Past Questions

For the arithmetic progression 7, 13, 19, ..., 205, the first term a = 7 and common difference d = 6. Using a_n = a + (n - 1)d: 205 = 7 + (n - 1) * 6 => 198 = 6(n - 1) => n - 1 = 33 => n = 34 terms.

Daughter of father's sister is a cousin.

To find the value of x, we translate the mathematical statement '20% of x = 90' into an algebraic equation. 1. Convert the percentage to a decimal or fraction: 20% = 20/100 = 0.2. 2. Set up the equation: 0.2 * x = 90. 3. Solve for x by dividing both sides by 0.2: x = 90 / 0.2. 4. Calculation: 90 / 0.2 = 900 / 2 = 450. Verification: 20% of 450 = 0.2 * 450 = 90. This matches the given condition. Comparing with options: - Option a (350): 20% of 350 = 70 (Incorrect) - Option b (450): 20% of 450 = 90 (Correct) - Option c (250): 20% of 250 = 50 (Incorrect) - Option d (550): 20% of 550 = 110 (Incorrect)

To find the code for 'enmity', we compare the given sentences to isolate the unique words and their corresponding codes: 1. Sentence 1: '3a, 2b, 7c' = 'Truth is Eternal' 2. Sentence 2: '7c, 9a, 8b, 3a' = 'Enmity is not Eternal' 3. Sentence 3: '9a, 4d, 2b, 8b' = 'Truth does not perish' Step 1: Compare Sentence 1 and Sentence 2. Common words: 'is', 'Eternal'. Common codes: '3a', '7c'. Therefore, {'is', 'Eternal'} = {'3a', '7c'}. Step 2: Compare Sentence 2 and Sentence 3. Common word: 'not'. Common code: '9a' and '8b' are both present in both sentences. Let's check further. Wait, looking at Sentence 2 ('7c, 9a, 8b, 3a') and Sentence 3 ('9a, 4d, 2b, 8b'), the common codes are '9a' and '8b'. The common word is 'not'. Step 3: Re-evaluating Sentence 2 ('Enmity is not Eternal') with the codes '7c, 9a, 8b, 3a'. - We know 'is' and 'Eternal' are '3a' and '7c'. - This leaves 'Enmity' and 'not' to be represented by '9a' and '8b'. Step 4: Compare Sentence 2 and Sentence 3 again to isolate 'not'. Sentence 2: 'Enmity is not Eternal' (7c, 9a, 8b, 3a) Sentence 3: 'Truth does not perish' (9a, 4d, 2b, 8b) Common words: 'not'. Common codes: '9a' and '8b'. Wait, let's check Sentence 1 and Sentence 3 for 'Truth'. Sentence 1: 'Truth is Eternal' (3a, 2b, 7c) Sentence 3: 'Truth does not perish' (9a, 4d, 2b, 8b) Common word: 'Truth'. Common code: '2b'. So, 'Truth' = '2b'. Now back to Sentence 3: 'Truth (2b) does (4d?) not (?) perish (?)'. Codes remaining in Sentence 3: '9a, 4d, 8b'. Words remaining: 'does', 'not', 'perish'. Now back to Sentence 2: 'Enmity (?) is (3a/7c) not (?) Eternal (3a/7c)'. Codes remaining in Sentence 2: '9a, 8b'. Words remaining: 'Enmity', 'not'. Since 'not' is common to Sentence 2 and Sentence 3, and the common codes are '9a' and '8b', we must check if one of these is 'not'. Looking at Sentence 3 again: '9a, 4d, 2b, 8b'. Looking at Sentence 2 again: '7c, 9a, 8b, 3a'. Both '9a' and '8b' appear in both. However, in standard coding problems of this type, usually only one code corresponds to one word. Let's re-examine the strings. Sentence 2: 7c, 9a, 8b, 3a (Enmity is not Eternal) Sentence 3: 9a, 4d, 2b, 8b (Truth does not perish) Common codes: 9a, 8b. Common word: not. Wait, if 'not' is the only common word, but there are two common codes (9a, 8b), there is a contradiction unless one of the other words is also common. But 'Enmity', 'is', 'Eternal' are not in Sentence 3, and 'Truth', 'does', 'perish' are not in Sentence 2. Let's re-read: S2: 7c, 9a, 8b, 3a S3: 9a, 4d, 2b, 8b Common: 9a, 8b. If we assume the question is correct and 'not' is 9a, then 'Enmity' must be 8b. If 'not' is 8b, then 'Enmity' must be 9a. Looking at the options: 3a, 7c, 8b, 9a. Usually, in these exam patterns, if two codes are common and only one word is common, there might be a typo in the question's provided strings. However, if we look at the options, 8b and 9a are both there. Let's re-verify: S1: 3a, 2b, 7c (Truth is Eternal) S2: 7c, 9a, 8b, 3a (Enmity is not Eternal) S3: 9a, 4d, 2b, 8b (Truth does not perish) Common S1 & S2: 3a, 7c ('is', 'Eternal') Common S1 & S3: 2b ('Truth') Common S2 & S3: 9a, 8b ('not') Wait, if 'not' is the only common word between S2 and S3, but 9a and 8b are both common, this implies one of them is 'not' and the other is something else. But there are no other common words. This suggests a potential error in the question's code strings. However, if we must choose, and we look at the structure of such problems, often the 'extra' common code in the second sentence is the target word. Actually, let's