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
The 1st three terms in the expansion of \({(4 + x)^{{3 \over 2}}}\) are
  • A
    \(8 + 3x + {3 \over 8}{x^2}\)
  • B
    \(4 + 3x + {3 \over {16}}{x^2}\)
  • C
    \(8 + 3x + {3 \over {16}}{x^2}\)
    Correct
  • D
    \(8 + 3x - {3 \over {16}}{x^2}\)
2
The coefficients of \({x^n}\)in the expansion of \({\left( {1 + 2x + 3{x^2} + ..........} \right)^{{1 \over 2}}}\) is
  • A
    1
    Correct
  • B
    -1
  • C
    n+1
  • D
    n
3
If \(z = {3 \over 4} + {3 \over 4}.{5 \over 8} + {3 \over 4}.{5 \over 8}.{7 \over {12}} + \ldots \ldots .,then{z^2} + 2z\) is equal to
  • A
    3
  • B
    7
    Correct
  • C
    1
  • D
    2
4
The index of the power of x that occurs in the \({{\rm{7}}^{{\rm{th}}}}\) term from the end in the expansion of \({\left( {{{2x} \over 3} - {3 \over {2x}}} \right)^9}\)is
  • A
    -5
  • B
    -3
  • C
    3
    Correct
  • D
    5
5
The index of the power of x that occurs in the \( {{\rm{6}}^{{\rm{th}}}}\) term in the expansion of \({\left( {{{4x} \over 5} - {8 \over {5x}}} \right)^9}\) is
  • A
    none of these
  • B
    1
  • C
    3
  • D
    -1
    Correct
6
If in the expansion of\({(1 + x)^{43}}\), the coefficients of (2r+1)th and (r+2)th terms are equal , then r is equal to
  • A
    1 or 14
    Correct
  • B
    7 or 1
  • C
    none of these
  • D
    21 or 1
7
The coefficient of \({x^7}\) in the expansion of \({(1 - x)^4}{\left( {1 + x} \right)^9}\) is
  • A
    \({}^9{C_7} - {}^9{C_3}\)
    Correct
  • B
    \({}^9{C_7}\)
  • C
    \({}^9{C_3}\)
  • D
    \(7{}^9{C_7} - 3{}^9{C_3}\)
8
If the three successive terms in the expansion of \({(1 + x)^n}\) have their coefficients as 28, 56, and 70, then n is equal to
  • A
    7
  • B
    8
    Correct
  • C
    5
  • D
    6
9
The index of the power of x that occurs in the 5th term in the expansion of \({\left( {2{x^2} - {1 \over {3{x^2}}}} \right)^8}\) is
  • A
    4
  • B
    12
  • C
    0
    Correct
  • D
    2
10
The expansion of \({\left( {8 - 3x} \right)^{{3 \over 2}}}\) in terms of powers of x is valid only if
  • A
    \({\text{ x | }} < {\text{ 8}}/{\text{3}}\)
    Correct
  • B
    \({\text{x }} > {\text{ 8 }}/{\text{3}}\)
  • C
    \({\text{x }} < {\text{ 3}}/{\text{8}}\)
  • D
    \({\text{x }} < {\text{ 8}}/{\text{3}}\)
11
If a and b are coefficients of \({x^n}and{x^{n + 1}}\) respectively in the expansion of \({(1 + x)^{2n + 1}}\),then
  • A
    a + b = 1
  • B
    a = b
    Correct
  • C
    a = 2b
  • D
    b = 2a
12
The coefficient of \({x^6}\) in the expansion of \({(1 + x + {x^2})^{ - 3}}\) is
  • A
    2
  • B
    none of these
  • C
    3
    Correct
  • D
    5
13
In Pascal’s triangle, each row begins with 1 and ends in
  • A
    -1
  • B
    0
  • C
    1
    Correct
  • D
    2
14
Coefficient of \({x^n}\) in the expansion of \({({{1 + x} \over {1 - x}})^{2}},n \in N \) is
  • A
    4n
    Correct
  • B
    none of these
  • C
    -4n
  • D
    4+n
15
Coefficient of \({x^n}\) in the expansion of \({({{1 - x} \over {1 + x}})^{2}},n \in N \) is
  • A
    none of these
  • B
    4+n
  • C
    4n
  • D
    \({( - 1)^n}4n\)
    Correct