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CBSE Questions for Class 11 Engineering Maths Principle Of Mathematical Induction Quiz 6 - MCQExams.com

If n is an odd positive integer, then an+bn is divisible by
  • ab
  • a+b
  • a2+b2
  • none of these
The value of 121.3+223.5++n2(2n1)(2n+1) is
  • n(n+1)2(2n+1)
  • n(n1)2(2n1)
  • n2(n1)22(2n+1)
  • none of these
The value of 11.2.3+12.3.4+....+1n(n+1)(n+2) is 
  • n(n+3)4(n+1)(n+2)
  • n(n+1)(n+2)
  • n(n+2)(n+1)(n+3)
  • All of these
The value of tan1(13)+tan1(17)++tan1(1n2+n+1) is
  • tan1(nn+2)
  • tan1(n+1n1)
  • tan1(n1n+2)
  • tan1(n+2n2)
By mathematical induction pn+1+(p+1)2n1 is divisible by
  • p2+p+1
  • p2+1
  • p+1
  • None of these
If a1=1,an+1=1n+1an,n1, then an =
  • 1n!
  • 1(n+2)!
  • 1(n+1)!
  • none of these
3+13+29+51+79+... to n terms =
  • 2n2+7n3
  • n2+5n3
  • n3+2n2
  • none of these
Using the principle of mathematical induction, find tanα+2tan2α+22tan22α+.... to n terms:
  • tanα2ntan(2nα)
  • cotα2ncot(2nα)
  • secα2nsec(2nα)
  • None of these
If p is a prime number, then npn is divisible by p for all n, where
  • nN.
  • n is odd natural number.
  • n is even natural number.
  • n is not a composite number.
For each nϵN, then 32n+1+1 is divisible by -
  • 2
  • 3
  • 7
  • None of these
For positive integer n, 3n<n! when
  • n6
  • n>7
  • n7
  • n7
nN, 1+12+13+......+1n is
  • n
  • n
  • >n
  • none of these
Let p(n)=x(xn1nan1+an(n1)) is divisible by (xa)2 for
  • n>1
  • n>2
  • nN
  • None of these
If 10n+34n+2+λ is exactly divisible by 9 for all nN, then the least positive integral value of λ is
  • 5
  • 3
  • 7
  • 1
For all nN, 10n+3.4n+2+5 is divisible  by
  • 23
  • 3
  • 9
  • 207
If 4nC2n:2nCn={1.3,.5,...(4n1)}:{1,3,5....(2n1)}λ,thenλ=
  • 1
  • 2
  • 3
  • none of these
If 283+k is divisible by 127, then the smallest positive integral value of k is:
  • 63
  • 31
  • 15
  • 64
 Using principle of mathematics induct or for all
n  N:1+2+3+....+n<18(2n+1)2
  • True
  • False
For all nN, 
12+22+32+42++n2=n(n+1)(2n+1)6
  • True
  • False
 112+122+332+......+1n23n+12n+2 for every natural number n
  • True
  • False
For any natural number n, xnyn is divisible by xy, where x and y are any integers with xy.
  • True
  • False
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