IBPS Clerk Prelims 2019 Question Paper with Answers & Explanations

Explanation

Arranging the persons according to their given month conditions gives the sequence: E in January, D in April, G in May, F in June, H in July, A in August, B in October, and C in December.

In this order, E is related to F with two persons (D and G) between them, and H is related to C with two persons (A and B) between them. Following the same pattern, D is related to the person placed three positions ahead with a gap of two persons (G and F), which is H.

Explanation

Months with 30 days are April and June, whereas January, May, July, August, October, and December have 31 days.

Since F and D watch movies in 30-day months, they occupy April and June. Placing F in April leaves no valid consecutive slots for H and A, so F must watch in June and D in April.

Three persons watch between F (June) and C, placing C in December. B watches just before C, placing B in October.

G watches after D (April), placing G in May and E in January. H watches in a 31-day month just before A and not in January, placing H in July and A in August.

The complete schedule from January to December is E, D, G, F, H, A, B, and C.

Explanation

Arranging the persons chronologically based on the month lengths gives: January (31 days): E April (30 days): D May (31 days): G June (30 days): F July (31 days): H August (31 days): A October (31 days): B December (31 days): C

F watches in June (30 days) and C in December, with three persons between them. B watches in October, immediately before C. D watches in April (30 days) and G in May after D. H watches in July (31 days) immediately before A in August, leaving E in January.

There is 1 person (G) watching the movie between D and F. Similarly, there is 1 person (A) watching the movie between B and H.

Explanation

Based on the given conditions, the schedule of persons according to their respective months is:

January (31 days): E April (30 days): D May (31 days): G June (30 days): F July (31 days): H August (31 days): A October (31 days): B December (31 days): C

H (July), C (December), B (October), and G (May) all watch the movie in months containing 31 days. In contrast, D watches the movie in April, which has 30 days. Thus, D is the odd one out because he is the only person among the group who watches the movie in a 30-day month.

Explanation

Arranging the eight months chronologically gives 1. January (31 days), 2. April (30 days), 3. May (31 days), 4. June (30 days), 5. July (31 days), 6. August (31 days), 7. October (31 days), and 8. December (31 days).

Placing F in June (30 days) puts C in December (8th position, keeping 3 persons between F and C), and B in October (just before C). Since H watches just before A, H is in a 31-day month (excluding January), and A is before B, H and A occupy July and August respectively. D takes the remaining 30-day month, April, and G watches after D in May, leaving E in January.

The final schedule from January to December is E, D, G, F, H, A, B, C.

The four persons watching the movie between D (April) and B (October) are G, F, H, and A.

Explanation

Eight persons sit to the left of Q, placing Q at the 9th position from the left end. F sits second to the right of Q, making F the 11th person from the left. One person sits between F and S, which places S at the 13th position from the left end, because position 9 is already occupied by Q. Since S is at the eighth position from one of the extreme ends, S must be the 8th person from the right end. Applying the position formula, Total persons = Left Position + Right Position - 1 = 13 + 8 - 1 = 20. Hence, the maximum number of persons in the row is 20.

Explanation

Let the positions from the left end be numbered sequentially starting from 1.

Since 8 persons sit to the left of Q, Q is at position 9. F sits second to the right of Q, placing F at position 11 (9 + 2). One person sits between F and S, so S is at position 13 (11 + 2). Four persons sit between P and Q to the right of Q, placing P at position 14 (9 + 5).

Since S is at position 13 and P is at position 14, P and S are sitting immediately adjacent to each other. Thus, zero persons sit between P and S.

Explanation

Eight persons sit to the left of Q, placing Q at position 9 from the left end. F sits second to the right of Q, putting F at position 11 (9 + 2). Since one person sits between F and S, and position 9 is occupied by Q, S must sit to the right of F at position 13 (11 + 2). D sits third to the right of S, placing D at position 16 (13 + 3). Subtracting F's position from D's position gives 16 - 11 = 5, which means D is located 5 places to the right of F, or fifth to the right.

Explanation

Since eight persons sit to the left of Q, Q is at the 9th position from the left end of the row. H sits fifth to the left of Q, placing H at position 9 - 5 = 4th from the left end. Consequently, there are exactly 3 persons sitting to the left of H.

Explanation

Since eight persons sit to the left of Q, Q is at position 9 from the left end. H sits fifth to the left of Q, placing H at position 4. F sits second to the right of Q, placing F at position 11. One person sits between F and S, placing S at position 13 (since position 9 is occupied by Q). D sits third to the right of S, placing D at position 16.

Four persons sit between P and Q. Since position 4 is occupied by H, P must be to the right of Q at position 14. A sits exactly in between P (position 14) and D (position 16), which places A at position 15. Comparing position 15 with S at position 13, A is sitting second to the right of S.

Explanation

Assigning alphabetical positions to the letters of CHLORINE gives C=3, H=8, L=12, O=15, R=18, I=9, N=14, E=5. A pair has the same number of letters between them in the word as in the alphabet when the difference between their positions in the word equals the difference between their alphabetical values.

Checking all pairs in both forward and backward directions:

For the pair (L, I), position difference in the word is 6 - 3 = 3, and alphabetical difference is 12 - 9 = 3. There are exactly 2 letters between L and I in the word (O, R) and 2 letters in the English alphabet (J, K).

No other pair satisfies this condition, giving only one such pair.

