A company is shut down due to… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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A company is shut down due to unavailability of electricity due to non payment of electricity Bill because of some unavoidable circumstances. Under which component of time series does this situation fall?

Official previous-year question

Held on 30 May 2025 · Verified 13 Jul 2026.

Options

A
Seasonal
B
Cyclic
C
Irregular
D
Secular

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Solution

For a system of equations to have infinite solutions, the determinant of the coefficient matrix must be zero.

The coefficient matrix is:

$A = \begin{vmatrix} 1 & -3 & 5 \\ 1 & -2 & 4 \\ 2 & -7 & \lambda \end{vmatrix}$

Expanding the determinant along Row 1:

$\det(A) = 1[(-2)(\lambda) - (4)(-7)] - (-3)[(1)(\lambda) - (4)(2)] + 5[(1)(-7) - (-2)(2)]$

$= 1[-2\lambda + 28] + 3[\lambda - 8] + 5[-7 + 4]$

$= -2\lambda + 28 + 3\lambda - 24 - 15$

$= \lambda + 28 - 24 - 15$

$= \lambda - 11$

Setting the determinant equal to zero:

$\lambda - 11 = 0$

$\lambda = 11$

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