Let's analyze the positional shifts of letters in each pair based on the English alphabet: <ul node="[object Object]"> <li node="[object Object]">OG – ML: First letter O (15) to M (13) is a shift of -2. Second letter G (7) to L (12) is a shift of +5.</li> <li node="[object Object]">GA – EF: First letter G (7) to E (5) is a shift of -2. Second letter A (1) to F (6) is a shift of +5.</li> <li node="[object Object]">KQ - IV: First letter K (11) to I (9) is a shift of -2. Second letter Q (17) to V (22) is a shift of +5.</li> <li node="[object Object]">CW - ZB: First letter C (3) to Z (26) is a shift of -3 (C $\to$ B $\to$ A $\to$ Z). Second letter W (23) to B (2) is a shift of +5 (W $\to$ X $\to$ Y $\to$ Z $\to$ A $\to$ B).</li> </ul> The common pattern for the first three pairs is a -2 shift for the first letter and a +5 shift for the second. The pair CW - ZB is the odd one out as its first letter undergoes a -3 shift.

<ul node="[object Object]"> <li node="[object Object]">Step 1: Calculate the day for 20 October 1986.</li> </ul> From 20 Oct 1981 to 20 Oct 1986, there are 5 full years (1982, 1983, 1984, 1985, 1986). Among these, 1984 is a leap year. Normal years contribute 1 odd day, leap years contribute 2 odd days. Total odd days = $(4 \times 1) + (1 \times 2) = 4 + 2 = 6$ odd days. Since 20 October 1981 was Tuesday, 20 October 1986 will be Tuesday + 6 days = Monday. <ul node="[object Object]"> <li node="[object Object]">Step 2: Calculate odd days from 20 October 1986 to 10 June 1987.</li> </ul> Days remaining in 1986 from Oct 20: Oct ($31-20=11$), Nov (30), Dec (31). Odd days in 1986 = $(11 \pmod 7) + (30 \pmod 7) + (31 \pmod 7) = 4 + 2 + 3 = 9 \pmod 7 = 2$ odd days. Days in 1987 till June 10 (1987 is a normal year): Jan (31), Feb (28), Mar (31), Apr (30), May (31), Jun (10). Odd days in 1987 = $(31 \pmod 7) + (28 \pmod 7) + (31 \pmod 7) + (30 \pmod 7) + (31 \pmod 7) + (10 \pmod 7) = 3 + 0 + 3 + 2 + 3 + 3 = 14 \pmod 7 = 0$ odd days. Total odd days from 20 Oct 1986 to 10 Jun 1987 = $2 + 0 = 2$ odd days. <ul node="[object Object]"> <li node="[object Object]">Step 3: Final day calculation.</li> </ul> The day on 10 June 1987 will be Monday + 2 days = Wednesday.

The statement indicates that the last date for payment without any penalty for late payment has been extended to September 30, 2025. <ul node="[object Object]"> <li node="[object Object]">Conclusion I: The statement only mentions penalty, not interest. Therefore, we cannot conclude anything about interest charges after September 30, 2025.</li> <li node="[object Object]">Conclusion II: The statement explicitly states that payment can be made up to September 30, 2025, without any penalty for late payment. This implies that any payment made on or before this date will not incur a penalty. Thus, this conclusion logically follows.</li> </ul>

Let's find the difference between consecutive numbers in the series: $325 - 306 = 19$ $306 - 289 = 17$ $289 - 274 = 15$ $274 - 261 = 13$ The pattern of differences is a decreasing sequence of odd numbers: 19, 17, 15, 13. The next difference in this sequence should be $13 - 2 = 11$. Therefore, the next number in the series is $261 - 11 = 250$.

<ol node="[object Object]"> <li node="[object Object]">V has the exam on Thursday.</li> <li node="[object Object]">Only five people have exams after S. This places S on Tuesday (Monday, S, Wednesday, Thursday, Friday, Saturday, Sunday).</li> <li node="[object Object]">Only four people have exams between Q and S. With S on Tuesday, Q must be on Sunday (Tuesday (S), Wednesday, Thursday, Friday, Saturday, Sunday (Q)). <ul node="[object Object]"> <li node="[object Object]">Schedule so far: _ _ S _ V _ _ Q</li> </ul> </li> <li node="[object Object]">R has the exam immediately after P (PR block). The only consecutive available slots are Friday and Saturday. So, P is on Friday and R is on Saturday. <ul node="[object Object]"> <li node="[object Object]">Schedule: _ S _ V P R Q</li> </ul> </li> <li node="[object Object]">T does not have the exam on Monday. The remaining slots are Monday and Wednesday. If T is not on Monday, T must be on Wednesday.</li> <li node="[object Object]">The last person, U, must take the exam on Monday.</li> </ol> Final Schedule: <ul node="[object Object]"> <li node="[object Object]">Monday: U</li> <li node="[object Object]">Tuesday: S</li> <li node="[object Object]">Wednesday: T</li> <li node="[object Object]">Thursday: V</li> <li node="[object Object]">Friday: P</li> <li node="[object Object]">Saturday: R</li> <li node="[object Object]">Sunday: Q</li> </ul> People between R (Saturday) and U (Monday) in chronological order are: S (Tuesday), T (Wednesday), V (Thursday), P (Friday). There are four people.

