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Home/JEE MAINS/mathematics/permutations and combinations
Curated PYQ Collection

Top 50 Most Repeated PERMUTATIONS AND COMBINATIONS PYQs | JEE MAINS

A curated collection of the most important questions from PERMUTATIONS AND COMBINATIONS, fully solved with step-by-step concepts to prepare for JEE MAINS.

Question #1

Practice Question

Concept Applied

Treat the pair as one unit: $4!$ arrangements. Pair can switch: $\times2$. Total: $3! \times 2 = 12$...

Read Full Step-by-Step Solution →

Question #2

Practice Question

Concept Applied

Fix one boy, arrange remaining 5 boys in 5! ways, 6 gaps for girls in 6! ways. Total = $5! \times 6! = 86400$....

Read Full Step-by-Step Solution →

Question #3

Practice Question

A.288
B.576
C.144
D.720

Concept Applied

Arrange 5 boys in circle: $4!$. Girls in gaps: $5!$. Total: $4! \times 5! = 576$....

Read Full Step-by-Step Solution →

Question #4

Practice Question

Concept Applied

Letters: E, H, M, O, R, T. Fix positions: Words starting with E, H → 5! each = 120. Then M: next letter E → 4! = 24, H → 24, O: now 'OT' → T then H → ...

Read Full Step-by-Step Solution →

Question #5

Practice Question

A.150
B.210
C.240
D.270

Concept Applied

Use inclusion-exclusion: $3^5 - 3\cdot2^5 + 3\cdot1^5 = 243 - 96 + 3 = 150$...

Read Full Step-by-Step Solution →

Question #6

Practice Question

Concept Applied

Use permutation formula $^5P_3 = 5!/(5-3)! = 5×4×3$....

Read Full Step-by-Step Solution →

Question #7

Practice Question

Concept Applied

Simplify using $6! = 720$, $5! = 120$, $4! = 24$: $(720 - 600)/24 = 5$ → Wait: recalculate: $6! = 720$, $5\cdot5! = 600$, diff=120,

20/24=5$ → Corre...

Read Full Step-by-Step Solution →

Question #8

Practice Question

Concept Applied

Use multinomial expansion; count combinations giving $x^4$....

Read Full Step-by-Step Solution →

Question #9

Practice Question

Concept Applied

Treat the pair as one unit: $4!$ arrangements. Pair can switch: $\times2$. Total: $3! \times 2 = 12$...

Read Full Step-by-Step Solution →

Question #10

Practice Question

Concept Applied

Fix one boy, arrange remaining 5 boys in 5! ways, 6 gaps for girls in 6! ways. Total = $5! \times 6! = 86400$....

Read Full Step-by-Step Solution →

Question #11

Practice Question

A.288
B.576
C.144
D.720

Concept Applied

Arrange 5 boys in circle: $4!$. Girls in gaps: $5!$. Total: $4! \times 5! = 576$....

Read Full Step-by-Step Solution →

Question #12

Practice Question

Concept Applied

Letters: E, H, M, O, R, T. Fix positions: Words starting with E, H → 5! each = 120. Then M: next letter E → 4! = 24, H → 24, O: now 'OT' → T then H → ...

Read Full Step-by-Step Solution →

Question #13

Practice Question

A.150
B.210
C.240
D.270

Concept Applied

Use inclusion-exclusion: $3^5 - 3\cdot2^5 + 3\cdot1^5 = 243 - 96 + 3 = 150$...

Read Full Step-by-Step Solution →

Question #14

Practice Question

Concept Applied

Use permutation formula $^5P_3 = 5!/(5-3)! = 5×4×3$....

Read Full Step-by-Step Solution →

Question #15

Practice Question

Concept Applied

Simplify using $6! = 720$, $5! = 120$, $4! = 24$: $(720 - 600)/24 = 5$ → Wait: recalculate: $6! = 720$, $5\cdot5! = 600$, diff=120,

20/24=5$ → Corre...

Read Full Step-by-Step Solution →

Question #16

Practice Question

Concept Applied

Use multinomial expansion; count combinations giving $x^4$....

