INDUCTION-QUIZ-4

MATHEMATICS INDUCTION 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. 

Q1. For each, n∈N, 10^2n-1+1 is divisible by

•  11
•  13
•  9
•  None of these

Solution

Q2.If 3+5+9+17+33+⋯ to n terms =2ⁿ⁺¹+n-2, then nth term of LHS is

•  3ⁿ-1
•  2n+1
•  2ⁿ+1
•  3n-1

Q3.  The remainder when 5⁹⁹ is divided by 13, is ∑y=50,∑xy=220,∑x² =200,∑y² =262,n=10 is

•  6
•  8
•  9
•  10

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

•  For all n
•  For all n>1
•  For all n>2
•  Nothing can be said

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

Q5.If n∈N, then 3²ⁿ+7 is divisible by

•  3
•  8
•  9
•  11

Solution  

 3²ⁿ+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

•  For all n
•  For n≥3
•  For n>4
•  None of these

Solution
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.

Q7.

• 6
•  11
•  24
•  26

Q8.

•  Aⁿ=2^n-1 A+(n-1)I
•  Aⁿ=nA+(n-1)I
•  Aⁿ=2^n-1 A-(n-1)I
•  Aⁿ=nA-(n-1)I

Solution

Q9.For natural number n,2ⁿ (n-1)!< nⁿ, if

•  n< 2
•  n>2
•  n≥2
•  never

Solution
The condition 2ⁿ(n-1)!< nⁿ is satisfied for n>2

Q10. 

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