MBA CET 2026 Attempt 2 Slot 2 question paper with solutions

Approach: Remainder method: add (divisor − remainder).

Solution:
1056 ÷ 23: 23 × 45 = 1035, remainder = 1056 − 1035 = 21.
Least number to add = 23 − 21 = 2.
Check: 1058 = 23 × 46.

Cetking shortcut: Nearest multiple above: 23 × 46 = 1058 → 1058 − 1056 = 2.

Answer: A

Approach: Two-digit number 10a + b; reversing gives 10b + a; difference = 9(a − b).

Solution:
(10a + b) − (10b + a) = 9(a − b) = 36.
a − b = 36 ÷ 9 = 4.

Cetking shortcut: Difference of a number and its reverse ÷ 9 = difference of digits → 36/9 = 4.

Answer: B

Approach: Form the equation x + 17 = 60/x and solve the quadratic.

Solution:
x + 17 = 60/x → x² + 17x − 60 = 0.
(x + 20)(x − 3) = 0 → x = 3 or x = −20.
Positive number = 3.
Check: 3 + 17 = 20 = 60/3. ✔

Cetking shortcut: Plug options: only 3 gives 20 on both sides (20 → 37 vs 3; 6 → 23 vs 10; 4 → 21 vs 15).

Answer: D

Approach: aⁿ + bⁿ is divisible by (a + b) when n is odd.

Solution:
Let a = 2³². Then 2⁹⁶ + 1 = a³ + 1 = (a + 1)(a² − a + 1).
So 2⁹⁶ + 1 is divisible by a + 1 = 2³² + 1.
Hence any number dividing 2³² + 1 also divides 2⁹⁶ + 1.

Why the other options are wrong:
A, B: 2¹⁶ ± 1 are smaller than 2³² + 1 and are factors of 2³² − 1, not multiples of 2³² + 1.
D: 2⁹⁶ − 1 = a³ − 1 is divisible by a − 1, not a + 1.
E: 23 is not a multiple of 32.

Cetking shortcut: Look for an option whose exponent is an ODD multiple of 32 with a '+1' → 96 = 3 × 32.

Answer: C

Approach: Square near a round number: (a − b)² = a² − 2ab + b².

Solution:
1397² = (1400 − 3)²
= 1400² − 2 × 1400 × 3 + 3²
= 1,960,000 − 8,400 + 9
= 1,951,609.

Cetking shortcut: Last digit 7² → 9 and last two digits 97² → 09 kill C and D; size ≈ 1.95 million kills A and E.

Answer: B

Approach: Rewrite as squares and use a² − b² = (a + b)(a − b).

Solution:
53 × 2 × 106 = 4 × 53² and 47 × 2 × 94 = 4 × 47².
Expression = 4(53² − 47²) = 4 × (53 + 47)(53 − 47)
= 4 × 100 × 6 = 2400.
(Direct check: 11236 − 8836 = 2400.)

Cetking shortcut: Spot 106 = 2 × 53 and 94 = 2 × 47 → 4(a² − b²) in one line.

Answer: B

Approach: Overlap in averages: the 5th number is counted in both groups.

Solution:
Sum of 9 numbers = 9 × 15 = 135.
First five sum = 5 × 13 = 65; last five sum = 5 × 17 = 85.
65 + 85 = 150 counts the 5th number twice.
5th number = 150 − 135 = 15.

Cetking shortcut: Deviation method: first five −2 each (−10), last five +2 each (+10) → 5th = 15 + 0 = 15.

Answer: C

Approach: Change in total = change in average × number of items.

Solution:
Wrong entry adds 83 − 63 = 20 to the total.
This raises the average by 0.5.
n × 0.5 = 20 → n = 40.

Cetking shortcut: Number of students = excess ÷ rise in average = 20 / 0.5 = 40.

Answer: C

Approach: Replacement in average: total drop = drop in average × team size.

Solution:
Average falls by 2 for 11 players → total falls by 22.
Removed ages = 32 + 30 = 62.
Two youngsters together = 62 − 22 = 40 → each = 20.

Cetking shortcut: Each youngster = (62 − 22) / 2 = 20 in one line.

Answer: B

Approach: Successive percentage increase: a + b + ab/100.

Solution:
Assume the article's cost (original price) = 100.
After +10%: 110. After a further +15%: 110 × 1.15 = 126.5.
Profit = 126.5 − 100 = 26.5%.

Why the other options are wrong:
A (25.5%) and C (22%) miss or mis-add the 1.5% compounding term; D, E have no basis.

Cetking shortcut: 10 + 15 + (10 × 15)/100 = 26.5%.

Answer: B

Approach: Gap between two percentages of CP equals the money gap.

Solution:
Loss 5% → SP = 0.95 CP; gain 25% → SP = 1.25 CP.
Difference = 30% of CP = Rs. 210 → CP = Rs. 700.
For 35% gain: SP = 1.35 × 700 = Rs. 945.

Cetking shortcut: 30% ↔ 210 → 1% = 7 → 135% = 945.

Answer: B

Approach: Work everything from the labeled (marked) price.

Solution:
SP = LP + 20% of LP = 1.2 LP = 2880 → LP = Rs. 2400.
Purchase price = LP − 15% = 0.85 × 2400 = Rs. 2040.

Cetking shortcut: 2880 ÷ 1.2 = 2400 (option A is the trap) → × 0.85 = 2040.

Answer: C

Approach: Split into boys/girls on a base of 100 students.

Solution:
Students = 100 → boys 40, girls 60.
Girls not reading Hindi = 20% of 60 = 12 → girls reading Hindi = 48.
Total reading Hindi = 70 → boys reading Hindi = 70 − 48 = 22.
% of boys reading Hindi = 22/40 × 100 = 55%.

Cetking shortcut: Take 100 students and fill a 2×2 table (boys/girls × Hindi/not).

Answer: C

Approach: Evaluate the percentages, then isolate x.

Solution:
88% of 370 = 325.6.
24% of 210 = 50.4.
325.6 + 50.4 − x = 118 → 376 − x = 118 → x = 258.

Cetking shortcut: The decimals .6 and .4 add to a whole number — 376 − 118 = 258.

Answer: B

Approach: Revenue = seats × price → successive percentage change.

Solution:
New revenue factor = 1.25 × 1.12 = 1.40.
Increase = 40%.

Cetking shortcut: 25 + 12 + (25 × 12)/100 = 25 + 12 + 3 = 40%.

Answer: B

Approach: Convert every group to work-hours and find relative efficiencies.

Solution:
Let m, w, b = work per hour of a man, woman, boy.
8m + 5w for 6 h × 4 days = 24 h: W = 24(8m + 5w).
4m + 5w for 8 h × 5 days = 40 h: W = 40(4m + 5w).
192m + 120w = 160m + 200w → 32m = 80w → m = 2.5w.
Take w = 2, m = 5 → W = 24(40 + 10) = 1200 units.
Boys: 5b × 8 × 30 = 1200 → b = 1.
4 men + 3 women + 4 boys = 20 + 6 + 4 = 30 units/hour.
At 5 h/day → 150 units/day → 1200 / 150 = 8 days.

Cetking shortcut: Fix units early: m : w : b = 5 : 2 : 1 and W = 1200 — then every sub-question is one division.

Answer: A

Approach: Total work ÷ maximum work one man can do in the allowed time.

Solution:
From the caselet: man = 5 units/hour, total work = 1200 units (woman 2, boy 1).
Max hours in 6 days = 6 × 9 = 54 hours per man.
One man does 5 × 54 = 270 units.
Men needed = 1200 / 270 = 4.44 → round up to 5 men.

Why the other options are wrong:
A (9), C (8), D (6) are more than needed — not minimum; E (4) does only 1080 < 1200 units.

Cetking shortcut: Men alone: 1200 / 5 = 240 man-hours; 240 / 54 = 4.4 → 5.

Answer: B

Approach: Equate the two scenarios in man/boy-days to get the efficiency ratio.

Solution:
10(6m + 8b) = 2(26m + 48b)
60m + 80b = 52m + 96b → 8m = 16b → m = 2b.
Work = 10(6 × 2b + 8b) = 10 × 20b = 200b.
15 men + 20 boys = 30b + 20b = 50b per day.
Days = 200b / 50b = 4 days.

Cetking shortcut: Once m = 2b, convert all to boys: 20 boys × 10 days = 200 boy-days; 50 boys → 4 days.

Answer: B

Approach: Distance per revolution = circumference = 2πr.

Solution:
Circumference = 2 × (22/7) × 0.25 = 11/7 m.
Distance = 11 km = 11,000 m.
Revolutions = 11,000 ÷ (11/7) = 11,000 × 7/11 = 7000.

Cetking shortcut: 11 km and 22/7 are built to cancel: 11000 × 7/11 = 7000.

Answer: C

Approach: Write the initial ratio with one variable and set up the new ratio.

Solution:
Start: males 3x, females x.
After break: males 3x − 12; females x − 4 + 6 = x + 2.
(3x − 12)/(x + 2) = 2 → 3x − 12 = 2x + 4 → x = 16.
Total at start = 3x + x = 4x = 64.

Cetking shortcut: Total must be a multiple of 4 (3 : 1) → 64, 48, 52, 72; test 64: 48 − 12 = 36 males, 16 + 2 = 18 females → 2 : 1 ✔

Answer: A

Approach: Find milk and water in each container on a common base, then add.

Solution:
Take capacities 3, 4, 5 litres.
Container 1 (4 : 1): milk 12/5, water 3/5.
Container 2 (3 : 1): milk 3, water 1.
Container 3 (5 : 2): milk 25/7, water 10/7.
Multiply all by 35: milk = 84 + 105 + 125 = 314; water = 21 + 35 + 50 = 106.
Milk : water = 314 : 106 = 157 : 53.

Cetking shortcut: Multiply every container by 35 (LCM of 5, 4, 7) at the start to avoid fractions.

Answer: B

Approach: Work = rate × time; use the efficiency ratio.

Solution:
Rates man : boy = 8 : 5 → combined 13 units/day.
Total work = 13 × 40 = 520 units.
Boy alone = 520 ÷ 5 = 104 days.

