SSC CGL Tier 1 2021 General Intelligence & Reasoning Questions with Solutions

Explanation

The relationship between the numbers follows the formula x = 2y + k, where x is the first number, y is the second number, and k is an adjustment constant. Arranging the pairs in ascending order of the first number x:

Pair 1 (11:6): 11 = 2(6) - 1, so k = -1 Pair 2 (16:8): 16 = 2(8) + 0, so k = 0

The values of x (11, 16, 21) form an arithmetic progression with a common difference of 5. Correspondingly, the values of k follow an arithmetic progression (-1, 0, 1) with a common difference of 1. Applying this pattern to the third pair (21:?):

21 = 2y + 1 20 = 2y y = 10

Explanation

The pattern follows a row-wise logic where the middle number is the sum of the square of the first number and the third number. The general formula is n₂ = n₁² + n₃.

In the first row, 3² + 4 = 9 + 4 = 13.

In the second row, 6² + 31 = 36 + 31 = 67.

Applying the same logic to the third row, the missing number is calculated as 5² + 20 = 25 + 20 = 45.

Explanation

The statement "Some mats are carpets" is a particular affirmative proposition (I-type). In syllogistic logic, an I-type proposition can be converted simply by interchanging the subject and predicate. Therefore, if "Some mats are carpets" is true, it is logically necessary that "Some carpets are mats", which is Conclusion III.

Conclusion I does not follow because the premises only establish that the portion of carpets belonging to the blanket category cannot be quilts; they do not provide information about the relationship between quilts and the rest of the carpets. Conclusion II does not follow because there is no direct or indirect logical link provided between blankets and mats. Consequently, only Conclusion III is a valid deduction from the given statements.

Explanation

The relationship between the first and second word is based on a part-to-whole analogy. An arc is a specific segment or a structural part of a circle. Similarly, a stem is a primary constituent part or organ of a plant. Just as an arc is a component that contributes to the physical structure of a circle, the stem is a fundamental component that forms the physical structure of a plant.

Explanation

To arrange the words in alphabetical order as they appear in a dictionary, we compare them letter by letter from left to right. All words begin with the letter P. Looking at the second letter, Palindrome (2), Pathetic (4), and Parking (5) contain the letter a, which precedes the letter r found in Protest (1) and Probability (3). Among the words starting with Pa, comparing the third letters l, t, and r shows that l in Palindrome (2) comes first, followed by r in Parking (5), and then t in Pathetic (4). For the words starting with Pr, both share the third letter o. Comparing their fourth letters, b in Probability (3) comes before t in Protest (1). Arranging these sequences together results in the order 2, 5, 4, 3, 1.

Explanation

Mayank's present age is 10, so in 6 years he will be 16. At that time, Ramesh will be 48 (3 times 16), which means Ramesh's present age is 42. Since Ramesh is 7 years older than Sangeeta, Sangeeta's present age is 35 (42 minus 7).

Explanation

The series follows a specific addition and subtraction pattern for each corresponding letter in the clusters.

For the first letter of each cluster, there is an increment of +5 in the alphabetical positions: C (3) + 5 = H (8) H (8) + 5 = M (13) M (13) + 5 = R (18) R (18) + 5 = W (23)

For the second letter of each cluster, there is a decrement of -4 in the alphabetical positions: U (21) - 4 = Q (17) Q (17) - 4 = M (13) M (13) - 4 = I (9) I (9) - 4 = E (5)

For the third letter of each cluster, there is an increment of +3 in the alphabetical positions: H (8) + 3 = K (11) K (11) + 3 = N (14) N (14) + 3 = Q (17) Q (17) + 3 = T (20)

Combining these results, the next cluster in the series is WET.

Explanation

The letters in the word PROFIT are coded using their positions in the alphabet (P=16, R=18, O=15, F=6, I=9, T=20) and their reverse alphabetical positions (27 - position).

