Recently Active Mathematics Questions

( 1+i )n + ( 1- i )n ...

Two n digit integers are said to be equivalent if one is a permutation of the other. for eg. 10075 and 01057 are equivalent. Find the number of 5 digit integers such that no two are equivalent ...

1) Show that the least value of 2 log 100 a - log a 0.0001, for a > 0 is 4. 2) If the equation x 4-4x 3+ax 2+bx+1=0 has four positive roots, then show that a=6 and b=-4 3) If S = a 1+a 2+a 3+..........+an then show that s/ ...

Q.1) prove : (n+1 / 2)n ≥ n! Q.2) prove : 2n + x Cn .2n-x Cn ≤ (2nCn)2 Q.3) If s be the sum of n +ve unequal quantities a,b,c,..... then prove that : s/s-a + s/s-b + s/s-c +...... > n2 / n2-1 ...

Find the coefficient of x50 in (1+x)+2(1+x)2+3(1+x)3+....+1000(1+x)1000 ...

1) If the equation x 4-4x 3+ax 2+bx+1=0 has four positive roots, then show that a=6 and b=-4 2) If S = a 1+a 2+a 3+..........+an then show that s/(s-a1) + s/(s-a2) +s/(s-a3) + ...............+ s/(s-a n) > n2 /( n-1). 3) If ...

If m is a prime number,and a,b ,two numbers less than m prove that am-2+am-3b+am-4b2+...bm-2 is a multiple of m ...

1) Find the values of a for which the eqn 3x4 + 4x3 -12x2 + a = 0 are real and distinct. 2) If f ' (sinx) < 0 and f '' (sinx) > 0 for x belonging to R, then find the intervals of monotonicity of the function g(x) = f(si ...

If x2+y2-14x-6y-6=0 ,then find maximum possible value of 3x+4y ...

Find the number of distinct solutions of equation sin5θcos3θ=sin9θcos7θ, θ ε [0,π/2] ...

If in ΔABC ,cosA+2cosB+cosC=2 then prove that a,b,c are in AP ...

Prove that : Any prime number of the form (4k+1) can be expressed as the sum of two perfect squares. [k∈I] ...

If φ(N) is the number of integers which are less than N and prime to it and if x is prime to N then show that xφ(N)-1≡0.mod(N) ...

In five throws with single die what is the chance of throwing a) three aces exactly b) three aces atleast ...

Show that ax+a and ax-a are always even whatever a and x may be I did it by taking four cases for a and x [EE,EO,OE,OO] where E and O denote even and odd respectively Is any shorter method available ? ...

If p is prime ,and x is prime to p,show that xpr-pr-1-1 is divisible by pr ...

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f(x+1) ≥ f(x) + 1 f(x+5) ≤ f(x) + 5 g(x) = f(x) + 1 - x find g(2008) ...

well watz sumation of n harmonic terms suppose 1/a 1/a+b 1/a+2b ..........1/a+<n-1>b ie for n terms . wat is sumation.>>>>>>>furmula<<<<<< ...

Find the angle? sin(sin-110) ...

If p and q are any two positive integers ,show that (pq)! is divisible by (p!)q.q! and by (q!)p.p! ...

1) Let f(x) = x3+x2+100x+7sinx then show that the eqn 1 / [y-f(!)] + 2 / [y-f(2)] + 3 / [y-f(3)] = 0 has exactly one root lying in (f(1) , f(2)). 2) Let f(x) and g(x) be two functions which cuts each other orthogonally. At th ...

Find general solution of congurence 98x-1≡0(mod 139) ...

Show that a12-b12 is divisible by 91 if a and b are both prime to 91 ...

If p is a prime number and a is prime to p,and if a square number c2 can be found such that c2-a is divisible by p, then show that a(p-1)/2-1 is divisible by p ...

1)AB is a chord of the circle x2+y2=25/2.P is a point such that PA=4 and PB=3.If AB=5,then the distance of P from the origin is _____ ...

Find the domain of the following:- (a) F(x) = sin -1{ (2-3[x] ) / 4 } (b) F(x) = sin |x| + sin -1 (tanx) + sin (sin -1 x) (c) F(x) = (x 2 - |x| - 2) 1/2 ...

Lim (x→∞) 2t-3t/xn where t= xn/ex and n ε N = a.ln(2/3) b.0 c.n ln(2/3) d. not defined ...

there is an amoeba....in every minute it has four options : (0) it dies (1) it remains as it is (2) it doubles (3) it triples find the probability that after 2 minutes the amoeba dies ....(.i.e. if it doubles or triples all o ...

Q. how would we prove that that the following statement is wrong n+n+n......n times = n2 differentiatng both sides w.r.t n we get 1+1+1+.....n times = 2n or n=2n or 1=2 ...