Cetking shortcut: Boy's days = 40 × 13/5 = 104.

Answer: B

Approach: Profit share ∝ capital × time.

Solution:
Capital: A = 1/4, B = 3/4 of total.
Profit: B gets 2/3 → A gets 1/3 → A : B = 1 : 2.
(1/4 × 15) : (3/4 × t) = 1 : 2
3t/4 = 2 × 15/4 = 30/4 → t = 10 months.

Cetking shortcut: Capital ratio 1 : 3, profit ratio 1 : 2 → time ratio = (1/1) : (2/3) = 15 : 10 → B = 10 months.

Answer: C

Approach: Rent shared in proportion to usage = discs × days.

Solution:
A = 27 × 19 = 513; B = 21 × 17 = 357; C = 24 × 23 = 552.
Total = 513 + 357 + 552 = 1422.
C's share = 552/1422 × 23,700.
23,700/1422 = 50/3 → 552 × 50/3 = Rs. 9,200.

Cetking shortcut: Notice 1422 × 50 = 71,100 = 3 × 23,700 → each unit = Rs. 50/3; C = 552 × 50/3 = 9200.

Answer: E

Approach: Find the cost price of the mixture, then alligation.

Solution:
SP = 44 at 10% profit → CP of mixture = 44 / 1.1 = Rs. 40/kg.
Alligation: cheap 31, dear 43, mean 40.
Cheap : Dear = (43 − 40) : (40 − 31) = 3 : 9 = 1 : 3.
Dear = 36 kg → cheap = 36/3 = 12 kg.

Cetking shortcut: Always convert SP to CP before alligation: 44 → 40.

Answer: A

Approach: Only nickel changes; copper and zinc stay fixed.

Solution:
100 kg in 5 : 3 : 2 → Cu 50, Zn 30, Ni 20 kg.
New ratio 5 : 3 : 3 with Cu = 50 → 1 part = 10 kg → Ni must be 30 kg.
Nickel to add = 30 − 20 = 10 kg.

Cetking shortcut: Cu and Zn parts unchanged → Ni goes from 2 parts to 3 parts = +1 part = 10 kg.

Answer: A

Approach: Weighted average price.

Solution:
Mixed price = (2 × 15 + 3 × 20) / (2 + 3) = (30 + 60)/5 = 90/5 = Rs. 18/kg.

Cetking shortcut: Mean lies 3/5 of the way from 15 to 20: 15 + 3 = 18.

Answer: A

Approach: CI − SI formulas: 2 years = P(r)², 3 years = P(r)²(3 + r), r as a fraction.

Solution:
Let r = rate as a fraction.
CI − SI (2 yrs) = P r².
CI − SI (3 yrs) = P r²(3 + r).
Ratio = (3 + r) : 1 = 25 : 8 → 3 + r = 25/8 → r = 1/8.
Rate = 12.5% p.a.

Cetking shortcut: Ratio of 3-yr to 2-yr difference = 3 + r → 25/8 − 3 = 1/8 = 12.5%.

Answer: C

Approach: Equal annual instalments: present value of all instalments = debt (compound interest).

Solution:
Read the debt of ₹50,440 as the amount owed today, to be repaid in 3 equal annual instalments x at 5% CI.
x/1.05 + x/1.05² + x/1.05³ = 50,440.
Multiply by 1.05³ = 1.157625: x(1.1025 + 1.05 + 1) = 50,440 × 1.157625.
x × 3.1525 = 58,390.6 → x = 18,522.
Check: 18,522 = 16,000 × 1.05³, and 16,000 × 3.1525 = 50,440 exactly.

Why the other options are wrong:
If ₹50,440 were the amount due at the END of 3 years, the instalment would be 50,440/3.1525 = ₹16,000 — not among the options; A, B, C and E match neither reading.

Cetking shortcut: Instalment = 50,440 × 1.05³ / 3.1525 = 16,000 × 1.157625 = 18,522.

Answer: D

Approach: Two-year CI factor: 8% → 16.64%, 12% → 25.44%.

Solution:
Let Scheme A = x, Scheme B = 20,000 − x.
CI on A in 2 yrs = 0.1664x; on B = 0.2544(20,000 − x).
0.1664x + 5088 − 0.2544x = 4538
0.088x = 550 → x = Rs. 6,250.

Why the other options are wrong:
B, C, D, E: plug in — e.g. D (5000): 832 + 3816 = 4648 ≠ 4538.

Cetking shortcut: If all 20,000 were at 12%, interest = 5088; actual is 550 less; each rupee moved to 8% loses 0.088 → 550/0.088 = 6250.

Answer: A

Approach: Convert every tap to a common rate (buckets per hour), then capacity = rate × time.

Solution:
A: 4 buckets in 24 min → 10 buckets/hour.
B: 8 buckets/hour.
C: 2 buckets in 20 min → 6 buckets/hour.
Together: 24 buckets/hour → in 2 hours 48 buckets drain the tank.
Capacity = 48 × 5 = 240 litres.

Cetking shortcut: Work per minute: 1/6 + 2/15 + 1/10 = 2/5 bucket/min → 120 min × 2/5 = 48 buckets.

Answer: E

Approach: Flow ∝ (diameter)²; add rates and divide the tank volume.

Solution:
Rates ∝ 1², (4/3)², 2² = 1, 16/9, 4.
Largest tap alone: 61 min → tank = 4 × 61 = 244 units.
Combined rate = 1 + 16/9 + 4 = 61/9 units/min.
Time = 244 ÷ (61/9) = 244 × 9/61 = 36 minutes.

Cetking shortcut: Time together = 61 × 4 ÷ (61/9) = 36 — the odd '61' is chosen so it cancels.

Answer: A

Approach: Work done together, then the remaining by B alone.

Solution:
In 4 min together: 4(1/15 + 1/20) = 4 × 7/60 = 28/60.
Remaining = 32/60 = 8/15 of the tank.
B alone: (8/15) × 20 = 32/3 min = 10 min 40 s.
Total = 4 + 10 min 40 s = 14 min 40 s.

Cetking shortcut: Take tank = 60 units: A = 4, B = 3/min. 4 min → 28; left 32 → 32/3 = 10⅔ min → total 14 min 40 s.

Answer: B

Approach: Same direction → relative speed = difference; opposite → sum.

Solution:
Total length = 130 + 110 = 240 m.
Same direction: 240/60 = 4 m/s = a − b.
Opposite: 240/3 = 80 m/s = a + b.
a = (80 + 4)/2 = 42 m/s; b = (80 − 4)/2 = 38 m/s.

Why the other options are wrong:
B: difference 4 but sum 76. C, D, E: sum/difference do not match 80 and 4.

Cetking shortcut: Options must sum to 80 and differ by 4: only 42, 38.

Answer: A

Approach: Passing a person: distance = train length; opposite direction → relative speed = sum.

Solution:
Relative speed = 280 m / 9 s = 280/9 m/s = (280/9) × 18/5 = 112 km/h.
Goods train speed = 112 − 50 = 62 km/h.

Cetking shortcut: 280/9 × 3.6 = 112 → subtract 50.

Answer: B

Approach: Same direction → relative speed = difference; distance = gap + train length.

Solution:
Relative speed = 45 − 9 = 36 km/h = 10 m/s.
Distance to cover = 240 + 120 = 360 m.
Time = 360 / 10 = 36 s.

Cetking shortcut: 36 km/h = 10 m/s is a must-know conversion.

Answer: A

Approach: Faulty clock: real time / clock time = 24 h / (24 h − loss).

Solution:
Clock loses 16 min per 24 h → in 24 real hours it shows 23 h 44 min = 1424 min.
From 5:00 a.m. (day 1) to 10:00 p.m. (day 4) on the clock = 3 days + 17 h = 89 h.
Real time elapsed = 89 × 1440/1424 = 89 × 90/89 = 90 h.
5:00 a.m. + 90 h = 5:00 a.m. + 3 days 18 h = 11:00 p.m. on day 4.

Cetking shortcut: 1424/1440 = 89/90 — so 89 clock-hours = 90 real hours; the clock is exactly 1 hour slow.

Answer: B

Approach: Angle = |30H − 5.5M|.

Solution:
H = 2, M = 30.
Angle = |30 × 2 − 5.5 × 30| = |60 − 165| = 105°.

Cetking shortcut: At 2:30 the minute hand is at 180°, hour hand at 60° + 15° = 75° → 105°.

Answer: A

Approach: Odd days: an ordinary year shifts the weekday by 1.

Solution:
Jan 12, 1979 to Jan 12, 1980 contains no 29 February (1979 is not a leap year; 29 Feb 1980 comes after 12 Jan) → 365 days = 1 odd day.
Going back one year: Saturday − 1 = Friday.

Cetking shortcut: Check for Feb 29 inside the span — none here, so shift by 1.

Answer: A

Approach: Percentage change = (new − old)/old × 100.

Solution:
55AH: 1992 = 108, 1998 = 145.
Increase = 37 → 37/108 × 100 ≈ 34.3% ≈ 34%.

Cetking shortcut: 37/108 is a bit more than 1/3 → 34%.

Answer: C

Approach: Add each column over the seven years.

Solution:
4AH: 75+90+96+105+90+105+115 = 676
7AH: 144+126+114+90+75+60+85 = 694
32AH: 114+102+75+150+135+165+160 = 901
35AH: 102+84+105+90+75+45+100 = 601
55AH: 108+126+135+75+90+120+145 = 799
Maximum = 32AH (901 thousand).

Cetking shortcut: 32AH has three values ≥ 150 in the last four years — check it against 55AH only.

Answer: C

Approach: Read two cells and subtract; table is in thousands.

Solution:
35AH: 1993 = 84 thousand, 1997 = 45 thousand.
Difference = 39 thousand = 39,000.

Cetking shortcut: Remember the unit (thousands).

Answer: D

Approach: Share = 4AH sales / year total; compare ratios.

Solution:
1994: 96/525 ≈ 18.3%
1995: 105/510 ≈ 20.6%
1996: 90/465 ≈ 19.4%
1997: 105/495 ≈ 21.2%
1998: 115/605 ≈ 19.0%
Maximum share in 1997.

