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Binomial Theorem Test - 4

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Binomial Theorem Test - 4
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  • Question 1
    1 / -0

    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

  • Question 2
    1 / -0

    The number of dissimilar terms in the expansion of (a+b+c)12 is


    Solution

  • Question 3
    1 / -0
     =
  • Question 4
    1 / -0

    If the rth term in the expansion of  contains x20, then r =

    Solution

     

  • Question 5
    1 / -0
    If x = , then is equal to
  • Question 6
    1 / -0

    The two consecutive terms in the expansion of (3+2x)74, which have equal coefficients, are

  • Question 7
    1 / -0
    The coefficient of the middle term in the expansion of (1 + x)2n is
  • Question 8
    1 / -0
    The sum of 12C1. + 12C2 + 12C3 + ................ upto 12 terms is
  • Question 9
    1 / -0

    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

     

  • Question 10
    1 / -0
    The value of x, for which the 6th term in the expansion of is 84, is equal to
  • Question 11
    1 / -0

    If n is a rational number, which is not a whole number, then the number of terms in the expansion of (1+x)n,|x|<1, is

    Solution

    (1+x)n=nC0 1n+nC1  1n−1x1+nC2 1n−2x2+................+nCn x

    ⇒(1+x)n=1+nC1 x+nC2 x2+................+nC xn

    Hence we have number of terms of (1+x)n=n+1 



  • Question 12
    1 / -0
    Sum of coefficients in the expansion of (1 + 2x - 4x2)1994 is
  • Question 13
    1 / -0
    If (1 + x)n = C0 + C1x + C1x + C2x2 +…+ Cnxn, then C0C2 + C1C3 + C2C4 +……..+ Cn - 2 Cn is equal to
  • Question 14
    1 / -0
    The constant term in the expansion of  is
  • Question 15
    1 / -0
    The sum of coefficients in the expansion (x + 2y + 3z)10 is
  • Question 16
    1 / -0
    If an =  equals
  • Question 17
    1 / -0
    If 1 + x2 = , then is equal to
  • Question 18
    1 / -0

    The term containing x3 in the expansion of (x−2y)7 is

  • Question 19
    1 / -0

    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

    Solution

  • Question 20
    1 / -0
    If A be the sum of the odd terms and B the sum of even terms in the expansion of (x + a)n, then the value of A2 - B2 is
  • Question 21
    1 / -0

    The two consecutive terms in the expansion of (3+2x)74, which have equal coefficients, are

    Solution

  • Question 22
    1 / -0
    If an = having n radical signs, then by the method of mathematical induction which of the following is true?
  • Question 23
    1 / -0
    If the number of terms in the expansion of (x - 2y + 3z)n is 45, then what is the value of n?
  • Question 24
    1 / -0
    If C0, C1, C2 …Cn denote the binomial coefficients in the expansion of (1 + x)n, then the value of . Cr is
  • Question 25
    1 / -0

    The number of dissimilar terms in the expansion of (a+b+c)12 is

    Solution

    We have the number  of dissimilar terms in the expansion of(x+y+z)n is (n+1)+n+(n−1)+...........+3+2+1=(n+1)(n+2)/2

    Hence the number of dissimilar terms in the expansion of (a+b+c)12=(12+1)(12+2)/2=13.14/2=91

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