Read Full Step-by-Step Solution →

Question #17

Practice Question

Concept Applied

Treat the pair as one unit: $4!$ arrangements. Pair can switch: $\times2$. Total: $3! \times 2 = 12$...

Read Full Step-by-Step Solution →

Question #18

Practice Question

Concept Applied

Fix one boy, arrange remaining 5 boys in 5! ways, 6 gaps for girls in 6! ways. Total = $5! \times 6! = 86400$....

Read Full Step-by-Step Solution →

Question #19

Practice Question

A.288
B.576
C.144
D.720

Concept Applied

Arrange 5 boys in circle: $4!$. Girls in gaps: $5!$. Total: $4! \times 5! = 576$....

Read Full Step-by-Step Solution →

Question #20

Practice Question

Concept Applied

Letters: E, H, M, O, R, T. Fix positions: Words starting with E, H → 5! each = 120. Then M: next letter E → 4! = 24, H → 24, O: now 'OT' → T then H → ...

Read Full Step-by-Step Solution →

Question #21

Practice Question

A.150
B.210
C.240
D.270

Concept Applied

Use inclusion-exclusion: $3^5 - 3\cdot2^5 + 3\cdot1^5 = 243 - 96 + 3 = 150$...

Read Full Step-by-Step Solution →

Question #22

Practice Question

Concept Applied

Use permutation formula $^5P_3 = 5!/(5-3)! = 5×4×3$....

Read Full Step-by-Step Solution →

Question #23

Practice Question

Concept Applied

Simplify using $6! = 720$, $5! = 120$, $4! = 24$: $(720 - 600)/24 = 5$ → Wait: recalculate: $6! = 720$, $5\cdot5! = 600$, diff=120,

20/24=5$ → Corre...

Read Full Step-by-Step Solution →

Question #24

Practice Question

Concept Applied

Use multinomial expansion; count combinations giving $x^4$....

Read Full Step-by-Step Solution →

Question #25

Practice Question

Concept Applied

Treat the pair as one unit: $4!$ arrangements. Pair can switch: $\times2$. Total: $3! \times 2 = 12$...

Read Full Step-by-Step Solution →

Question #26

Practice Question

Concept Applied

Fix one boy, arrange remaining 5 boys in 5! ways, 6 gaps for girls in 6! ways. Total = $5! \times 6! = 86400$....

Read Full Step-by-Step Solution →

Question #27

Practice Question

A.288
B.576
C.144
D.720

Concept Applied

Arrange 5 boys in circle: $4!$. Girls in gaps: $5!$. Total: $4! \times 5! = 576$....

Read Full Step-by-Step Solution →

Question #28

Practice Question

Concept Applied

Letters: E, H, M, O, R, T. Fix positions: Words starting with E, H → 5! each = 120. Then M: next letter E → 4! = 24, H → 24, O: now 'OT' → T then H → ...

Read Full Step-by-Step Solution →

Question #29

Practice Question

A.150
B.210
C.240
D.270

Concept Applied

Use inclusion-exclusion: $3^5 - 3\cdot2^5 + 3\cdot1^5 = 243 - 96 + 3 = 150$...

Read Full Step-by-Step Solution →

Question #30

Practice Question

Concept Applied

Use permutation formula $^5P_3 = 5!/(5-3)! = 5×4×3$....

Read Full Step-by-Step Solution →

Question #31

Practice Question

Concept Applied

Simplify using $6! = 720$, $5! = 120$, $4! = 24$: $(720 - 600)/24 = 5$ → Wait: recalculate: $6! = 720$, $5\cdot5! = 600$, diff=120,

20/24=5$ → Corre...

Read Full Step-by-Step Solution →

Question #32

Practice Question

Concept Applied

Use multinomial expansion; count combinations giving $x^4$....

Read Full Step-by-Step Solution →

Question #33

Practice Question

Concept Applied

Treat the pair as one unit: $4!$ arrangements. Pair can switch: $\times2$. Total: $3! \times 2 = 12$...