The vowels O and I are coded by their reverse alphabetical positions: O: 27 - 15 = 12 I: 27 - 9 = 18

The consonants F, T, R, and P are coded as follows: F is coded by its original position: 6 T is coded by its reverse position: 27 - 20 = 7 R is coded by its reverse position: 27 - 18 = 9 P is coded by the sum of the digits of its reverse position: 27 - 16 = 11 → 1 + 1 = 2

Combining these values in the specific sequence used in the code results in 12 (O), 18 (I), 6 (F), 7 (T), 9 (R), and 2 (P), forming the code 12186792.

Explanation

Vision is a physical sense or a cognitive faculty related to the ability to see or plan for the future. In contrast, Zeal, Fury, and Devotion are all terms that describe intense human emotions or psychological states of feeling. Since Vision pertains to sensory perception or mental foresight rather than an emotional state, it is the odd word out in the group.

Explanation

Kamal is the father of Piyush because Rani and Piyush are siblings and Kamal is Rani's father. Aryan is the brother of Kamal. In kinship terms, the brother of one's father is defined as the paternal uncle. Therefore, Aryan is the paternal uncle of Piyush.

Explanation

The coding logic follows the formula: Code = (Sum of reverse alphabetical positions of letters) × (Number of vowels in the word). The reverse alphabetical position of any letter is determined by subtracting its forward position from 27.

For VIRTUE: The reverse positions are V = 5, I = 18, R = 9, T = 7, U = 6, and E = 22. Sum of reverse positions = 5 + 18 + 9 + 7 + 6 + 22 = 67. Vowels in VIRTUE are I, U, and E, making the count 3. Final Code = 67 × 3 = 201.

For TRAGEDY: The reverse positions are T = 7, R = 9, A = 26, G = 20, E = 22, D = 23, and Y = 2. Sum of reverse positions = 7 + 9 + 26 + 20 + 22 + 23 + 2 = 109. Vowels in TRAGEDY are A and E, making the count 2. Final Code = 109 × 2 = 218.

For PROFANE: The reverse positions are P = 11, R = 9, O = 12, F = 21, A = 26, N = 13, and E = 22. Sum of reverse positions = 11 + 9 + 12 + 21 + 26 + 13 + 22 = 114. Vowels in PROFANE are O, A, and E, making the count 3. Final Code = 114 × 3 = 342.

Explanation

The words Advance, Headway, and Growth are synonyms that signify progress, forward movement, or positive development. In contrast, Deteriorate means to become progressively worse or to decline in quality or condition. Therefore, Deteriorate is the odd one out because it represents a negative state or regression, while the other three words describe improvement or moving forward.

Explanation

The numbers in the set follow a specific mathematical relationship where the second number is derived by multiplying the first number by 2.5, and the third number is obtained by multiplying the second number by 2 and adding 1.

In the given set (12, 30, 61): 12 × 2.5 = 30 30 × 2 + 1 = 61

Applying the same logic to the numbers in the selected option (18, 45, 91): 18 × 2.5 = 45 45 × 2 + 1 = 91

Alternatively, the relationship can be viewed as a function of the first number n, represented by the triplet (n, 2.5n, 5n + 1). Substituting n = 18 into this pattern gives 18, 2.5 × 18 = 45, and 5 × 18 + 1 = 91.

Explanation

Let the present ages of Anamika, Malini, and Srinidhi be A, M, and S respectively. From the first condition, Anamika's age in seven years will equal Malini's age four years ago: A + 7 = M - 4, which simplifies to M = A + 11.

Since Srinidhi was born 2 years ago, her present age S = 2. The problem states that the average age of the three individuals 10 years from now will be 33 years. Therefore, the sum of their ages in 10 years will be 33 × 3 = 99 years.

The relationship between their present ages and their ages in 10 years is expressed as (A + 10) + (M + 10) + (S + 10) = 99, which simplifies to A + M + S + 30 = 99, or A + M + S = 69.

Substituting the values of M and S in terms of A: A + (A + 11) + 2 = 69 2A + 13 = 69 2A = 56 A = 28

The present age of Anamika is 28 years.

