If n is a +ve integer, then 3^{3n}−26n−1 is divisible by
If n is a +ve integer, then 2^{3n}−7n−1 is divisible by
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If n is a +ve integer, then 3.5^{2n+1}+2^{3n+1} is divisible by
If n is a +ve integer, then 7^{2n}−4 is divisible by
Let P (k) = 1 + 3 + 5 + …………….+ (2k – 1) = (3+k^{2}).Then which of the following is true ?
The inequality 2^{n}<n!,n∈N is true for :
For each n ∈ N,a^{2n−1}+b^{2n−1} is divisible by :
For each n ∈ N, n (n + 1) (2n + 1) is divisible by :
For each n ∈ N, 3(5^{2n+1})+2^{3n+1 }is divisible by :
For each n ∈ N, 2^{3n}−1 is divisible by :
For each n ∈ N, 3^{2n}−1 is divisible by :
The statement P (n) : “(n+3)^{2 }> 2^{n+3} “ is true for :
The smallest positive integer ‘n‘ for which 2^{n}(1×2×3×...............×n) < n^{n} holds is :
If 10^{n}+3×4^{n+1}+k is divisible by 9 for all n ∈ N, then the least positive integral value of k is
The smallest positive integer n, for which ( 1 × 2 × 3 ×……×n )
Let P(n) : n^{2}−n+41 is a prime number . then :
Let that P(n) ⇒ P(n+1) for all natural numbers n. also, if P (m) is true, m ∈ N, then we conclude that
Consider the statement P (n) : “n^{2 }≥ 100 “. Here P(n) ⇒ P(n+1) for all natural numbers n. Does it mean
The smallest positive integer ‘n‘ for which P (n) : 2^{n }< (1×2×3×............×n) holds is :
If x^{n}−1 is divisible by x – k for all n belongs to natural numbers N, then the least positive integral value of k is :
A student was asked to prove a statement P (n) by method of induction. He proved P (k + 1) is true whenever P (k) Is true for all k ≥ 5 , k ∈ N and P (5) is true. On the basis of this he could conclude that P (n) is true
If a,b,c ∈ N, a^{n}+b^{n} is divisible by c, when n is odd but not when n is even, then the value of c is :
1.2.3 + 2.3.4 + 3.4.5 + ………..up to n terms is equal to :
The number of terms in the expansion of (x+y+z)^{n} is
The sum of the terms in the nth bracket of the series 1 + (2+3+4) + (5+6+7+8+9) ….is
447 docs930 tests

JEE Advanced (Single Correct Type): Mathematical induction & Binomial Theorem Doc  8 pages 
JEE Advanced (One or More Correct Option): Mathematical induction & Binomial Theorem Doc  3 pages 
JEE Advanced (Subjective Type Questions): Mathematical Induction & Binomial Theorem Doc  23 pages 
JEE Advanced (Fill in the Blanks): Mathematical Induction & Binomial Theorem Doc  2 pages 
Integer Answer Type Questions for JEE: Mathematical induction & Binomial Theorem Doc  5 pages 
447 docs930 tests

JEE Advanced (Single Correct Type): Mathematical induction & Binomial Theorem Doc  8 pages 
JEE Advanced (One or More Correct Option): Mathematical induction & Binomial Theorem Doc  3 pages 
JEE Advanced (Subjective Type Questions): Mathematical Induction & Binomial Theorem Doc  23 pages 
JEE Advanced (Fill in the Blanks): Mathematical Induction & Binomial Theorem Doc  2 pages 
Integer Answer Type Questions for JEE: Mathematical induction & Binomial Theorem Doc  5 pages 