## MATHEMATICS INDUCTION QUIZ-5

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

Q1. If m,n are any two odd positive integer with n< m, then the largest positive integers which divides all the numbers of the type m2-n2 is
•  4
•  6
•  8
•  9
Solution

Q2.If a,b are distinct rational numbers, then for all n∈N the number an-bn is divisible by
•  a-b
•  a+b
•  2a-b
•  a-2b

Q3.  23n-7n-1 is divisible by ∑y=50,∑xy=220,∑x2 =200,∑y2 =262,n=10 is
•  64
•  36
•  49
•  25
Solution

Q4. If n∈N, then x2n-1 y2n-1 is divisible by
•  x+y
•  x-y
•  x2+y2
•  None of these

Q5.If xn-1 is divisible by x-k, then the least positive integral value of k is
•  1
•  2
•  3
•  4

Q6. (23n-1) will be divisible by (∀n∈N)
•  25
•  8
•  7
•  3
Solution

Q7.For all n∈N,49n+16n-1 is divisible by
• 64
•  8
•  16
•  4
Solution
We observe that 49n+16n-1 takes values 64
Hence, 49n+16n-1 is divisible by 64

Q8.For all n∈N,33n-26n-1 is divisible by
•  24
•  64
•  17
•  676
Solution

Q9.If 10n+3.4n+2+Î» is exactly divisible by 9 for all n∈N, then the least positive integral value of Î» is
•  5
•  3
•  7
•  1

Q10. For all n∈N,52n-1 is divisible by
•  6
•  11
•  24
•  26
Solution

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