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 greatest coefficient in the expansion of \({(1 + x)^{12}}\) is
  • A
    C ( 12, 4)
  • B
    C ( 12, 5)
  • C
    C ( 12, 6)
    Correct
  • D
    none of these
2
In the expansion of \({(1 + x)^{60}},\) the sum of coefficients of odd powers of x is
  • A
    \({2^{60}}\)
  • B
    none of these.
  • C
    \({2^{59}}\)
    Correct
  • D
    \({2^{61}}\)
3
Let n \( \in \) Q an n \( \notin \;N,n \ne 0,\) a \(>\) 0, then the expansion of \({\left( {a + x} \right)^n}\) in powers of x is valid if
  • A
    \(\left| x \right| \ge a\)
  • B
    \(\left| x \right| > a\)
  • C
    \(\left| x \right| < a\)
    Correct
  • D
    \(\left| x \right| = a\)
4
The expansion of \({1 \over {\sqrt {6 - 3x} }},\) in powers of x, is valid if
  • A
    \(\left| x \right| > 2\)
  • B
    \(\left| x \right| < 2\)
    Correct
  • C
    x \(<\) 2
  • D
    x \(>\) 2
5
The middle term in the expansion of \({(1 + x)^{2\;\;n}}\) is
  • A
    \(2\;{\;^n}{C_{n\; + \;1}}{x^{n\; + \;1}}\)
  • B
    \(2\;{\;^n}{C_n}\)
  • C
    \(\frac{{1.3.5...(2n - 1)}}{{\left| \!{\underline {\, n \,}} \right. }}{.2^n}{x^n}\)
    Correct
  • D
    \(2\;{\;^n}{C_{n - 1}}{x^{n - 1}}\)
6
The coefficient of\({x^{99}}in\left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 5} \right) \ldots \ldots \ldots ..\left( {x + 199} \right)is\)
  • A
    none of these
  • B
    1.3.5…………..199
  • C
    1+2+3+………+99
  • D
    1+3+5+……….+199
    Correct
7
If the expansion of \({\left( {x + {1 \over {{x^4}}}} \right)^{n - 5}}\) in powers of x contains the term \({x^{2r}}\) \(,thenn - 2ris\)
  • A
    none of these
  • B
    even
  • C
    a positive integral multiple of 5
    Correct
  • D
    odd
8
\({\left( {\sqrt 5 + 1} \right)^4} + {\left( {\sqrt 5 - 1} \right)^4}\) is
  • A
    none of these
  • B
    a rational number
    Correct
  • C
    a negative integer
  • D
    an irrational number
9
If rth ,(r+1)th and (r+2)th terms in the expansion of \({(1 + x)^n}\) are in A.P. then
  • A
    none of these
  • B
    \({\left( {n + 2r} \right)^3} = n - 2\)
  • C
    \({\left( {n + 2r} \right)^2} = n + 2\)
  • D
    \({\left( {n - 2r} \right)^2} = n + 2\)
    Correct
10
Coefficient of \({a^2}{b^5}\) in the expansion of {/tex}{(a + b)^3}{(a - 2b)^4}is{/tex}
  • A
    -24
    Correct
  • B
    48
  • C
    96
  • D
    24
11
In the expansion of\({(1 + x)^{11}}\), the \( {{\rm{5}}^{{\rm{th}}}}\) term is 24 times the \( {{\rm{3}}^{{\rm{rd}}}}\) term . The value of x is
  • A
    \( \pm 5\)
  • B
    \( \pm 2\)
    Correct
  • C
    \( \pm 3\)
  • D
    \( \pm 4\)
12
The sum of coefficients in the expansion of \({\left( {x + 2y + z} \right)^n}\) is ( n being a positive integer )
  • A
    3n
  • B
    1
  • C
    2n
  • D
    none of these
    Correct
13
If the rth term in the expansion of \({\left( {{x \over 3} - {2 \over {{x^2}}}} \right)^{10}}\) contains \({x^4}\) then r is equal to
  • A
    1
  • B
    2
  • C
    3
    Correct
  • D
    4
14
If a+b = 1 , then \(\sum\limits_{r = 0}^n {C(n,r){a^r}{b^{n - r}}} \) is equal to
  • A
    n
  • B
    0
  • C
    \({3^6}\)
Answer
Not Available
15
If a+b = 1 , then \(\sum\limits_{r = 0}^n {rC(n,r){a^r}{b^{n - r}}} \) is equal to
  • A
    na
    Correct
  • B
    1
  • C
    nab
  • D
    0