Recently Active Algebra Questions

pl tell hw 2 do Q .Let n be a positive integer and f(n) = 1! + 2! + 3! +........n! and R(x) and Q(x) be polynomials in x such that f(n+2)= R(n)f(n+1) + Q(n)f(n) for all n≥1 Now let P(x) = - Q(x)/R(x) (for all x ≥ 1) denot ...

was number theory ever a part of jee syllabus??if yes,then till which year? ...

I've a doubt and want it to be clearied... Let us suppose... (a - 3)2 + (b - 4)2 + (c - 8)2 + (d - 14)2 + (e - 19)2 = 0 then we've to find a + b + c + d + e...?? Now, clearly, a = 3, b = 4, c = 8, d = 14 and e = 19 and thus, ...

Let n be a positive Integer. 0<\theta _{i}<90 , such that cos^{2}\theta _{1}+cos^{2}\theta _{2}+cos^{2}\theta _{3}+.....+cos^{2}\theta _{n} = 1 PROVE THAT: tan \theta _{1}+tan \theta _{2}+tan \theta _{3}+...+tan \theta ...

Closed forms of the sum of powers for fixed values of m S_m(n) = \sum_{k=1}^n k^m = 1^m + 2^m + \cdots + n^m \, are always polynomials in n of degree m + 1. Note that Sm(0) = 0 for all m ≥ 0 because in this case the sum is ...

no. of ways to place x things in y boxes. what does word place mean here either (i)to distribute OR (ii)to arrange i have seen most book authors have given answer with reasoning (i) to be correct...i.e. finding no of division ...

find the h.c.f(or clasically g.c.d [3]) of 2nC1,2nC3,2nC5,.......,2nC2n-1 where n=2m * q, where q is an odd integer. ...

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in expansion of (3-x/4+35x/4)n the sum of the binomial coefficients is 64.find n. ...

a perfect cubic die is thrown large number of times in sets of 8.occurence of or 6 is calle d a success.in what proportion of the sets would you expect three successes? ...

Evaluate: \sum_{r=0}^{n}{^{n}C_{r}\left(r-nx \right)^{2}x^{r}\left(1-x \right)^{n-r}} ...

Consider (n+1)n/nn+1 (1+1/n)n < 2 +1/2 + 1/22 + 1/23 + ...... ∞ = 3, provided n>3 Please explain me the above step. I can prove that the expression in LHS is greater than 2 by Binomial expression. How does this come? ...

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If the integers m and n r chosen at random with replacement frm 1 to 100 , then what is the probability that a no. of the form 7^m + 7^n is divisible by 5? ...

p is the probability that a man aged x years will die in a year.find the probability that out of n men A1,A2,.......,An each aged x years,A1 will die in a year and will be first to die. ...

Prove that 100400 can be written as the sum of two squares of integers....!! Such an easy one....... but a good one though.......!! ...

1.If A and B are two distinct matries such that A3=B3 and A2B=B2A,find the det(A3+B3) and det(A2+B2). 2.Suppose A and B are two non-singular matrices such that B≠I,A6=I and AB2=BA.find the least value of k for Bk=I. ...

If x1,x2 are the roots of x2-3x+a=0, and x3,x4 are those of the equationx2-12x++b=0, and x1,x2,x3 and x4 are in increasing G.P.,find a and b. ...

Show that C12 - 2C22 + 3C32............-2n.C2n2 = (-1)n-1.nCn where Cr stands for 2nCr ...

z1,z2,z3 are three complex numbers such that (z3-z1)/(z3-z2)=∂ find ∂ such that it represents an equilateral triangle i got 0.5±i√3/2 as the answer.in fact these both were in the options too.but the final answer was gi ...

what is the probability that sin-1 ( sin x ) + cos-1 ( cos y ) is an integer x , y belongs to { 1 , 2 , 3 , 4 }? ...

write following functions as a function g(w) where w=(z+z-1) (1)f(z)=z10+z9+z8+....+z+1 (2)f(z)=z8-z7+z5-......+z3-z+1 ...

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1. Find the no. of three element set of positive integers (a,b,c) satisfying the abc = 2310 2. Find the no. of distinct throws that can be made with 'n' 6 faced fair dices which are indistinguishable among them? NOTE: Please ...

Sir, I need help with those special type of questions like - 1. Find the maximum no. of planes in which n circles can divide a plane? 2. Find the maximum no. of point of intersection of n circles and n straight lines? 3. Tota ...

is rank of matrix in jee syllabus or not ...

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in book its given that the number of ways to distribute 3 identical A's into 2 different groups ( when empty groups are allowed) is 4, which is correct.... also the no. of ways to distribute and arrange A,B,C into two differe ...

Let a, b, c, d, e be real numbers satisfying a+ 16b+ 81c + 256d + 625e = 1 16a + 81b + 256c + 625d + 1296e = 12 81a + 256b + 625c + 1296d + 2401e = 123 256a + 625b + 1296c + 2401d + 4096e = 1234 625x1 + 1296x2 + 2401x3 + 4096 ...