Explanation

This analogy represents the relationship between a tool and the professional who primary uses it. A sculptor employs a chisel to carve and shape materials like stone, wood, or clay into artistic forms. Similarly, an anvil is a heavy iron or steel block that serves as the essential workspace for a blacksmith, providing a hard surface upon which heated metal is hammered and forged into various shapes.

Explanation

The relationship between the given words is that of a physical quantity and its standard unit of measurement. Resistance is a property of a conductor that opposes the flow of electric current, and its SI unit is the Ohm. Similarly, an Angle is a geometric quantity representing the figure formed by two rays, and its standard SI unit of measurement is the Radian. Both pairs follow the specific order of naming the physical property first followed by the unit used to quantify it.

Explanation

The series follows a specific pattern for each letter position in the cluster. For the first letter, the sequence moves forward by one position in the English alphabet: M → N → O → P → Q. The second letter remains constant as C throughout the series. For the third letter, the sequence also moves forward by one position: N → O → P → Q → R. Combining these patterns, the next cluster in the series is QCR.

Explanation

The relationship in the given pair is based on the city and the primary river situated on its banks. Varanasi is one of the most prominent cities located along the Ganga. Similarly, Mathura, an ancient city in Uttar Pradesh, is situated on the banks of the Yamuna. The Yamuna is the main river flowing through Mathura and is central to the city's geographical and cultural identity.

Explanation

To arrange words in alphabetical dictionary order, compare them letter by letter from left to right. All five words begin with the letters Hy. Comparing the third letters, p in Hypodermic, Hypocrite, Hypothermia, and Hypotense comes before s in Hysterical, meaning word 3 must appear last in the sequence. Among the four words beginning with Hypo, the fifth letters are c in Hypocrite, d in Hypodermic, and t in both Hypothermia and Hypotense. Alphabetically, c precedes d, and d precedes t, so word 2 comes first, followed by word 1. To determine the order between word 4 and word 5, compare their subsequent letters. Both share the first six letters Hypote. At the seventh letter, n in Hypotense comes before r in Hypothermia. This places word 5 before word 4. Arranging all parts together results in the sequence 2, 1, 5, 4, 3.

Explanation

Omprakash and Mani are brothers. Madhurima is the wife of Omprakash. Since the family consists of two couples and Mani is a male, he must be married to Komali. This is further confirmed by the fact that Komali has two children and Mani has a son, Tarun. In this family structure, Omprakash and Mani are the husbands in the two couples. Because Madhurima is the wife of Omprakash and Komali is the wife of Omprakash's brother Mani, Madhurima and Komali are related to each other as sisters-in-law.

Explanation

The coding logic involves calculating the sum of the positional values of the letters in the word according to the English alphabet (A=1, B=2, ..., Z=26) and then multiplying this sum by the total number of letters in that word.

For RAJ: R = 18, A = 1, J = 10 Sum = 18 + 1 + 10 = 29 Number of letters = 3 Code = 29 × 3 = 87

For GITA: G = 7, I = 9, T = 20, A = 1 Sum = 7 + 9 + 20 + 1 = 37 Number of letters = 4 Code = 37 × 4 = 148

Applying the same logic to VARUN: V = 22, A = 1, R = 18, U = 21, N = 14 Sum = 22 + 1 + 18 + 21 + 14 = 76 Number of letters = 5 Code = 76 × 5 = 380

Explanation

Goitre, Scurvy, and Anaemia are all classified as deficiency diseases, which occur when the body lacks specific essential vitamins or minerals over a prolonged period. Goitre is caused by a deficiency of iodine, Scurvy results from a lack of Vitamin C, and Anaemia is most commonly caused by a deficiency of iron. Diarrhoea is not a deficiency disease but is instead a condition typically caused by infections from bacteria, viruses, or parasites, often transmitted through contaminated food or water.

Explanation

Let the monthly incomes of Ankit, Sanjay, and Roshan be 12x, 9x, and 7x respectively, and let their expenditures be 15y, 9y, and 8y. Ankit's savings are given as 25% of his income, which leads to the equation 12x - 15y = 0.25 × 12x. Simplifying this gives 12x - 15y = 3x, resulting in 9x = 15y, or the ratio (x)/(y) = ⁵⁄₃.