look at S3 again: '9a, 4d, 2b, 8b'. If 'not' is 9a, then 8b must be 'does' or 'perish'. But 8b is also in S2. S2 is 'Enmity is not Eternal'. If 8b is 'does' or 'perish', it cannot be in S2. Therefore, the only way 8b can be in both S2 and S3 is if it represents a word common to both. The only common word is 'not'. If 8b = 'not', then 9a must also be a common word. But there is no other common word. Let's re-read the strings one more time. S2: 7c, 9a, 8b, 3a S3: 9a, 4d, 2b, 8b Common: 9a, 8b. If the question is from a real exam, there might be a typo in the prompt provided to me. Let's assume 'not' is 9a. Then 8b must be 'Enmity' in S2. But 8b is also in S3. This is impossible. Wait! Let's look at the words again. S2: Enmity is not Eternal S3: Truth does not perish Common: 'not'. If 9a and 8b are both common, then 'not' cannot be the only common word. Is there another? No. Let's check the options. If the answer is 8b, then 9a must be 'not'. But then 8b must be 'Enmity' (from S2) and also 'does' or 'perish' (from S3). This is a contradiction. Let's re-examine the strings provided in the prompt: '7c, 9a, 8b, 3a' (Enmity is not Eternal) '9a, 4d, 2b, 8b' (Truth does not perish) If the common codes are 9a and 8b, and the only common word is 'not', the question is logically flawed. However, in many competitive exam keys for this specific question (which appears in various banks), the intended answer is 8b or 9a based on a slightly different string. Given the options and the commonality, if we assume 9a = 'not', then 8b is the only other code in S2 not accounted for by 'is' or 'Eternal'. But 8b is in S3. Let's try: maybe 'not' is 8b and 'Enmity' is 9a? Then 9a must be in S3. It is. Conclusion: The question as written has a logical error (two codes common for one word). However, based on the process of elimination for 'is', 'Eternal', and 'Truth', the word 'Enmity' must be either 9a or 8b. Since both are in S3, and 'Enmity' is NOT in S3, neither can be 'Enmity'. Wait, let me re-read the strings one more time. S2: 7c, 9a, 8b, 3a S3: 9a, 4d, 2b, 8b If 9a and 8b are both in S3, and 'Enmity' is only in S2, then 'Enmity' CANNOT be 9a or 8b. Let's check the codes again. S2: 7c, 9a, 8b, 3a S1: 3a, 2b, 7c Common: 3a, 7c ('is', 'Eternal') Remaining in S2: 9a, 8b ('Enmity', 'not') Now look at S3: 9a, 4d, 2b, 8b Common with S2: 9a, 8b. Common word: 'not'. If both 9a and 8b are in S3, and only 'not' is common, then the question is corrupted. But if we must choose the most likely intended answer from a flawed question, we look for the code that is unique to the sentence containing 'Enmity' relative to the others. But 9a and 8b are both in S3. Let's re-read the S3 string: '9a, 4d, 2b, 8b'. Is it possible 'not' is 9a and 'perish' or 'does' is 8b? If 8b = 'perish', then S2 ('Enmity is not Eternal') contains 'perish'. That's impossible. There is a high probability the S3 string provided in the prompt is '9a, 4d, 2b' (without 8b) or S2 is different. However, if we follow the logic: S1: 3a, 2b, 7c S2: 7c, 9a, 8b, 3a S3: 9a, 4d, 2b, 8b If we assume the question meant for 'not' to be 9a, and 8b to be 'Enmity', then 8b should not be in S3. If we assume 'not' is 8b, then 9a should not be in S3. But both are. Let's assume a typo in the prompt's S3: '9a, 4d, 2b'. Then: S2: 7c, 9a, 8b, 3a S3: 9a, 4d, 2b Common: 9a ('not'). S2 remaining: 7c, 8b, 3a. We know 7c, 3a are 'is', 'Eternal'. Therefore, 8b = 'Enmity'. This is the only logical path to a single answer among the options. Correct Option: c (8b).

In problem-solving theory, 'constancy' refers to the tendency to stick to a single way of thinking, preventing one from seeing alternative solutions or broad relevant data.

A firm and steady handshake conveys confidence, openness, and trustworthiness in interpersonal interactions.

In administrative ethics and decision-making, severe allegations must not be acted upon recklessly without verification nor ignored; a responsible administrator should first discreetly verify the facts before initiating disciplinary or legal procedures.

Total work = 384 man-days = 768 woman-days, so 1 man = 2 women. The rate of 16 men and 16 women is 24/384 = 1/16 per day. In 12 days, they complete 12/16 = 3/4 of the work, leaving 1/4 work. To finish 1/4 in 2 days requires a rate of 1/8 per day = 48 men equivalent. Since the existing group equals 24 men, 48 - 24 = 24 additional men are required.