Cetking shortcut: 1995 vs 1997: same numerator 105, smaller total in 1997 (495 < 510) → 1997 beats 1995; others are clearly below 20%.

Answer: D

Approach: Scan each column from 1992 to 1997 for a strictly falling run.

Solution:
7AH: 144 → 126 → 114 → 90 → 75 → 60 — falls every year.
4AH rises (75 → 90 …); 32AH and 55AH rise in 1993/1994; 35AH rises in 1994 (84 → 105).

Why the other options are wrong:
A and E rise in the first year (75 → 90; 108 → 126); C falls at first but rises in 1995 (75 → 150); D (35AH) rises from 84 to 105 in 1994.

Cetking shortcut: Reject a column at the first rise you see.

Answer: B

Approach: Add each city's column (1 kg of each fruit).

Solution:
Delhi: 83+55+98+75+102+69 = 482
Mumbai: 96+59+99+34+28+98 = 414
Bangalore: 90+47+88+79+65+79 = 448
Amritsar: 66+72+81+69+65+91 = 444
Agra: 88+55+83+75+100+105 = 506
(Chennai: 374)
Highest = Agra.

Cetking shortcut: Delhi vs Agra only: Agra beats Delhi by +5, 0, −15, 0, −2, +36 = +24.

Answer: E

Approach: Read the three rates, multiply by quantities, add.

Solution:
Banana, Amritsar: 2 × 72 = 144.
Apple, Mumbai: 4 × 96 = 384.
Mango, Delhi: 3 × 102 = 306.
Total = 144 + 384 + 306 = Rs. 834.

Why the other options are wrong:
A (798), B (807), D (877), E (896) do not match 144 + 384 + 306.

Cetking shortcut: Unit digits: 4 + 4 + 6 = 14 → answer ends in 4 → only 834.

Answer: C

Approach: Compute each total cost; four are equal, one is not.

Solution:
A: 84 × 75 (Grapes, Delhi) = 6300.
B: 70 × 90 (Carrot, Chennai) = 6300.
C: 63 × 100 (Mango, Agra) = 6300.
D: 95 × 65 (Mango, Bangalore) = 6175.
E: 60 × 105 (Orange, Agra) = 6300.
Odd one = D.

Why the other options are wrong:
A, B, C, E all cost exactly Rs. 6300.

Cetking shortcut: 6300 = 2² × 3² × 5² × 7; 95 × 65 has no factor 3 or 7 → it cannot be 6300.

Answer: D

Approach: Compute each cost from the table and pick the minimum.

Solution:
A: 4 × 90 = 360.
B: 5 × 55 = 275.
C: 7 × 34 = 238.
D: 4 × 81 = 324.
E: 8 × 32 = 256.
Cheapest = C (Rs. 238).

Why the other options are wrong:
A 360, B 275, D 324, E 256 — all costlier than Rs. 238.

Cetking shortcut: Only C and E are under 260 — compare 238 vs 256.

Answer: C

Approach: Average = sum of the row ÷ number of cities.

Solution:
Orange: 69 + 98 + 32 + 79 + 105 + 91 = 474.
Average = 474 / 6 = Rs. 79.

Cetking shortcut: Deviation from 80: −11, +18, −48, −1, +25, +11 = −6 → 80 − 1 = 79.

Answer: E

Approach: Prime-number series: every alternate prime.

Solution:
Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 …
The series takes the 3rd, 5th, 7th, 9th, 11th primes → next is the 13th prime = 41.
(Equivalently: each term skips exactly one prime — after 31 skip 37 → 41.)

Why the other options are wrong:
A (37): the prime right after 31 — but the series always skips one prime.
B (39): not prime (3 × 13).
D (43): skips two primes.
E (47): skips three primes.

Cetking shortcut: When the gap breaks from a steady +6 (23 → 31), test the prime list.

Answer: C

Approach: Specific detail — locate the keyword 'coexist peaceably'.

Solution: Para 2 says the body's defences do not attack tissues carrying a self-marker; 'immune cells and other body cells coexist peaceably in a state known as self-tolerance.' The passage names the state directly.

Why the other options are wrong:
A: 'equilibrium' is a general word; the passage gives a specific term.
C: 'harmony' paraphrases 'peaceably' but is not the named state.
D, E: 'patience' and 'indifference' never appear and do not fit.

Cetking shortcut: When the stem says 'what is the state…', look for 'known as' / 'called' in the passage.

Answer: B

Approach: Specific detail — find 'ragweed pollen'.

Solution: Para 3: 'Antigens are not to be confused with allergens, which are most often harmless substances (such as ragweed pollen or cat hair) that provoke … the inappropriate and harmful response known as allergy.' So the substance is an allergen.

Why the other options are wrong:
A: Antigen triggers a normal immune response; the passage explicitly contrasts it with allergen.
B, E: Microbes/viruses are examples of antigens, not harmless triggers.
D: Autoimmune disease is the body attacking itself, not a substance.

Cetking shortcut: 'Harmless substance + harmful response' = allergen; the passage itself warns not to confuse it with antigen.

Answer: C

Approach: Specific detail — how an antigen 'announces its foreignness'.

Solution: Para 3: 'An antigen announces its foreignness by means of intricate and characteristic shapes called epitopes, which protrude from its surface.' Option D restates this exactly.

Why the other options are wrong:
A: Allergy is a wrong response, not a recognition mechanism.
B: Blood type is never mentioned.
C: The epitopes are 'shapes', not 'fine hairs' — a distortion of 'protrude'.
E: Neurons are unrelated to antigen recognition here.

Answer: D

Approach: Main idea — find the sentence the whole passage is built around.

Solution: Para 2 opens: 'At the heart of the immune system is the ability to distinguish between self and non-self.' Self-tolerance, memory of non-self molecules, antigens/epitopes, transplant rejection and autoimmune disease all illustrate this self vs non-self distinction. Option B is the only option built on that theme (its wording 'function of the antigen' is loose — the passage credits the immune system — but it carries the central idea).

Why the other options are wrong:
A: Definition of antigen is a supporting detail of para 3, not the main idea.
C: 'Central system of the body' is never claimed; the passage only compares its complexity with the brain.
D: Contradicts the passage — failure is only in 'abnormal situations'.
E: Microbes are a passing mention.

Cetking shortcut: Main-idea questions: look for 'At the heart of…' / 'The key…' sentences.

Answer: B

Approach: Inference from a stated rule — transplants and self-markers.

Solution: Para 3: tissues from another individual act as antigens and are rejected, 'except an identical twin, whose cells carry identical self-markers.' A father's tissue carries different self-markers, so the daughter's immune system reads it as non-self; a twin's tissue reads as self.

Why the other options are wrong:
A: Age of tissue is never a factor in the passage.
C: Sex difference is not mentioned; the reason is self-markers.
D: Immune memory is not inherited/shared, and is irrelevant to rejection.
E: Environment plays no role in self-markers.

Answer: B

Approach: Main idea — problem stated, solution emphasised.

Solution: Para 1: green plants soothe. Para 2: household chemicals cause Multiple Chemical Sensitivity — 'what has this got to do with green plants? Everything healthy!' Para 3: ferns and palms pull chemicals from the air (even NASA found palms removed formaldehyde). The thrust is that certain plants can purify the home.

Why the other options are wrong:
A, E: Only the problem half of the passage.
B: Allergy-like symptoms are mentioned, but the passage says it is actually MCS, and this is a detail.
C: 'All plants' is extreme; only ferns and palms are discussed.

Cetking shortcut: Main idea = where the passage lands (the 'solution'), not where it starts.

Answer: D

Approach: Specific detail — effect of household chemicals in closed air.

Solution: Para 2: in winter with windows shut we breathe these chemicals, causing allergy-like symptoms; 'The truth is that we are experiencing a syndrome that is called Multiple Chemical Sensitivity.' So the chemicals together contribute to MCS.

Why the other options are wrong:
A: The passage says people only mistake it for allergy.
B: 'Monumental task' is not stated.
D: Formation of new compounds is not mentioned.
E: Photosynthesis is what plants do to remove chemicals, not an effect of chemicals.

Cetking shortcut: 'The truth is…' signals the author's correction — the answer usually sits there.

Answer: C

Approach: True-statement check — test each option against the text.

Solution: Para 2: 'Research has been conducted with two types of plants that have actually removed much of these harmful chemicals.' Para 3 names them — ferns and palms. So the research cited used specific plants only: A is true.

Why the other options are wrong:
B: 'Only by NASA' is false — 'Even NASA' shows NASA was one of the researchers.
C: Sources are identified — dry-cleaned clothes, cleansers, home products.
D: The benefit is to homes; space exploration was only the context of NASA's experiment.
E: 'Logic of machines' is not in the passage.

Cetking shortcut: 'Even NASA' kills any 'only NASA' option instantly.

Answer: A

Approach: Inference — what the author links to the plants' antiquity.

Solution: Last para: both species are ancient (over 100 million years) and long-lived, then the closing line: 'Perhaps it is their primal qualities that have contributed to their ability to purify their environment.' 'Primal qualities' = antiquity; the link drawn is to air purification.

Why the other options are wrong:
A, C: Long life and long-lived leaves are listed alongside antiquity as other shared traits, not as its result.
D: Research success is not linked to their age.
E: Rebirth is never mentioned.

Answer: B

Approach: Title — must cover the passage's main point, neither too narrow nor too broad.

Solution: The passage moves from the hazards of indoor chemicals to its real point: ferns and palms (common houseplants) can pull these chemicals from the air. 'Common Houseplants May Purify Your Home' captures both the subject and the claim, with an appropriately tentative 'may' (the author says 'perhaps', 'seem to be').

Why the other options are wrong:
A: Too broad and vague.
B, E: Cover only the problem half.
D: 'Finds the Cure' overstates; NASA is a single supporting example.

Cetking shortcut: Title = main idea in headline form; reuse your answer to the main-idea question (D).

Answer: C

Approach: Primary purpose — the option must cover the whole passage.

Solution: Para 1: pain travels through complex circuitry. Para 2: prostaglandins sensitise nerve endings; aspirin blocks their synthesis. Para 3: impulses go to the spinal cord, substance P relays them; local anaesthetics block transmission. Para 4: endorphins block signals in the brain. So the passage describes how pain signals are conveyed and the ways they can be blocked — option C.

