Popular Mathematics Questions

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Given six real numbers a,b c,x y,z , , such that 0<b-c<a<b+c and ax+by+cz=0. What is the sign of the sum ayz+bzx+cxy ? o promise u if u really try this question sincerely , you are bound to learn a new concept ...

Prove that in every triangle we have: ma*mb>=ra*rb*rc. ma is length of median drawn from A, same is mb. ra= exradius of A ...

On a bookcase there are n ≥ 3 books side by side by different authors. A librarian considers the first and second book from left and exchanges them iff they are not alphabetically sorted. Then he is doing the same operation ...

Find all real values of parameter a for which the equation in x \[ 16x^{4}-ax^{3}+(2a+17)x^{2}-ax+16 = 0 \] has four solutions which form an arithmetic progression. ...

Prove that for positive real numbers a, b, c, d, we have \[ \frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{c}+\frac{1}{d}}\le\frac{1}{\frac{1}{a+c}+\frac{1}{b+d}} \] ...

Find all polynomial P(x) with real coefficients satisfying P^2(x)+P^2(x-1)=2(P(x)-x)^2 ...

Prove that √(7/2) ≤ |1 + z| + |1 − z + z2| ≤ 3√(7/6) for all complex numbers with |z| = 1. ...

Could anyone please post a copy of all B.Stat Subjective Questions? ...

circles are described on any two focal chords of a parabola as diameters . prove that their common chord passes through the vertex of the parabola . ...

find the locus of the the point of the intersection of the normals to the parabola x2=8y which are at right angles to each other . ...

in expansion of 1/(1-ax)(1-bx) = a0 + a1x +... an then wat is an? ...

sveral numbers are written in a row. in each move, john choses any 2 adjacent numbers in which one on the left is greater than one on the right, doubles each of them and switches around. prove that roberts cn make only a fini ...

A device consists of 4n elements, any two of which are joined by either a red or a blue wire. The numbers of red and blue wires are the same. The device is disabled by removing two wires of the same color connecting four di e ...

In a society of n people, any two persons who do not know each other have exactly two common acquaintances, and any two persons who know each other don’t have other common acquaintances. Prove that in this society every per ...

Twenty-one girls and twenty-one boys took part in a mathematics competition. It turned out that (i) each contestant solved at most six problems, and (ii) for each pair of a girl and a boy, there was at least one problem that ...

Find all positive integral solutions (a,b,c) to the equation (a+1)(b+1)(c+1)=2(abc + 1) ...

Find all positive integral solutions (a,b,c) to the equation (a+1)(b+1)(c+1)=2(abc + 1) ...

From a point P, perpendicular PM and PN are drawn to two straight lines OM and ON. If the area OMPN, be constant, then prove that the locus of point P is a hyperbola. ...

In an ellipse, the tangent at P meets in T and t, and CY is the pependicular on it from the centre; prove thet 1) Tt.PY = a2 - b2 and 2) the least value of Tt is a+b. ...

Find all positive integers, representable uniquely as \frac{x^{2}+y}{xy+1} where x and y are positive integers. ...

Suppose that p is a prime number and is greater than 3 . Prove that 7^{p}-6^{p}-1 is divisible by 43. ...

The integers a and b have the property that for every nonnegative integer n, the number 2^{n}a+b is the square of an integer. Show that a=0. ...

i find it hard to these questions........... so plz help 1) (2cos40 -cos20)/sin20 2) tan10-tan50+tan70 ...

If \alpha =e^{2i\pi/11 } and f(x)=5+\sum_{K=1}^{60}{A_K{x^{K}}} then find value of 100\sum_{r=0}^{10}{f(\alpha ^{r}x}) ...

wrong post sorry ...

I was seeing a website.. which I recommend everyone to see... for the sake of mathematics not JEE.. These are many ways you can look(prove) AM-GM inequality! http://jwilson.coe.uga.edu/EMT725/AMGM/AMGM.html *Image* ...

A town has several clubs. Given any two residents there is exactly one club that both belong to. Given any two clubs, there is exactly one resident who belongs to both. Each club has at least 3 members. At least one club has ...

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suppose there are 997 points given in a plane. if every two points are joined by a line segment with its mid point coloured in red, show that there are atleast 1991 red points in the plane. can u find a special case with exac ...