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Find n ,if(n+1)! =12xx(n-1)!dot...

Find `n ,if(n+1)! =12xx(n-1)!dot`

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Find the sum 1 xx 2 xx .^(n)C_(1) + 2 xx 3 xx .^(n)C_(2) + "….." + n xx (n+1) xx .^(n)C_(n) .

Find the sum of 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+ ...,

If U_n=(sqrt(3)+1)^(2n)+(sqrt(3)-1)^(2n) , then prove that U_(n+1)=8U_n-4U_(n-1)dot

Find the coefficient of x^n in the expansion of (1-9x+20 x^2)^(-1)dot

Find the sum of n terms of the series whose nth term is T(n)=tanx/(2^n)xxsecx/(2^(n-1)dot)

If a > b and n is a positive integer, then prove that a^n-b^n > n(a b)^((n-1)//2)(a-b)dot

Prove that (.^n C_0)/1+(.^n C_2)/3+(.^n C_4)/5+(.^n C_6)/7+ . . . =(2^n)/(n+1)dot

Find the sum of the coefficients in the expansion of (1+2x+3x^2+ n x^n)^2dot

Find the equation of the line passing through the points (1,2,3)a n d(-1,0,4)dot

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CENGAGE PUBLICATION-PERMUTATIONS AND COMBINATIONS-All Questions
  1. If 9^(th) term of an A.P. is zero, prove that its 29^(th) term is doub...

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  2. In how many ways can four people, each throwing a dice once, make a su...

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  3. Find n ,if(n+1)! =12xx(n-1)!dot

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  4. Three numbers are in AP. If theirsum is 27 and their product is 648. F...

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  5. Find the total number of integers 'n' such that 2 le n le 2000 and ...

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  6. The number of polynomials of the form x^3 + ax^2 + bx + c which are di...

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  7. Find the number of diagonals in a polygon with n sides.

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  8. Find the total number of n -digit number (n >1) having property that n...

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  9. Prove that (n !)^2 < n^n n! < (2n)!, for all positive integers n.

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  10. Find the sum of the series sum(r=1)^n r/((r+1) !)dot

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  11. Find the exponent of 80 in 200!.

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  12. Prove that .^nPr = ^(n-1)Pr + r^(n-1)P(r-1)

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  13. How many ways are there to seat n married couples (ngeq3) around a tab...

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  14. A round-table conference is to be held among 20 delegates belonging fr...

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  15. How many numbers can be formed from the digits 1, 2, 3, 4 when repetit...

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  16. Find the three-digit odd numbers that can be formed by using the digit...

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  17. If ^ n P5=20 ^nP3 find the value of n

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  18. Find the total number of ways of selecting five letters from the word ...

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  19. Passengers are to travel by a double decked bus which can accommodate ...

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  20. Simplify the following and express it in the form (a+ib): (3+4i)(2-3i...

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