UGCNET Questions

The rule states that each letter is replaced by the next letter in the alphabet. For the word NET, N is followed by O, E is followed by F and T is followed by U. Replacing each letter accordingly, N becomes O, E becomes F and T becomes U, giving the code OFU. This maintains the same pattern that was used to convert WORD into XPSE.

Option A:
Option A correctly shifts every letter of NET forward by one position, providing O from N, F from E and U from T. It applies the coding rule consistently to all positions and thus matches the example given.

Option B:
Option B, OEU, shifts only some letters correctly and uses E instead of F for the second position. This breaks the uniform next-letter rule for the middle letter.

Option C:
Option C, MFS, shifts N backwards to M instead of forwards and only partially follows the pattern. It does not consistently apply the specified direction of shift.

Option D:
Option D, NEU, keeps N unchanged, which contradicts the rule that each letter must be replaced by its immediate successor in the alphabet.

A strong argument should be relevant, logical and address the purpose of the statement. Entrance tests aim to provide a common measure to compare candidates from different backgrounds. A standardized test can help identify merit and readiness for professional study. This argument connects the use of tests directly with fairness and objectivity in selection, making it strong.

Option A:
Option A highlights the core rationale behind entrance tests: fairness and standardization in assessing merit. It justifies the policy by linking it with transparent and comparable evaluation across diverse applicants, which is a central concern in admissions.

Option B:
Option B claims that tests completely remove stress, which is unrealistic and exaggerated. Tests often create some stress; this argument therefore undermines its own credibility.

Option C:
Option C rejects all testing categorically, which is extreme and does not engage with the practical need to assess suitability for professional courses.

Option D:
Option D states that professional courses do not require any ability, which is obviously false and dismisses the seriousness of such education. It cannot be considered a strong argument.

The contrapositive of a statement of the form “If p then q” is “If not q then not p,” and these two are logically equivalent. Here, p is “the number is divisible by 6” and q is “the number is divisible by 3.” The contrapositive is therefore “if a number is not divisible by 3, then it is not divisible by 6.” This preserves the logical structure of the original implication while reversing and negating its components.

Option A:
Option A negates p but not q and forms the inverse “If not p then not q,” which is not logically equivalent to the original statement in general.

Option B:
Option B correctly follows the contrapositive pattern ¬q → ¬p, matching the structure of the initial implication about divisibility. It reflects the fact that if a number is not divisible by 3, it cannot possibly be divisible by 6.

Option C:
Option C is the converse q → p, which need not be true simply because the original implication is true; many numbers are divisible by 3 but not by 6.

Option D:
Option D contradicts the original statement directly by combining p with not q, which cannot be true if the original implication holds.

A is given as the mother of B. B and C are siblings because B is the brother of C, so A is also the mother of C. C is the father of D, which means D is A’s grandchild through C. Hence, combining these links, A’s relationship to D is that of a grandmother.

Option A:
Option A correctly traces the family relations step by step: A is parent to C, and C is parent to D, making A one generation above D’s parent. This is precisely the definition of a grandparent, and since A is female, the correct term is grandmother.

Option B:
Option B, aunt, would be appropriate if A were a sibling of D’s parent, but the problem clearly states A is the mother of B and C, not their sister. Therefore, she stands one generation above, not at the same generation as D’s parent.

Option C:
Option C, sister, would require A and D to share the same parents or at least be in the same generation. The information places A two generations above D, so this description is incompatible.

Option D:
Option D, mother, would mean A directly gave birth to D, but the statement shows that C is the father of D, and A is C’s mother, so the relationship has an extra generational step.

The days of the week repeat in a cycle of 7. To find the day after 10 days from Monday, we compute 10 modulo 7, which gives a remainder of 3. This means the day will be 3 days ahead of Monday. Counting forward, Monday plus 3 days is Thursday. Thus, after 10 days, it will be Thursday.

