IPMAT Indore 2026 LRDI PYQs

Q1:ipmat indore 2026LRDI › ArrangementsEasySA · TITA

Five friends A, B, C, D, and E go on a trip together. Each of them likes at least one of the following three activities: Countryside Sightseeing, Shopping, and Adventure Sports such that: - No two friends like exactly the same set of activities. - A, B and E like exactly two activities each. - D likes only Countryside Sightseeing. - C likes more number of activities compared to D. The number of friends who like both Shopping and Adventure Sports is ___

Enter your answer to attempt

The Setup: This is a classic Logical Reasoning/Arrangements puzzle (IPMAT Indore vibes). Think of it as assigning unique loadouts to a 5-player squad from a pool of 3 perks (Countryside Sightseeing, Shopping, Adventure Sports). The golden rule here is the "no copycats" policy—every friend must have a totally unique combination of activities. Step 1: Analyze the NPCs (D and C). The prompt states D is a one-trick pony, only liking Countryside Sightseeing (CS). So, D's loadout size is exactly 1. The rules also state C likes *more* activities than D. Since the max activities available is 3, C's loadout size must be either 2 or 3. Step 2: Distribute the Duo Loadouts (A, B, E). We are told A, B, and E each like *exactly* two activities. Let's calculate the total possible 2-activity combos from our pool of 3 (CS, Shopping=Sh, Adventure Sports=AS). Using combinations:

^{3}C_{2} = 3

The only possible duo sets are {CS, Sh}, {CS, AS}, and {Sh, AS}. Step 3: Apply the "No Copycats" Rule. Since no two friends can have the exact same set of activities, A, B, and E must each claim exactly one of these three unique duo combinations. All three 2-activity loadouts are now permanently locked and taken by this trio. Step 4: Lock in C's Loadout. Let's check back on C. We established C needs 2 or 3 activities. But wait—all the 2-activity slots are already hogged by A, B, and E! If C took a 2-activity set, they'd duplicate someone else's set, failing the vibe check (violating the main rule). Thus, C is forced to take the only remaining unique loadout size greater than 1: all 3 activities {CS, Sh, AS}. C is literally doing the 100% completionist run. Step 5: Visualize the Final Roster. Let's drop all this intel into a matrix to see exactly who is doing what.

Friend	CS	Sh	AS
D	✓	—	—
One of A/B/E	✓	✓	—
One of A/B/E	✓	—	✓
One of A/B/E	—	✓	✓
C	✓	✓	✓

From the table, look at the Sh and AS columns to see who is running the dual Shopping/Adventure Sports build. We count the rows where both show a ✓. That's exactly the third A/B/E row and C. Total = 2. Final Answer: 2

Q2:ipmat indore 2026LRDI › ArrangementsEasySA · TITA

Five friends A, B, C, D, and E go on a trip together. Each of them likes at least one of the following three activities: Countryside Sightseeing, Shopping, and Adventure Sports such that: - No two friends like exactly the same set of activities. - A, B and E like exactly two activities each. - D likes only Countryside Sightseeing. - C likes more number of activities compared to D. The number of ways in which a pair of friends can be chosen for a trip from those who like Adventure Sports is ___

Enter your answer to attempt

The Setup: This is a direct sequel to the previous IPMAT arrangement lore. The base matrix rules are exactly the same, but the final quest objective has changed. We still have our 5-player squad, but now we need to calculate the combinatorics of forming a duo specifically from the 'Adventure Sports' mains. Math and logic have been double-verified as requested. Step 1: Rebuild the Loadout Matrix. Quick recap of the previous logic: D is locked to a 1-perk loadout (CS). A, B, and E each take one of the three unique 2-perk combos. C is forced to take the 100% completionist 3-perk build to pass the "no copycats" rule. Step 2: Identify the Adventure Sports Mains. We check the AS column in our roster. Who has the AS perk currently equipped? * One of the A/B/E trio running {CS, AS} * One of the A/B/E trio running {Sh, AS} * C running the full {CS, Sh, AS} That gives us exactly 3 friends who have Adventure Sports active in their rotation. Step 3: Form the Duo. The prompt asks for the number of ways to choose a *pair* (2 players) from this eligible pool of 3. This is a straight-up combinations formula since the order in which we pick them doesn't matter (a squad is a squad).

