Mathematical Economics and Optimization - Statistics, Econometrics and Mathematical Economics - Economics Previous Year Questions

1

2021 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2021

Given below is an inter-industry transactions matrix. If final demand for the agriculture sector changes from 150 units to 300 units and for the manufacturing sector changes from 120 units to 200 units, then the output of the agriculture sector should be __________ units (in integer).

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2

2022 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2022

Consider the following system of equations in three variables \( x, y, z \):
\( -x - y - z = 3 \)
\( x + y + z = 10 \)
\( 2x - 3y = 6 \)
This system of equations has

A

no combination of values of \((x, y, z) \) that satisfy this system simultaneously

B

only one combination of values of \((x, y, z) \) that satisfy this system simultaneously

C

only two combinations of values of \((x, y, z) \) that satisfy this system simultaneously

D

infinitely many combinations of values of \((x, y, z) \) that satisfy this system simultaneously

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3

2022 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2022

Let \( f(x, y) \) be a continuously differentiable homogeneous function of degree 4. Which of the following is necessarily true?

A

\(x \frac{\partial f(x, y)}{\partial x} + y \frac{\partial f(x, y)}{\partial y} = f(x, y) \)

B

\(x \frac{\partial f(x, y)}{\partial x} + y \frac{\partial f(x, y)}{\partial y} = 2 f(x, y) \)

C

\(x \frac{\partial f(x, y)}{\partial x} + y \frac{\partial f(x, y)}{\partial y} = 4 f(x, y) \)

D

\(x \frac{\partial f(x, y)}{\partial x} + y \frac{\partial f(x, y)}{\partial y} = 8 f(x, y) \)

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4

2022 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2022

Suppose \(\alpha\) is a real number between 0 and 1. Rohit is choosing \(x\) and \(y\) to maximize the following utility function:
\(U(x, y) = x^2 + 2xy + y^2 + 4\alpha^2 + 8\alpha + 10\)
subject to the following constraints:
\(2x + y = 10\),
\(x, y \ge 0\)
Then the optimal value of \(y\) chosen by Rohit is ______ (in integer).

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5

2023 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2023

Match the following:

A

I → P ; II → Q ; III → R ; IV → S

B

I → P ; II → S ; III → Q ; IV → R

C

I → R ; II → S ; III → Q ; IV → P

D

I → S ; II → P ; III → R ; IV → Q

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6

2024 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2024

For the function \(F: \mathbb{R}^2 \to \mathbb{R}\) specified as \(F(x, y) = x^3 - y^3 + 9xy\), which of the following options is/are correct

A

one saddle point

B

one strict local minimum

C

one strict local maximum

D

one global maximum

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7

2025 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2025

Let \( f(x, y, z) = x^2 y^3 z \).
Then,
\[ x \frac{\partial f}{\partial x} (x, y, z) + y \frac{\partial f}{\partial y} (x, y, z) + z \frac{\partial f}{\partial z} (x, y, z) = \]

A

\(f(x, y, z) \)

B

\(2 f(x, y, z) \)

C

\(3 f(x, y, z) \)

D

\(6 f(x, y, z) \)

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8

2025 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2025

Let \( f(x) = -3x^2 (1 - x) - 3x(1 - x)^2 - (1 - x)^3 \).
Then, \[ \frac{df(x)}{dx} = \]

A

\(3x^2 \)

B

\(3(1 - x)^2 \)

C

\(3x(1 - x) \)

D

\(x \)

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9

2025 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2025

Consider the following system of linear equations:
\[ \begin{aligned} x + 2y + 3z &= 0 \\ 2x + py &= 0 \\ 3x + 2y + pz &= 0 \end{aligned} \]
The value(s) of \( p \) for which the system of equations have infinitely many solutions is/are

A

\(p = 1 \)

B

\(p = 2 \)

C

\(p = 6 \)

D

\(p = 12 \)

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10

2025 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences-Economics (XH-C1) 2025

Let \(f(x, y) = −x^2 − y^2 + 2x + 4y + 5\). Let \((x^*, y^*)\) denote the solution to the following optimization problem: Maximize \(f(x, y)\) subject to \(x \geq 0\), \(y \geq 0\), \(2x + y \leq 6\). Then the value of \(f(x^*, y^*)\) is __________ (in integer)

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11

2026 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences - Economics (XH-C1) 2026

A is an \( n \times n \) matrix. Consider the following two statements
Statement 1: Columns of matrix A are linearly independent
Statement 2: Inverse of matrix A exists
Which one of the following statements is TRUE?

A

Statement 1 is true if and only if Statement 2 is true

B

Statement 1 and Statement 2 can be individually true or false

C

Statement 1 implies Statement 2 but not the other way round

D

Statement 2 implies Statement 1 but not the other way round

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12

2026 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences - Economics (XH-C1) 2026

Match Column I with Column II

A

(P → 2), (Q → 3), (R → 1), (S → 4)

B

(P → 4), (Q → 3), (R → 1), (S → 2)

C

(P → 2), (Q → 1), (R → 3), (S → 4)

D

(P → 4), (Q → 1), (R → 3), (S → 2)

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13

2026 · Economics · Statistics, Econometrics and Mathematical Economics · Mathematical Economics and Optimization

Humanities & Social Sciences - Economics (XH-C1) 2026

Consider the function G(x,y,z) = 0. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function G(x,y,z) exist everywhere. Then, the value of \(\left(\frac{\partial z}{\partial x} \times \frac{\partial x}{\partial y} \times \frac{\partial y}{\partial z}\right)\) is _____ (in integer)

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