By substituting x = 5 and y = 3 into the expressions for savings (Income - Expenditure): Savings of Ankit = 12(5) - 15(3) = 60 - 45 = 15 Savings of Sanjay = 9(5) - 9(3) = 45 - 27 = 18 Savings of Roshan = 7(5) - 8(3) = 35 - 24 = 11

The ratio of their savings is 15:18:11.

Explanation

The logic followed in the given pairs is that the second number is the square of the sum of the digits of the first number. For the number-pair (547, 258), the sum of the digits of the first number is 5 + 4 + 7 = 16. The square of this sum is 16² = 256. This pair is the odd one out because the second number is 258 instead of 256, which does not conform to the pattern observed in the other pairs.

Explanation

The pattern followed in the given pairs is that the second number is the square of the first number minus two. Mathematically, the relationship is expressed as (n₁ - 2)² = n₂.

In the first pair 11:81, subtracting 2 from the first number gives 11 - 2 = 9. Squaring this result yields 9² = 81. In the third pair 8:36, subtracting 2 from the first number gives 8 - 2 = 6. Squaring this result yields 6² = 36.

Applying this same logic to the missing number x in the second pair x:121, we set up the equation (x - 2)² = 121. Since 121 is the square of 11, we have x - 2 = 11. Adding 2 to both sides of the equation gives x = 11 + 2 = 13.

Explanation

The statements can be represented using set theory or Venn diagrams. Let M be medals, L be lockets, C be chains, and R be rings. The statements give M ⊂ L, L ⊂ C, and R ∩ C ≠ ∅. Combining the first two relations, we get M ⊂ L ⊂ C, which implies all medals are chains.

Conclusion I states that all chains are medals (C ⊂ M). This is not logically certain because while all medals are contained within chains, the set of chains can contain elements that are not medals. Thus, C ⊂ M is not a necessary consequence of the given information.

Conclusion II suggests a possibility that all medals are rings (M ⊂ R). The statements establish a relationship between rings and chains (R ∩ C ≠ ∅) but provide no specific information regarding the relationship between rings and medals or rings and lockets. Since there is no negative statement (like No medal is a ring) that forbids an overlap, a configuration where the entire set of medals is contained within the set of rings is logically possible and does not contradict any given statement. Therefore, the possibility exists.

Explanation

The given series can be divided into four groups of five letters each. In each group, four letters (J, P, N, and D) remain constant, while the fifth letter follows an alphabetical progression (L → M → N → O).

The blocks are formed as follows: Group 1: J L (P) N (D) Group 2: J (M) P N D Group 3: (J) N P (N) D Group 4: (O) J (N) P D

By sequentially placing the letters from option c (P, D, M, J, N, O, N) into the blanks: The first and second blanks (at positions 3 and 5) are filled by P and D, completing the first block: JL P ND. The third blank (at position 7) is filled by M, completing the second block: JM PND. The fourth and fifth blanks (at positions 11 and 14) are filled by J and N, completing the third block: JN PND. The sixth and seventh blanks (at positions 16 and 18) are filled by O and N, completing the final block: OJ NPD.

The variable letter in each block increments alphabetically (L → M → N → O), while the other letters maintain the core set of {J, P, N, D}.

Explanation

The relationship in the given pair is that of a medical specialist and the specific organ or system they study and treat. A pulmonologist is a physician who specializes in the anatomy, functions, and diseases of the respiratory system, primarily the lungs. Similarly, an endocrinologist is a medical professional who specializes in the endocrine system, which is composed of various glands that produce and secrete hormones to regulate body functions.

Explanation

The given series consists of the squares of consecutive odd numbers starting from 11. The pattern is as follows: 11² = 121 13² = 169 15² = 225 17² = 289 The next odd number in the sequence after 17 is 19. Calculating the square of 19 gives 19² = 361.

Explanation

The coding logic follows a specific pattern based on the position of the letters in the 7-letter word. The first three letters are shifted forward by one position in the alphabet (+1), the middle (fourth) letter remains unchanged, and the last three letters are shifted backward by one position (-1).