Explanation

The statement "No picnic is mystery" directly implies that no mystery is picnic, which logically means "Some mystery are not picnic" is definitely true, so Conclusion I follows. The statement "Only a few home is picnic" means both "Some home is picnic" and "Some home is not picnic". Since it is a definite fact that some home is not picnic, it is impossible for all homes to be picnic, so Conclusion II does not follow. Thus, only conclusion I logically follows.

Explanation

"Only a few strong is tough" implies both "Some strong are tough" and "Some strong are not tough". Similarly, "Only a few tough is dark" implies both "Some tough are dark" and "Some tough are not dark".

Conclusion I states "Some strong is not dark." Since no statement directly connects 'strong' and 'dark', all strong could potentially be dark. A definite conclusion cannot be drawn without a direct relationship between the terms, so conclusion I does not follow.

Conclusion II states "No tough is strong." Since the first statement guarantees that some strong are tough, it automatically implies that some tough are strong. This renders conclusion II directly contradictory and invalid.

Explanation

From the statement "No network is dull", it follows that no dull is network, which directly implies that "Some dull are not network". Therefore, conclusion II logically follows.

From the statements "Only a few dull is fast" and "All fast is memory", the elements that are fast belong to both dull and memory. Since "No network is dull", the portion of memory that overlaps with dull can never be network. Hence, "Some memory are definitely not network", making conclusion I logically follow as well.

Both conclusions I and II follow.

Explanation

Using set inclusion and transitivity rules from the given statements:

Tennis ⊆ Football ⊆ Basketball, and Basketball ∩ Cricket = ∅.

Conclusion I: Since Football is entirely contained within Basketball, and Basketball shares no element with Cricket, Football can have no overlap with Cricket. Therefore, "No football is cricket" logically follows.

Conclusion II: Since Tennis is entirely contained within Football, which is in turn entirely contained within Basketball, Tennis is completely contained within Basketball by transitivity. Therefore, "All tennis is basketball" logically follows.

Explanation

Based on the given conditions, the seating arrangement from left to right for both parallel rows is:

Row 1 (Facing North): B, F, D, A, E, C Row 2 (Facing South): R, S, P, T, Q, U

Evaluating the positions: B and C occupy the extreme left and right ends of Row 1, while R and U occupy the extreme left and right ends of Row 2. P occupies an internal seat (position 3 in Row 2) rather than an extreme end, making P the odd one out among the group.

Explanation

Based on the given conditions, the step-by-step seating arrangement from left to right (positions 1 to 6) is determined as follows:

Row 1 (facing North): B (pos 1), F (pos 2), D (pos 3), A (pos 4), E (pos 5), C (pos 6) Row 2 (facing South): R (pos 1), S (pos 2), P (pos 3), T (pos 4), Q (pos 5), U (pos 6)

Since E sits 4th to the right of B, B is at position 1 and E is at position 5 in Row 1. Q faces E at position 5 in Row 2, leaving U at position 6. One person sits to the left of Q (facing South), so one person sits to the right of S, placing S at position 2 and R at position 1 in Row 2. F sits immediately to the left of D, occupying positions 2 and 3 respectively in Row 1. A sits to the left of C and right of F, placing A at position 4 and C at position 6. P faces D (an immediate neighbor of A) at position 3, and T occupies position 4 in Row 2.

Matching the opposite pairs at position 2, S faces F.

Explanation

In Row 1, all six persons (A, B, C, D, E, F) face North, which means Left is to the west and Right is to the east.

Placing the persons in Row 1 from left to right (positions 1 to 6): E sits 4th to the right of B, which means B is at position 1 and E is at position 5. F sits immediate to the left of D, meaning F and D occupy adjacent seats in the sequence (F, D). Placing F at position 2 and D at position 3 satisfies this condition. A sits to the left of C and to the right of F. Placing A at position 4 and C at position 6 satisfies both conditions, as A (position 4) is to the right of F (position 2) and to the left of C (position 6).

The complete arrangement of Row 1 from position 1 to 6 (left to right) is: B, F, D, A, E, C.

Since B is at position 1 and F is at position 2, F sits immediate to the right of B.

Explanation

Numbering positions 1 to 6 from left to right for both rows:

In Row 1 (facing North), B is at position 1, making E (4th to its right) at position 5. Placing F immediately to the left of D, and A between F and C gives the complete arrangement for Row 1 from position 1 to 6 as B, F, D, A, E, C.

In Row 2 (facing South), Q faces E at position 5, and U is at position 6. Since one person sits to the left of Q (facing South), one person sits to the right of S, putting S at position 2. P faces D (an immediate neighbor of A), putting P at position 3. Since R sits to the right of T, R is at position 1 and T is at position 4, giving Row 2 from position 1 to 6 as R, S, P, T, Q, U.

For South-facing persons in Row 2, right is towards the viewer's left. P is at position 3, so S at position 2 sits to the immediate right of P.

Explanation

Row 1 faces North (positions 1 to 6 from left to right) and Row 2 faces South (positions 1 to 6 from West to East, where West is Right and East is Left).

Since E sits 4th to the right of B, B is at position 1 and E is at position 5 in Row 1. Q faces E, placing Q at position 5 in Row 2. U sits at position 6 as the end-of-row neighbor. Since 1 person sits to the left of Q, 1 person sits to the right of S, placing S at position 2 in Row 2.

