Binomial Theorem CBSE Questions & Answers

Binomial Theorem

This is Mathematics Class 11 Binomial Theorem CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Sum of the coefficients in the expansion of \({(1 + 2x - 4{x^2})^{1994}}is\)
  • A
    none of these
  • B
    1
    Correct
  • C
    \({2^{1994}}\)
  • D
    -1
2
The statement \({3^n} > 4n\) is true for all
  • A
    \({\text{n }} > {\text{3}}\), \(n \in N\)
  • B
    \({\text{n }} > {\text{ 1}}\), \(n \in N\)
    Correct
  • C
    \({\text{n }} > {\text{ 2}}\), \(n \in N\)
  • D
    \(n \in N\)
3
The statement \({2^n} > 3n\) is true for all
  • A
    \({\text{n }} > {\text{ 3}}\)
    Correct
  • B
    \({\text{n }} \geq {\text{ 3}}\)
  • C
    none of these
  • D
    \(n \in N\)
4
The coefficient of \({x^n}\) in the expansion of \(\left( {1 + x} \right){(1 - x)^{ - 2}}\) is
  • A
    ( 2n + 1)
    Correct
  • B
    2n - 1
  • C
    2n
  • D
    none of these
5
The coefficient of \({x^{11}}\) in the expansion of \({(1 + x + {x^2} + \ldots + {x^{10}})^{2}}\) is equal to
  • A
    10
    Correct
  • B
    12
  • C
    none of these
  • D
    11
6
\({(\sqrt 5 + 1)^{2n + 1}} - {(\sqrt 5 - 1)^{2n + 1}}\)is
  • A
    none of these
  • B
    an even positive integer
    Correct
  • C
    an odd positive integer
  • D
    not an integer
7
\({(\sqrt 3 + 1)^{2n}} + {(\sqrt 3 - 1)^{2n}}\)is
  • A
    an odd positive integer
  • B
    not an integer
  • C
    none of these
  • D
    an even positive integer
    Correct
8
\({(\sqrt 3 + 1)^{2n + 1}} + {(\sqrt 3 - 1)^{2n + 1}}\) is
  • A
    an irrational number
    Correct
  • B
    a rational number
  • C
    an odd positive integer
  • D
    an even positive integer
9
\({(\sqrt 3 + 1)^{2n}} - {(\sqrt 3 - 1)^{2n}}\) is
  • A
    an odd positive integer
  • B
    a rational number
  • C
    an irrational number
    Correct
  • D
    none of these
10
If n is a positive integer, then \({(\sqrt 3 + i)^n} + {(\sqrt 3 - i)^n}\) is
  • A
    a positive real number
  • B
    a non real number
  • C
    a real number
    Correct
  • D
    none of these
11
The statement \({2^{n + 2}} < {3^n}\) is true for all
  • A
    all \({\text{n }} > {\text{ 2}}\)
  • B
    none of these
  • C
    all \(n \in N\)
  • D
    all \({\text{n }} > {\text{ 3}}\)
    Correct
12
The smallest positive integer for which the statement \({3^{n + 1}} < {4^n}\) is true for all
  • A
    4
    Correct
  • B
    2
  • C
    3
  • D
    1
13
The integral part of \({(\sqrt 2 + 1)^6}is\)
  • A
    163
  • B
    197
    Correct
  • C
    196
  • D
    198
14
The greatest term in the expansion of \({(3 + 2x)^9}\),when x = 1, is
  • A
    \({{\rm{4}}^{{\rm{th}}}}\) and \({{\rm{5}}^{{\rm{th}}}}\)
    Correct
  • B
    \({{\rm{6}}^{{\rm{th}}}}\)
  • C
    \({{\rm{5}}^{{\rm{th}}}}\)
  • D
    \({{\rm{4}}^{{\rm{th}}}}\)
15
The number 111111…………..1 (91 times) is
  • A
    none of these
  • B
    not a prime
    Correct
  • C
    not an odd number
  • D
    an even number