Recently Active Algebra Questions

Find all pairs (a,b) of real numbers such that whenever α is a root of x2 + ax + b = 0, α2 - 2 is also a root of the equation. I am confused with the solution of this question... case1 : When α = β So there is only one po ...

Show that \sum_{k=0}^{n}{C(n,k)sinkx cos(n-k)x} = 2^{n-1}sinnx ...

Find the last term of the A.P formed by the common terms of both the A.P's 15,17,19....... 135 and, 21,27,33........ 561 ...

1.There are n≥4 points situated on the plane such that no two of the lines joining them are parallel and no three of lines joining them are concurrent except at the given points.Find the number of points of intersection, ot ...

Prove that among any 16 distinct digit +ve integer not exceeding 100 there are four distinct ones a,b,c,d such that a+b=c+d ...

x4 -(x - 1)2 \ (x2 + 1)2 + x2 - (x2 -1)2 \ x2 (x +1)2 - 1 + x2 (x -1)2 -1 \ x4 -(x+1)2 ...

If the angle between the hands of a clock be 54 degrees and the time it reads be between 7 and 8.Find the time indicated by the clock. ...

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Find the sum of all numbers greater than 10,000 formed by using the digits 0,2,4,6,8, no digit being repeated in any number. ...

Can any one explain me how to find the coeff. of x5 in the expression (1+x)(1+x+x2)(1+x+x2+x3+x4)2 I did not start Binomial Expansions yet. So please explain in easy language. ...

I would be grateful to anyone who could explain me in detail. 1) No. of ways in which 6 diff. toys can be given to 2 children so that all toys donot go to the same child. 62 2) No of ways in which 6 diff. toys may be distribu ...

when we say the confition for a number k to be greater than both the roots of ax2+bx+c (whether a is less or greater than 0), one of the conditions is af(k)>0. Why do we multiply a with f(k) and why not simply check whethe ...

if a girl stands on a rotating platform and then suddenly if she getz her hands inwards towardz her then angularmomentum increases angular velocity decreases moment of inertia decreases moment of inertia increses wch of the f ...

y=( 1/x )2(x)2 wt is its max. value?? it is an easy one.. let us see euclid who seems himself to be genius solves it in wt time . it is very easy ...

I got this doubt while solving a problem- \sum_{r=2}^{n}{}\left|A_{1} A_{r}\right| = 2\sum_{r=2}^{n}{}sin(r-1)\frac{\Pi }{n} I got the answer as 2cot\frac{\Pi }{2n} The answer given is 4cosec\frac{\Pi }{n} Please help ...

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Let P(x)=1+x+x2+x3+x4+x5 What is the remainder when P(x12) is divided by P(x)?? (A)0 (B)6 (C)1+x (D)1+x+x2+x3+x4 ...

If x, y are 2 independent variables, find rho(x,y) or R(x,y) ...

NOT A DOUBT! :D is it possible to have a QUADRATIC equation of the form (a+1)x2+2(a+1)x+(a-2)=0 to have 2 equal roots? is the same possible for the eqn (a-1)x2+2(a+1)x+(a+1)=0 if yes then find values for a in both cases and i ...

Q1)Solve: 4x - 3(x-1/2)= 3(x-1/2)-2(2x-1) Q2)If (1-p)is the root of quadratic equation x2+px+(1-p)=0.the the roots are?? Q3)Inthe proof of common roots it is given for eq1:aα2+bα+c=0 eq2:a'α2+b'α+c'=0 by cross multiplying ...

1.In how many ways can 6 boys and 4 girls sit in a row so that no boy is between two girls? 2.How many five digits number divisible by 4 can be formed by digits 1,2,3,4 and 5 if the digits can be repeated in the same number? ...

The number of ways of dividing 15 men and 15 women into 15couples,each consisting of man and woman is a. 1240 b.1840 c.1820 d.2005 ...

Q1)Solve:(x+3)5-(x-1)5≥244. Q2)Find all real a such that 5a2-3a-2, a2+a-2 and 2a2+a-1 are the lengths of sides of Triangle. ...

A boat has a crew of 10 men of which 3 can row only on one side and 2 only on the other.In how many ways,can the crew be arranged?? ...

z has property that |z-5i|=1 find z1 with the property that |z-z1| is maximum Pls also if u can explain little bit.. ...

1. 1+22+333+4444+......... upto n terms 2. Find the sum of Products of 1st n natural numbers taken 2 at a time. 3. Show that 49,4489,44489,........, the no's obtained by inserting 48 in the middle of the subsequent terms are ...

1)Two cards are drawn at random from a well shuffled pack of 52 cards & thrown away.Find the probability of drawing an ace from the remaining 50 cards. 2)A & B play alternately with an unbiased die.He who first throws a 'six' ...

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0≤i<j<k<l≤nΣΣΣΣn ans: n(n+1C4) ...

OUT OF 30 TICKETS MARKED WITH NUMBERS 1 TO 30 , 3 ARE DRAWN AT RANDOM ; FIND THE PROBABILITY THAT THESE ARE IN GEOMETRIC PROGRESSION. PLS. HELP ME WITH THESE SUM. pls... tell how the answer comes... ...