Learners' Club (Combined Aptitude Test)

Two particular girls are fixed, so we only need to choose 3 more students from the remaining 18 students. The number of ways to choose 3 students from 18 is calculated using combinations, which is 18C3. This equals 816. Other options do not correctly apply combination logic. Therefore, 816 is the correct answer because it accounts for fixed selections and remaining combinations accurately.

Let correct answers be x. Then incorrect answers are 75 minus x. Total marks equation becomes 4x minus (75 minus x) equals 125. Simplifying gives 5x equals 200, so x equals 40. This matches one of the options. Therefore, the student answered 40 questions correctly. The method uses algebraic equation formation and simplification to determine the correct value.

Economic growth generally leads to improved income, employment, and purchasing power, which increases the standard of living. Therefore, the growth of the Indian economy acts as the cause, while the rising standard of living is the effect. Hence, Statement II is the cause and Statement I is the effect. Other options fail to correctly establish the logical cause-and-effect relationship between economic growth and societal improvement.

Illiteracy is reduced or controlled through education. Similarly, floods are controlled or prevented using dams. Therefore, the correct analogy is flood and dam. Rain causes floods but does not control them, so it is not correct. The analogy focuses on problem and solution relationship. Hence, dam is the correct answer because it performs the same function as education in the analogy.

In a standard die, opposite faces remain constant regardless of position. Based on given rotations, pairs of opposite faces can be identified by observing which faces never appear together. From such analysis, A is opposite to E. The logic depends on visual reasoning and elimination. Therefore, E is the correct answer because it consistently appears opposite A in all possible orientations derived from the figure.

Once ice melts due to heat, it changes from solid to liquid form and cannot be seen again as an ice cube under the same conditions. The statement refers to something that has already melted. Therefore, it is impossible to see it as an ice cube again. Hence, “Never” is the correct answer, as it reflects the irreversible change under the described conditions.

From the information, Q has the same profession as U, and no two people share professions except defined roles. Since they match and are not in conflicting roles, they must be technicians. Logical elimination of other roles confirms this. Therefore, Q and U form the pair of technicians. This conclusion is reached by matching profession conditions and eliminating incompatible pairings.

The pattern alternates into two sequences. Odd positions increase by 3: 3, 6, 9, 12, 15. Even positions decrease by 2: 7, 5, 3, 1. The next number continues the even pattern: 1 minus 2 equals negative 1. Therefore, -1 is correct. Other options do not follow this alternating sequence rule. This requires identifying two interwoven number patterns.

Let sum of sons be S. Then father’s age is 3S. After 5 years: 3S plus 5 equals 2(S plus 10). Solving gives S equals 15. Therefore, father’s age equals 3 times 15, which is 45. This matches one option. The earlier solution was incorrect. Proper equation formation and solving yields the correct answer as 45 years.

Time taken by runners to complete one lap are 4, 6, and 3 hours respectively. They meet again when all complete whole laps together. This occurs at the least common multiple of 4, 6, and 3, which is 12. Therefore, they meet again after 12 hours. This solution uses LCM to synchronize periodic motion in circular paths.