Binomial Theorem - Algebra -Integer Type Questions(JEE ADVANCED) Part 1

 Q.1

Correct Answer is: [3]  
Solution Explain:








Q.2

Correct Answer is: [310]  
Solution Explain:








Q.3

Correct Answer is: [22]  
Solution Explain:







Q.4

Correct Answer is: [31]  
Solution Explain:








Q.5

Correct Answer is: [4]  
Solution Explain:








Q.6

Correct Answer is: [6]  
Solution Explain:








Q.7

Correct Answer is: [0]  
Solution Explain:










Q.8

Correct Answer is: [9]  
Solution Explain:










Q.9

Correct Answer is: [9]  
Solution Explain:









Q.10

Correct Answer is: [8]  
Solution Explain:








Q.11

Correct Answer is: [6]  
Solution Explain:










Q.12

Correct Answer is: [129]  
Solution Explain:








Q.13

Correct Answer is: [84]  
Solution Explain:









Q.14

Correct Answer is: [0]  
Solution Explain:









Q.15

Correct Answer is: [6]  
Solution Explain:










Q.16

Correct Answer is: [12]  
Solution Explain:











Q.17

Correct Answer is: [3]  
Solution Explain:










Q.18

Correct Answer is: [4]  
Solution Explain:








Q.19

Correct Answer is: [9]  
Solution Explain:










Q.20

Correct Answer is: [4]  
Solution Explain:










Q.21

Correct Answer is: [84]  
Solution Explain:









Q.22

Correct Answer is: [6]  
Solution Explain:








Q.23

Correct Answer is: [4]  
Solution Explain:









Q.24

Correct Answer is: [1]  
Solution Explain:










Q.25

Correct Answer is: [646]  
Solution Explain:







Q.26

Correct Answer is: [1]  
Solution Explain:










Q.27

Correct Answer is: [11]  
Solution Explain:







Q.28

Correct Answer is: [1458]  
Solution Explain:








Q.29

Correct Answer is: [118]  
Solution Explain:










Q.30

Correct Answer is: [7]  
Solution Explain:









Q.31

Correct Answer is: [2]  
Solution Explain:

As (3053)456 – (2417)333 = (339 × 9 + 2)456 – (269 × 9 – 4)333
Remainder of given number is same as remainder of 2456 + 4333
and 2456 + 4333 = (64)76 + (64)111
= (1 + 63)76 + (1 + 63)111 = (1 + 9 × 7)76 + (1 + 9 × 7)111
Hence the remainder is 2.










Q.32

Correct Answer is: [6]  

Solution Explain:









Q.33

Correct Answer is: [7]  
Solution Explain:











Q.34

Correct Answer is: [0]  
Solution Explain:







Q.35

Correct Answer is: [201]  
Solution Explain:









Q.36

Correct Answer is: [15]  
Solution Explain:








Q.37

Correct Answer is: [7]  
Solution Explain:










Q.38

Correct Answer is: [49]  
Solution Explain:










Q.39

Correct Answer is: [3]  
Solution Explain:










Q.40

Correct Answer is: [40]  
Solution Explain:




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