In Row 1, F sits immediately to the left of D, placing F at 2 and D at 3. A sits to the right of F and left of C, placing A at position 4 and C at position 6. P faces A's neighbor D, so P is at position 3 in Row 2. R sits to the right of T, placing T at position 4 and R at position 1.

The seating in Row 2 from positions 1 to 6 is R, S, P, T, Q, U. Facing South, moving to the right of T (position 4) means moving toward position 1: 1st is P (position 3), 2nd is S (position 2), and 3rd to the right of T is R (position 1).

Explanation

Arranging the eight persons around the square table according to the given clues placing middle-facing-in and corner-facing-out positions:

Placing F at a middle position facing inside, J occupies a corner position facing outside such that two persons sit between them. V sits at the immediate right of J at a middle position, and N sits at the immediate left of V at a corner position facing outside. S sits directly opposite N with three persons between them. M is an immediate neighbor of S but not J, placing M at the middle position between F and S. Since P faces inside, P takes the middle position between S and J, leaving K at the remaining corner position between F and M.

The clockwise sequence starting from F is F, K, M, S, P, J, V, N. Because F faces inside towards the center, counting from the left of F means moving in the clockwise direction. The persons sitting between F and J in this direction are K, M, S, and P, making a total of four persons.

Explanation

Based on the given conditions, the seating positions and facing directions of all eight persons are determined as follows:

Persons sitting at the middle of the sides and facing towards the center (inside): F, M, P, V Persons sitting at the corners and facing away from the center (outside): S, J, K, N

Among the given persons, S, J, K, and N all sit at the corners of the table and face away from the center, whereas F sits at the middle of a side and faces towards the center. Therefore, F does not belong to the group.

Explanation

Placing F at a middle position facing inside, J is positioned at a corner position facing outside such that two persons sit between them. Since V sits at the immediate right of J, V occupies a middle position, and N sits at the immediate left of V at a corner position. S sits directly opposite to N as three persons sit between them. M is an immediate neighbor of S but not of J, placing M at the middle position adjacent to S. P faces inside, so P occupies the last remaining middle position, leaving K to take the remaining corner position. In this completed seating arrangement, J and K occupy diagonally opposite corners of the table, confirming that J sits opposite to K.

Explanation

Arranging the eight persons around the square table based on their seating positions and facing directions:

F sits at top-middle facing inside. Two positions away, J sits at bottom-left corner facing outside. V sits at immediate right of J at left-middle facing inside. N sits at immediate left of V at top-left corner facing outside. S sits opposite N at bottom-right corner. M sits adjacent to S but not J, which places M at right-middle facing inside. Since P faces inside, P takes bottom-middle facing inside, leaving K at top-right corner.

With M seated at right-middle facing inside, moving two places clockwise gives the second position to the left of M, which is occupied by P at bottom-middle.

Explanation

Based on the given conditions, persons at the middle side face inside and persons at the corners face outside.

Placing F at the North middle side (facing inside), two persons sit between F and J, which places J at a corner. Since V sits at the immediate right of J and N sits at the immediate left of V, J is positioned at the South-West corner (facing outside), V at the West middle side (facing inside), and N at the North-West corner (facing outside).

Three persons sit between S and N, so S sits directly opposite N at the South-East corner (facing outside).

M is an immediate neighbor of S but not of J, placing M at the East middle side (facing inside).

Since P faces inside, P must sit at the remaining middle side, which is the South middle side. The remaining person K sits at the North-East corner (facing outside).

The final arrangement clockwise starting from North is: North: F (facing inside) North-East: K (facing outside) East: M (facing inside) South-East: S (facing outside) South: P (facing inside) South-West: J (facing outside) West: V (facing inside) North-West: N (facing outside)

P is seated at the South middle side, directly opposite F at the North middle side.

Explanation

Since K is the child of L and L is married to J, J is a parent of K. Because G is married to K, J becomes the parent-in-law of G. However, the gender of J is not specified anywhere in the information. Without knowing whether J is male or female, it is impossible to specify whether J is the father-in-law or mother-in-law of G, so the exact relationship cannot be determined.

Explanation

A is the mother of P and G. Since A is married to R, R is male and the father of P and G. K is married to G, making G and K a married couple. S is the sister of K and the aunt of M, which means M is the child of the couple G and K. As R is the father of G, R is the grandfather of M.

Explanation

K is married to G, making K the spouse of G. S is the sister of K, which means S is the sister of G's spouse. Therefore, S is the sister-in-law of G.

Explanation

The letters at the 2nd, 5th, 8th, and 9th positions of the word "TRANSLATION" are R, S, T, and I respectively. Using these four letters, the only meaningful four-letter English word that can be formed is STIR. In the word STIR, counting from the left, the first letter is S and the second letter is T.

Explanation

Removing all numerical digits (8, 9, 6, 7, 5, 4, 2) from the original arrangement gives the sequence: R, Q, D, H, L, O, P, T, E, F, M, I, A, J, B, U, G.

Counting from the left end of this modified sequence, the first ten letters are: 1st R, 2nd Q, 3rd D, 4th H, 5th L, 6th O, 7th P, 8th T, 9th E, and 10th F.

Explanation

Counting 7 elements from the left end of the given arrangement gives L.

Counting 9 elements from the right end gives A.

The question asks for the number of English alphabet letters positioned between A and L in standard alphabetical order.

