Recently Active Algebra Questions

$\textrm{Show that for any real numbers }$ $a_{3 } ,a_{4},........,a_{85 }, $ $\textrm{the roots of the equation }$ $a_{85}x^{85 }+ a_{84}x^{84}+ ..........+a_{3}+ 3x^2+ 2x+ 1=0$ $ \textrm{are not real}$ ...

in a certain test ,ai students gave wrong answers to at least i questions where i=1,2,3,4,5,....................k. no student gave more than k wrong answers. the total number of wrong answers given is__________ (A) a1+a2+a3+. ...

long time since posted ques.............here are some for 2011 aspirants daily updates..... Day1 Q1 Express 1*3*5*...*(2n-1)/2*4*6*8....*(2n) as a/2w where a is odd and w<2n Q2 Prove that there is no prime number in sequen ...

LET A={123},THEN THE NO OF RELATIONS CONTAING (!,2),(2,3) WHICH ARE REFLEXIVE AND TRANSITIVE BUT NOT SYMMETRIC ARE.GUYS PLS EXPLAIN BRIEFLY..................... ...

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If three positive real numbers a, b, c are in A.P. and abc = 4 then minimum possible value of b is ...

prove that xyz >(y+z-x)(z+x-y)(x+y-z) i have found one solution but i am sure a better is existing in someones brain :) ...

Prove the criteria for divisibility by 9. ...

find the domain and range of function f(x)= 2x+2y =2 ...

If a,b,c are in H.P. and n>1 , then show that an+cn > 2bn. ...

Let a_0 = a_1 = 1 and a_{n+1} = 1 + \frac{a_1^2}{a_0} + \frac{a_2^2}{a_1} + ...+ \frac{a_n^2}{a_{n-1}} Find a closed formula for an (i.e. express an as a function of n) ...

2n points are chosen on a circle. In how many ways can one join pairs of points by non-intersecting chords? ...

a plane with parallal straight lines with separation 2a is spread till infinity,a needle of length 2l (2l<2a) is thrown here at random find the probability of the needle to hit one of the line ...

1. Give the continued fractions expansions of a = d2±1 , d element of Z 2. Determine the least positive solution of x2 − ny2 = 1, where n = d2 + 2 ...

Why is a^0 = 1 ?? Where a is any number. ...

Three numbers are chosen at random from 1 to 20. The probability that they are consecutive is ...

If x,y,z are in H.P,prove that log(x+z)+log(x+z-2y)=2log(x-z). ...

prove that 32n+7 is a multiple of 8 ...

Find the sum of 2+5+10+17+26+.......to n terms. ...

1) Suppose that x1,x2....xn are reals. Given xi=-xn-i+1 S=ΣΣΣxixjxk summation is over all distinct i,j,k belonging to [1,n] Find S. 2) Consider the smallest number in each of the subsets of size r of the set X={1,2,3,4,5.. ...

IF ef(X)=10+x/10-x, x belongs to (-10.10) and f(x)=k f[200x/100+x2] ,then find k. ...

IF a2x4 + b2y4=c6 then max value of xy is ...

A has n distinct elements.find no. of distinct functions from A to A i m getting answer as nn.is it correct?? ...

Q1. Every one of the 10 available lamps can be switched on to illuminate a certain hall. The total number of ways in which the hall can be illuminated is -: a) 55 b) 1023 c) 210 d) 10! My Working : Each lamp can or cannot ill ...

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1) Every living person has shaken hands with a certain number of other persons . prove that the count of the number of the people who have shaken hands an odd number of time must yield an even number. 2) In a chess is it poss ...

3a=(b+c+d)^3 3b=(e+c+d)^3 3c=(e+a+d)^3 3d=(e+a+b)^3 3e=(c+a+b)^3 . find all reals (a,b,c,d,e). Source - INMO. ...

Prove if gcd(a,b)=1,then gcd(a^2,b^2)=1. ...

The values of α for which the system of equations x+y+z=1 x+4y+10z=α2. x+2y+4z=α....is consistent are given by.. Ans.(1.2) ...

FIND ALL THE INTEGRAL TRIANGLES WHOSE PERIMETER EQUALS THERE AREA . ...