Option A:
Option A, Wednesday, is only 2 days ahead of Monday and would correspond to a remainder of 2, not 3, when dividing the number of days by 7.

Option B:
Option B aligns the remainder of 3 with a three-day forward move from Monday, giving Thursday. It uses the cyclic nature of the week correctly and therefore identifies the correct resulting day.

Option C:
Option C, Friday, is 4 days ahead and would correspond to a remainder of 4, which is not obtained when dividing 10 by 7.

Option D:
Option D, Sunday, is 6 days after Monday and would match a remainder of 6, not the remainder of 3 that arises here.

A prime number has exactly two distinct positive divisors, 1 and itself. The numbers 11, 13 and 17 each have no divisors other than 1 and themselves and are therefore prime. The number 15, however, is divisible by 1, 3, 5 and 15, so it has more than two divisors and is composite. Hence 15 is the odd one out in the list.

Option A:
Option A, 11, is a prime number because its only positive divisors are 1 and 11. It shares this property with 13 and 17 and therefore does not stand out in this group.

Option B:
Option B, 13, is also prime and fits the same classification as 11 and 17. It does not have additional factors that would make it different.

Option C:
Option C, 15, clearly deviates from the prime pattern, since it can be expressed as 3 × 5. Its composite nature makes it unique among the options and justifies treating it as the different number.

Option D:
Option D, 17, remains prime since no integer between 2 and 16 divides it without remainder. It aligns with 11 and 13 rather than differing from them.

Let the original price be 100 units. A 10% decrease takes it to 90. A further 10% decrease is now applied to 90, resulting in a reduction of 9, so the new price is 81. The overall decrease from 100 to 81 is 19 units, which is a 19% reduction. This shows that successive equal percentage decreases do not simply add arithmetically.

Option A:
Option A, 19%, correctly reflects the multiplicative effect of two successive 10% decreases. It uses the idea that the combined factor is 0.9 × 0.9 = 0.81, corresponding to a 19% drop.

Option B:
Option B, 20%, comes from the mistaken belief that decreases add directly (10% + 10%), but this ignores that the second decrease is on an already reduced base.

Option C:
Option C, 21%, overestimates the net effect and does not correspond to the computed final value of 81.

Option D:
Option D, 25%, greatly overstates the combined impact and has no support in the actual price sequence produced by the successive reductions.

A statement that is always true under every possible assignment of truth values to its components is called a tautology. The disjunction “p or not p” covers all possibilities: if p is true, the first part is true; if p is false, not p is true. Thus, in all cases the compound statement evaluates to true. This makes “p or not p” a classic example of a tautology.

Option A:
Option A, “p and not p,” is instead a contradiction because it asserts that p is both true and false simultaneously. There is no assignment of truth values that can make both p and not p true together, so this statement is never true.

Option B:
Option B, “p or not p,” correctly spans all truth possibilities for p. Since one of p or not p must be true, their disjunction is always true, demonstrating tautological status.

Option C:
Option C, “p → not p,” is not always true. If p is true, the implication would require not p to be true as well, which is impossible, so the statement can be false.

Option D:
Option D, “not p → p,” also fails to be always true; there are assignments where it becomes false, so it is not a tautology.

The days of the week repeat every 7 days. We find the effective shift by computing 50 mod 7. Since 50 = 7 × 7 + 1, the remainder is 1, meaning the day moves forward by 1 from Wednesday. One day after Wednesday is Thursday, so 50 days from now it will be Thursday.

Option A:
Option A, Thursday, is exactly one day after Wednesday and corresponds to a remainder of 1 in the modulo-7 calculation, so it matches the correct reasoning.

Option B:
Option B, Saturday, is three days after Wednesday and would be correct only if the remainder were 3, not 1.

Option C:
Option C, Sunday, is four days after Wednesday and would require a remainder of 4, which does not arise from 50 ÷ 7.

Option D:
Option D, Monday, is five days after Wednesday, again inconsistent with the actual remainder of 1.