Why the other options are wrong:
A: 'Pleasure' is never discussed.
B: Endorphins help the body — the passage never calls them harmful.
D: Acupuncture blocks pain; pleasure is not mentioned.
E: The passage is about one signal pathway, not 'kinds' of pain.

Cetking shortcut: 'Completely' in the stem = the option must cover both halves (transmission + blocking).

Answer: C

Approach: Sequence detail — the first event after injury.

Solution: Para 2: 'When a cell is injured, a rush of prostaglandins sensitizes nerve endings at the injury.' 'A flood of prostaglandins' = 'a rush of prostaglandins'. Option D.

Why the other options are wrong:
A: Electrical flow is broken only by local anaesthetics, not by injury.
B: Substance P is released later, at the spinal cord.
C: Endorphins block signals in the brain; they do not 'speed up' nerve cells.
E: Quiescence is caused by anaesthetics.

Answer: D

Approach: Application — match the scenario to the mechanism the passage gives.

Solution: Last para: 'techniques for blocking chronic pain — such as acupuncture and electrical stimulation of the central brain stem — involve the release of endorphins.' A chronic back-pain patient relieved after acupuncture is exactly this case.

Why the other options are wrong:
A, C: Novocaine/local anaesthetics block nerve transmission (sodium ions), not endorphins.
B: Ibuprofen is an aspirin-like drug — blocks prostaglandin synthesis.
D: Vaccines concern immunity, not pain.

Cetking shortcut: Each blocker in the passage has its own mechanism: aspirin → prostaglandins, anaesthetic → sodium ions, acupuncture → endorphins.

Answer: E

Approach: Inference from a proportional rule.

Solution: Para 2: aspirin-type drugs block prostaglandin synthetase, and 'the drugs' effectiveness against pain is proportional to their success in blocking this enzyme.' Partial blocking → some prostaglandins are still made → some nerve endings are sensitised → some signals travel on (substance P is released at the spinal cord) → some pain reaches the brain. Option B states this outcome. (Note: B's label 'pain killing' is loose — substance P is a pain-signalling chemical — but its conclusion is the only correct inference.)

Why the other options are wrong:
A: Endorphins are not produced by this pathway, and signals would be reduced, not intensified.
C: Sodium ions are blocked by anaesthetics, not by aspirin.
D: If some prostaglandins are produced, signals continue, so substance P is not prevented.
E: Peptides (endorphins) regulating traffic is unrelated to the enzyme.

Cetking shortcut: Partial cause → partial effect: look for 'some … so some …'.

Answer: B

Approach: Vocabulary in context.

Solution: Para 3: anaesthetics inhibit sodium flow, 'making the nerves electrically quiescent; thus no pain signals are sent.' Quiescent = inactive, at rest, temporarily quiet — i.e. dormant.

Why the other options are wrong:
B, C, E: vibrant/busy/energetic are opposites.
D: 'dead' is too strong — the nerves recover when the anaesthetic wears off.

Answer: A

Approach: Title — find what most of the passage discusses.

Solution: Diseases and Zika are only the opening context. The bulk of the passage explains how GM A. aegypti mosquitoes are made (lethality gene tTAV, fluorescence gene, tetracycline antidote), how their offspring die, and the Brazil release that cut the population by 80–95%. Title: 'Genetically modified mosquitoes'.

Why the other options are wrong:
A: Zika is only the motivation, too narrow.
C: Symptoms take one line.
D: Brazil is only the study site.
E: Honey bees are never mentioned.

Answer: B

Approach: Tone — judge word choice and purpose.

Solution: The author gives WHO statistics, explains genes (tTAV, fluorescence), lab rearing and a field study, and even points to a teaching activity. No opinion, humour, irony or apology — the purpose is to inform.

Why the other options are wrong:
B, C: No humour or sarcasm.
D: Nothing is apologised for.
E: No one-sided judgement; facts and a hypothesis are reported neutrally.

Cetking shortcut: Science-explainer passages with data and processes = informative/objective tone.

Answer: A

Approach: NOT-correct question — verify each statement against the text.

Solution: The passage says 'Zika fever is caused by a virus transmitted to humans primarily by the bite of Aedes Aegypti mosquitoes.' Option A swaps 'Zika' with 'Malarial fever' — the passage never says malaria is a virus spread by Aedes aegypti. So A is not correct.

Why the other options are wrong:
B: Stated — 'The fluorescence gene is used to identify GM mosquitoes.'
C: Stated word for word.
D: Stated — 'scientists released GM mosquitoes into a neighborhood in Brazil.'
E: Stated word for word.

Cetking shortcut: In NOT/EXCEPT questions, look for a swapped noun inside a copied sentence.

Answer: A

Approach: Vocabulary in context — closest meaning of 'transcription' among the options.

Solution: In the passage, tTAV 'blocks the transcription of several other genes' — transcription is the copying of a gene's information into a record (RNA). In general use, a transcription (transcript) is a written copy or record of something, and a record is what serves as evidence. None of the other options carries the sense of a copied record, so evidence is the closest.

Why the other options are wrong:
A: Introduction — a beginning, not a copy.
C: Variation — a change, the opposite of a faithful copy.
D, E: Induction/deduction — modes of reasoning.

Answer: B

Approach: Antonym in context.

Solution: 'Sustained release over the course of a year led to a reduction…' — sustained = continuous, kept up without break. The opposite is sporadic = occurring irregularly, now and then.

Why the other options are wrong:
A: nourished — a different sense of 'sustain' (to feed), and a near-synonym, not an antonym.
C: 'back' — unrelated.
D: relieved — unrelated to continuity.
E: prolonged — a synonym.

Cetking shortcut: Antonym questions: first eliminate synonyms (prolonged, nourished).

Answer: B

Approach: 'Wish' + would — wishing for a change in someone's habitual behaviour.

Solution: 'I wish he wouldn't be so rude to people when we go out.' To complain about another person's repeated present/future behaviour that we want changed, English uses wish + would/wouldn't + base verb. 'When we go out' shows a habitual, recurring situation, not a past one.

Why the other options are wrong:
A, D, E: will/won't/shall are not used after 'wish'.
C: 'hadn't been' expresses regret about the past, but 'when we go out' is present/habitual.

Cetking shortcut: After 'wish': past → had + V3; present state → were/past simple; someone's annoying habit → would.

Answer: B

Approach: Articles — specific (the) vs one-of-many (a/an), and sound rule.

Solution: 'Put the bag on the table' — a particular bag and table both speakers can see. 'Give me an apple and a bar of chocolate' — any one apple / bar; 'apple' begins with a vowel sound → an, 'bar' with a consonant sound → a. Pattern: the … the … an … a.

Why the other options are wrong:
A: 'a table' — the table here is a specific one in the room.
B: 'a bag' — the instruction refers to a specific bag.
C: 'the apple / the bar' — no particular apple or bar is identified.
D: 'a bag … a table' — both should be definite.

Cetking shortcut: Fix the easy pair first: apple → an, bar → a; only A, B, D, E survive, then decide the/a for bag/table.

Answer: E

Approach: Time conjunction — 'as soon as' + present simple for a future event.

Solution: 'I'll send it to you as soon as I get the money.' The sentence needs a conjunction linking the sending to the moment of getting the money; 'as soon as' = immediately when, and takes the present simple ('get') for a future meaning.

Why the other options are wrong:
B: 'immediately' alone is an adverb, not a standard conjunction here.
C: 'unless' gives the opposite sense (send only if I don't get the money).
D: 'until' (misspelt 'untill') means up to that time — illogical: I'd send it before getting the money.
E: 'in case' = as a precaution, illogical.

Answer: A

Approach: Modal of general possibility — 'can'.

Solution: 'Winters here can be really cold sometimes.' 'Can' expresses something that is possible or happens from time to time; 'sometimes' signals occasional possibility, and the advice 'bring warm clothes' fits.

Why the other options are wrong:
B: 'won't' contradicts the advice to bring warm clothes.
C: 'shall' is for future intention/offers, not general facts.
D, E: 'was/is' are singular; the subject 'Winters' is plural.

Cetking shortcut: 'sometimes' + general statement → can.

Answer: A

Approach: Second conditional — If + past simple, would + base verb.

Solution: 'If I had more time' (past simple for an unreal present) must be followed by would + base verb: 'I would do more exercise.'

Why the other options are wrong:
A: 'am bound to' expresses certainty/obligation, not a hypothetical result.
B: 'am ought to' is ungrammatical ('ought to' takes no 'am').
D, E: will/can belong to the first conditional (If I have …).

Cetking shortcut: Spot 'If + had/were' → result clause takes would/could/might.

Answer: C

Approach: Participle phrase — check the subject and tense.

Solution: 'Having received your letter this morning, we are writing to thank you.' The perfect participle 'having received' shows the earlier action and correctly refers to the subject 'we'. 'Are writing' (action in progress) and 'to thank you' (purpose) are both correct. No part has an error.

Why the other options are wrong:
A: Correctly attached to 'we' — not dangling.
B: 'this morning' fits the past action of receiving.
C: Present continuous is correct for the current act of writing.
D: Infinitive of purpose is correct.

Answer: E

Approach: Preposition/phrase usage — 'on the part of'.

Solution: The delay is due to inefficiency and poor management on the part of the railways (= by the railways). 'Infront of' means physical position, which makes no sense here — and is also wrongly written as one word ('in front of'). Correct: '…lack of good management on the part of the railways.'

Why the other options are wrong:
A: 'A lot of travel delay is caused' — acceptable.
B: 'due to the inefficiency' — acceptable in this exam context.
C: 'and lack of good management' — correct.

Cetking shortcut: Responsibility of a person/organisation → 'on the part of'.

Answer: D

Approach: Linking (sense) verbs take adjectives, not adverbs.

Solution: 'Smell' here describes the roses' quality (a linking verb, like look/taste/feel/seem), so it needs an adjective: 'Do the roses in your garden smell sweeter than those in ours?' 'More sweetly' (adverb) is wrong — part C.