The letters between A (1st alphabet) and L (12th alphabet) are B, C, D, E, F, G, H, I, J, and K.

Counting these letters gives a total of 10 alphabets.

Explanation

To find the element that is 3rd to the right of the 11th element from the left end, add the positions from the left end: 11 + 3 = 14th element from the left end. Counting to the 14th position from left to right in the sequence R Q D 8 H 9 L O P T E F M 6 I A 7 J 5 4 B U 2 G gives 6.

Explanation

To find numbers that are immediately preceded by a consonant and immediately followed by a consonant, search for the pattern Consonant + Number + Consonant in the given arrangement.

In the sequence R Q D 8 H 9 L O P T E F M 6 I A 7 J 5 4 B U 2 G, the numbers that fulfill this pattern are 8 (preceded by consonant D and followed by consonant H) and 9 (preceded by consonant H and followed by consonant L).

The remaining numbers do not satisfy the condition: 6 is followed by vowel I, 7 is preceded by vowel A, 5 is followed by number 4, 4 is preceded by number 5, and 2 is preceded by vowel U.

Therefore, there are exactly 2 such numbers.

Explanation

The given number is 485794362. Applying the operations according to position from left to right:

1st digit (odd): 4 − 1 = 3 2nd digit (even): 8 + 1 = 9 3rd digit (odd): 5 − 1 = 4 4th digit (even): 7 + 1 = 8 5th digit (odd): 9 − 1 = 8 6th digit (even): 4 + 1 = 5 7th digit (odd): 3 − 1 = 2 8th digit (even): 6 + 1 = 7 9th digit (odd): 2 − 1 = 1

The resulting number is 394885271. In this number, only the digit 8 appears more than once (at the 4th and 5th positions), while all other digits appear exactly once.

Explanation

In all other letter groups, each consecutive letter is formed by moving 3 positions forward in the English alphabetical series (+3, +3 pattern). In KOP, the alphabetical positions are K = 11, O = 15, and P = 16, which have positional differences of +4 and +1. Because KOP fails to follow the consistent +3 step rule, it is the odd one out.

Explanation

Square both sides of the equation to remove the square root:

124 + ? + 169 = 18²

124 + ? + 169 = 324

293 + ? = 324

? = 324 − 293 = 31

Explanation

Simplify the left-hand side by performing exponentiation and division first: 136 ÷ 2² × ? = 136 ÷ 4 × ? = 34 × ?

Simplify the right-hand side by evaluating the percentage first, followed by division: 17% of 500 ÷ 10 = (17 ÷ 100) × 500 ÷ 10 = 85 ÷ 10 = 8.5

Equate the simplified left-hand side and right-hand side to solve for the unknown: 34 × ? = 8.5 ? = 8.5 ÷ 34 ? = 85 ÷ 340 ? = 1 ÷ 4 ? = 0.25

Explanation

Using the order of operations (BODMAS):

Evaluate the Left Hand Side (LHS): 115 ÷ 5 + 12 × 6 = 23 + 72 = 95

Evaluate the Right Hand Side (RHS): ? + 64 ÷ 4 - 35 = ? + 16 - 35 = ? - 19

Equating LHS and RHS: 95 = ? - 19 ? = 95 + 19 = 114

Explanation

41% of 600 = 41 × 6 = 246 77% of 900 = 77 × 9 = 693

Substituting these values into the given equation: 246 - 250 = ? - 693 -4 = ? - 693 ? = 693 - 4 = 689

Explanation

First, evaluate the exponent on the right hand side of the equation: 3³ = 27

Adding 73 to 27 yields: 73 + 27 = 100

Now substitute this value back into the equation: 360 / ? = 100

Rearranging to solve for the unknown value: ? = 360 / 100 = 3.6

Explanation

To find the missing value (?), rearrange the given equation:

? = ½ - ⅗ + 4 ⅔ - 5/6

Separate the integer and fractional components: ? = 4 + (½ - ⅗ + ⅔ - 5/6)

Find the Least Common Multiple (LCM) of the denominators 2, 5, 3, and 6, which is 30: Fractional part = (15 - 18 + 20 - 25) / 30 = -8/30 = -4/15

Combine the integer and fractional parts: ? = 4 - 4/15 = (60 - 4) / 15 = 56/15 = 3 11/15

Explanation

Using the BODMAS rule, simplify both sides of the equation step-by-step:

Left Hand Side: (65 × 3 ÷ 13) + 67 - ?² = (65 ÷ 13) × 3 + 67 - ?² = (5 × 3) + 67 - ?² = 15 + 67 - ?² = 82 - ?²

Right Hand Side: (81 ÷ 9) × 2 = 9 × 2 = 18

Equating the Left Hand Side to the Right Hand Side: 82 - ?² = 18 ?² = 82 - 18 ?² = 64 ? = √64 = 8

Explanation

Evaluate each term in the equation (2744)⅓ + 18² - 121 = ? - 69 × 5:

Since 14³ = 2744, (2744)⅓ = 14. 18² = 324. 69 × 5 = 345.

Substitute these values into the given equation: 14 + 324 - 121 = ? - 345

Simplifying the left-hand side gives: 338 - 121 = 217

Now, solve for ?: 217 = ? - 345 ? = 217 + 345 = 562

Explanation

According to the standard order of operations (BODMAS), division takes precedence over addition. Evaluate each term separately:

1111 ÷ 11 = 101 2002 ÷ 26 = (2002 ÷ 2) ÷ 13 = 1001 ÷ 13 = 77 750 ÷ 25 = 30

Now, sum the results of the individual division operations: 101 + 77 + 30 = 208

Thus, the evaluated result of the given mathematical expression is 208.

