Recently Active Mathematics Questions

If A and B throw 2 dice such that if A gets a sum of 6, he wins and if B gets a sum of 7, he wins. Find the probability of there victory if A throws the dice first. They throw dices alternatively. That might be simple...but p ...

Give a good approximation for i^i^i^..... ans:0.43+0.36i ...

Let P, Q, R and S cut a pack of 52 cards successively in the order given. If the person who cuts heart first receives Rs. 700. Then match the expectations of P, Q, R, S 1. Expectation of P A. Rs. 144 2. Expectation of Q B. Rs ...

The sum of the first few terms in a geometric progression is 11, the sum of their squares is 341, and sum of their cubes is 3641. Find the terms of the sequence. ...

prove this inequality *Image* conditions:plz dont use titu lemma,tchebychef and cauchy-schwatz.... only alowwed inequality's are a.m >g.m >h.m and mean power............ i am imposing these conditions because i proved i ...

if a+\frac{1}{a}=-1 find the value of (a^2+a+1)+(a^4+a^2+1)+(a^6+a^3+1)+(a^8+a^4+1)+...+(a^{2006}+a^{1003}+1) ...

try these 2 questions :) 1). if z + 1/z =2cos3° then find the value of z2009 + 1/z2009 2) if x= 4/((51/2 +1)(51/4+1)(51/8+1)(51/16 +1)) then find the last digit of (x+1)48....... ...

A continuation of what b555 started, I'm posting here another theorem namely the Totient theorem or the famous "EULER'S-PHI-FUNCTION-FORMULA" to ease the mod-bashings....beleive me this is another tool to ease rem calculation ...

Which of the following definition is correct? A square matrix A is called nilpotent if there exists a positive integer m such that Am= 0 , where m is the least positive integer such that Am = 0 , then m is called the index of ...

1)Evaluate \sum_{0}^{infinity}{sin(n\alpha )/n} = ??? (n varies from 0 to infinity) [\alpha\varepsilon (0,2\pi )] 2)Find the sum of \sum_{r=00}^{infity}{\frac{sinr\alpha }{sin^{r}\alpha }} ...

Determine all 2 by 2 matrices "A" such that AX=XA for any 2 by 2 matrix X. Aside: I have often said this.. Uptil a long time I used to think why we are taught that (a+b)+c = a+(b+c) and a+b=b+a .. etc etc... We used to laugh ...

Evaluate: \lim_{x\rightarrow 0} \frac{tan^{-1}x}{sin^{-1}x} ...

"Give two different numbers, each of which is the square of the other." and i dont want o and 1 as the answer ...

An AP and a GP have the same first and last terms as well as the same number of terms. Is the sum of terms greater for the AP or GP? ...

Find the condition that the straight line cx-by+b^{2}=0 may touch the circle x^{2}+y^{2}=ax+by and find the point of contact. ...

If 0 <x < π/2, then the Minimum Value of.... \frac{cos^{3}x}{sin \ x} + \frac{sin^{3}x}{cos \ x} is ... a) √3 b) 1/2 c) 1/3 d) 1 ...

The orthogonal trajectory of x2 + y2 = a2 , where'a' is arbitrary constant is a circle. IS THE STATEMENT RIGHT??????? ...

Let us consider a real valued function f:R --->R f(x+y) = f(x) + f(y) + f(x)f(y) , x,y ε R The sum and difference of two continuous/differentiable functions is also continuous (differentiable) over their common domain. Us ...

I need a graph of eq [x]+[y]=5 ,where [ ]represents greatest integer function ...

STATEMENT : (a.b)c - (a.c)b is perpendicular to a or b x c where (a.b)c - (a.c)b = a x (b x c) is it or (or) and ...

[x] + [x+1/n] +[x+ 2/n] +........[x+ (n-1)/n]=[nx] is true a)for any real no x b)for any integer x c){x} is multiple of 1/n d)for no n. ...

If C0, C1, C2, ........., Cn are the binomial coefficients, then 2 C 1 + 2 3 C 3 + 2 5 C 5 +............... equals (a) 3 n + (-1) n/2 (b) 3n - (-1) n/2 (c) 3 n +1/2 (d) 3 n -1/2 ...

∫ tan-1x/1+x [lower limit 0 and upper limit 1]= (pi ln2)/k find k ...

Find the domain of k if nCr = (k2 - 2k - 7 )n+1Cr+1. ...

if f(x) nd g(x) r twice differentiable functions on [0,2] nd if f''(x) = g''(x) nd f' (1) =4 , g' (1)=2 nd f(2)=3 , g(2)=9 then find g(4)- f(4)?? ...

ai>0;i=1,2,3,4.........n (n-1)s=a1+a2+a3+a4+..............an prove that a1.a2a3..........an>= (n-1)n(s-a1).(s-a2).(s-a3)(s-a4).........(s-an) ...

If the roots of ax2 + 2bx + c = 0 be possible and different then the roots of (a+c)(ax2+2bx+c) = 2(ac-b2)(x2+1) will be impossible and vice-versa.............prove it. ...

given g(f(x))=x.then f(x) is one-one/onto/both/one one but not necessarily onto ...

If 7^103 is divided by 25, then what is the remainder? ...

Ques) If a,b,c are in A.P, then ax +by +c =0 represents : (a)a straight line (b) a family of concurrent lines (c) a family of parallel lines (d) none of these ...