Why the other options are wrong:
A: 'Do the roses' — plural subject with 'do', correct.
B: 'in your garden smell' — base form after 'do', correct.
D: 'those in ours' — correct pronoun comparison.

Cetking shortcut: Replace the verb with 'are': 'Are the roses sweeter?' makes sense → adjective needed.

Answer: C

Approach: Fixed preposition — 'prejudicial to'.

Solution: The adjective 'prejudicial' (= harmful) takes 'to': 'prejudicial to the interests of his client.' 'Prejudicial against' is incorrect, so the error is in part D.

Why the other options are wrong:
A: 'It is easy to see that' — correct.
B: 'a lawyer's demeanour in court' — correct possessive.
C: 'may be prejudicial' — correct modal + adjective.

Cetking shortcut: Learn the pair list: prejudicial to, detrimental to, averse to, prior to.

Answer: D

Approach: One-word substitution — showing off learning.

Solution: Pedantic = excessively concerned with displaying one's learning or minor rules. A pedantic style is one in which the writer makes a display of his knowledge.

Why the other options are wrong:
B: Verbose — using too many words.
C: Pompous — self-important in manner; not specifically about knowledge.
D: Sarcastic — mocking.
E: Succinct — brief and clear.

Answer: A

Approach: One-word substitution — 'cannot be corrected'.

Solution: Incorrigible (in- = not + corrigible = correctable) = that which cannot be corrected or reformed.

Why the other options are wrong:
A: Unintelligible — cannot be understood.
B: Indelible — cannot be erased.
C: Illegible — cannot be read.
E: Irregular — not following a pattern.

Cetking shortcut: Root 'corrig-' = correct (as in 'corrigendum').

Answer: D

Approach: One-word substitution — insisting on something.

Solution: A stickler is a person who insists firmly on a particular quality or standard ('a stickler for punctuality').

Why the other options are wrong:
A: Disciplinarian — enforces strict discipline on others; narrower.
C: Instantaneous — an adjective meaning immediate.
D: Boaster — one who brags.
E: Literate — able to read and write.

Answer: B

Approach: One-word substitution — direction relative to a centre.

Solution: Centrifugal (centr- + -fugal, from Latin fugere = to flee) = tending to move away from the centre or axis.

Why the other options are wrong:
B: Centripetal (-petal from petere = to seek) — towards the centre.
C: Awry — out of the normal position.
D: Axiomatic — self-evident.
E: Central — at the centre.

Cetking shortcut: fugal = flee (fugitive) → away; petal = seek → towards.

Answer: A

Approach: One-word substitution — pretending to be someone else.

Solution: An impostor (also spelt imposter) is a person who pretends to be somebody he/she is not, in order to deceive.

Why the other options are wrong:
A: Hypocrite — pretends to have virtues or beliefs he lacks, not another identity.
B: Rogue — a dishonest person.
C: Liar — tells untruths, not necessarily posing as someone.
E: Linguist — one skilled in languages.

Answer: D

Approach: Idiom meaning — from the fable 'The Boy Who Cried Wolf'.

Solution: 'To cry wolf' = to raise a false alarm. The shepherd boy kept shouting 'Wolf!' when there was none, so no one believed him when the wolf really came.

Why the other options are wrong:
A: To listen eagerly — 'be all ears'.
C: To turn pale — unrelated.
D: To keep off starvation — 'keep the wolf from the door'.
E: To take a difficult task — unrelated.

Cetking shortcut: Don't confuse 'cry wolf' (false alarm) with 'keep the wolf from the door' (avoid hunger).

Answer: B

Approach: Idiom meaning — knights' custom.

Solution: 'Throw down the gauntlet' = to issue a challenge. A medieval knight threw his gauntlet (armoured glove) on the ground to challenge an opponent; picking it up meant accepting.

Why the other options are wrong:
A: To refer to — unrelated.
C: To raise objections — not a challenge to compete.
D: To be discussed — 'be on the table'.
E: To put someone at ease — opposite in spirit.

Cetking shortcut: Throw down = challenge; take up the gauntlet = accept the challenge.

Answer: B

Approach: Idiom meaning.

Solution: 'A black sheep' = a member of a family or group who is regarded as odd, a disgrace, or disreputable compared with the rest.

Why the other options are wrong:
B: An unlucky person — 'jinx'.
C: An ugly person — literal misreading.
D: A partner taking no profits — 'sleeping partner' is close but different.
E: A worthy fellow — opposite.

Answer: A

Approach: Idiom meaning.

Solution: 'To smell a rat' = to suspect that something is wrong — trickery, deceit or foul dealing.

Why the other options are wrong:
A, B: Literal readings about rats/plague.
D: To be in a bad mood — unrelated.
E: To teach someone a lesson — unrelated.

Cetking shortcut: Literal options in idiom questions are almost always traps.

Answer: C

Approach: Idiom meaning.

Solution: 'To hit the nail (right) on the head' = to say or do exactly the right thing; to describe a situation or cause precisely. Among the options, 'to do the right thing' carries this sense.

Why the other options are wrong:
B: To destroy one's reputation — unrelated.
C: To announce fixed views — 'lay down the law'.
D: To look steadily — 'stare'.
E: To judge by appearance — unrelated.

Answer: A

Approach: Para jumble — pronoun links and time markers.

Solution: S1 introduces the Chairman → Q 'On him rests much of the responsibility…' (him = Chairman). → S 'As the meeting opens, he runs briskly through formalities.' → R 'While this is happening we … get the feel of this committee' (this = the formalities). → P 'For a committee is not just a mere collection of individuals' — explains why it has a 'feel', and leads into S6 'it begins to have a … life of its own'. Order: QSRP.

Why the other options are wrong:
B (QSPR): P cannot precede R — 'While this is happening' needs S directly before it.
C (QRPS): R's 'this' would have nothing to refer to.
D (PQSR), E (RQSP): Q's 'him' must come right after S1's Chairman.

Cetking shortcut: Lock pronoun links: S1→Q (him), S→R (this is happening), P→S6 (it = committee).

Answer: A

Approach: Para jumble — narrative sequence of a ship fire.

Solution: S1: smoke oozes up. → S 'Flames broke out here and there' (smoke turns into visible fire). → R 'Everyone now knew there was fire on board' (the flames make it known). → Q 'The rising gale fanned the smouldering fire' (it spreads, the danger grows). → P 'Passengers were told to be ready to quit the ship' — the order to which S6 'Most people bore the shock bravely' reacts. Order: SRQP.

Why the other options are wrong:
A (QPSR), B (PSRQ): evacuation (P) cannot come before everyone knows about the fire (R).
D (QRSP): R's 'now knew' needs a visible cause — flames (S) — before it.
E (SPQR): the order to quit (P) must lead into S6, so P is last.

Cetking shortcut: Fix the ends first: P must be last (it sets up 'bore the shock'), and 'now knew' (R) needs S before it → S R … P.

Answer: C

Approach: Para jumble — contrast marker and pronoun chain.

Solution: S1: the city is almost a slum and stinks. → S 'Even so, it looked beautiful to tourists' (contrast with S1). → P 'The slush on the road did not deter them' (them = tourists). → Q 'The occasional slips and falls were … a small price to pay' (slips follow from slush). → R 'They were excited, fascinated by the sight of fresh snow' — the upbeat note that S6 contrasts with 'But some visitors came away with … young labourers scantily clad.' Order: SPQR.

Why the other options are wrong:
B (RSPQ): 'They' in R has no referent after S1.
C (QSPR), E (PSQR): 'Even so' (S) must directly answer S1's slum description.
D (SQRP): 'slips and falls' (Q) needs the slush (P) before it.

Cetking shortcut: 'Even so' signals the sentence right after the negative opener → S first; then 'slush → slips'.

Answer: A

Approach: Para jumble — past vs present contrast.

Solution: S1: the heart is the pump of life. → S 'If the heart stops we die in about five minutes' (why it is vital). → R 'A few years ago it was impossible to operate on a patient whose heart was not working' (past). → Q 'Nowadays surgeons are able to stop a patient's heart and operate' (present). → P 'They have even succeeded in heart transplants' (the climax). → S6 'All this was made possible by the heart-lung machine.' Order: SRQP.

Why the other options are wrong:
A (SPRQ): 'They' in P (surgeons) appears before surgeons are mentioned.
C (SQRP): 'Nowadays' (Q) should follow the 'few years ago' (R) contrast, not precede it.
D (PRQS), E (RPQS): S explains S1 and must come first; P cannot open.

Cetking shortcut: Time pair rule: 'a few years ago' → 'nowadays' → 'even' (climax).

Answer: B

Approach: Para jumble — concession ('Yes…') then rebuttal ('But…').

Solution: S1: America has been called a melting pot. → S 'Yes, immigrants … did cast off vestiges of their native lands and become … woven into the American fabric' (the part that is true). → Q 'The term has long been a cliché and half-truth' (only half true). → R 'But homogenisation was never achieved' (the untrue half). → P 'Differences remained — in appearance, mannerisms, customs…' → S6 'such differences … have become something to celebrate.' Order: SQRP.

Why the other options are wrong:
A (QRSP): 'Yes, immigrants did…' (S) cannot come after 'homogenisation was never achieved' (R).
C (PQRS), D (PQSR): 'Differences remained' (P) must come just before S6's 'such differences'.
E (SQPR): R's 'But homogenisation…' must precede P, which illustrates it.

Cetking shortcut: Anchor P before S6 ('differences' → 'such differences'), then R before P.

Answer: B

Approach: Active → passive with a participle phrase.

Solution: Active: 'After driving Professor Kumar to the museum, she dropped him at his hotel.' Make Professor Kumar the subject: the participle 'driving' becomes passive 'being driven', and 'she dropped him' becomes 'Professor Kumar was dropped … by her' (past simple → was + V3). Result: 'After being driven to the museum, Professor Kumar was dropped at his hotel by her.'

Why the other options are wrong:
B: Ungrammatical ('was being driven dropped') and drops the museum.
C, E: Still active voice, with a needless tense change to 'had dropped'.
D: Mixed and wrong ('she was driven Professor Kumar').

Cetking shortcut: In voice change, the options still in active voice (C, E) are out at once.