Explanation

Simplify each term on the left-hand side of the equation:

(5/11) × 121 = 5 × 11 = 55

Convert the mixed fraction 1 4/9 to the improper fraction 13/9: (13/9) × 288 = 13 × 32 = 416

Sum of the terms on the left-hand side: 55 + 416 = 471

Now, substitute this value into the given equation: 471 = 141 + ? ? = 471 - 141 = 330

Explanation

When two items are sold at the same selling price with equal profit percentage and loss percentage x%, the overall loss percentage is given by:

Overall Loss % = x² / 100

Given overall loss percentage = 6.25%: x² / 100 = 6.25 x² = 625 x = 25%

Cost price of the pen sold at 25% profit: CP₁ = 300 / (1 + 0.25) = 300 / 1.25 = Rs. 240

Cost price of the pen sold at 25% loss: CP₂ = 300 / (1 - 0.25) = 300 / 0.75 = Rs. 400

Difference between cost prices = CP₂ - CP₁ = 400 - 240 = Rs. 160

Explanation

Simple Interest formula gives: SI = (P × R × T) / 100 3456 = (P × 12 × 3) / 100 3456 = 0.36 × P P = 3456 / 0.36 = Rs. 9600

The new principal is P + 4400 = 9600 + 4400 = Rs. 14000.

For compound interest at 15% p.a. for 2 years, the net effective rate is: 15 + 15 + (15 × 15) / 100 = 32.25%

Interest received = 14000 × 32.25% = 14000 × 0.3225 = Rs. 4515.

Explanation

Total time for the round trip = 14 hours 24 minutes = 14.4 hours = 72/5 hours.

Let the speed of the boat in still water be u km/hr. Given stream speed v = 6 km/hr, downstream speed is (u + 6) km/hr and upstream speed is (u - 6) km/hr.

Using Time = Distance / Speed: 162/(u + 6) + 162/(u - 6) = 72/5 162 × 2u / (u² - 36) = 72/5 324u / (u² - 36) = 72/5

Simplifying by dividing both sides by 36: 9u / (u² - 36) = 2/5 2u² - 45u - 72 = 0 (2u + 3)(u - 24) = 0

Since speed cannot be negative, u = 24 km/hr.

Upstream speed = 24 - 6 = 18 km/hr.

Time taken to cover 240 km upstream = 240 / 18 = 40/3 = 13 1/3 hours.

Explanation

Since C is 100% more efficient than B, the efficiency ratio C : B = 2 : 1, which means the ratio of combined efficiency (B + C) to B is 3 : 1.

B and C together complete the work in 2⅔ days = 8/3 days. Combined 1-day work of (B + C) = 1 / (8/3) = 3/8.

Since B's efficiency is 1/3 of (B + C)'s efficiency: B's 1-day work = (1/3) × (3/8) = 1/8.

Given A completes the work alone in 9 days, A's 1-day work = 1/9.

Combined 1-day work of A and B = 1/9 + 1/8 = (8 + 9) / 72 = 17/72.

Work completed by A and B together in 4 days = 4 × (17/72) = 17/18.

Explanation

Let P and R be the present ages of P and R respectively.

Given that the average of present ages of P and R is 39 years: P + R = 39 × 2 = 78

From the age ratio condition: (P - 2) / (R + 2) = 1 / 2 2P - 4 = R + 2 R = 2P - 6

Substituting R in the sum equation: P + (2P - 6) = 78 3P = 84 P = 28 years

Substituting P to find R's present age: R = 2(28) - 6 = 50 years

P's age 5 years hence = 28 + 5 = 33 years. Difference between R's present age and P's age 5 years hence = 50 - 33 = 17 years.

Explanation

From the first equation, x² - 2x - 143 = 0, factoring gives (x - 13)(x + 11) = 0, which yields x = 13 and x = -11.

From the second equation, y² - 169 = 0, taking the square root gives y = 13 and y = -13.

Comparing the values: When x = 13 and y = 13, x = y. When x = 13 and y = -13, x > y. When x = -11 and y = 13, x < y.

Since x is greater than y in one case and less than y in another, no clear relationship can be established between x and y.

Explanation

For equation I: x² - 7x - 18 = 0 Factoring gives (x - 9)(x + 2) = 0, so x = 9, -2.

For equation II: y² - 19y + 90 = 0 Factoring gives (y - 10)(y - 9) = 0, so y = 10, 9.

Comparing the roots: When x = 9, y = 9 gives x = y, and y = 10 gives x < y. When x = -2, x is less than both 9 and 10 (x < y).

Therefore, comparing all pairs yields x ≤ y.

Explanation

For equation I: 2x² + 5x + 3 = 0 Splitting the middle term gives 2x² + 2x + 3x + 3 = 0, which factors into (2x + 3)(x + 1) = 0. Thus, x = -1.5 and x = -1.

For equation II: y² + 4y - 12 = 0 Splitting the middle term gives y² + 6y - 2y - 12 = 0, which factors into (y + 6)(y - 2) = 0. Thus, y = -6 and y = 2.

