S_2 = {(x, y) ∈ R^2 ∶ x + y ≥ 1, x + y ≤ 2, y ≤ x^2, x, y ≥ 0}.$ Then, which of the following is CORRECT ?

Let ∫ sin⁹ 𝑥 cos(11𝑥) 𝑑𝑥 = cos(10𝑥) 𝑓(𝑥) + 𝑐 , where 𝑐 is a constant. If 𝑓 ′′ (\(\frac{\pi}{4}\)) − 𝑘𝑓 ′(\(\frac{ \pi}{4}\)) = 0, then 𝑘 is equal to ______ (in integer)

Let [𝑡] denote the greatest integer ≤ 𝑡. The number of points of discontinuity of the function 𝑓(𝑥)= [𝑥²−3𝑥+2] for 𝑥∈[0, 4] is _______ (in integer)

Let 𝑀 = \(\begin{bmatrix} K & 1 & 1 \\ 1 & K & 1 \\ 1 & 1 & K \end{bmatrix}\)and I₃ be the identity matrix of order 3. If the rank of the matrix 10 𝐼₃ − 𝑀 is 2 then 𝑘 is equal to _____ (in integer).

Let 2𝑧=-3+√3 𝑖 , 𝑖 = √−1. Then 2z ⁸ is equal to

Let an = \((1+\frac{1}{n})^{\frac{n}{2}}\) be the n^𝑡ℎ term of the sequence 〈a_n 〉, n = 1, 2, 3, …. Then which one of the following is NOT CORRECT?

For α, β ∈ R , α ≠ β, if −2 and 5 are the eigenvalues of the matrix 𝑀=[1−𝛼1+𝛽𝛽 𝛼+𝛽] and 𝑋 = [𝑥1 𝑥2 ] is an eigenvector of 𝑀 associated to −2, then\(M=\begin{bmatrix} 1-α& 1+β\\ β & a+B& \end{bmatrix}\)
and 𝑋 = \(\begin{bmatrix}  X_1\\ X_2 \end{bmatrix}\) is an eigenvector of 𝑀 associated to −2, then

Let 𝑓: R² → R be the function defined by

Then

Among the following statements which one is CORRECT?
S1: 𝑥²+𝑦²=6 is a level curve of 𝑓(𝑥, 𝑦)=\(\sqrt{𝑥^2+𝑦^2}\)−𝑥²−𝑦²+2 
S2: 𝑥²−𝑦2=−3 is a level curve of 𝑔(𝑥, 𝑦) =\(𝑒−{^𝑥}^{2} 𝑒{^y}^{2}\)+𝑥⁴−2−2𝑥²𝑦²+y⁴

Let 𝐸 be the area of the region bounded by the curves 𝑦 = 𝑥² and 𝑦 = \(8\sqrt𝑥\), 𝑥≥0. Then 30𝐸 is equal to ________ (round off to 1 decimal place).

Which of the following is NOT CORRECT?

Let 𝑓, 𝑔∶ℝ → ℝ be defined by

Then

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

Let 𝑆 be a feasible set of a linear programming problem (𝑃). If the dual problem of (𝑃) is unbounded then

Let 𝑦 = 𝑦(𝑥) be a solution curve of the differential equation
\(𝑥 \frac{𝑑𝑦}{d𝑥} = 𝑦 \) ln ( \(\frac{y}{x}\) ) , 𝑦 > 𝑥 > 0. 
If 𝑦(1) = 𝑒 ² and 𝑦(2) = 𝛼, then the value of \(\frac{𝑑𝑦}{𝑑𝑥}\) at (2, 𝛼) is equal to