Recently Active Algebra Questions

find .... [ k = 1Σ80( 1/√k ) ] .. where [.] denotes greatest integer function ... ...

please give detailed solution ... find the orthocentre of triangle whose vertices are z1 z2 z3 ... ...

2 different lines meet a circle |z| =r in the points p , q , r ,s lines are not parrallel . then prove that these lines meet in the point z given by \frac{p^{-1} + q^{-1} -r^{-1}-s^{-1}}{p^{-1}q^{-1} -r^{-1}s^{-1} } =z ...

f(x) is a bijective function .. g(x) is inverse of that function .. f '(x) = 1/ (1 + x2009) find g ' (x) in terms of g(x) ? ...

please give a detailed solution... dont give me hints i tried it many times before editing [2] can u please tell me equation of line perpendicular to az + \bar{a}\bar{z}+b=0 yaar actually i cant make out difference b/w two eq ...

1. let f(x)=x2+bx+c,where b,c ε R.if f(x) is a factor of both x4+6x2+25 and 3x4+4x2+28x+5,then least value of f(x) is a. 2 b. 3 c. 5/2 d. 4 2. the number of ordered pair of positive integers x,y such that x2+3y and y2+3x are ...

find the number of the natural numbers less than or equal to 2985984,which are neither perfect squares nor perfect cubes . ...

*Image* try d 7th and 8th one ...

This is a fun problem. May i request that only the students attempt this one? If a,b and c are all distinct real numbers, then find values of a,b and c such that \frac{a-b}{1+ab} + \frac{b-c}{1+bc} + \frac{c-a}{1+ca} = 0 ...

find the min value of \left|a+b\omega +c\omega ^{2} \right| where a,b,c are not equal integers and ω≠1 is cube root of unity.. ...

let S be the set of 6 -digit numbers a1 a2 a3 a4 a5 a6 (all digits are distinct) where a1≥ a2≥ a3≥ a4≤ a5≤ a6.then n(S) is equal to NOTE :PLEASE IGNORE THE EQUALITY AND CONSIDER ONLY THE INEQUALITY RELATIONS .(i cou ...

dont give me official solm..........i cant understand that,,,,,,and i cant do it myself either.... *Image* ...

find the degree of the following expression: ( 2x2+1 + 2x2-1 )6+ 26[ 2x2+1 + 2x2-1 ]-6 ...

Let f(x)=x2+bx+c,where b,c \in R . If f(x) is a factor of both x4+6x2+25 and 3x4+4x2+28x+5 , then the least value of f(x) is ...

if r,s t are prime nos. and p,q,r are +ve integers such dat LCM of p,q is r2t4s2 then the no. of ordered pairs (p,q) is.....patha nahin...y nothin strikes my big head ...

S1, S2.... be squares such that for each n>=1, the length of the side of Sn equals to the length of the diagonal of Sn+1... If side of S1 is 10 cm, for which of these values of n is the area of Sn less than 1 sq. cm? ...

maximum no of sets obtainable frm A and B by applyin sum n differnce operations ...

A box contains n coins,If P(E_i) = k ( i(i+1)) for 1\leq i\leq n , where P(E_i) denotes the probability of the event that i out of n coins are biased, find k ...

find the remainder when 2740 is divided by 12 ...

The real numbers x1,x2,x3 satisfying the equation x3-x2+bx+c=0 are in AP find the interval in which b and c lie! ...

S1, S2, S3.... Sn are sums of infinite Geometric series whose first terms are 1,2,3,....n and common ratios are 1/2, 1/3... 1/n+1 respectively then S12+S22+S3.... +Sn2=? ...

If thotal number of runds scored in n matches is \left(\frac{n+1}{4} \right)\left(2^{n+1} -n-2\right) where n >1, and the runs scored in the kth match are given by k.2n+1-k, 1≤k≤n. Find n ...

Sun of the first n terms of a the series 12+2.22+32+2.42+52+2.62.... is n(n+1)2/2 when n is even what is the sum when n is odd? ...

If a, b, c, are in AP. a2, b2, c2 are in HP prove that either a=b=c or a,b,-c/2 are in GP ...

An infinite GP has first term x and sum 5 then x belongs to ? ...

a, b, c, are +ve real numbers prove (1+a)7(1+b)7(1+b)7>77a4b4c4 ...

two persons ach make a thrw wid a pair of cubical die n let p denote d prob dat their thrws r equal then find d value of 648p Given by Integrations! ...

Total no. of ways in which 256 identical balls can be placed in '16' numbered boxes (1,2,3,...16) such that rth box contains atleast 'r' balls is (1≤r≤16) ...

NUMBER OF ORDERED TRIPLETS l,m,n ( l,m.n are positive integers and 1≤ l,m,n≤ 8 ) such that 2l + 3m + 5nis divisible by 4 is _______________ [94] a> 224 b>288 c> 60 d> 256 ...

The land of Hogwarts school of magic is different. The no. of girls and boys are equal . All the boys have two hands, while all the girls have only one {:)} . Dumbledore, the principal of the school arranged a party on new ye ...