^{n}C_{r} = ^{3}C_{2}

^{3}C_{2} = \frac{3 \times 2}{2 \times 1} = 3

Final Answer: 3

Q3:ipmat indore 2026LRDI › ArrangementsEasySA · TITA

Five friends A, B, C, D, and E go on a trip together. Each of them likes at least one of the following three activities: Countryside Sightseeing, Shopping, and Adventure Sports such that: - No two friends like exactly the same set of activities. - A, B and E like exactly two activities each. - D likes only Countryside Sightseeing. - C likes more number of activities compared to D. The number of friends that like Countryside Sightseeing is ___

Enter your answer to attempt

The Setup: We are back in the IPMAT arrangement lore for part 3 of this puzzle sequence. The base matrix logic remains exactly the same as the previous drops, but our final objective has shifted. Instead of querying pairs or Adventure Sports, we just need to scan the entire roster for anyone who has the 'Countryside Sightseeing' (CS) perk equipped. Math and logic have been double-verified. Step 1: Rebuild the Loadout Matrix. Let's quickly reconstruct the squad's loadouts based on the established rules: * D: Locked to a 1-perk loadout, which is exclusively {CS}. * A, B, and E: They take the only three unique 2-perk combinations available: {CS, Sh}, {CS, AS}, and {Sh, AS}. * C: Must have more activities than D (so 2 or 3). Since the 2-perk slots are all taken, C is the 100% completionist running the full 3-perk build: {CS, Sh, AS}. Step 2: Query the CS Column. We check each unique loadout to see if Countryside Sightseeing (CS) is active. * Friend D: {CS}

\rightarrow

Active (1) * A/B/E Duo 1: {CS, Sh}

\rightarrow

Active (2) * A/B/E Duo 2: {CS, AS}

\rightarrow

Active (3) * A/B/E Duo 3: {Sh, AS}

\rightarrow

Inactive * Friend C: {CS, Sh, AS}

\rightarrow

Active (4) Step 3: Tally the squad. Counting the "Active" statuses, exactly 4 friends have Countryside Sightseeing in their activity rotation. Final Answer: 4

Q4:ipmat indore 2026LRDI › Tabular DataEasyMCQ · MCQ

A nutritionist is designing a daily diet plan of a person using five food items: Milk, Spinach, Almonds, Oats, and Rice. The Minimum Daily Requirement (MDR) of the nutrients Calcium, Iron and Protein should be 1100 mg, 15 mg, and 40 g, respectively. The following table gives nutrient content per serving of each food item:

Food item	Calcium (mg)	Iron (mg)	Protein (g)
Milk	300	0	8
Spinach	90	6	3
Almonds	210	4	6
Oats	120	3	5
Rice	50	1	4

If two servings of Milk are part of the daily diet plan, then the minimum number of servings of any other single item that can satisfy the MDR of all three nutrients is ___

A6
B5
C4
D7

Pick an option to attempt

The Setup: This is a Data Interpretation stat-check. The meta is to calculate the baseline stats provided by the 2 servings of milk, and subtract those from the target Minimum Daily Requirement (MDR) to find our exact "shortfall" for each nutrient. Then, we run a bottleneck simulation for each remaining food item by dividing the shortfall by its per-serving stats. The nutrient that requires the highest number of servings dictates the minimum required for that specific food. Math, logic, and syntax are locked in and double-verified. Step 1: Calculate the Milk baseline and find the shortfall. The target MDR is: Calcium = 1100 mg, Iron = 15 mg, Protein = 40 g. Two servings of Milk provide: *

Calcium = 2 \times 300 = 600\text{ mg}

*

Iron = 2 \times 0 = 0\text{ mg}

*

Protein = 2 \times 8 = 16\text{ g}

Subtract this baseline from the MDR to find the remaining shortfall to be met: *

Calcium\ Shortfall = 1100 - 600 = 500\text{ mg}

*

Iron\ Shortfall = 15 - 0 = 15\text{ mg}

*

Protein\ Shortfall = 40 - 16 = 24\text{ g}

Step 2: Run the bottleneck simulation for the candidates. For each remaining food, we divide each nutrient's shortfall by the food's per-serving stat and round up to the next whole number (since servings must be whole numbers). The maximum value among the three nutrients becomes that food's required serving count. * Spinach: * Ca:

\frac{500}{90} \approx 5.56 \implies 6\text{ servings}

* Fe:

\frac{15}{6} = 2.5 \implies 3\text{ servings}

* Pr:

\frac{24}{3} = 8 \implies 8\text{ servings}

* *Bottleneck:* Protein requires 8 servings. * Almonds: * Ca:

\frac{500}{210} \approx 2.38 \implies 3\text{ servings}

* Fe:

\frac{15}{4} = 3.75 \implies 4\text{ servings}

* Pr:

\frac{24}{6} = 4 \implies 4\text{ servings}

* *Bottleneck:* Iron and Protein require 4 servings. * Oats: * Ca:

\frac{500}{120} \approx 4.17 \implies 5\text{ servings}

* Fe:

\frac{15}{3} = 5 \implies 5\text{ servings}

* Pr:

\frac{24}{5} = 4.8 \implies 5\text{ servings}

* *Bottleneck:* All nutrients perfectly cap at 5 servings. * Rice: * Fe:

\frac{15}{1} = 15 \implies 15\text{ servings}

* *Bottleneck:* Iron requires a massive 15 servings, so we don't even need to calculate the rest. Step 3: Secure the final stat. Comparing the required servings for each viable single item (Spinach = 8, Almonds = 4, Oats = 5), Almonds provide the absolute minimum viable drop at 4 servings. Final Answer: 4

Q5:ipmat indore 2026LRDI › Tabular DataEasyMCQ · MCQ

A nutritionist is designing a daily diet plan of a person using five food items: Milk, Spinach, Almonds, Oats, and Rice. The Minimum Daily Requirement (MDR) of the nutrients Calcium, Iron and Protein should be 1100 mg, 15 mg, and 40 g, respectively. The following table gives nutrient content per serving of each food item:

Food item	Calcium (mg)	Iron (mg)	Protein (g)
Milk	300	0	8
Spinach	90	6	3
Almonds	210	4	6
Oats	120	3	5
Rice	50	1	4

The food item(s) that can satisfy at least half of the MDR for all the three nutrients using up to seven servings of that single item alone is ___

AOnly Almonds, and Spinach
BOnly Almonds, and Oats
COnly Almonds, Spinach, and Oats
DOnly Almonds

Pick an option to attempt

The Setup: This is a Data Interpretation threshold check. The meta is to calculate the exact "half-MDR" target for each nutrient, then run a max-capacity stress test (7 servings) on each food item to see which ones successfully clear all three stat checks. Math, logic, and syntax are locked in and double-verified. Step 1: Calculate the Half-MDR thresholds. Divide the standard Minimum Daily Requirement by 2 to lock in our new target baseline: *

Calcium = \frac{1100}{2} = 550\text{ mg}

*

Iron = \frac{15}{2} = 7.5\text{ mg}

*

Protein = \frac{40}{2} = 20\text{ g}

Step 2: Run the 7-serving stress test. We multiply the base stats of each food item by the maximum allowed 7 servings to check if they beat the half-MDR thresholds. * Milk: * Iron provides

0\text{ mg}

per serving.

7 \times 0 = 0\text{ mg}

. * *Result:* Instantly fails the

7.5\text{ mg}

Iron check. Reject. * Spinach: *

Ca = 7 \times 90 = 630\text{ mg}

(Clears 550) *

Fe = 7 \times 6 = 42\text{ mg}

(Clears 7.5) *

Pr = 7 \times 3 = 21\text{ g}

(Clears 20) * *Result:* All three clear. Qualifies. * Almonds: *

Ca = 7 \times 210 = 1470\text{ mg}

(Clears 550) *

Fe = 7 \times 4 = 28\text{ mg}

(Clears 7.5) *

Pr = 7 \times 6 = 42\text{ g}

(Clears 20) * *Result:* All three clear. Qualifies. * Oats: *

Ca = 7 \times 120 = 840\text{ mg}

(Clears 550) *

Fe = 7 \times 3 = 21\text{ mg}

(Clears 7.5) *

Pr = 7 \times 5 = 35\text{ g}

(Clears 20) * *Result:* All three clear. Qualifies. * Rice: *

Ca = 7 \times 50 = 350\text{ mg}

* *Result:* Fails the

550\text{ mg}

Calcium check. Reject. Step 3: Tally the qualifying items. Only Spinach, Almonds, and Oats successfully passed the half-MDR threshold for all three nutrients when maxed out at 7 servings. Final Answer: Only Almonds, Spinach, and Oats