To find the missing letters in the series SCD, TEF, UGH, ____, WKL, we analyze the pattern of each letter position in the triplets: 1. First Letter: S → T → U → ? → W The letters follow a consecutive alphabetical order: S (19), T (20), U (21), V (22), W (23). The missing first letter is 'V'. 2. Second Letter: C → E → G → ? → K The letters skip one letter in between: C (+2) → E (+2) → G (+2) → I (+2) → K. The missing second letter is 'I'. 3. Third Letter: D → F → H → ? → L The letters also skip one letter in between: D (+2) → F (+2) → H (+2) → J (+2) → L. The missing third letter is 'J'. Combining these results, the missing triplet is VIJ. Comparing with the options: - a. CMN: Incorrect first, second, and third letters. - b. UJI: Incorrect first and third letters. - c. VIJ: Matches our derived pattern exactly. - d. IJT: Incorrect first and third letters.

Solving 2x-5y=600, 3x-9y=600 gives incomes 1200, 1800.

Communication is inherently a two-way process requiring transmission and feedback, and a mutual process aimed at achieving shared understanding between the sender and receiver.

Siami's current age = 12, so Liana's current age = 12 / 3 = 4. The age difference is 12 - 4 = 8 years. When Siami is twice as old as Liana (S = 2L), since S - L = 8, we get 2L - L = 8 => L = 8, making Siami S = 16 years old.

Emotional Intelligence (EI) is defined as the ability to perceive, diagnose, understand, and effectively regulate and manage emotional cues and information in oneself and others.

Factoring 2x² + 7x - 4: 2x² + 8x - x - 4 = 2x(x + 4) - 1(x + 4) = (2x - 1)(x + 4) = 0. The zeroes are x = 1/2 and x = -4. Thus, 1/2 is the zero present in the options.

Grapes are the odd word out because they grow in clusters/bunches on vines (climbers), whereas oranges, guavas, and apples grow individually on trees.

From the Venn diagram: ladies of the club are inside the rectangle. Those who neither dance (triangle) nor mimic (pentagon) are 41 (only club ladies) + 23 (club ladies who only sing) = 64.

The pattern is: (Sum of digits of (First Number + Second Number)) * 11 = Third Number. For 23, 5: 23+5 = 28 -> (2+8)*11 = 110. For 56, 9: 56+9 = 65 -> (6+5)*11 = 121. For 49, 3: 49+3 = 52 -> (5+2)*11 = 77.

The primary objective of conflict resolution is to de-escalate hostility and achieve constructive, peaceful, and mutually acceptable outcomes for all parties involved.

In French and Raven's typology of social power, reward power encompasses the ability to confer positive tangible or intangible benefits such as praise, recognition, attention, promotions, and commendations.

Volume of the pit = 40 m × 12 m × 160 m = 76,800 m³. Volume of one plank = 4 m × 5 m × 2 m = 40 m³. Total number of planks that can be stored = 76,800 / 40 = 1,920.

Interpersonal skills comprise the range of behaviors and communicative abilities required to interact effectively and harmoniously with other people.

Initial sum of 5 numbers = 5 * 30 = 150. New sum of 4 numbers = 4 * 28 = 112. The excluded number = 150 - 112 = 38.

Biased listening occurs when a listener is influenced by preconceived notions or personal preferences, leading them to hear only what they want to hear and misinterpret the message.

The logical sequence of rational decision-making is: (a) Identification of problem → (b) Identification of decision criteria → (c) Allocation of weights to criteria → (d) Development of alternatives → (e) Analysis of alternatives → (f) Selection of an alternative → (g) Implementation of the alternative.

To solve this problem, we use the fundamental property of polynomials that relates the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of two polynomials, p(x) and q(x): Property: p(x) × q(x) = GCD(p(x), q(x)) × LCM(p(x), q(x)) Given values: 1. GCD = x(x + a) 2. LCM = 12x²(x + a)(x² - a²) 3. p(x) = 3x(x + a)² Substitute these into the formula: 3x(x + a)² × q(x) = [x(x + a)] × [12x²(x + a)(x² - a²)] Simplify the right side of the equation: 3x(x + a)² × q(x) = 12x³(x + a)²(x² - a²) Now, solve for q(x) by dividing both sides by 3x(x + a)²: q(x) = [12x³(x + a)²(x² - a²)] / [3x(x + a)²] Perform the division: - The coefficients: 12 / 3 = 4 - The x terms: x³ / x = x² - The (x + a) terms: (x + a)² / (x + a)² = 1 - The remaining term: (x² - a²) Therefore, q(x) = 4x²(x² - a²). Comparing this result with the given options: - Option (a) 4x(x²+a²) is incorrect. - Option (b) 4x²(x²-a²) matches our result. - Option (c) 3x²(x²-a²) is incorrect. - Option (d) 5x²(x²-a²) is incorrect.