Substitute the symbols with their respective mathematical operations: <ul node="[object Object]"> <li node="[object Object]">P = $\div$</li> <li node="[object Object]">Q = $\times$</li> <li node="[object Object]">R = +</li> <li node="[object Object]">S = -</li> </ul> Now, evaluate Option 2 using the order of operations (BODMAS): $38 \text{ S } 16 \text{ Q } 3 \text{ R } 96 \text{ P } 4$ $= 38 - 16 \times 3 + 96 \div 4$ $= 38 - 48 + 24$ $= -10 + 24$ $= 14$ This matches the required resultant.

Break down the relationship string from right to left: <ol node="[object Object]"> <li node="[object Object]">$R+T$: R is the mother of T.</li> <li node="[object Object]">$G\%R$: G is the father of R. Since R is T's mother, G is T's maternal grandfather.</li> <li node="[object Object]">$V\times G$: V is the wife of G. Since G is T's maternal grandfather, V is T's maternal grandmother.</li> <li node="[object Object]">$N\#V$: N is the daughter of V. Since V is T's maternal grandmother, N is the daughter of T's maternal grandmother.</li> </ol> Therefore, N is T's mother's sister.

Establish the height relationships: <ol node="[object Object]"> <li node="[object Object]">Z is shorter than J but taller than C: J &gt; Z &gt; C</li> <li node="[object Object]">L is shorter than C but taller than P: C &gt; L &gt; P</li> </ol> Combine these two sequences to form a complete order from tallest to shortest: J &gt; Z &gt; C &gt; L &gt; P The friends in order of height from tallest to shortest are J, Z, C, L, P. The second tallest among them is Z.

Let Y be the origin $(0,0)$. <ol node="[object Object]"> <li node="[object Object]">Drives 28 km West: Current position $(-28, 0)$.</li> <li node="[object Object]">Right turn, drives 55 km (North): Current position $(-28, 55)$.</li> <li node="[object Object]">Left turn, drives 69 km (West): Current position $(-28-69, 55) = (-97, 55)$.</li> <li node="[object Object]">Left turn, drives 76 km (South): Current position $(-97, 55-76) = (-97, -21)$.</li> <li node="[object Object]">Left turn, drives 35 km (East): Current position $(-97+35, -21) = (-62, -21)$.</li> <li node="[object Object]">Left turn, drives 21 km (North) to stop at Z: Current position $(-62, -21+21) = (-62, 0)$.</li> </ol> Point Z is at $(-62, 0)$ and Point Y is at $(0,0)$. To reach Y from Z, Ravi must drive $62-0=62$ km in the positive X-direction, which is East.

<ol node="[object Object]"> <li node="[object Object]">Statement I: Some mirrors are angles. This indicates an overlap between the set of mirrors and the set of angles.</li> <li node="[object Object]">Statement II: All ellipses are angles. This means the entire set of ellipses is a subset of the set of angles.</li> </ol> Conclusion (I): Some ellipses are mirrors. This does not logically follow. While both mirrors and ellipses are related to angles, there's no information to suggest an overlap between ellipses and mirrors. Ellipses could be a subset of angles that does not intersect with the portion of angles that are mirrors. Conclusion (II): All angles are ellipses. This is the converse of Statement II and is not necessarily true. If all ellipses are angles, it does not imply that every angle must be an ellipse. There can be angles that are not ellipses (e.g., those angles that are mirrors but not ellipses).

iimb-bbadbe 2025 Complete Paper Solution | LR Slot 1

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iimb-bbadbe 2025 Complete Paper Solution | LR Slot 1

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<div><div class="latex-wrapper">If 20 October 1981 is Tuesday then what will be the day of the week on 10 June 1987?<br /></div></div>

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<div><div class="latex-wrapper">What should come in place of '?' in the given series? 325, 306, 289, 274, 261, ?<br /></div></div>

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<div><div class="latex-wrapper">If 'P' stands for '÷', 'Q' stands for 'x', 'R' stands for '+' and 'S' stands for '-', then the resultant of which of the following would be 14?<br /></div></div>

Instructions

<div><div class="latex-wrapper">In a certain code language,<br />A+ B means 'A is the mother of B'<br />A-B means 'A is the brother of B'<br />A x B means 'A is the wife of B'<br />A% B means 'A is the father of B'<br />A# B means 'A is the daughter of B'<br /></div></div>

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<div><div class="latex-wrapper">Based on the above, how is N related to T if 'N # V x G % R+T' ?<br /></div></div>

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<div><div class="latex-wrapper">Five friends C, J, L, P and Z are of different heights. Z is shorter than J but taller than C. L is shorter than C but taller than P. Who among them is the second tallest?<br /></div></div>

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