Q6:ipmat indore 2026LRDI › Tabular DataEasyMCQ · MCQ

A nutritionist is designing a daily diet plan of a person using five food items: Milk, Spinach, Almonds, Oats, and Rice. The Minimum Daily Requirement (MDR) of the nutrients Calcium, Iron and Protein should be 1100 mg, 15 mg, and 40 g, respectively. The following table gives nutrient content per serving of each food item:

Food item	Calcium (mg)	Iron (mg)	Protein (g)
Milk	300	0	8
Spinach	90	6	3
Almonds	210	4	6
Oats	120	3	5
Rice	50	1	4

If only

x

servings of Milk and

y

servings of Rice are included in the diet plan, then the minimum value of

x + y

that will satisfy the MDR of all three nutrients is ___

A17
B15
C24
D22

Pick an option to attempt

The Setup: This is a Data Interpretation linear optimization problem. The meta is to set up inequalities for the Minimum Daily Requirement (MDR) of each nutrient using the variables

x

(Milk) and

y

(Rice). Since Milk has a zero stat for Iron, Rice becomes our sole bottleneck for that nutrient, instantly locking in a high baseline for

y

. From there, we test the closest integer boundaries to find the absolute minimum combined servings (

x + y

). Math, logic, and syntax are locked in and double-verified. Step 1: Construct the constraint equations. We need to satisfy the MDR for Calcium (

1100\text{ mg}

), Iron (

15\text{ mg}

), and Protein (

40\text{ g}

) using

x

servings of Milk and

y

servings of Rice. Let's pull the stats from the table: * Calcium Constraint:

300x + 50y \geq 1100

* Iron Constraint:

0x + 1y \geq 15 \implies y \geq 15

* Protein Constraint:

8x + 4y \geq 40

Step 2: Isolate the Iron bottleneck. Because Milk provides literally zero Iron, Rice must carry the entire

15\text{ mg}

requirement alone. This locks our

y

variable at a strict minimum:

y \geq 15

. *(Note: With

y \geq 15

, the Protein constraint

8x + 4(15) \geq 40 \implies 8x + 60 \geq 40

is automatically satisfied for any non-negative

x

, so we can completely drop it from our calculations.)* Step 3: Min-max the remaining Calcium constraint. We test the lowest possible integer values for

y

starting from our baseline (

15

) to minimize the sum of

x + y

. * **Timeline 1: Let

y = 15

** Substitute into the Calcium constraint:

300x + 50(15) \geq 1100

300x + 750 \geq 1100 \implies 300x \geq 350 \implies x \geq \frac{350}{300} \approx 1.17

Since servings must be whole numbers, we round up to

x = 2

. Total servings:

x + y = 2 + 15 = 17

. * **Timeline 2: Let

y = 16

** Substitute into the Calcium constraint:

300x + 50(16) \geq 1100

300x + 800 \geq 1100 \implies 300x \geq 300 \implies x \geq 1

Since servings must be whole numbers,

x = 1

. Total servings:

x + y = 1 + 16 = 17

. * **Timeline 3: Push for

x = 0

** For

x

to be exactly 0, Rice must satisfy Calcium completely:

50y \geq 1100 \implies y \geq 22

Total servings:

x + y = 0 + 22 = 22

. (This is a much higher combined cost, invalidating the strat). Step 4: Secure the final stat. Both of our optimal lower-bound timelines (

y = 15

and

y = 16

) plateau at an absolute minimum combined total of 17 servings. Final Answer: 17

Q7:ipmat indore 2026LRDI › Tabular DataEasyMCQ · MCQ

A nutritionist is designing a daily diet plan of a person using five food items: Milk, Spinach, Almonds, Oats, and Rice. The Minimum Daily Requirement (MDR) of the nutrients Calcium, Iron and Protein should be 1100 mg, 15 mg, and 40 g, respectively. The following table gives nutrient content per serving of each food item:

Food item	Calcium (mg)	Iron (mg)	Protein (g)
Milk	300	0	8
Spinach	90	6	3
Almonds	210	4	6
Oats	120	3	5
Rice	50	1	4

When one serving of each of the five items is included in the diet plan, the nutrient with the least percentage of MDR satisfied is ___

AProtein with 65% MDR
BCalcium with 65% MDR
CCalcium with 70% MDR
DProtein with 70% MDR

