Recently Active Mathematics Questions

This has been discussed before but it is important... a+b+c=4 a2+b2+c2=6 a3+b3+c3=8 Find [a4+b4+c4] where [] denotes G.I.F? P.s:I know a method but i'm not sure if it's the shortest one to do this problem....thus sharing this ...

Let 0 < a < b. Consider two circles with radii a and b and centers (a, 0) and (b, 0) respectively with 0 < a < b. Let c be the center of any circle in the crescent shaped region M between the two circles and tange ...

\hspace{-16}\bf{(1)\;\; \int_{e^{e^{e}}}^{\infty}\frac{1}{x.(\log x).({\log \log x}).(\log \log \log x)^{\frac{4}{3}}}dx}$\\\\\\ $\bf{(2)}$ For Which Integer $\bf{ 1\leq m\leq 10}$ is it true that\\\\\\ $\bf{\int_{0}^{\pi}(\c ...

Find the least number which when divided by 24,32 and 36 leaves the remainder 19,27,31 respectively. ...

The grid is 4X3 rectangular Determine the number of paths from the lower-left corner of the left grid to the upper-right corner. ...

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. The number of ways in which we can place the balls in the boxes ( order is not considered in the box) so th ...

The total number of three digit numbers, the sum of whose digits is even, is equal to: (A) 450 (B) 350 (C) 250 (D) 325 ...

Find the least number which when divided by-------------10--9--8--7--6--5--4--3--2--1 leaves remainder-----9--8--7--6--5--4--3--2--1--0 ...

Prove that if 3 prime numbers greater than are in AP then common difference is divisible by 6. ...

Suppose n is a natural number such that i + 2i^2 + 3i^3 +................+ ni^n=18√2,where i is √-1.Then n is... ...

Let a,b,c be three distinct real numbers such that the expression ax2+bx+c, bx2+cx+a, and cx2+ ax+b is positive for each x belongs to R and let α =(bc+ca+ab)/(a2+b2+c2) Then (a) α<4 (b) α<1 (c) α>1/4 (d) α>1 ...

limx→0 {(1+3x)1/3-1-x} / {(1+x)101- 1-101x} has the value equal to? ...

easy one... Find the minimum value of the sum of squares of all trigonometric ratios? Hint:Integer-type answer... :P ...

ATTENTION Q7 ) added i'm weak in algebra Pleasse help.So Posting the questions VERY VERY WEAK Q1) Prove that 22225555 + 55552222 is divisible by 7 Q2) If 7 divides 323232 then find the remainder . ans is 4 Q3) Show that 19921 ...

x2+y2= 2013 How many solutions (x,y) exist such that x and y are positive integers? ...

show that ∫[sspi][/ss0]|(sin nx)/x|dx ≥ (2/pi)|1+(1/2)+(1/3)+.......(1/n)| ...

The number of points in space (x, y, z), whose each coordinate is a negative integer such that x+y+z+12=0 is ...

43. The number of times the function f (x) = 2009 Σ x/x-r vanishes is r=1 (A) 0 (B) 2008 (C) 2010 (D) 1 ...

If a,b,c are integers and are the sides of a right angle triangle,where c is the largest,prove that the area of that triangle is divisible by 6. ...

Find the number of ordered triplets of natural numbers (x, y, z) satisfying xyz≤10 ...

The equations of the common tangents to the circles x2 + y2-2x-6y+9=0 and x2+y2+6x-2y+1=0 is/are ? ...

let a1,a2,........an be integers.Show that there exists integers k and r such that the sum ak,ak+1,ak+2+.........ak+r is divisible by n. ...

let nCk denote the binomial coefficient and F[m] be the mth fibonaki number given by F[1]=F[2]=1 and F[m+2]=F[m]+F[m+1] for m≥1.Show that ∩(nCk)=F[m+1] for all m≥1. where n≥k≥0 and n+k=m ...

Prove that if the equation a_{0}x^{n} + a_{1}x^{n-1} + ... + a_{n-1}x = 0 has a positive root x0 then the equation na_{0}x^{n-1} + (n-1)a_{1}x^{n-2} + ... + a_{n-1} = 0 has a positive root less than x0 ...

let f(x)=∫(0 to 1)|t-x|tdt for all real x. What is the minimum value of f(x). ...

Let the range of the function f: R→ R f(x) = | x-1| + |x - a| + | x| + |x+1| + |x+ 2a - 21 | a being a real parameter given by [α,∞).Then find the no. of integral values of a for which there is exactly one x0ε R such th ...

i,j positive integers f(i,i+1)=1/3(for all i) f(i,j)=f(i,k)+f(k,j)-2f(i,k)(k,j) Find the value of f(1,100) ...

How many integers between 1 & 1000000 have the sum of the digits equal to 18? ...

limx→0+ (sin x)sin x = ? ...

C0/2+2C1/3+3C2/4+...+(n+1)Cn/(n+2) ...