Recently Active Mathematics Questions

1)For n≥3 determine all real solutions of the system of n equations x1+ x2+...+xn-1 = 1/xn ............ x1+ x2+ ...+xi-1+ xi+1+...xn= 1/xi ....... x2+ ...+ xn-1+ xn = 1/x1 2)Suppose P(x) is a polynomial with real coefficien ...

The Product (1 + tan1°) (1 + tan2°) (1 + tan3°) ........ (1 + tan45°) equals: a) 221 b) 222 c) 223 d) 224 ...

If K= sin (pi/18) sin (5pi/18) sin ( 7pi/18) , then numerical value of K is ...

\lim_{x\rightarrow \propto } [ 1^{1}+2^{1/2} + 3^{1/3} + ...... + x^{1/x} ] ...

Find the sum of the series:- 1+ 1/12 + 1/22 + 1+ 1/22 + 1/32 ..... 1+ 1/20072 + 1/20082 a)2008- 1/2008 b)2007- 1/2007 c)2007- 1/2008 d)2008- 1/2007 e)2008- 1/2009 ...

A man started from his home at 14:30 hrs and drove to a village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes he drove back by a different route of length (5/4) times the 1st route ...

Three vertices are chosen at randomly from seven vertices of regular seven sided polygon. Probability that they form vertices of an isosceles triangle is: a) 1/7 b) 1/3 c) 3/7 d) 3/5 ...

generalization of a past jee q Let p(x) be a polynomial over R of even degree n for which for which p(x)≥0 for all x. Prove that p(x) + p'(x) +...+ p(n)(x)≥0 for all x. source :Polynomials, E.J.Barbeau ...

Calculate; 1) 4cos20° - 3 cot20° 2) ( 2cos40° - cos20°)/sin 20° ...

The digit in the unit position of the integer 1!+2!+3!+.....+99! is: a)3 b)0 c)1 d)7 ...

1))fIND THE SUM upto n terms-2 +12+36+80+150+252..... 2))if a,b,c, r in HP then bc,ca,ab r in? ...

esinx+e-sinx=4 Find the maximum value of x. ...

Limitm→∞ Limitn→∞ (1+cos2m(n!πx)) where n! denotes factorial of n.. Answer=2 if x is rational and 1 if x is irrational.. ...

An automatic machine makes paper clips from wire coiling. If on an average 1 in 400 paper clips are defective and 100 clips are packed in each box, What are the probabilities that any box of clips will contain : a) No defecti ...

find the least positive value of a+b,where a,b are positive integers and such that 11divides a+13b and 13 divides a+11b ...

Let ABC be the triangle formed by intersection of the lines x-y=0 , y=0 and 7x+y = 56. Find the minimum possible perimeter of the family of triangles inscribed in ABC. ...

Q. Find the number of ways of selecting 10 objects out of 30 objects of which 10 are alike and rest are different? ...

Help me friends.I am not able to solve it. If tan( (pi/4) + y/2) = tan3 ( (pi/4) + x/2), prove that sin(y)/ sin(x) = (3 + sin2x)/ (1+ 3sin2x) ...

if (9,23) and (49,53) are the 2 focii of an ellipse. and x- axis is tangent to it.then find the length of major axis.?? ...

Ltx→0Ltn→∞ 1/n3 ∫nr=1[r2 (sin x)x] ,[x] is greatest integer fn2 ;∫ is summation ...

If a number n can be expressed as sum of two perfect squares prove that 2^{17^{17^{17^{17}}}}n can also be expressed as sum of two squares. ...

1 . Solve - x 3 - 3 x = x + 2 ...

find the number of digits in 5^30. given log 210 = 0.3010 ...

this sum came in AIEEE 2009.. ∫[cotx]dx from 0 to pi where [.]denotes greatest integer fnctn ...

Combinatorics marathon Inspired from artofproblemsolving we are gonna start a combithread maybe some questions will go above iitjee but i would like everyone to participate Rules 1) u need to post solution to the question uns ...

lt e-1/x/x x→0 ...

i am not able to solve this sum,someone help ∫√tanx dx = ? ...

what is the difference in these two statements.... >> a point dividing a line internally >> a point dividing a line externally let us suppose P divides AB in the ratio m:n and A = (x1,y1), B = (x2,y2) then coordin ...

Let I be an open interval of R. Let f : I--> R be a differentiable functiin such that f does not vanish on I. Prove that f is one-one on I. is the question correct as it stands or instead of f does not vanish on I it shoud ...

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