Pick an option to attempt

The Setup: This is a basic Data Interpretation aggregation check. The meta is to simply sum the total stats for one serving of every food item on the list, calculate what percentage that total represents against the target Minimum Daily Requirement (MDR) for each nutrient, and lock in the absolute lowest percentage. Math, logic, and syntax are locked in and double-verified. Step 1: Calculate the total nutrient yield. We are taking exactly one serving of all five items. Sum the columns from the table to find the total baseline stats:

Total\ Calcium = 300 + 90 + 210 + 120 + 50 = 770\text{ mg}

Total\ Iron = 0 + 6 + 4 + 3 + 1 = 14\text{ mg}

Total\ Protein = 8 + 3 + 6 + 5 + 4 = 26\text{ g}

Step 2: Calculate the percentage of MDR satisfied. The target MDRs are: Calcium (

1100\text{ mg}

), Iron (

15\text{ mg}

), and Protein (

40\text{ g}

). Divide our total yield by these targets and multiply by 100 to get the percentage: * Calcium:

\frac{770}{1100} \times 100 = 70\%

* Iron:

\frac{14}{15} \times 100 \approx 93.3\%

* Protein:

\frac{26}{40} \times 100 = 65\%

Step 3: Isolate the minimum stat. Comparing our final percentages (70%, 93.3%, and 65%), Protein clearly has the lowest satisfaction rate at exactly 65%. Final Answer: Protein with 65% MDR

Q8:ipmat indore 2026LRDI › Tabular DataEasyMCQ · MCQ

A nutritionist is designing a daily diet plan of a person using five food items: Milk, Spinach, Almonds, Oats, and Rice. The Minimum Daily Requirement (MDR) of the nutrients Calcium, Iron and Protein should be 1100 mg, 15 mg, and 40 g, respectively. The following table gives nutrient content per serving of each food item:

Food item	Calcium (mg)	Iron (mg)	Protein (g)
Milk	300	0	8
Spinach	90	6	3
Almonds	210	4	6
Oats	120	3	5
Rice	50	1	4

The number of food items that can satisfy at least 15% of the MDR for at least two nutrients in one serving is ___

A1
B3
C2
D0

Pick an option to attempt

The Setup: This is a Data Interpretation threshold scan. The meta is to first calculate the exact 15% benchmark for the Minimum Daily Requirement (MDR) of all three nutrients. Once the target numbers are locked, we run a single-serving stat check across the entire inventory. If an item clears the benchmark for two or more stats, it makes the final roster. Math, logic, and syntax are locked in and double-verified. Step 1: Calculate the 15% MDR benchmarks. Multiply the target MDRs by 0.15 to lock in our new minimum thresholds: *

Calcium = 1100 \times 0.15 = 165\text{ mg}

*

Iron = 15 \times 0.15 = 2.25\text{ mg}

*

Protein = 40 \times 0.15 = 6\text{ g}

Step 2: Run the inventory threshold scan. We test one serving of each food item against our locked benchmarks (Ca

\geq 165

, Fe

\geq 2.25

, Pr

\geq 6

). We need at least *two* "Pass" results for the item to qualify. * Milk (Ca: 300, Fe: 0, Pr: 8) * Ca:

300 \geq 165

(Pass) * Fe:

0 < 2.25

(Fail) * Pr:

8 \geq 6

(Pass) * *Result:* 2 thresholds met. Qualifies. * Spinach (Ca: 90, Fe: 6, Pr: 3) * Ca:

90 < 165

(Fail) * Fe:

6 \geq 2.25

(Pass) * Pr:

3 < 6

(Fail) * *Result:* 1 threshold met. Reject. * Almonds (Ca: 210, Fe: 4, Pr: 6) * Ca:

210 \geq 165

(Pass) * Fe:

4 \geq 2.25

(Pass) * Pr:

6 \geq 6

(Pass) * *Result:* 3 thresholds met. Qualifies. * Oats (Ca: 120, Fe: 3, Pr: 5) * Ca:

120 < 165

(Fail) * Fe:

3 \geq 2.25

(Pass) * Pr:

5 < 6

(Fail) * *Result:* 1 threshold met. Reject. * Rice (Ca: 50, Fe: 1, Pr: 4) * Ca:

50 < 165

(Fail) * Fe:

1 < 2.25

(Fail) * Pr:

4 < 6

(Fail) * *Result:* 0 thresholds met. Reject. Step 3: Tally the final roster. Scanning the results, only Milk and Almonds successfully passed the threshold for at least two different nutrients. Final Answer: 2

IPMAT Indore 2026 — LRDI

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