Answer: A

Approach: Indirect → direct speech — reverse the pronoun and tense shifts.

Solution: Indirect: 'She said that her brother was getting married.' In direct speech the speaker refers to herself: 'her brother' → 'my brother'; the backshifted 'was getting' → 'is getting'; 'said that' → said, "…". Result: She said, "My brother is getting married."

Why the other options are wrong:
A: 'Her brother' — the speaker would say 'my'.
B: 'told' needs an object (told me/him); and 'Her' is wrong.
D: 'was getting' keeps the indirect backshift.
E: 'Our brother' changes the meaning.

Answer: C

Approach: Indirect → direct speech of an exclamation.

Solution: 'Exclaimed with sorrow that was a very miserable plight' → an exclamatory sentence: What a miserable plight it is! 'that was' → 'it is' (tense and demonstrative restored); 'exclaimed with sorrow' becomes the reporting verb 'said', with sorrow carried by the exclamation. Result: She said, "What a miserable plight it is!"

Why the other options are wrong:
A: 'pity' changes the content.
B: 'mystery' changes the content.
C: 'sight' changes 'plight'.
E: 'cried' suggests shouting/weeping — a different reporting verb, not the standard conversion.

Cetking shortcut: In narration questions, first eliminate options that change the content words (pity, mystery, sight).

Answer: D

Approach: Direct → indirect speech of a yes/no question.

Solution: Yes/no question → 'asked if/whether'; 'you' → 'I' (the person addressed is the narrator 'me'); 'are' → 'was'; question order → statement order; the vocative 'my son' is dropped. The reporting detail 'close behind me' is kept. Result: 'A soft voice close behind me asked if I was alone.'

Why the other options are wrong:
A: Adds 'what I was doing there' — changes the question.
B: Still direct-question form, no tense/pronoun change.
C: 'from my back' changes 'close behind me'.
E: 'yelled' contradicts 'soft voice'.

Answer: D

Approach: Direct → indirect statement with an embedded question.

Solution: 'Said to her friend' → 'told her friend'; 'I' → 'she'; 'know' → 'knew'; the embedded clause 'where is everyone' must take statement order and backshift: 'where everyone was'. Result: 'She told her friend that she knew where everyone was.'

Why the other options are wrong:
A: Drops 'her friend' (told needs an object) and keeps question order 'where was everyone'.
C: 'where is everyone' — no backshift, question order.
D: 'knows' not backshifted; 'where was everyone' wrong order.
E: 'asked' — the original is a statement, not a question.

Cetking shortcut: Embedded questions never keep question word order: 'where everyone was'.

Answer: B

Approach: Subject–verb agreement with a collective noun.

Solution: 'The committee' acts as one unit making a single decision, so it takes a singular verb: 'The committee has decided to postpone the annual meeting due to unavoidable circumstances.' The error is in part (B) 'have decided'.

Why the other options are wrong:
A: 'The committee' — correct subject.
C: 'to postpone' — correct infinitive.
D: 'the annual meeting' — correct.
E: the final part is correct (here E also stands for 'no error', which is ruled out).

Cetking shortcut: Collective noun acting as one body → singular verb; members acting separately → plural.

Answer: B

Approach: Direction tracking with coordinates (left of South = East, left of East = North).

Solution:
Start at O(0, 0).
25 m South → (0, −25).
Facing South, left turn = East; 20 m → (20, −25).
Facing East, left turn = North; 25 m → (20, 0).
Facing North, right turn = East; 15 m → (35, 0).
Final point is on the same horizontal line as O, 20 + 15 = 35 m away, towards East.

Why the other options are wrong:
B, E: he ends exactly back on the start's East–West line (the 25 m South and 25 m North cancel), so no North-East component.
C, D: 40 / 60 m add distances wrongly; only the East moves (20 + 15) count.

Cetking shortcut: The two 25 m legs (South and North) cancel; just add the East legs 20 + 15 = 35 m East.

Answer: A

Approach: Decode the relation from the speaker outwards, one link at a time.

Solution:
'Husband of my mother' = Aradhya's father.
'Mother-in-law of Aradhya's father' = mother of his wife.
His wife is Aradhya's mother, so the lady is the mother of Aradhya's mother.
Mother's mother = Maternal Grandmother.

Why the other options are wrong:
A: Paternal grandmother is the father's mother, not his mother-in-law.
B, D, E: Aunt, sister and grand-daughter are not two generations above via the mother.

Cetking shortcut: 'Mother-in-law of my father' is always 'my mother's mother'.

Answer: C

Approach: Collective-noun analogy (animal : name of its group).

Solution:
A group of fish is called a 'school'.
Applying the same relation, a group of birds is called a 'flock'.
So Fish : School :: Bird : Flock.

Why the other options are wrong:
A: Nest is a bird's home, not its group.
C, D: Water and Sky are the habitats/mediums of fish and birds.
E: Feather is a body part.

Answer: B

Approach: Classification — find the item whose category differs (endocrine glands vs brain part).

Solution:
Pituitary, Pancreas, Adrenal and Testis are endocrine glands — they secrete hormones into the blood.
Thalamus is a part of the brain (forebrain) that relays sensory signals; it is not a gland.
So Thalamus is the odd one out.

Why the other options are wrong:
A, B, D, E: all four are hormone-secreting glands, so they form the group.

Cetking shortcut: Hypothalamus is endocrine-related, but Thalamus is purely a brain relay centre — don't confuse the two.

Answer: C

Approach: Blood relation — identify the common person and place both sides around him.

Solution:
'The only son of my mother's father' = Ben's mother's only brother = Ben's maternal uncle (call him U).
Ben says the girl's mother's brother is U, so the girl's mother is a sister of U.
U's sisters are Ben's mother and Ben's mother's sisters.
Ben speaks of 'her mother' as a separate person from his own mother, so the standard reading is that she is another sister of U, i.e. Ben's mother's sister.
Mother's sister = Ben's Aunt.

Why the other options are wrong:
A: this would make the girl Ben's own sister, but the question treats the girl's mother as a different person from Ben's mother.
B, E: the girl's mother is one generation above Ben, so she cannot be his sister or brother.
D: grandmother is two generations above.

Cetking shortcut: Same maternal uncle for both ⇒ the two mothers are sisters ⇒ the girl's mother is Ben's (maternal) aunt.

Answer: C

Approach: Facing-direction tracking (right of South = West, left of West = South).

Solution:
Walks South → facing South.
Turns right: right of South is West; walks 3 km facing West.
Turns left: left of West is South; walks 5 km.
He is now facing South.

Why the other options are wrong:
A: West was the direction of the middle leg only.
C, D: no diagonal movement is involved.
E: East would need a right turn from South twice.

Cetking shortcut: A right turn followed by a left turn cancels out — he faces his original direction, South.

Answer: B

Approach: Venn diagram classification — check which pairs overlap and which are disjoint.

Solution:
Passengers and Airplane: some passengers travel by airplane → overlap.
Passengers and Taxi: some passengers travel by taxi → overlap.
Airplane and Taxi: two different vehicles, no common member → disjoint.
So Passengers is a middle circle overlapping both, while the end circles do not touch: three circles in a chain.
Figure D shows exactly this.

Why the other options are wrong:
A: three separate circles — ignores the passenger overlaps.
B: three mutually overlapping circles — would need something that is both airplane and taxi.
C: concentric circles — would mean one class wholly contains another.
E: two disjoint sets inside one big set — would mean all airplanes and taxis are passengers.

Cetking shortcut: Two unrelated items + one item linked to both = chain diagram.

Answer: D

Approach: Letter coding — vowels become a number, consonants shift +1.

Solution:
Decode REQUEST → S2R52TU letter by letter:
R → S (+1), E → 2, Q → R (+1), U → 5, E → 2, S → T (+1), T → U (+1).
Vowels are numbered A=1, E=2, I=3, O=4, U=5; consonants move to the next letter.
ACID: A → 1, C → D, I → 3, D → E.
Code = 1D3E.

Why the other options are wrong:
A: 1394 codes C and D by alphabet rank instead of shifting them.
B: IC94 follows no consistent rule.
D: B3J4 shifts the vowels and ranks the consonants — the reverse of the rule.
C: shifts every letter by +1, ignoring the vowel-number rule.

Cetking shortcut: Vowels become 1-5 and every consonant moves up one letter: C→D, D→E, so only E (1D3E) fits.

Answer: E

Approach: Split-half letter shift coding.

Solution:
TERMINAL = TERM | INAL; code SDQL | JOBM.
First half: T→S, E→D, R→Q, M→L (each −1).
Second half: I→J, N→O, A→B, L→M (each +1).
CREDIBLE = CRED | IBLE.
CRED −1 → BQDC; IBLE +1 → JCMF.
Code = BQDCJCMF.

Why the other options are wrong:
B: second half shifted −1 (HAKD) instead of +1.
C: first half shifted +1 instead of −1.
D: both halves shifted the wrong way.
E: halves swapped and shifted wrongly.

Cetking shortcut: Check just the first and fifth letters: C−1 = B and I+1 = J → only A starts 'B…J'.

Answer: A

Approach: Alphanumeric series — letter jumps +2 and the number is the letter's alphabet position.

Solution:
Letters: D, F, H, J → +2 each → L, N.
Numbers: 4, 6, 8, 10 = positions of D, F, H, J.
L = 12, N = 14.
Next two terms: L-12, N-14.

Why the other options are wrong:
A, D: K is +1 from J, not +2; also M-13 breaks the position rule.
B: M is only +1 from L.
E: B-12 — B is not the 12th letter.

Cetking shortcut: The number always equals the letter's rank — only C keeps both letters and numbers consistent.

Answer: C

Approach: Rotated direction pole — find the rotation, then apply it to the pointer followed.

Solution:
The West pointer now points South. Going from West to South is a 90° anticlockwise turn.
So every pointer has turned 90° anticlockwise: North→West, East→North, South→East, West→South.
Harish follows the pointer marked 'East'.
That pointer now actually points North, so he is travelling North.

Why the other options are wrong:
A: South is where the West pointer points, not the East pointer.
C: West is where the North pointer now points.
D: East would mean the pole had not turned.
E: a 90° turn cannot produce a diagonal direction.

