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 coefficient of \({x^n}\) in the expansion of \({(1 - x)^{ - 1}}\) is
  • A
    \({( - 1)^n}n\)
  • B
    n
  • C
    1
    Correct
  • D
    \({( - 1)^n}\)
2
The term independent of x in the expansion of \({\left( {2x - {1 \over {2{x^2}}}} \right)^{12}}\) is
  • A
    \({ - ^{12}}{C_5}{2^2}\)
  • B
    \({}^{12}{C_3}{2^6}\)
  • C
    \(^{12}{C_4}{2^4}\)
    Correct
  • D
    \({}^{12}{C_6}\)
3
The coefficient of y in the expansion of \({\left( {{y^2} + {c \over y}} \right)^5}\) is
  • A
    10 c
  • B
    20 c
  • C
    \(20{c^2}\)
  • D
    \(10{c^3}\)
    Correct
4
the number o subsets of a set containing n distinct elements is
  • A
    \({2^n}\)
    Correct
  • B
    n
  • C
    2 n
  • D
    \({n^2}\)
5
The number of terms in the expansion of \({[{(x + 4y)^3}{(x - 4y)^3}]^2}\) is
  • A
    32
  • B
    8
  • C
    6
  • D
    7
    Correct
6
\(\sqrt 5 \left\{ {{{(\sqrt 5 + 1)}^{50}} - {{\left( {\sqrt 5 - 1} \right)}^{50}}} \right\}\)is
  • A
    none of these
  • B
    0
  • C
    an irrational number
  • D
    a natural number
    Correct
7
Coefficient of \({x^5}\) in the expansion of \({(1 + {x^2})^5}{(1 + x)^4}\) is
  • A
    61
  • B
    60
    Correct
  • C
    0
  • D
    59
8
If three successive terms in the expansion of \({(1 + x)^n}a\) have their coefficients in the ratio 6 : 33 : 110, then n is equal to
  • A
    none of these
  • B
    10
  • C
    12
    Correct
  • D
    11
9
\({(1.003)^4}\)is nearly equal to
  • A
    none of these
  • B
    1.014
  • C
    1.012
    Correct
  • D
    0.988
10
5th term from the end in the expansion of \({\left( {{{{x^3}} \over 2} - {2 \over {{x^2}}}} \right)^{12}}\)is
  • A
    \(7920{x^4}\)
  • B
    \(7920{x^{ - 4}}\)
    Correct
  • C
    \( - 7920{x^4}\)
  • D
    \( - 7920{x^{ - 4}}\)
11
The coefficient of second, third and fourth terms in the binomial expansion of \({(1 + x)^n}\) ( ‘n’, a + ve integer) are in A.P.., if n is equal to
  • A
    4
  • B
    5
  • C
    7
    Correct
  • D
    6
12
The coefficient of \({x^3}\) in the binomial expansion of \({\left( {x - {m \over x}} \right)^{11}}\) is
  • A
    \(942{m^7}\)
  • B
    \(792{m^6}\)
  • C
    \(792{m^5}\)
  • D
    \(330{m^4}\)
    Correct
13
The coefficient of \({x^{17}}\) in the expansion of ( x- 1) ( x- 2) …..( x – 18) is
  • A
    - 171
    Correct
  • B
    342
  • C
    684
  • D
    \({{171} \over 2}\)
14
If the coefficients of (r +1)th term and ( r + 3)th term in the expansion of \({(1 + x)^2}^{\;n}\)be equal then
  • A
    n = r – 1
  • B
    n + r – 1 = 0
  • C
    n = r + 1
    Correct
  • D
    none of these.
15
If \(x = {99^{50}} + {100^{50}}\) and \(y = {(101)^{50}},\) then
  • A
    x = y
  • B
    none of these
  • C
    x \(>\) y
  • D
    x \(<\) y
    Correct