Read Full Step-by-Step Solution →

Question #34

Practice Question

Concept Applied

Fix one boy, arrange remaining 5 boys in 5! ways, 6 gaps for girls in 6! ways. Total = $5! \times 6! = 86400$....

Read Full Step-by-Step Solution →

Question #35

Practice Question

A.288
B.576
C.144
D.720

Concept Applied

Arrange 5 boys in circle: $4!$. Girls in gaps: $5!$. Total: $4! \times 5! = 576$....

Read Full Step-by-Step Solution →

Question #36

Practice Question

Concept Applied

Letters: E, H, M, O, R, T. Fix positions: Words starting with E, H → 5! each = 120. Then M: next letter E → 4! = 24, H → 24, O: now 'OT' → T then H → ...

Read Full Step-by-Step Solution →

Question #37

Practice Question

A.150
B.210
C.240
D.270

Concept Applied

Use inclusion-exclusion: $3^5 - 3\cdot2^5 + 3\cdot1^5 = 243 - 96 + 3 = 150$...

Read Full Step-by-Step Solution →

Question #38

Practice Question

Concept Applied

Use permutation formula $^5P_3 = 5!/(5-3)! = 5×4×3$....

Read Full Step-by-Step Solution →

Question #39

Practice Question

Concept Applied

Simplify using $6! = 720$, $5! = 120$, $4! = 24$: $(720 - 600)/24 = 5$ → Wait: recalculate: $6! = 720$, $5\cdot5! = 600$, diff=120,

20/24=5$ → Corre...

Read Full Step-by-Step Solution →

Question #40

Practice Question

Concept Applied

Use multinomial expansion; count combinations giving $x^4$....

Read Full Step-by-Step Solution →

Question #41

Practice Question

Concept Applied

Treat the pair as one unit: $4!$ arrangements. Pair can switch: $\times2$. Total: $3! \times 2 = 12$...

Read Full Step-by-Step Solution →

Question #42

Practice Question

Concept Applied

Fix one boy, arrange remaining 5 boys in 5! ways, 6 gaps for girls in 6! ways. Total = $5! \times 6! = 86400$....

Read Full Step-by-Step Solution →

Question #43

Practice Question

A.288
B.576
C.144
D.720

Concept Applied

Arrange 5 boys in circle: $4!$. Girls in gaps: $5!$. Total: $4! \times 5! = 576$....

Read Full Step-by-Step Solution →

Question #44

Practice Question

Concept Applied

Letters: E, H, M, O, R, T. Fix positions: Words starting with E, H → 5! each = 120. Then M: next letter E → 4! = 24, H → 24, O: now 'OT' → T then H → ...

Read Full Step-by-Step Solution →

Question #45

Practice Question

A.150
B.210
C.240
D.270

Concept Applied

Use inclusion-exclusion: $3^5 - 3\cdot2^5 + 3\cdot1^5 = 243 - 96 + 3 = 150$...

Read Full Step-by-Step Solution →

Question #46

Practice Question

Concept Applied

Use permutation formula $^5P_3 = 5!/(5-3)! = 5×4×3$....

Read Full Step-by-Step Solution →

Question #47

Practice Question

Concept Applied

Simplify using $6! = 720$, $5! = 120$, $4! = 24$: $(720 - 600)/24 = 5$ → Wait: recalculate: $6! = 720$, $5\cdot5! = 600$, diff=120,

20/24=5$ → Corre...

Read Full Step-by-Step Solution →

Question #48

Practice Question

Concept Applied

Use multinomial expansion; count combinations giving $x^4$....

Read Full Step-by-Step Solution →

Question #49

Practice Question

Concept Applied

Treat the pair as one unit: $4!$ arrangements. Pair can switch: $\times2$. Total: $3! \times 2 = 12$...

Read Full Step-by-Step Solution →

Question #50

Practice Question

Concept Applied

Fix one boy, arrange remaining 5 boys in 5! ways, 6 gaps for girls in 6! ways. Total = $5! \times 6! = 86400$....

Read Full Step-by-Step Solution →
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