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Questions › CUET-PG › CUET-PG 2023 Shift 1 › Q71
4 marks, −1Mathematics › Difference and differential equations › Difference equationsModerateabout 1 min

CUET-PG 2023 Shift 1 Question 71: Difference and differential equations

The solution of the difference equation xt=12xt−1+3x_t = \frac{1}{2}x_{t-1} + 3xt​=21​xt−1​+3 is

  1. xt=(12)t(x0−6)+6x_t = \left(\frac{1}{2}\right)^t (x_0 - 6) + 6xt​=(21​)t(x0​−6)+6
  2. xt=(12)t(x0−3)−2x_t = \left(\frac{1}{2}\right)^t (x_0 - 3) - 2xt​=(21​)t(x0​−3)−2
  3. xt=(12)t(x0−6)−6x_t = \left(\frac{1}{2}\right)^t (x_0 - 6) - 6xt​=(21​)t(x0​−6)−6
  4. xt=(12)(x0+6)+2x_t = \left(\frac{1}{2}\right)(x_0 + 6) + 2xt​=(21​)(x0​+6)+2

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Plain-text version

The solution of the difference equation xₜ = 1/2xₜ₋₁ + 3 is 1. xₜ = (1/2)^t (x₀ - 6) + 6 2. xₜ = (1/2)^t (x₀ - 3) - 2 3. xₜ = (1/2)^t (x₀ - 6) - 6 4. xₜ = (1/2)(x₀ + 6) + 2 (A) xₜ = (1/2)^t (x₀ - 6) + 6 (B) xₜ = (1/2)^t (x₀ - 3) - 2 (C) xₜ = (1/2)^t (x₀ - 6) - 6 (D) xₜ = (1/2)(x₀ + 6) + 2

Also written as: The solution of the difference equation x_t = 1/2x_(t-1) + 3 is 1. x_t = (1/2)^t (x_0 - 6) + 6 2. x_t = (1/2)^t (x_0 - 3) - 2 3. x_t = (1/2)^t (x_0 - 6) - 6 4. x_t = (1/2)(x_0 + 6) + 2

Difference and differential equations has come up 20 times in 5 exams since 2014.

What this question tests

This question is on Difference equations, part of Difference and differential equations in Mathematics.

Solving equations that link a variable to its past values.

TestStop has 5 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q16Let a second order difference equation be yₙ₊₂ + 4yₙ = 4yₙ₊₁, n = 2, 3, 4, …, with y₀ = 1, y₁ = 4. Then the…
  • IIT JAM 2021 · Q45Consider xₙ = ((n+1)/n)xₙ₋₁ for n = 1, 2, 3, … with x₀ = 2. Then x₁₀₀ - x₅₀ equals _ (in integer).
Take this paper as a timed mockMore on Difference equations

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Question from the CUET-PG 2023 Shift 1 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.