Comparing the values: When x = -1.5 and y = -6, x > y. When x = -1.5 and y = 2, x < y.

Since x is greater than y in one case and smaller than y in another, no clear relationship can be established between x and y.

Explanation

Simplifying equation I by dividing by 3 gives 3x + y = 5, which means y = 5 - 3x.

Substituting y into equation II: 4x + 5(5 - 3x) = 14 4x + 25 - 15x = 14 -11x = -11 x = 1

Substituting x = 1 back into y = 5 - 3x: y = 5 - 3(1) = 2

Since x = 1 and y = 2, it clearly follows that x < y.

Explanation

Solving equation I: 2x² - x - 1 = 0 2x² - 2x + x - 1 = 0 (2x + 1)(x - 1) = 0 x = 1, -0.5

Solving equation II: 3y² - 5y + 2 = 0 3y² - 3y - 2y + 2 = 0 (3y - 2)(y - 1) = 0 y = 1, ⅔ (≈ 0.67)

Comparing the roots: When x = 1 and y = 1, x = y. When x = 1 and y = ⅔, x > y. When x = -0.5 and y = 1, x < y.

Since both x > y and x < y hold true for different pairs of roots, no fixed relation can be established.

Explanation

The pattern of the given number series involves multiplying each term by successive increments of 0.5:

2 × 1.5 = 3 3 × 2 = 6 6 × 2.5 = 15 15 × 3 = 45 45 × 3.5 = 157.5 157.5 × 4 = 630

Following this rule, the term following 45 should be 157.5. Therefore, 156.5 is the wrong number in the series.

Explanation

The pattern in the given series is obtained by halving each term and adding 2, or equivalently, by subtracting halving differences:

36 ÷ 2 + 2 = 20 20 ÷ 2 + 2 = 12 12 ÷ 2 + 2 = 8 8 ÷ 2 + 2 = 6 6 ÷ 2 + 2 = 5 5 ÷ 2 + 2 = 4.5

Alternatively, looking at the differences between consecutive terms: 36 − 16 = 20 20 − 8 = 12 12 − 4 = 8 8 − 2 = 6 6 − 1 = 5 5 − 0.5 = 4.5

Following this rule, the term after 6 should be 5 instead of 5.5, making 5.5 the wrong number in the sequence.

Explanation

The pattern governing the series is:

1 × 1 + 2 = 3 3 × 2 + 3 = 9 9 × 3 + 4 = 31 31 × 4 + 5 = 129 129 × 5 + 6 = 651 651 × 6 + 7 = 3913

Each term is obtained by multiplying the preceding term by n and adding (n + 1), starting from n = 1. Thus, 31 × 4 + 5 yields 129 instead of 128.

Explanation

The pattern followed in the given number series is × 1 + 1², × 2 + 2², × 3 + 3², × 4 + 4², and so on.

2 × 1 + 1² = 3 3 × 2 + 2² = 10 10 × 3 + 3² = 39 39 × 4 + 4² = 172 172 × 5 + 5² = 885 885 × 6 + 6² = 5346

Therefore, 40 is the wrong term in the series and should be replaced by 39.

Explanation

The series follows the relation: Next term = (Current term × 2) - 2.

5 × 2 - 2 = 8 8 × 2 - 2 = 14 14 × 2 - 2 = 26 26 × 2 - 2 = 50 50 × 2 - 2 = 98 98 × 2 - 2 = 194

Replacing 16 with 14 satisfies the entire pattern.

Explanation

Area of the path = Total cost / Rate = 273 / 0.5 = 546 m²

Let the width of the garden be W meters. Its length L = W + 3 meters.

When a path of width 3 m surrounds the garden, the outer length becomes L + 6 and the outer width becomes W + 6.

Area of the path = Outer Area − Garden Area (L + 6)(W + 6) − LW = 546 LW + 6(L + W) + 36 − LW = 546 6(L + W) + 36 = 546 6(L + W) = 510 L + W = 85

Substituting L = W + 3 into the equation: (W + 3) + W = 85 2W = 82 W = 41 m

Length of the garden, L = 41 + 3 = 44 m

Area of the garden = L × W = 44 × 41 = 1804 m²

Explanation

Let total students = 100. Passed students = 60% of 100 = 60 Failed students = 100 - 60 = 40

Since an equal number of boys and girls passed: Passed boys = Passed girls = 60 ÷ 2 = 30

Let the number of girls who failed be x. Boys who failed are 200% more than girls who failed, so failed boys = x + 2x = 3x.

Total failed students = x + 3x = 4x 4x = 40 x = 10

The percentage of girls who failed out of total students = (10 ÷ 100) × 100 = 10%.

Explanation

Simple Interest formula is SI = (P × R × T) / 100.

Interest from first investment = (X × 15 × 4) / 100 = 0.60X Interest from second investment = (1.35X × 18 × 3) / 100 = 0.729X

Total interest = 0.60X + 0.729X = 1.329X

Given total interest = 15948 1.329X = 15948 X = 15948 / 1.329 = 12000

Required value = 3.12X = 3.12 × 12000 = 37440.

