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****MATHEMATICS ****INDUCTION**** QUIZ-4**

**MATHEMATICS**

**QUIZ-4**

## Dear Readers,

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.

**Q2.**If 3+5+9+17+33+⋯ to n terms =2

^{n+1}+n-2, then nth term of LHS is

**Q3.**The remainder when 5

^{99}is divided by 13, is ∑y=50,∑xy=220,∑x

^{2}=200,∑y

^{2}=262,n=10 is

Solution

**Q4.**If P(n) is a statement (n∈N) such that, if P(k) is true, P(k+1) is true for k∈N, then p(n) is true

Solution

Unless we prove P(1) is true, nothing can be said.

Unless we prove P(1) is true, nothing can be said.

**Q5.**If n∈N, then 3

^{2n}+7 is divisible by

Solution

3

^{2n}+7is divisible by 8. This can be checked by putting n=1,2,3 etc.**Q6.**If P(n) is a statement such that P(3) is true. Assuming P(k) is true ⇒P(k+1) is true for all k≥3, then P(n) is true

Solution

Since, P(3) is true.

Since, P(3) is true.

Assume P(k) is true

⇒P(k+1) is true means,

if P(3) is true

⇒P(4) is true

⇒P(5) is true and so on.

So, statement is true for all n≥3.

**Q9.**For natural number n,2

^{n}(n-1)!< n

^{n}, if

Solution

The condition 2

The condition 2

^{n}(n-1)!< n^{n}is satisfied for n>2