Recently Active Mathematics Questions

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let P[x] = x3 - rx + r + 11 be a polynomial , where r is a +ve integer . Let r vary [Q1] the no . positive integral solutions of p[x] = 0 are [a] 6 [b) 3 [c] nil [d] infinitely many [Q2] the sum of all +ve integral roots of p ...

Prove that 2[\frac {1}{2n^2-1} + \frac {1}{3(2n^2-1)^3}+\frac {1}{5(2n^2-1)^5}+..........]=\frac {1}{n^2} +\frac {1}{2n^4} +\frac {1} {3n^6} +.........=2log_en-log_e(n+1)-log_e(n-1) ...

Show taht 1+\frac {2n}{3} + \frac {2n(2n+2)}{3.6}+\frac {2n(2n+2)(2n+4)}{3.6.9}+... \infty=3^n and 2^n[1+\frac {n}{3} + \frac {n(n+1)}{3.6}+\frac {n(n+1)(n+2)}{3.6.9}+... \infty]=3^n ...

Two straight lines cut the axis of x at distances a and -a and the axis of y at distances b and b° respectively; find the coordinates of their point of intersection. Ans:- { a(b-b°)/(b+b°) , 2bb°/(b+b°) } From: S.L.Loney ...

1.Find the remainder when 2710 +751 is divided by 10. PLEASE TELL ME THE GENERAL METHOD TO THIS SUM 2.determine constant term in expansion ok (1+ x + (1/x)2 + (1/x)3)10 ...

Q1 let A be set of digit nos. a1a2a3a4 where a1>a2>a3>a4,then n(A) = ???????? Q2 All possible 2 factor products are formed form nos. 1,2,3...200.The number of factors of hte total obtained which are multiple of 5 ?? ...

find no. of distinct rational nos. x such that 0<x<1 and x=p/q where p,qε {1,2..6} ...

f(x)=x^2+bx+c. If f(x) assumes only interger values for all integer x then : a)b must be integer but c may not be. b)c must be integer but b may not be. c)b+c must be integer. d)None of these. ...

let A={1,2....n}.If X denotes subsets of A containing exactly 3 elements,then find \sum_{p\in X}{min(P)} ...

If r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is r2 t4s2, then the number of ordered pair (p, q) is (a) 252 (b) 254 (c) 225 (d) 224 ...

do we have non integral index in ur sylbaus n also -ve index FOT IIT JEE.......... ...

WELCOME all tiitians this thread is open to all good Qs on Vectors & 3D & discussions on them PLZ dont post qs out of IIT JEE's level ...

find the value of *Image* ...

Eleven scientists are working on a secret research project of ISRO. They wish to lock up all the documents regarding the project in a cabinet such that the cabinet can be opened if and only if atleast six of these scientists ...

Got this one from goiit.. (Nice that i went there and browsed a couple of posts :) 21 = x^y + y^x Find the values of x and y . (Restrict to the integral solutions only) Discuss the other cases too... ...

In how many ways can you color a cube with a) one color b) two colors c) three colors d) 4 colors e) 5 colors f) 6 colors Each of them is easy ... just needs a bit of thinking :) ...

If m and n are any 2 odd positive integers with n<m then largest positive integer which divides all numbers of the form (m2-n2).(my ans is cumin 4 but it is given 8). ...

Find the number of rectangles excluding squares from a rectangle of size 9 X 6.. ...

There are 10 points in a plane of which no three are collinear and 4 points are concyclic.Find the number of different circles that can be drawn through atleast 3 of these points.. Kindly explain also.. ...

There are n concurrent lines and another line parallel to one of them.Find the number of different triangles that will be formed by the (n+1) lines.. ...

\int_{-1}^{0}{\int_{-\sqrt{1-x^{2}}}^{0}{\frac{2}{1+\sqrt{x^{2}+y^{2}}}}}dydx ...

There are n people at a party. Prove that there are two of them such that of the remaining n − 2 people, there are at least \left[\frac{n}{2} \right]-1 of them each of whom knows both or else knows neither of the two. [ .] ...

prove 3^{n}>n^{3} for all positive integers `n`. note: open for all ...

in a book there is some formula if f(x+y)=f(x)+f(y) then f(x)=xf(1).how does this come?? ...

Let A=\left( \begin{array}{cc} a & b \\ 0 & a \end{array} \right) , by judging from A^2,\ A^3,\ \cdots to expect An for every positive integer n, then prove that the expectation is true by induction. Src: 1976 Hitotsubashi Un ...

This is another question from Larson's book.. .(Today I have given 2-3 from it) I_n=\int_{0}^{\pi/2}{\sin^nx dx} Show that I_{2n}=\frac{1.3.5....(2n-1)}{2.4.6....2n}\times \frac{\pi}{2} and I_{2n+1}=\frac{2.4.6....(2n-2)}{1.3 ...

Prove that: \begin{vmatrix}\frac{1}{p+1}&\frac{1}{p+2}&\ldots &\frac{1}{p+n}\\ \frac{1}{p+2}&\frac{1}{p+3}&\ldots &\frac{1}{p+n+1}\\ \vdots &\vdots &\ddots &\vdots\\ \frac{1}{p+n}&\frac{1}{p+n+1}&\ldots &\frac{1}{p+2n-1}\end{ ...

find the number of solutions : x^{2}+4x+1=\sqrt{x+3}-2 ...

There's a square ABCD.....inscribed in a circle, this square is now partitioned into non-overlapping rectangles, and for each rectangle it's circum-circle is drawn. If the sum of areas of all these circles equals the area of ...