In the example DOLPHIN: D + 1 = E O + 1 = P L + 1 = M P + 0 = P H - 1 = G I - 1 = H N - 1 = M This results in the code EPMPGHM.

Applying this same logic to the word CORDIAL: C + 1 = D O + 1 = P R + 1 = S D + 0 = D I - 1 = H A - 1 = Z L - 1 = K

Following this sequence, the coded form of CORDIAL is DPSDHZK.

Explanation

The pattern followed in the set (12, 121, 169) is (n, (n - 1)², (n + 1)²). For the first number n = 12, the second number is (12 - 1)² = 11² = 121 and the third number is (12 + 1)² = 13² = 169.

Applying the same logic to the set (17, 256, 324), where n = 17: The second number is (17 - 1)² = 16² = 256. The third number is (17 + 1)² = 18² = 324.

Explanation

The coding logic involves splitting the word into consecutive pairs of letters, reversing the order of letters within each pair, and then applying a +4 shift to the first letter and a -4 shift to the second letter of each reversed pair based on their positions in the alphabet.

For the word INHALE, the pairs are (I, N), (H, A), and (L, E). Reversing these gives (N, I), (A, H), and (E, L). Applying the +4 and -4 shift to each pair: the first pair becomes N + 4 = 18 (R) and I - 4 = 5 (E); the second pair becomes A + 4 = 5 (E) and H - 4 = 4 (D); the third pair becomes E + 4 = 9 (I) and L - 4 = 8 (H). Combining these results in the code REEDIH.

Applying this same logic to MIGHTY, the pairs are (M, I), (G, H), and (T, Y). Reversing these gives (I, M), (H, G), and (Y, T). Applying the shifts: for the first pair, I + 4 = 13 (M) and M - 4 = 9 (I); for the second pair, H + 4 = 12 (L) and G - 4 = 3 (C); for the third pair, Y + 4 = 29 (which corresponds to 29 - 26 = 3, or C in a circular alphabet) and T - 4 = 16 (P). The resulting code is MILCCP.

Explanation

In the expression X2M8Y, we decode the relationships step by step using the given definitions. The term X2M indicates that X is the wife of M. The term M8Y indicates that M is the father of Y. Since X is the wife of Y's father, she is naturally the mother of Y. This satisfies the requirement for X to be the mother of Y.

Explanation

The letter-cluster HJMP is different because its third and fourth letters do not form a reverse pair. Alphabetical opposites, or reverse pairs, are defined by the property that the sum of their numerical positions in the alphabet is exactly 27. In HJMP, the letters correspond to the positions H(8), J(10), M(13), and P(16). While the first three letters follow a positional increment of +2 and +3 (8 + 2 = 10 and 10 + 3 = 13), the sum of the positions for the third letter M and the fourth letter P is 13 + 16 = 29. This cluster does not maintain the relationship where the third and fourth letters are alphabetical opposites.

Explanation

The relationship between Cat and Kitten is that of an animal and its young offspring. Similarly, a calf is the offspring or young one of a cow. While the word cow appears as a typographical error written as caw, it maintains the identical biological relationship of parent and offspring found in the original pair.

Explanation

In dictionary order, words are arranged alphabetically letter by letter. All five words begin with the prefix Relat. Comparing the sixth letter of each word, Relatable (5) comes first as it has a, followed by Related (3) which has e. For the remaining words, the sixth letter is i. Comparing the seventh letter of these remaining words, Relation (2) comes next because o precedes v. Between Relativai (1) and Relative (4), both share the same letters up to the seventh position Relativ. Comparing the eighth letter, Relativai (1) comes before Relative (4) because a precedes e. The final alphabetical sequence is 5, 3, 2, 1, 4.

Explanation

The numbers in the given set (4, 7, 359) follow a pattern where the third number is the sum of the square of the first number and the cube of the second number. Using the formula x² + y³ = z:

4² + 7³ = 16 + 343 = 359

In the set (6, 8, 548), the same logic applies:

6² + 8³ = 36 + 512 = 548

The calculation confirms that adding the square of the first digit to the cube of the second digit yields the third digit in the sequence.