Explanation

Using Time = Distance ÷ Speed, the time taken for each section of the journey is calculated as follows:

Bus distance = 6¼% of 640 = 40 km Bus time = 40 ÷ 80 = ½ hour

Car distance = 25% of 640 = 160 km Car time = 160 ÷ 120 = 4/3 hours

Bicycle distance = 30% of 640 = 192 km Bicycle time = 192 ÷ 32 = 6 hours

Train distance = 640 − (40 + 160 + 192) = 248 km Train time = 248 ÷ 62 = 4 hours

Total time = ½ + 4/3 + 6 + 4 = 10 + 11/6 = 71/6 hours.

Explanation

Using the weighted average relation, the total weight ratio is: Class Average = (Boys Ratio × Boys Average + Girls Ratio × Girls Average) ÷ (Total Ratio)

Substituting the given ratio of boys to girls (5 : 4) and the respective averages: 60 = (5 × 80 + 4 × Average weight of girls) ÷ 9 540 = 400 + 4 × Average weight of girls 140 = 4 × Average weight of girls Average weight of girls = 140 ÷ 4 = 35 kg

Explanation

The passage explicitly states that the balance of an ecosystem depends on the presence of every type of animal because if even one type of animal becomes too numerous (abundant) or scarce, the entire balance of the ecosystem changes and gets disturbed. Therefore, maintaining the population stability of each animal type is essential for sustaining ecological balance.

Explanation

According to the passage, a natural community depends on carnivores to maintain ecological balance by controlling the populations of other animals. Carnivores achieve this population control by feeding on herbivores (grass and plant eaters), omnivores (plant and meat eaters), as well as other carnivores within the ecosystem. Since all these statements accurately reflect the roles and feeding habits described in the text, all three given points are correct.

Explanation

According to the passage, carnivores depend heavily on having sufficient prey in the food chain to obtain the nutrients they need to stay alive. A shortage of prey directly jeopardizes their food supply. Furthermore, a decline in the population of herbivores or other carnivores in the ecosystem reduces the overall availability of their prey, which can prevent carnivores from surviving. Consequently, both an insufficient amount of prey in the food chain and a decline in herbivore and carnivore populations constitute direct threats to their survival.

Explanation

All statements regarding herbivores are explicitly supported by the passage. The text confirms that herbivores eat plants exclusively, meaning their diet consists solely of vegetation. It also notes that their survival relies on plant availability, as a decline in plants directly threatens their numbers. Furthermore, the passage explicitly states that many herbivores spend the majority of their lives eating to stay alive, and that they possess specialized biological systems enabling them to digest a variety of different plants. Therefore, all the listed statements are true.

Explanation

According to the passage, omnivores have an advantage in an ecosystem because their diet is the most diverse, allowing them to vary what they eat depending on which food source is most plentiful at any given time. Because both a diverse diet and the ability to adapt their feeding habits based on abundant food sources contribute to this advantage, both statements are correct.

Explanation

In the given sentence, the word filling blank (1) must function as an adjective to modify the noun "plants". "Abundant" means present in large quantities or plentiful, which fits both grammatically and contextually. The passage emphasizes that an ecosystem needs a plentiful supply of plant life to support herbivores, as any decline in plant availability directly threatens their survival. Words like "largely" and "quite" are adverbs, while "diversity" is a noun, making "abundant" the only grammatically appropriate and meaningful choice to describe the quantity of plants required.

Explanation

In the context of the passage, "balance" refers to the stable condition of an ecosystem maintained when different animal populations exist in proper proportion to one another. "Equilibrium" denotes a state of balance between opposing forces or elements within a system, making it the precise synonym for "balance" in ecological contexts.

Explanation

The term sufficient refers to having enough or an adequate amount of something to satisfy a particular need or condition. The word inadequate represents the exact antonym, as it describes a state of being insufficient, lacking, or not enough to fulfill a requirement.

Explanation

The auxiliary verb "have" in the present perfect tense requires the past participle form of the verb (V3). "Stabilized" is the past participle that completes the verb phrase "have stabilized" grammatically. Contextually, "stabilized" accurately describes how the operational procedures of the mid-day meal scheme have become established and settled over two decades, setting up a clear contrast with the clause "but accidents continue to occur."

Explanation

The noun blunder means a severe mistake, gross error, or careless oversight. In the context of the passage, diluting a single litre of milk with a bucketful of water to serve over eighty children represents a grave administrative lapse and gross mismanagement in executing the mid-day meal scheme. Contextually and grammatically, blunder fits perfectly as the noun subject following the superlative adjective latest to describe this reported error.

Explanation

The word suffice means to be enough, adequate, or sufficient to satisfy a need. In the context of the passage, diluting one litre of milk with a bucketful of water was done so that the small quantity of milk would be enough or serve adequately for all the 80 children present. Grammatically, the base verb suffice correctly follows the modal verb would and naturally collocates with the preposition for.

Explanation

The context refers to administrative officers responsible for overseeing and managing the execution of the mid-day meal scheme. The verb supervise means to observe, inspect, and direct the implementation of a project or system. In this sentence, officers who supervise the mid-day meal scheme logically describes the official authority charged with monitoring the program's daily operation in government schools, making supervise the grammatically and contextually appropriate word to complete the sentence.

Explanation

The word reflexive means done as an automatic response or reflex, without conscious thought or deliberation. In the context of the passage, officials repeatedly issue the same predictable, routine statement whenever a scandal or revelation regarding the mid-day meal scheme comes to light. Therefore, reflexive appropriately describes this habitual, unthinking reaction of the authorities.