Cetking shortcut: Opposite pointers stay opposite: West→South means East→North.

Answer: B

Approach: Venn diagram region reading — inside the required shapes, outside the excluded one.

Solution:
Men educated and employed but not married = inside Triangle AND Rectangle AND Circle, but outside Square.
Regions in Triangle + Rectangle + Circle: 5 and 9.
Region 9 is also inside the Square (married); region 5 lies above the square's top edge.
So the required region is 5.

Why the other options are wrong:
A: 3 is triangle + rectangle only — not employed.
B: 9 is in all four shapes — married.
D: 8 is triangle + rectangle + square — married and not employed.
E: 11 is circle + square only — neither male nor educated.

Cetking shortcut: List the regions common to the three 'yes' shapes first (5, 9), then strike the one inside the 'no' shape.

Answer: C

Approach: Number series with ×2 + 2 rule (differences doubling).

Solution:
10 × 2 + 2 = 22
22 × 2 + 2 = 46
46 × 2 + 2 = 94
94 × 2 + 2 = 190
Check: differences 12, 24, 48 double → next 96; 94 + 96 = 190.

Cetking shortcut: Differences 12, 24, 48 double each time — add 96.

Answer: C

Approach: Time comparison in a race — certain event has probability 1.

Solution:
A runs the full 400 m: time = 400 ÷ 10 = 40 s.
B starts 50 m ahead, so runs 350 m: time = 350 ÷ 8 = 43.75 s.
A always finishes 3.75 s earlier — no chance involved.
An event that is certain has probability 1.

Why the other options are wrong:
A: 0 would mean A can never win.
C, D, E: fractional values imply uncertainty, but the speeds fix the result.

Cetking shortcut: Head start 50 m at 8 m/s is worth 6.25 s, but A already gains 10 s over 400 m (50 vs 40 s) — A wins for sure.

Answer: B

Approach: Number-pair classification — each pair is (n, n²).

Solution:
15² = 225 ✓, 13² = 169 ✓, 14² = 196 ✓, 12² = 144 ✓.
19² = 361, but the pair shows 227 ✗.
So (19, 227) is the odd pair.

Cetking shortcut: Unit digit check: 19² must end in 1 — 227 ends in 7.

Answer: C

Approach: Ranking by chaining 'before/behind' clues.

Solution:
Raj finished before Mohit but behind Gaurav: Gaurav > Raj > Mohit.
Ashish finished before Sanchet but behind Mohit: Mohit > Ashish > Sanchet.
Join at Mohit: Gaurav > Raj > Mohit > Ashish > Sanchet.
Gaurav finished first.

Why the other options are wrong:
A: Raj is behind Gaurav.
C, D, E: Mohit, Ashish, Sanchet are all behind Raj.

Cetking shortcut: The winner is the one never said to be 'behind' anyone — Gaurav.

Answer: B

Approach: Rank arithmetic with a boys–girls split.

Solution:
Girls = 2 × Boys and total 60 → Boys = 20, Girls = 40.
Ashwini is 27th from top → 26 students ahead of her.
Boys ahead = 9 → Girls ahead = 26 − 9 = 17.
Ashwini is a girl, so girls up to and including her = 17 + 1 = 18.
Girls after her = 40 − 18 = 22.

Why the other options are wrong:
A: 23 forgets to exclude Ashwini herself.
B, D: arithmetic slips around 22.
E: 27 is her rank, not a count of girls.

Cetking shortcut: Girls after = Total girls − girls ahead − 1 (herself) = 40 − 17 − 1.

Answer: C

Approach: Syllogism — 'No' + 'Some' statements; check only definite conclusions.

Solution:
No women teacher can play: the women-teacher circle is separate from 'players'.
Some women teachers are athletes: athlete circle overlaps women teachers.
Those athletes who are women teachers cannot play; about other athletes nothing is known.
I. 'Male athletes can play' — males are never mentioned → does not follow.
II. 'Some athletes can play' — only a possibility, not certain → does not follow.

Why the other options are wrong:
A, E: I introduces a new term (male athletes).
B, E: II is possible but not definite.
C: I and II are not a complementary pair, so 'either-or' cannot apply.

Cetking shortcut: From 'Some A are B' + 'No A is C' the valid conclusion is 'Some B are not C' — here 'Some athletes cannot play', which is neither option.

Answer: D

Approach: Syllogism — 'All' + 'No' gives a definite 'No'.

Solution:
All mangoes are golden; no golden thing is cheap.
Mangoes sit fully inside 'golden', which has no overlap with 'cheap' → no mango is cheap.
I. All mangoes are cheap — contradicts the result → does not follow.
II. Golden-coloured mangoes are not cheap — every mango is golden and not cheap → follows.

Why the other options are wrong:
A, E: I is directly contradicted.
C: 'either-or' needs one of the two always true while neither is certain; here II is certain.
D: II does follow.

Cetking shortcut: All A are B + No B is C ⇒ No A is C — a standard valid form.

Answer: B

Approach: Input–output word sorting — fix one word per step, left to right.

Solution:
Rule from the illustration: longer (5-letter) words come first in alphabetical order, then the shorter words in alphabetical order; words are placed one by one from the left.
Target for the new input: cough, fight, sough (5 letters, a→z) then acts, cats, idea, more (4 letters, a→z).
Input: more fight cats cough sough acts idea
Step I: cough more fight cats sough acts idea
Step II: cough fight more cats sough acts idea
Step III: cough fight sough more cats acts idea
Step IV: cough fight sough acts more cats idea
Step V: cough fight sough acts cats more idea
Step VI: cough fight sough acts cats idea more — final arrangement.
No word is already in its final place, so all six placements are needed.

Why the other options are wrong:
A, B, C: stopping at III, IV or V leaves the 4-letter words unsorted.
E: VII would mean placing the last word too, but it falls into place automatically.

Cetking shortcut: Count how many of the first (n − 1) positions hold the wrong word in the input — here all 6 → 6 steps.

Answer: D

Approach: Linear arrangement — build the row from the 'left of / right of' clues.

Solution:
D is left of C and A is right of C → D … C … A.
B is left of D → B … D … C … A.
B is right of E → E … B … D … C … A.
Five people, five seats: E B D C A, with E at a corner as given.
Middle (3rd) seat = D.

Why the other options are wrong:
A, E: A and E are at the two ends.
B, C: B and C are 2nd and 4th.

Cetking shortcut: E at one end and the chain E-B-D-C-A uses all five — the 3rd letter is the answer.

Answer: D

Approach: Linear arrangement of 8 houses — fix the Paul–Mike–Harry–Larry block, then place the rest.

Solution:
Paul is in house 4 or 5; Mike is between Paul and Larry; Harry is immediately left of Larry, and someone lives to Larry's left.
'Harry is not between Taud and Larry' means Taud is not on Harry's left, so Taud is to the right of Larry.
Take Paul = 4, Mike = 5, Harry = 6, Larry = 7, Taud = 8.
Robert must have someone on his right, and Jack is not Simon's neighbour, so houses 1–3 hold Simon, Robert, Jack with Robert in the middle (house 2).
Row: Simon, Robert, Jack, Paul, Mike, Harry, Larry, Taud.
Statement C says Taud lies between Paul and Jack. Taud is at the far right end, beyond Larry, while Jack is on Paul's left, so Taud is not between them — this statement is not correct.

Why the other options are wrong:
A: Robert is in house 2, not at the left end — correct statement.
B: Robert lies between Simon and Taud — correct statement in this arrangement.
D, E: they only describe who stands to the right of Paul; the statement that fails because of Taud's forced position is C, which is the official answer.

Cetking shortcut: Turn 'Harry is not between Taud and Larry' into 'Taud is right of Larry' at once — it pushes Taud to the far end, away from Paul and Jack.

Answer: C

Approach: Row counting — positions from both ends.

Solution:
Total books = 64.
Western Music is 25th from left; Classical Music is 30th from right.
25 + 30 = 55 < 64, so the two books do not overlap and the gap lies between them.
Books between = 64 − 55 = 9.

Cetking shortcut: Between = Total − (left rank + right rank) when the sum is less than the total.

Answer: D

Approach: Match the diagram: one class inside another + one completely separate class.

Solution:
Diagram: a small circle wholly inside a bigger circle, and a third circle outside both.
A: every Thief is a Criminal (Thief inside Criminal); a Judge is neither, so Judge is separate. ✓
So Judge, Thief, Criminal fits the diagram.

Why the other options are wrong:
B: Father and Mother are two separate classes both inside Parents.
C: Teacher, College, Students are different kinds of things with no subset pattern matching.
D: Squares ⊂ Rectangles ⊂ Polygons — three nested circles, no separate one.
E: Birds ⊂ Animals ⊂ Living Things — again three nested circles.

Cetking shortcut: Look for exactly one subset pair plus one unrelated item — only A has an outsider.

Answer: A

Approach: Syllogism with four conclusions — accept only definite ones.

Solution:
Cups ⊂ Glasses; Glasses overlap Bowls; Bowls and Plates are disjoint.
I. No cup is a plate — cups and plates are never linked; a cup may or may not be a plate → does not follow.
II. No glass is a plate — glasses that are not bowls may be plates → does not follow.
III. Some plates are bowls — contradicts 'No bowl is a plate' → false.
IV. Some cups are not glasses — contradicts 'All cups are glasses' → false.
None of the conclusions follows.

Why the other options are wrong:
A: I and III are not complementary (III is outright false), so 'either-or' fails.
B, C, D: each includes a conclusion that is only possible or plainly false.

Cetking shortcut: 'No' links only the two terms named; it cannot be extended through a 'Some' link to cups or glasses.

Answer: E

Approach: Assertion–Reason — test each statement's truth first.

Solution:
A: Bangladesh is the world's largest exporter of raw jute; India imports raw jute from Bangladesh, not the other way round → A is false.
R: At Partition (1947) the jute-growing areas went to East Bengal (now Bangladesh) while most jute mills stayed in West Bengal (India) → R is false.
Both A and R are false.

Why the other options are wrong:
A, B, C: each needs A to be true.
E: needs R to be true, but the mills were largely in India.

