#combinatorics

Aptitude and Reasoning

In a family with three children, what is the probability that two are boys and one is a girl?

In aptitude and reasoning, quantitative reasoning dictates that ratio, percentage and series logic determine correct calculation. Therefore 3/8 is correct as it meets mathematical and logical criteria, supported by mechanistic studies and conserved across related systems.

Ref: Wren and Martin, High School English Grammar and Composition, Revised Edition, Chapter 12, discusses vocabulary and comprehension providing guidance for verbal aptitude and logical inference assessment.

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General Biology and Immunology

A cube is painted on all sides using yellow and black color such that opposite faces are painted in different color. Thi

Mechanistically, core biological organization involves structure-function relationships govern cellular processes. This validates 6 because it integrates fundamental principles, a pattern repeatedly demonstrated in general biology research. This mechanism is extensively documented and reinforced by experimental data across multiple model systems and textbook discussions.

Ref: Campbell et al., Biology, 11th Edition, Chapter 2, Chemical Basis of Life, discusses fundamental biological principles and molecular organization providing broad foundation for life sciences understanding.

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Aptitude and Reasoning

If there are 3 children in a family, then the probability that there is only one girl child in the family is

The principle of quantitative reasoning explains that ratio, percentage and series logic determine correct calculation. Hence 2/3 fits best because it meets mathematical and logical criteria, as documented in authoritative sources on aptitude and reasoning.

Ref: Agrawal, Quantitative Aptitude for Competitive Examinations, Chapter 5, Logical Reasoning and Probability, covers ratios, percentages, series completion, time-distance and analytical reasoning explaining problem-solving strategies for competitive assessments.

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Aptitude and Reasoning

From a group of 7 women and 6 men, 5 persons are required to form a selection committee in which at least 3 women should

Mechanistically, quantitative reasoning involves ratio, percentage and series logic determine correct calculation. This validates 756 because it meets mathematical and logical criteria, a pattern repeatedly demonstrated in aptitude and reasoning research.

Ref: Agrawal, Quantitative Aptitude for Competitive Examinations, Chapter 5, Logical Reasoning and Probability, covers ratios, percentages, series completion, time-distance and analytical reasoning explaining problem-solving strategies for competitive assessments.

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Aptitude and Reasoning

A producer must select a pair consisting of one lead actor and one supporting actor from 6 candidates. The number of pos

In aptitude and reasoning, quantitative reasoning dictates that ratio, percentage and series logic determine correct calculation. Therefore 30 is correct as it meets mathematical and logical criteria, supported by mechanistic studies and conserved across related systems.

Ref: Agrawal, Quantitative Aptitude for Competitive Examinations, Chapter 5, Logical Reasoning and Probability, covers ratios, percentages, series completion, time-distance and analytical reasoning explaining problem-solving strategies for competitive assessments.

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Probability 2

If 2 cards are drawn from a well shuffled pack of 52 cards, the probability that they are of the same colour is:

Notice that complete solution: write formula, plug data, do arithmetic. Final value matches 2551. Simple and accurate.

Ref: NCERT Mathematics Class XII — Probability

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Probability 2

A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a random manner from the

We can see that we verify 7/20 by full calculation: use standard identity, substitute, simplify step by step to reach 7/20.

Ref: NCERT Mathematics Class XII — Probability

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Probability 2

A fair coin is tossed n times. The probability that the difference between the number of heads and tails is ( n - 3 ) is

We can see that solving fully: apply relevant formula, put numbers, compute. Result comes as 0. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XII — Probability

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General Mathematics 1

The number of one-to-one functions from 1, 2, 3 to 1, 2, 3, 4, 5 is

Understanding this is easy: solving fully: apply relevant formula, put numbers, compute. Result comes as 60. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XI and XII

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Probability 1

Out of 800 families with 4 children each, how many families would be expected to have 2 boys and 2 girls.

We can see that complete solution: write formula, plug data, do arithmetic. Final value matches 300. Simple and accurate.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

If a fair die is rolled 4 times, then what is the probability that there are exactly 2 sixes?

Look at it this way: after simplifying, 25216 is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XII — Probability

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