Explanation

The relationship between the numbers follows the pattern: y = (x(x + 1))/(3), where x is the first number and y is the second number in each pair.

Applying this logic to the given numerical pairs:

For the first pair (8 : 24): (8 × (8 + 1))/(3) = (8 × 9)/(3) = 8 × 3 = 24

For the third pair (18 : 114): (18 × (18 + 1))/(3) = (18 × 19)/(3) = 6 × 19 = 114

For the middle pair (? : 52), let the unknown number be x: (x(x + 1))/(3) = 52 x(x + 1) = 156

To solve the quadratic equation x² + x - 156 = 0, we find the factors of 156 that differ by 1: 12 × 13 = 156

Thus, x = 12.

Explanation

The terms Hinder, Forbid, and Impede all share a similar meaning related to obstructing, slowing down, or prohibiting an action. Permit is the only word in the set that means to allow or grant permission, making it the semantic opposite of the other three words which form a group based on the concept of restriction.

Explanation

The logical relationship between the categories can be determined by combining the first two statements. From the second statement, some coolers are fans. Since the first statement asserts that all fans are heaters, it follows that the specific group of coolers that are fans must also be heaters. This establishes a definite intersection between the set of heaters and the set of coolers, validating the conclusion that some heaters are coolers. The third statement regarding purifiers does not provide a guaranteed link to fans or heaters, as purifiers are only established as a subset of coolers without any defined overlap with the fan category. Therefore, only conclusion III is logically certain.

Explanation

The pattern shared by the majority of the number-pairs is a constant difference of 118 between the first and second numbers. Calculations for the other pairs show that 797 - 679 = 118, 373 - 255 = 118, and 727 - 609 = 118. The pair 191:177 is different because the difference between its numbers is 191 - 177 = 14, which does not conform to the common rule of 118.

Explanation

The relationship hierarchy is as follows: Gaurav is married to Kamini, and they have a daughter named Gouri. Gouri's children are Akshara and Anil. Since Swati is the daughter of Akshara, she belongs to the third generation descending from Gaurav. Specifically, Gouri is the first generation (daughter), Akshara is the second generation (granddaughter), and Swati is the third generation, making her Gaurav's great-granddaughter.

Explanation

The series consists of 20 characters which can be divided into four equal groups of five letters each to identify a repeating pattern. The structure of the divided series is: m _ t q _ | m l _ q r | m _ t q _ | m _ t _ r

By comparing these groups, it is evident that each segment follows the consistent five-letter sequence m-l-t-q-r. Filling the blanks according to this pattern: The first group (m _ t q _) requires l at the second position and r at the fifth position. The second group (m l _ q r) requires t at the third position. The third group (m _ t q _) requires l at the second position and r at the fifth position. The fourth group (m _ t _ r) requires l at the second position and q at the fourth position.

Sequentially arranging the letters filled in the blanks results in the combination: l, r, t, l, r, l, q.

Explanation

The given numbers follow a row-wise pattern where the square of the difference between the third and first numbers, minus one, equals the middle number: (n₃ - n₁)² - 1 = n₂. In the first set, (13 - 7)² - 1 = 6² - 1 = 35. In the second set, (14 - 9)² - 1 = 5² - 1 = 24. For the final set, letting the unknown be x, the equation is (x - 13)² - 1 = 120. This leads to (x - 13)² = 121, so x - 13 = 11 and x = 24.

Explanation

The coding logic involves a two-step process: dividing the word into blocks and then applying specific numeric transformations after sorting each block alphabetically.

Division of the word: The 7-letter words are split into two blocks: the first four letters and the remaining three letters. Alphabetical Sorting: Each block is rearranged so its letters are in alphabetical order. Numeric Transformation: Vowels (A, E, I, O, U) are replaced by their corresponding positional values in the alphabet (A=1, E=5, I=9, O=15, U=21). Consonants are replaced by twice their positional value (Value = 2 × Position).

