Recently Active Algebra Questions

For all real numbers a; b; c prove the following chain inequality 3(a2 + b2 + c2) ≥  (a + b + c)2  ≥ 3(ab + bc + ca): ...

What are the roots of x3+px2+q=0 in terms of p and q ...

If a, b, c, d are unequal +ve numbers then the roots of the equation x/x-a + x/x-b + x/x-c +x+d=0 are necessarily a)all real b)all imaginary c)2 real 2 imaginary d)atleast 2 real ...

If Cr=nCr,the sum of the series 2[( n/2 )fact)2]/nfact [C02-2C12+3C22-......(-1)n(n+1)2Cn2] where n is even integer,is (a)0 (b)(-1) n/2 .(n+1) (c)(-1)n.(n+2) (d)(-1)n.n (e)none of these Ans is (e)..however..pls provide the so ...

If x is real,then the maximum value of y=2(a-x)(x+√(x2+b2) ...

pls give the shortest method to solve this quickly *Image* ...

What shoud be the minimum thickness of a coin of radius 'r' so that there is a 1/3 probability that the coin will stand straight? ...

if D = diag(a1 , a2 , a3 , ...... an), where ai ≠0 for all i = 1,2....,n, then show that D-1 = diag(a1-1 , a2-1 , a3-1 , .......... an-1). ...

*Image* ...

The number of 5 digit numbers such that the sum of their digits is even is? ...

Number of permutations of 1,2,3,4,5,6,7,8 and 9 taken all at a time ,such that the digit 1 appearing somewhere to left of 2 3 appearing to the left of 4 and 5 somewhere to the left of 6 (e.g.815723946 would be one such permut ...

the number of four digits having only two consecutive digits identical is ?? ...

Find the coefficient of x99 and x98 in the polynomial (x-1)(x-2)(x-3).........(x-100). ...

Represent m6+n6 as a sum of 2 squares other than (m3)2+(n3)2. Think its easy....give it a try!:P ...

x1, x2, x3, x4 are real nos. x1 < x2 < x3 < x4. Product of any three chosen at a time + the remaining = 130. Find the sum of all possible values of x4 rounded to the nearest decimal place. ...

If a0, a1, a2,... are the coefficients in the order of expression of (1+x+x2)n, prove that a02-a12+a22-.....+(-1)n-1an-12=(1/2)an(1-(-1)nan) ...

A 10-digit number has one 1, two 2's, three 3's and four 4's as its digits in some order. Prove that it can never be a perfect square. ...

all possible three digits even numbers which can be firmed with the condition that if 5 is one of the digit,then 7 is the next digit is? ...

The number of ways in which 2 boys can take 4 subjects if each boy takes atleast one subject is? ...

Let abcd is 4 digit number which satisfy the equation 4*abcd=dcba find the abcd ...

number of 9 digits numbers divisible by 9 using the digits from 0 to 9 if each digit is used atmost once is K.8!, then k has value equal to? ...

in how many ways can the letters of the word CINEMA be arranged so that the order of vowels do not change ...

2 frnds after a long time decided to meet at a particular coffee shop between 5:00 pm to 6:00 pm on a specified day.they also decided that the person whho comes earlier will not wait for the second person for more than 10mins ...

The number of right angled triangles with integer sides and inradius r=2013 is (a) 13 (b) 17 (c) 27 (d) 39 ...

Nine hundred distinct n-digit positive number are to be formed using only the digits 2, 5 & 7. The smallest value of n for which this is possible is (a) 6 (b) 7 (c) 8 (d) 9 ...

I know something is wrong in the following proofs.Can't figure out which step is wrong. Proof of -1 =1: *Image* Proof of 1=3: *Image* ...

In a binomial distribution B(n, p=1/4), if the probability of at least one success is greater than or equal to 9/10, then prove that n is greater than 1/(log10 4 - log10 3) ...

a,b ε N. The number of ordered pairs (a,b), a<b such that 1/a + 1/b = 1/2013 is (a) 11 (b) 13 (c) 17 (d) 21 ...

\hspace{-16}$If $\bf{a,b}$ and $\bf{c}$ are different real no. such that\\\\\\ \begin{Vmatrix} \bf{a^3=3b^2+3c^2-25} \\\\ \bf{b^3=3a^2+3c^2-25} \\\\ \bf{c^3=3a^2+3b^2-25} \end{Vmatrix}\\\\\\ Then find value of $\bf{abc=}$ ...

For real x, let f(x)=x3 +5x+1, then prove that f is one-one and onto R. ...