## MATHEMATICS INDUCTION QUIZ-3

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. For all n∈N,72n-48n-1 is divisible by
•  25
•  26
•  1234
•  2304
Solution

Q2.The greatest positive integer, which divides (n+2)(n+3)(n+4)(n+5)(n+6) for all n∈N, is
•  4
•  120
•  240
•  24

Q3.  For n∈N,10n-2≥81n is ∑y=50,∑xy=220,∑x2 =200,∑y2 =262,n=10 is
•  n>5
•  n≥5
•  n< 5
•  n>8
Solution

Q4. Let P(n) denotes the statement that n2+n is odd. It is seen that P(n)⇒P(n+1),P(n) is true for all
•  n>1
•  n
•  n>2
•  None of these
Solution
P(n)=n2+n It is always odd but square of any odd number is always odd and also sum of two odd number is always even. So, for no any n for which this statement is true.

Q5.If n is an odd positive integer, then an+bn is divisible by
•  a+b
•  a-b
•  a2+b2
•  None of these

Q6.

•

•

•

•  None of the above
Solution

Q7.If n is a positive integer, then n3+2n is divisible by
• 2
•  6
•  15
•  3
Solution

Q8.For all n∈N,n4 is less than
•  10n
•  4n
•  5n
•  1010

Q9.For all n∈N,cos⁡Î¸ cos⁡2Î¸ cos⁡4Î¸…cos⁡2n-1 Î¸ equals to
•

•

•

•

Q10.

•  Equal to √n
•  Less than or equal to √n
•  Greater than or equal to √n
•  None of these

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