Home
Class 11
MATHS
Using binomial theorem (without using th...

Using binomial theorem (without using the formula for `.^n C_r`) , prove that `.^nC_4+^m C_2-^m C_1.^n C_2 = .^m C_4-^(m+n)C_1.^m C_3+^(m+n)C_2.^m C_2-^(m+n)C_3^m.C_1 +^(m+n)C_4dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

Similar Questions

Explore conceptually related problems

Prove that ^m C_1^n C_m-^m C_2^(2n)C_m+^m C_3^(3n)C_m-=(-1)^(m-1)n^mdot

Show that: ^mC_1+^(m+1)C_2+^(m+2)C_3+…….+^(m+n-1)C_n=^nC_1+^(n+1)C_2+^(n+2)C_3+…+^(n+m-1)C_m .

If m in N and mgeq2 prove that: |1 1 1\ ^m C_1\ ^(m+1)C_1\ ^(m+2)C_1\ ^m C_2\ ^(m+1)C_2\ ^(m+2)C_2|=1 .

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2m+1) 2^(n) .

[(^nC_0+^n C_3+)-1/2(^n C_1+^n C_2+^n C_4+^n C_5]^2 + 3/4(^n C_1-^n C_2+^n C_4 +)^2= a. 3 b. 4 c. 2 d. 1

Prove that 1/(n+1)=(.^n C_1)/2-(2(.^n C_2))/3+(3(.^n C_3))/4- . . . +(-1^(n+1))(n*(.^n C_n))/(n+1) .

If alpha=^m C_2,t h e n^(alpha)C_2 is equal to a. ^m+1C_4 b. ^m-1C_4 c. 3^(m+2)C_4 d. 3^(m+1)C_4

((1 + ""^nC_1 + ""^nC_2 + ""^nC_3+…….+nC_n)^2)/(1 + ""^(2n)C_1 + ""^(2n)C_2 + ""^(2n)C_3 + ……… + ""^(2n)C_(2n)) =

Statement 1: a fair coin tossed 15 times, then the probability of getting head as many times in the first ten throws as in the last five is 3003/32768. Statement 2: Sum of the series ^m C_r^n C_0+^m C_(r-1)^n C_1++^m C_0^n C_r=^(m+n)C_r .

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

    Text Solution

    |

  2. Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

    Text Solution

    |

  3. Using binomial theorem (without using the formula for .^n Cr) , prove ...

    Text Solution

    |

  4. Prove that .(r+1)*^n Cr-r*^n Cr+ ... +(-1)^r.^n Cr=(-1)^r.^(n-2)Crdot

    Text Solution

    |

  5. Find the sum .^n C0+^n C4+^n C8 + . . .

    Text Solution

    |

  6. Find the value of ^4nC0+^(4n)C4+^(4n)C8++""^(4n)C(4n) .

    Text Solution

    |

  7. Find the coefficient of x^n in the polynomial (x+^n C0)(x+3^n C1)xx(x+...

    Text Solution

    |

  8. If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15), then find the value of C2+2C...

    Text Solution

    |

  9. Prove that (.^n C0)/1+(.^n C2)/3+(.^n C4)/5+(.^n C6)/7+ . . . =(2^n)/(...

    Text Solution

    |

  10. Find the sum sumsum(0lt=ilt=jlt=n)^n Ci^n Cj

    Text Solution

    |

  11. Find the sum sumsum(i!=j)^n ^nCi^n Cj

    Text Solution

    |

  12. Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as ...

    Text Solution

    |

  13. Prove that (1^2)/3""^n C1+(1^2+2^2)/5^n C2(1^1+2^2+3^2)/7^n C3+ +(1^2+...

    Text Solution

    |

  14. Prove that 1/(n+1)=(.^n C1)/2-(2(.^n C2))/3+(3(.^n C3))/4- . . . +(-1^...

    Text Solution

    |

  15. Find the sum 2C0+(2^3)/2C1+(2^3)/3C2+(2^4)/4C3++(2^(11))/(11)C(10)dot

    Text Solution

    |

  16. If in the expansion of (2x+5)^(10) , the numerically greatest tem in ...

    Text Solution

    |

  17. Find the value of 1/(81^n)-(10)/(81^n)^(2n)C1+(10^2)/(81^n)^(2n)C2-(10...

    Text Solution

    |

  18. Find the value of 5C3 + 4C2

    Text Solution

    |

  19. Find the sum 1C0+2C1+3C2++(n+1)Cn ,w h e r eCr=^n Crdot

    Text Solution

    |

  20. If (1+x+x^2++x^p)^n=a0+a1x+a2x^2++a(n p)x^(n p), then find the value o...

    Text Solution

    |