CUET UG 2025 — General Test Quantitative Reasoning

The first 100 integers are: 1, 2, 3, 4, ..., 100

Total integers = 100

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A perfect cube is a number that can be expressed as $n^3$n3 where $n$n is an integer.

The perfect cubes from 1 to 100:

$$1^3 = 1$$13=1

$$2^3 = 8$$23=8

$$3^3 = 27$$33=27

$$4^3 = 64$$43=64

$5^3 = 125$53=125 (exceeds 100)

Perfect cubes from 1 to 100: {1, 8, 27, 64}

Total perfect cubes = 4

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Probability = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$Total number of outcomesNumber of favorable outcomes​

Probability = $\dfrac{4}{100}$1004​

Probability = $\dfrac{1}{25}$251​

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Therefore, the probability that a randomly chosen number from the first 100 integers is a perfect cube is $\dfrac{1}{25}$251​.