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Find `n` if `n P_1=2`

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Let int_x^(x+p)f(t)dt be independent of x and I_1=int_0^p f(t) dt , I_2 = int_(10)^(p^n+10) f(z) dz for some p , where n in N . Then evaluate (I_2)/(I_1) .

Find the value of n such that (""^(n)P_(4))/(""^(n-1)P_(4))=(5)/(3), n gt 4

Let f(n)=|n n+1 n+2 ^n P_n^(n+1)P_(n+1)^n P_n^n C_n^(n+1)C_(n+1)^(n+2)C_(n+2)| , where the symbols have their usual meanings. Then f(n) is divisible by a. n^2+n+1 b. (n+1)! c. n ! d. none of these

Find the value of n such that ""^(n)P_(5)=42""^(n)P_(3), n gt 4

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If the number of permutations of n different things taken r at time be denoted by .^(n)P_(r) , show that , (.^(n)P_(1))/(1!)+(.^(n)P_(2))/(2!)+(.^(n)P_(3))/(3!)+...+(.^(n)P_(n))/(n!)=2^(n)-1

Find the sum of the series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^2+5((2n+1)/(2n-1))^3+.....

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Statement 1: In the expansion of (1+x)^(41)(1-x+x^2)^(40), the coeffic...

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  2. The coefficient of x^(n) in (1+x+(x^(2))/(2!) + (x^(3))/(3!) +"….." + ...

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  3. Evaluate the following .^3C2

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  4. Evaluate .^5C2

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  5. The value of sum(r=0)^(10)r""^(10)C(r)3^(r)(-2)^(10-r) is (a) 20 (b) 1...

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  6. Find n if n P1=2

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  7. Evaluate .^5P2

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  8. The value of (.^(n)C(0))/(n)+(.^(n)C(1))/(n+1)+(.^(n)C(2))/(n+2)+"..."...

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  9. The value of .^(20)C(0)+.^(20)C(1)+.^(20)C(2)+.^(20)C(3)+.^(20)C(4)+.^...

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  10. If (3+x^(2008)+x^(2009))^(2010)=a0+a1x^2+....+anx^n, a0-1/2 a1-1/2 a2+...

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  11. Find the seventh term of the G.P: 1, √3, 3, 3 √3, …..

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  12. Find the 10th term of the G.P. : 12, 4, 1 1/3,....

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  13. If (1+x)^(n) = C(0) +C(1)x+C(2)x^(2) + "….." + C(n)x^(n), then C(0)C(2...

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  14. The value of (lim)(n->oo)sum(r=1)^(n)(sum(t=0)^(r-1)1/(5^n).^n Cr.^r C...

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  15. If n gt 2, then prove that C(1)(a-1) - C(2) xx (a-2) + "….." + (-1)^(...

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  16. Find the nth term of the series: 1, 2, 4, 8, ……

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  17. The remainder, if 1+2+2^2+2^3+....+2^1999 in divided by 5 is

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  18. Largest real value for x such that underset(k=0)overset(4)sum((3^(4-k)...

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  19. If in the expansion of (a-2b)^(n), the sum of 5^(th) and 6^(th) terms ...

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  20. The number of real negative terms in the binomial expansion of (1+ix)^...

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