Cetking shortcut: Remember the Partition fact: Bangladesh got the jute fields, India got the mills — so India buys jute from Bangladesh.

Answer: D

Approach: Assertion–Reason — check truth, then whether R explains A.

Solution:
A: Plastic harms animals and the environment — true.
R: Many animals eat plastic, mistaking it for food or swallowing it accidentally — true.
Ingestion causes choking, gut blockage and poisoning, which is a direct way plastic harms animals → R explains A.

Why the other options are wrong:
B: R is not unrelated — it gives the mechanism of the harm.
C, D, E: both statements are true.

Cetking shortcut: Ask 'A happens because R?' — 'Plastic harms animals because animals eat it' reads naturally → A.

Answer: A

Approach: Letter series — alternate terms move +2; each even term is the reverse of the term before it.

Solution:
Odd terms: FAG → HAI → ?: outer letters +2 each (F→H, G→I), A stays.
Even terms: GAF = FAG reversed, IAH = HAI reversed.
The 5th term is the next odd term: H+2 = J, A, I+2 = K → JAK.

Why the other options are wrong:
A, B: HAK / HAL keep H as first letter — no +2 move.
D: JAI moves only the first letter.
E: KAH does not follow either pattern.

Cetking shortcut: Pairs (FAG, GAF), (HAI, IAH): new word then its mirror — the 5th term starts a new pair: JAK.

Answer: C

Approach: Alphanumeric analogy — letter rank shift and number shift.

Solution:
P21 → J28: P (16) → J (10) is −6; 21 → 28 is +7.
Apply to G19: G (7) − 6 = 1 → A.
19 + 7 = 26.
So G19 : A26.

Why the other options are wrong:
A: T17 — T is +13 and 17 is −2.
B: C16 — C is −4 and 16 is −3.
D: O19 — number unchanged.
E: K11 — K is +4 and 11 is −8.

Cetking shortcut: Fix the number part first: only A26 has 19 + 7 = 26.

Answer: C

Approach: Number classification — divisibility by 11.

Solution:
253 = 11 × 23 ✓
473 = 11 × 43 ✓
143 = 11 × 13 ✓
847 = 11 × 77 ✓
633: alternating sum 6 − 3 + 3 = 6, not 0 or 11 → not divisible by 11 ✗
633 is the odd one.

Cetking shortcut: For a 3-digit number abc, it is a multiple of 11 when a + c = b (or a + c = b + 11): 2+3=5, 4+3=7, 1+3=4, 8+7=15=4+11; 6+3=9 ≠ 3.

Answer: D

Approach: Coded blood relations — decode each option, looking for 'M is father of C' and 'C is male'.

Solution:
Need: M is the father (or mother) of C, and C is male.
D: M x N → M is father of N.
N – C → N is sister of C, so C is also M's child.
C + F → C is brother of F, so C is male.
Hence C is the son of M.

Why the other options are wrong:
A: M – N x C → M is sister of N, who is C's father → M is C's aunt.
B: N x M → N is father of M; C is N's brother → C is M's uncle.
C: F x C → F is C's father; M is F's sister → M is C's aunt.
E: F–N+C does not mention M at all.

Cetking shortcut: Start from options where M is followed by 'x' (father) — only D begins 'M x'.

Answer: D

Approach: Assertion–Reason — check truth of each statement.

Solution:
A: Business finance (raising and using funds) is essential to achieve business objectives — true.
R: Financial decisions (investment, financing, dividend) directly decide growth and expansion; saying they have 'no impact' is false.
So A is true, R is false.

Why the other options are wrong:
A, B: need R to be true.
D: A is clearly true.
E: A is true and R is false, the reverse.

Cetking shortcut: Absolute words like 'no impact' in R usually signal a false statement.

Answer: C

Approach: Letter series — position-wise patterns in 5-letter groups.

Solution:
Position 1: A, D, G, J → +3 → M
Position 2: Y, W, U, S → −2 → Q
Position 3: B, E, H, K → +3 → N
Position 4: Z, X, V, T → −2 → R
Position 5: C, F, I, L → +3 → O
Next group: MQNRO.

Why the other options are wrong:
A: MQORN swaps the 3rd and 5th letters.
C, D, E: wrong first letter (must be M = J + 3).

Cetking shortcut: Positions 1, 3, 5 just run through the alphabet (ABC, DEF, GHI, JKL → MNO); slot Q and R into positions 2 and 4.

Answer: B

Approach: Alphanumeric series — letters step back by 1, numbers rise by 10.

Solution:
Letters: Z, Y, X, W → −1 each → V.
Numbers: 10, 20, 30, 40 → +10 → 50.
Next term: V50.

Why the other options are wrong:
A, D, E: U and T skip letters.
B: 60 skips a step of 10.

Answer: C

Approach: Calendar — count odd days between two dates of the same month.

Solution:
Rohit's birthday: 1 May = Sunday.
Shekhar's birthday: 20 May → 20 − 1 = 19 days later.
19 ÷ 7 = 2 weeks + 5 odd days.
Sunday + 5 days = Friday (Mon 1, Tue 2, Wed 3, Thu 4, Fri 5).

Why the other options are wrong:
B: Tuesday is Sunday + 2 — a counting slip.
A, C, D: Sunday + 1, 3 or 4.

Cetking shortcut: Same weekday repeats every 7 days: 1, 8, 15 May are Sundays → 15 + 5 = 20 is Friday.

Answer: E

Approach: Row ranking — get one person's rank from both ends, then total = left + right − 1.

Solution:
Aman is 16th from left; Gagan is 11th to the right of Aman → Gagan is 16 + 11 = 27th from left.
Vivek is 18th from right; Gagan is 3rd from Vivek towards the right end → Gagan is 18 − 3 = 15th from right.
Total boys = 27 + 15 − 1 = 41.

Why the other options are wrong:
A, B: off by one — forgetting or double-subtracting Gagan.
C, E: adding ranks of different people.

Cetking shortcut: Convert everything to the common person (Gagan), then Total = L + R − 1.

Answer: D

Approach: Date range intersection.

Solution:
Charu: after 24, before 29 → 25, 26, 27, 28.
Sister: after 27, before 31 → 28, 29, 30.
Common dates: 28 only.
Brother: even date — 28 is even ✓.
Birthday = 28 May.

Why the other options are wrong:
A: 30 is outside Charu's range.
C, E: 26 and 24 are outside the sister's range (24 is outside Charu's too).
D: 29 is excluded by Charu and is odd.

Cetking shortcut: 'After 24' and 'before 29' are exclusive limits — list only the dates strictly between.

Answer: B

Approach: Symbol substitution, then BODMAS.

Solution:
Replace: + → ÷, − → ×, × → +, ÷ → −.
45 + 9 − 3 × 15 ÷ 2 becomes 45 ÷ 9 × 3 + 15 − 2.
45 ÷ 9 = 5; 5 × 3 = 15.
15 + 15 − 2 = 28.

Cetking shortcut: Rewrite the whole expression first, then solve — never substitute and compute at the same time.

Answer: B

Approach: Letter-to-operator substitution, then BODMAS.

Solution:
K = −, L = ÷, M = +, D = ×.
117 L 3 K 5 M 12 D 8 = 117 ÷ 3 − 5 + 12 × 8.
117 ÷ 3 = 39; 12 × 8 = 96.
39 − 5 + 96 = 130.

Cetking shortcut: Division and multiplication first: 39 and 96, then 39 + 96 − 5.

Answer: B

Approach: Logical sequence — arrange by increasing size.

Solution:
Sizes: Mosquito (3) < Cat (2) < Tiger (4) < Elephant (1) < Whale (5).
Sequence: 3, 2, 4, 1, 5.

Why the other options are wrong:
A: puts Whale before Elephant and Tiger last.
B, D, E: start from a larger animal and break the size order.

Cetking shortcut: Smallest (mosquito) first and largest (whale) last — only C starts with 3 and ends with 5.

Answer: C

Approach: Logical sequence — order of human technological ages.

Solution:
Stone Age came first (3).
Then the Metallic Age — copper/bronze/iron (2).
Then the Alloy Age — mixed metals like steel (4).
Finally the modern Atomic Age (1).
Sequence: 3, 2, 4, 1.

Why the other options are wrong:
A, D: the same sequence (4,3,2,1); it starts with Alloy Age.
B: starts with Metallic Age, before Stone Age.
E: puts Atomic Age before Alloy Age.

Cetking shortcut: Stone Age must come first and Atomic Age last — only C does both.

Answer: C

Approach: Age equations with two sons.

Solution:
Let father = F, elder son = E, younger son = Y.
F = 2E → E = F/2.
E − Y = 15 → Y = F/2 − 15.
Ten years hence: F + 10 = 3(Y + 10) = 3(F/2 − 5) = 1.5F − 15.
0.5F = 25 → F = 50.
Check: E = 25, Y = 10; after 10 years 60 = 3 × 20 ✓.

Cetking shortcut: Test options: F must be even; F = 50 → Y = 10 → 60 = 3 × 20 ✓ in one line.

Answer: A

Approach: Group counting — add every group containing the language.

Solution:
Stated groups: 10 + 5 + 10 + 12 + 13 + 5 = 55.
Remaining (Bengali and Hindi) = 60 − 55 = 5.
Bengali speakers = only Bengali 10 + Bengali & Hindi 5 = 15.
Marathi speakers = Marathi & Hindi 12 + English, Tamil & Marathi 13 = 25.
Ratio = 15 : 25 = 3/5.

Why the other options are wrong:
A: 15/32 adds the wrong groups to Marathi.
B, C: wrong group totals.
E: 5/3 is the ratio inverted.

Cetking shortcut: Find the 'remaining' group first — it is the only missing number.

Answer: D

Approach: Equal sharing — fixed total, fewer people, higher share.

Solution:
Let the planned number be x; share = 96/x.
4 dropped out → share = 96/(x − 4).
96/(x − 4) − 96/x = 4 → 96 × 4 = 4x(x − 4) → x² − 4x − 96 = 0.
(x − 12)(x + 8) = 0 → x = 12.
People who turned up = 12 − 4 = 8. Check: 96/8 = 12, 96/12 = 8, extra 4 ✓.