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JEE Advanced

Explore popular questions from Permutations and Combinations for JEE Advanced. This collection covers Permutations and Combinations previous year JEE Advanced questions hand picked by experienced teachers.

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Permutations and Combinations

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Q 1. {tex} ^ n C _ { r - 1 } = 36 , ^ { n } C _ { r } = 84 {/tex} and {tex} ^ { n } C _ { r + 1 } = 126 , {/tex} then {tex} r {/tex} is

A

1

B

2

3

D

None of these

Explanation

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Q 2. The value of the expression {tex} ^ { 47 } C _ { 4 } + \sum _ { j = 1 } ^ { 5 }{^{ 52 - j }C _ { 3 }} {/tex} is equal to

A

{tex} ^ { 47 } C _ { 5 } {/tex}

B

{tex} ^ { 52 } C _ { 5 } {/tex}

{tex} ^ { 52 } C _ { 4 } {/tex}

D

none of these

Explanation

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Q 3. If the LCM of {tex} p , q {/tex} is {tex} r ^ { 2 } t ^ { 4 } s ^ { 2 } , {/tex} where {tex} r , s , t {/tex} are prime numbers and {tex} p , q {/tex} are the positive integers then the number of ordered pair {tex} ( p , q ) {/tex} is

A

252

B

254

225

D

224

Explanation

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Q 4. The number of seven digit integers, with sum of the digits equal to {tex}10{/tex} and formed by using the digits {tex} 1,2 {/tex} and {tex}3{/tex} only, is

A

55

B

66

77

D

88

Explanation

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Q 5. Six cards and six envelopes are numbered {tex} 1,2,3,4,5,6 {/tex} and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered {tex}1{/tex} is always placed in envelope numbered {tex} 2 . {/tex} Then the number of ways it can be done is

A

264

B

265

53

D

67

Explanation