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CBSE Questions for Class 11 Engineering Maths Principle Of Mathematical Induction Quiz 2 - MCQExams.com

nN;102n1+1 is divisible by
  • 2
  • 3
  • 7
  • 11
nN;3n5+5n3+7n is divisible by
  • 3
  • 5
  • 10
  • 15
If xn1 is divisible by xk, then the least positive integral value of k is
  • 1
  • 2
  • 3
  • 4
nN,n4 is less than
  • 10n
  • 4n
  • 4n
  • 1010
If  n  N, then x2n1+y2n1 is divisible by
  • x+y
  • xy
  • x2+y2
  • none of these
For all nN,n is
  • <(2n+1)28
  • >(2n+1)28
  • =(2n+1)28
  • none of these
If 49n+16n+λ is divisible by 64 for all nN, then the least negative integral value of λ is
  • 12
  • 1
  • 3
  • 4
Let P(m) be the statement m2>100, the statement P(k+1) will be true if
  • P(1) is true
  • P(2) is true
  • P(k) is true
  • none of these
The product of three consecutive natural numbers is divisible by
  • 3
  • 8
  • 6
  • 11
Let P(n) be a statement such that truth of P(n) the truth of P(n+1) for all nϵN, then P(n) is true
  • n>1
  • n
  • nothing can be said
  • n>k (k is some fixed positive integer)
x3n+y3n is divisible by x+y, if 
  • n is any integer 0
  • n is an odd positive integer
  • n is an even positive integer
  • n is a rational number
Statement  1 : For each natural number n,(n+1)7n71 is divisible by 7.
Statement  2 : For each natural n, n7n is divisible by 7.
  • A) Statement - 1 is True, Statement - 2 is True; Statement -2 is a correct explanation for Statement - 1
  • B) Statement - 1 is True, Statement - 2 is True; Statement -2 is NOT a correct explanation for Statement - 1
  • C) Statement - 1 is True, Statement-2 is False
  • D) Statement - 1 is False, Statement-2 is True
For nN,xn+1+(x+1)2n1 is divisible by
  • x
  • x+1
  • x2+x+1
  • x2x+1
Let P(n)=n(n+1) is an even number, then which of the following satisfy P(n)
  • P(3)
  • P(100)
  • P(50)
  • All of these
For each natural number, the statement P(n)=23n1 is divisible by
  • 10
  • 6
  • 7
  • None of these.
Let P(n):n2+n is an odd integer
P(k)P(k+1) is true
Then P(n) is true for all
  • n>2
  • n>1
  • n
  • none of these
If P(n) be the statement n(n+1)+1 is odd, then which of the following is false?
  • P(2)
  • P(3)
  • P(4)
  • none of these
Let P(n)=23n7n1 then P(n) is divisible by
  • 63
  • 36
  • 49
  • 25
Let P(n) be the statement representing the sum of next three successive natural numbers of n, nN, then the smallest value of n to which P(n) is divisible by 9 is
  • 1
  • 3!
  • 3
  • 9!
Let P(n)=1+14+19+...+1n2<21n is true for
  • n
  • for n=1
  • n=2
  • none of these
P(n):2n+2<3n, is true for
  • nN
  • n>3,nN
  • n>2,nN
  • none of these.
Let P(k):2+4+6+...+2k=k(k+1)+2, then the statement P(m+1) will be true if
  • P(1) is true
  • P(2) is true
  • P(m) is true
  • none of these
Let P(n) be the statement that n2n+41 is prime, then which of the following is not true ?
  • P(2)
  • P(3)
  • P(41)
  • none of these
Let P(n):2n>n,nN and 2k>k,n=k, then which of the following is true k2?
  • 2k>5k>1
  • 2k+1>2k>k+1
  • 2k>2(k+1)>k
  • None of these.
The inequality, P(n)=n!>2n is true for
  • n4
  • n>1
  • n>2
  • nN
Let P(n):an+bn such that a,b are even, then p(n) will be divisible by a+b if
  • n>1
  • n is odd
  • n is even
  • none of these
Let f(n)=8n3n, if n is odd natural number then f(n) is divisible by
  • 2
  • 3
  • 5
  • none of these
If P(n)=12+32+52+...+(2n1)2=n(4n21)3, then which of the following does NOT hold good?
  • P(1)
  • P(2)
  • P(3)
  • None of these.
If P(n)=1+2+3++n is a perfect square, N is less than 100, then possible values of n is/are
  • only 1
  • 1 and 8
  • only 8
  • 1,8,49
Let the statement P(n):2n3n, the truth of P(k),kN truth of,
  • P(1)
  • P(2)
  • P(3)
  • P(k+1)
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