Recently Active Algebra Questions

let a,b,c be 3 real no.s such that 1>a^-1+b^-1+c^-1=1/2 2>a+b+c=2 3>a^-2+b^-2+c^-2=1/4 match the following:- I)abc is greater than a)6 II)ac+ab+bc is less than b)8 III)a^2+b^2+c^2 is less than c)-2 IV)a^3+b^3+c^3 is ...

Q1: No. of ordered pair (x,y) satisfying the Eqn x2+1=y and y2+a=x is: Q2: If the Eqn ax2+bx+c=0 and x3+3x2+3x+2=0 has two common roots, then: A) a = b (Not Equal to) c B) a (Not equal to) b = c C) a=b=c D) a=-b=c Please Expl ...

If the complex sequence of numbers z0, z1, z2........satisfy z_0=i+\frac{1}{137} and for n≥1 z_{n+1}=\frac{z_n+i}{z_n-i} then find the value of z2007 ...

a well known one, but still very amusing(i think this has been already been discussed but still): An airplane has 100 seats, and 100 passengers were assigned seats. The first passenger enters the plane and rather than sitting ...

This qsn cud have been in the MO section, but it's way easier than an Olympiad problem, as such. Define a function f over the set of naturals as f(n)=n! Now let a positive real a have the decimal representation as a=0.f(1)f(2 ...

ltn---∞ cos( x/2 ).cos( x/4 ).cos( x/8 ).................cos( x/2n ) find the value.... ...

ltx---∞ { x-sinx/x-cosx }1/2 ...

ltx→0+ xm(log x)n where m,n are natural no.s find the value.... ...

1) If f(x) = x2 - x3 find f -1(x) 2) The remainder when the polynomial x+x3+x9+x27+x81+x243 is divided by x2 -1 3) If | x | + x + y =10 x + | y | - y =12 find x + y ...

Number of quadratic equations with real roots which remain unchanged even after sqaring their roots is 1. 1 2. 2 3. 3 4. 5 ...

find coefficient of x49 in expansion of (x+1)(x+2)(x+3)......(x+99) ...

A function f(x) is a polynomial function in sin-1x ( ie f(x) = a(sin-1x )n + b(sin-1x )n-1 + c(sin-1x )n-2..........+ k) the conditions given on f(x) are: 1. f(x) is an onto function. 2. f o f o f o f o f o f o...........o f ...

Find least no. of digits in x , When f(f(f(f(x)))) = 1 whre f(x) is the sum of the digits in x x > f(x) f(x) > f(f(x)) f(f(x)) > f(f(f(x))) > 1 ...

can some one plz tell me what is a palindrome & what kind of sums on palindromes come in iitjee. ...

*** Q3 is dbt only.....rest i have done... *** Q1 Determine sign of roots of equation x2+(3-2a)x-3a+2=0 Q2 If a,b,c are odd integers prove that both roots of ax2+bx+c=0 can not be rational Q3 ax2+bx+c=p has both roots integer ...

find the value of summation \sum_{r=0}^{2008}\left [ \frac{2^r}{3} \right ] \\ \\\textup{where [.] is GIF} ...

if p and q are the 2 roots of the eqns a(x2-x)+x+5=0. If a1 and a2 are the two values of a for which the roots p and q are related by p/q + q/p = 4/5 theb find the value of a1/a2 + a2/a1 my answer: without even calculating ca ...

how many faces of rubik's cube can be simultaneously solved ??? ...

A class test has maximum marks equal to 50 . It should contain 7 questions each having marks in the range of 2(min. marks for a ques.) to 14(max marks of a ques.). Find the possible number of ways to prepare the test. ...

A train has to stop at any 3 stations in the shown fixed lot such that no two stations are adjacent. Find the number of ways this is possible. *Image* ...

prove that for all integers n>1, 1/n+1+1/n+2+/n+3.....1/2n>1/2 ...

1.find the condition that the expression ax2+2hxy+by2 may have two factors of the form (y-mx) and (my+x) respectively. ans: a+b=0 2.find the condition that ax2+2hxy+by2 and a1x2+2h1xy+b1y2 may have factors of the form (y-mx) ...

solve for x 16x+30\sqrt{1-x^2}=17\sqrt{1+x}+17\sqrt{1-x} where 0<x<1 ...

Among the following which pair of quadratic equations have the same nature of roots? a) 13x2+41x+37 and 912+67x+13 b) 11x2+23x+25 and 59x2+45x+11 c) 31x2+14x+7 and 52x2+76x+31 d) all Finding out the discriminant is a tedious ...

if 1/a+1/b=1/c,and a,b,c have no common factor...then prove that a+b is a perfect square. ...

help me out!.. the number f positive integral solutions of x4- y4 = 3789108 ...

if the sequence {an} ,satisfies the recurrence , an+1 = 3an -2an-1 for n>=2 a0 = 2 a1 = 3 Find a2007 ...

*Image* ...

let x,y,z be complex numbers such that x + y+ z=2 x2 +y2+z2=3 xyz= 4 Find the value of *Image* ...

solve for x and y: x + y = 11 y + x = 7 ...