Applying this to 'REFUSAL': Split 'REFUSAL' into two blocks: (R, E, F, U) and (S, A, L). Sort the first block (R, E, F, U) alphabetically: E, F, R, U.

• E (Vowel): 5
• F (Consonant): 6 × 2 = 12
• R (Consonant): 18 × 2 = 36
• U (Vowel): 21 Resulting code for block 1: 5123621. Sort the second block (S, A, L) alphabetically: A, L, S.
• A (Vowel): 1
• L (Consonant): 12 × 2 = 24
• S (Consonant): 19 × 2 = 38 Resulting code for block 2: 12438.

Combining the two blocks yields the final code: 512362112438.

Explanation

The series follows a specific addition and subtraction pattern for each letter position in the clusters.

For the first letters, the sequence is D (4), I (9), N (14), S (19). The pattern is an addition of 5 to the positional value of the preceding letter: 4 + 5 = 9, 9 + 5 = 14, and 14 + 5 = 19. Following this, 19 + 5 = 24, which corresponds to the letter X.

For the second letters, the sequence is V (22), T (20), R (18), P (16). The pattern is a subtraction of 2 from the positional value of the preceding letter: 22 - 2 = 20, 20 - 2 = 18, and 18 - 2 = 16. Following this, 16 - 2 = 14, which corresponds to the letter N.

For the third letters, the sequence is G (7), M (13), S (19), Y (25). The pattern is an addition of 6 to the positional value of the preceding letter: 7 + 6 = 13, 13 + 6 = 19, and 19 + 6 = 25. Following this, 25 + 6 = 31. Since there are 26 letters in the alphabet, 31 - 26 = 5, which corresponds to the letter E.

Explanation

The relationship between the first pair of words, Elated and Dejected, is that of antonyms. Elated refers to a state of being extremely happy or in high spirits, while Dejected refers to being sad, depressed, or dispirited. To maintain the same relationship for the second pair, the word that follows Alleviate must be its antonym. Alleviate means to make suffering, deficiency, or a problem less severe or more bearable. Aggravate means to make a problem, injury, or offense worse or more serious. Therefore, Aggravate is the correct antonym to complete the analogy.

Explanation

The series consists of two alternating sequences. The terms at the odd positions (1ˢᵗ, 3ʳᵈ, 5ᵗʰ) are 18, 36, and 54, which follow the pattern 18 × 1 = 18, 18 × 2 = 36, and 18 × 3 = 54. The terms at the even positions (2ⁿᵈ, 4ᵗʰ, 6ᵗʰ) are 3, 6, and 9, following the pattern 3 × 1 = 3, 3 × 2 = 6, and 3 × 3 = 9. The missing number (?) is the 7ᵗʰ term in the series, which belongs to the sequence of odd-positioned terms. Continuing the multiplication pattern for the odd positions, the next term is 18 × 4 = 72. Alternatively, the odd terms can be viewed as an arithmetic progression with a common difference of 18, where 54 + 18 = 72.

Explanation

By applying the signs in the order ÷, ×, -, +, = to the expression 221 ∗ 17 ∗ 12 ∗ 130 ∗ 24 ∗ 50, we follow the BODMAS rule to solve the equation.

First, calculate the division: 221 ÷ 17 = 13

Second, calculate the multiplication: 13 × 12 = 156

Third, perform the subtraction and addition: 156 - 130 + 24 = 26 + 24 = 50

The left-hand side simplifies to 50, which matches the right-hand side, thus balancing the equation.

Explanation

Alekha is 6 years old. Her father is 25 years older than her, so his current age is 6 + 25 = 31 years. Since the father is two years elder than the mother, the mother's current age is 31 - 2 = 29 years. Alekha was born one year after her mother's marriage, which means the marriage took place one year before Alekha's birth. As Alekha is 6 years old, she was born 6 years ago, and the marriage occurred 6 + 1 = 7 years ago. Subtracting this duration from the mother's current age gives her age at the time of marriage: 29 - 7 = 22 years.