Explanation

The word customary means routine, standard, or done according to established practice. In the given context, the text describes how authorities routinely react to such exposed scandals by carrying out standard, predictable administrative actions like firing a low-level worker. Therefore, customary fits the blank appropriately both contextually and grammatically to describe the standard procedural measures taken by the administration.

Explanation

The word transitioning means moving or changing from one state, stage, or condition to another. In the sentence, the continuous verb phrase has been transitioning into accurately conveys the ongoing shift in Maharashtra's political landscape toward a new party system. It fits both grammatically and contextually with the idea of a political dynamic evolving over time as one party seeks to replace another as the dominant force in the state.

Explanation

The structure "enough to + base verb" requires a verb in its infinitive form that pairs naturally with the noun "memories." Both "evoke" and "recall" are base form verbs that mean to bring past experiences, feelings, or images back to mind. Using either "evoke memories" or "recall memories" completes the sentence with complete grammatical accuracy and meaningful context.

Explanation

The noun proposal refers to a formal plan, scheme, or offer put forward for consideration. In the context of government policy, considering a proposal to boost vegetable cultivation is both grammatically correct after the indefinite article a and semantically appropriate for describing an administrative scheme aimed at stabilizing market prices.

Explanation

Both effectiveness and utilisation fit contextually and grammatically into the sentence. In railway management, speeding up trains allows tracks and physical assets to handle higher traffic volumes, thereby maximising the utilisation of infrastructure and increasing the overall effectiveness of the transport network. Collecting does not make logical sense when paired with infrastructure in this context. Thus, both effectiveness and utilisation correctly complete the sentence.

Explanation

When economic growth has not yet bottomed out, a central bank aims to stimulate economic activity by easing monetary policy and reducing borrowing costs. Lowering interest rates encourages investment and consumer spending to boost growth. Contextually and grammatically, "cuts" is the precise term used to denote a reduction in interest rates by the RBI.

Explanation

Swapping the words accounts and capacity places thermal capacity together as the correct subject noun phrase, followed by the phrasal verb accounts for, which means to make up or constitute. This restores the grammatically correct and contextually meaningful structure: Today, thermal capacity accounts for about two-thirds the installed generation capacity in the country.

Explanation

The given sentence is grammatically sound and contextually meaningful as written. The verb "followed" correctly indicates that the IMF acted after the World Bank. The gerund "reducing" appropriately follows the preposition "in" to denote the action taken. The adjective "economic" correctly modifies "growth," and "financial" appropriately describes "year." Since all four highlighted words are placed in their proper positions, no interchange of words is required.

Explanation

In the given sentence, swapping the words at positions (B) and (D) restores two standard English idioms. The phrase "draw attention to" correctly means to attract notice, while "caught on the wrong foot" is an established idiom meaning to be taken by surprise or unprepared. Placing "attention" at position (B) and "caught" at position (D) makes the sentence grammatically accurate and contextually meaningful.

Explanation

Swapping the word 'power' with 'economic' restores both grammatical structure and contextual meaning to the sentence. In the original position, 'economic' acts as an adjective without a noun to modify, rendering 'demand for economic' ungrammatical. Exchanging the positions of 'power' and 'economic' yields 'With economic growth, the demand for power in India is only going to increase further.' Here, 'economic growth' forms a standard meaningful noun phrase, and 'power' correctly functions as the noun object following the preposition 'for'.

Explanation

Swapping B and C makes the sentence grammatically and contextually correct. The verb "stayed" properly pairs with "worsened" as a past tense action indicating that the Air Quality Index remained in the "poor" category. Meanwhile, "expected" correctly completes the passive structure "is expected to", which accurately describes a future prediction about the quality deteriorating further.

Explanation

The correct spelling is "necessary", which contains a single 'c' and double 's'. The sentence incorrectly includes an extra 'c' in "neccessary".

Explanation

All four words—provisions, incomes, redistributing, and equitable—are spelled correctly and used in their appropriate grammatical forms within the sentence. "Provisions" means legal or official stipulations, "incomes" refers to financial earnings, "redistributing" means distributing again or differently, and "equitable" means fair and impartial. Since there is no spelling error present in any of the specified words, all words in the sentence are correctly spelled.

Explanation

All four words—rejected, decades, liberalisation, and circulation—are spelled correctly in standard English. "Rejected" means dismissed or refused, "decades" refers to periods of ten years, "liberalisation" refers to the process of making laws or rules less strict, and "circulation" refers to being passed from place to place or person to person. Since none of these words contain any spelling mistakes, all the highlighted words in the given sentence are accurate.

Explanation

All four highlighted words in the sentence are spelled correctly according to standard English rules: "establish" (meaning to set up or create), "overarching" (meaning comprehensive or all-encompassing), "permeate" (meaning to spread throughout), and "applauded" (meaning praised or approved). Since none of the words contain any grammatical or spelling errors, the sentence is entirely free of misspellings.

Explanation

The word "Essentail" is misspelled. The correct spelling is "essential", which ends with "-tial" rather than "-tail". All other highlighted words in the sentence are spelled correctly.

Explanation

All four words—bureau, abuse, exploitation, and investigation—are spelled correctly in standard English. "Bureau" refers to an organization or department, "abuse" refers to improper usage or treatment, "exploitation" refers to the action of treating someone unfairly in order to benefit from their work, and "investigation" refers to a formal inquiry. As every highlighted word is spelled accurately, there are no spelling errors in the sentence.