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
If n is a rational number, which is not a whole number, then the number of terms in the expansion of \({(1 + x)^n},\left| x \right| < 1,\) is
  • A
    n + 1
  • B
    Infinitely many
    Correct
  • C
    nothing can be said
  • D
    n
2
If n is a +ve integer, then the binomial coefficients equidistant from the beginning and the end in the expansion of \({(x + a)^n}\) are
  • A
    multiplicative inverse of each other
  • B
    nothing can be said
  • C
    additive inverse of each other
  • D
    equal
    Correct
3
If the rth term in the expansion of \({\left( {{{{x^3}} \over 3} - {2 \over {{x^2}}}} \right)^{10}}\)contains \({x^{20}},\) then r =
  • A
    5
  • B
    4
  • C
    2
  • D
    3
    Correct
4
If the coefficients of \({x^{ - 7}}\) and \({x^{ - 8}}\) in the expansion of \({\left( {2 + {1 \over {3x}}} \right)^n}\) are equal then n =
  • A
    55
    Correct
  • B
    15
  • C
    56
  • D
    45
5
The largest term in the expansion of \({(1 + x)^{19}}\) when \(x = {1 \over 2}\) is
  • A
    \({{\rm{8}}^{{\rm{th}}}}\)
  • B
    \({{\rm{6}}^{{\rm{th}}}}\)
  • C
    none of these
  • D
    \({{\rm{7}}^{{\rm{th}}}}\)
    Correct
6
If coefficients of three successive terms in the expansion of \({(x + 1)^n}\) are in the ratio 1 : 3 : 5, then n is equal to
  • A
    8
  • B
    7
    Correct
  • C
    9
  • D
    none of these
7
The exponent of power of x occurring in the \({{\rm{7}}^{{\rm{th}}}}\) term of expansion of \({\left( {{{3x} \over 2} - {8 \over {7x}}} \right)^9}\) is
  • A
    - 3
    Correct
  • B
    5
  • C
    3
  • D
    - 5
8
The term independent of x in the expansion of \({\left( {x - {3 \over {{x^2}}}} \right)^{18}}\) is
  • A
    \({}^{18}{C_6}\;{3^6}\)
    Correct
  • B
    \({3^6}\)
  • C
    \({}^{18}{C_6}\)
  • D
    \({}^{18}{C_{12}}\)
9
The number of dissimilar terms in the expansion of \({(a + b)^n}\) is n + 1, therefore number of dissimilar terms in the expansion of \({(a + b + c)^{12}}\) is
  • A
    39
  • B
    78
  • C
    91
    Correct
  • D
    13
10
The term containing \({x^3}\) in the expansion of \({(x - 2y)^7}\) is
  • A
    \({{\rm{4}}^{{\rm{th}}}}\)
  • B
    \({{\rm{3}}^{{\rm{rd}}}}\)
  • C
    \({{\rm{6}}^{{\rm{th}}}}\)
  • D
    \({{\rm{5}}^{{\rm{th}}}}\)
    Correct
11
The coefficients of \({x^p}\) and \({x^q}\) ( p, q are + ve integers) in the binomial expansion of \({(1 + x)^{p\; + \;q}}\) are
  • A
    equal
    Correct
  • B
    equal numerically
  • C
    None of these
  • D
    reciprocal of each other
12
If 2nd, 3rd and 4th terms in the expansion of \({(x + a)^n}\) are 240, 720 and 1080 respectively, then the value of n is
  • A
    15
  • B
    5
    Correct
  • C
    10
  • D
    20
13
If the first three terms in the expansion of \({(x + a)^n}\) are 729, 7290 and 30375 respectively, then the value of n is
  • A
    8
  • B
    none of these
  • C
    9
  • D
    6
    Correct
14
The coefficient of \({x^n}\) in the expansion of \({(1 - x)^{ - 2}}\) is
  • A
    ( n + 1)
    Correct
  • B
    none of these
  • C
    \({( - 1)^n}(n + 1)\)
  • D
    \({( - 1)^n}n\)
15
The two consecutive terms in the expansion of \({(3 + 2x)^{74}}\), which have equal coefficients, are
  • A
    none of these
  • B
    )7th and 8th
  • C
    11th and 12th
  • D
    30th and 31st
    Correct