Recently Active Mathematics Questions

if ab+bc+ca=0,show that the lines x/a+y/b=1/c, x/b+y/c=1/a, and x/c+y/a=1/b are concurrent? ...

find the area of the triangle which the straight line 3x+4y-12=0forms with the co-ordinate axes? ...

find the co-ordinates of the foot of the perpendicular drawn from the point (2,-5) on the straight line x=y+1 ? ...

show that the equation of the straight line passing through (acos3θ,asin3θ) and perpendicular to the straight line xsecθ+ycosecθ=a is xcosθ-ysinθ=acos2θ ? ...

a straight line AB intersects the y-axis at B and the perpendicular to AB at B intersects the x-axis at C.If the equation of the straight line AB is x/3-y/4=-1 find the co-ordinates of the point C ? ...

if the co-ordinates of the points P,Q,R are respectively (-7,5),(3,8),(-5,13) and if RN is perpendicular to PQ and RT parallel to PQ, find the equations of RN and RT ? ...

In a triangle with BC = 3 & AC = 4 & circle with AB as diameter passes thru the centroid of a triangle then AB is (A) 5 (B) 5 (C) 3 (D) None ...

Please can anyone please show me a detailed explanation of the method to find the co-eff. of x11 in the expansion : (1+x+x2+x3+.......+x6)3 ...

the estimated value of 1/1000 + 1/1001 + 1/1002 +.............. 1/2000 ...

If - Z= \frac{1}{^nC_0} + \frac{1}{^nC_1} +....+ \frac{1}{^nC_n} Then, find the value of - Z= \frac{1}{^nC_1} + \frac{2}{^nC_2} + \frac{3}{^nC_3}+....+ \frac{n}{^nC_n} in terms of "n" and "Z". ...

Ques) Find the solution of x + y dy/dx/y - x dy/dx = x sin 2 (x2+y2)/y3 . ...

If f(x+y+z)=f(x)+f(y)+f(z) with f(1)=1,f(2)=2 and x,y,z εR,thne evaluate \lim_{n\rightarrow\infty }\frac{\sum_{r=1}^{n}{(4r).f(3r)}}{n^3} ...

The no. of irrational solutions of the equation - \sqrt{x^2 + \sqrt{x^2 + 11}} + \sqrt{x^2 - \sqrt{x^2 + 11}} = 4 are - a) 0 b) 2 c) 4 d) Infinite ...

The remainder when ... .^5 x= .^. 5^5 (24 times 5 ) is divided by 24 is _______ . ...

Let f : A-->B be an onto function where A={1,2,3,4} B = {x,y,z} also f(!) = x Let M be total such functions then find value of M/2 ...

Let f(x) = lim (n--->∞) cosx/[1+(tan-1x)n] Then the value of ∫[0--->∞] f(x)dx is equal to (A) cos(tan1) (B) sin(tan1) (C) tan(tan1) (D) None ...

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The number of pairs of (x,y) satisfying the equation sinx+siny=sin(x+y) and lxl+lyl=1 is ? ...

First look this might seem an olympiad problem that may scare some of you... but try this problem to get an insight on how to solve such problems... x+y+z = w 1/x + 1/y + 1/z = 1/w Solve for x, y and z... (Not that you have t ...

√(1+1/12+1/22) + √(1+1/22+1/32) +....√(1+1/20072+1/20082) ...

These are few sums on probability from Chinese Olympiad.. 1. If a stick is broken in two at random,what is the average length of the smaller piece ?? 2. A railroad numbers its locomotives in order, 1,2,....N. One day you see ...

A sequence is defined as a1 = a2 = 1 and an = an-1 + an-2 for all n ≥ 3 then { an } is an increasing sequence TRUE / FALSE ...

If a,b,c be the three consecutive coefficients in the expansion of a power of (1+x), prove that the index of the power is 2ac + b(a+c)/b2 - ac ...

let f(x) , x ε [0,∞) be a non negative continuous function. If f '(x) cosx ≤ f(x) sinx for all x≥0 then value of f(2π) is- a)0 b)1 c)Πd)none ...

P(x) be a polynomial of degree at the most 5 which leaves the reaminders -1 and 1 upon division by (x-1)3 and (x+1)3 1)....find the no of real roots of p(X)=0 2)....the max value of y=P''(x) can be obtained at x 3).....the su ...

if (1+2x+2x2)n=a0+a1x+a2x2+........a2n2n then prove that : ar=nC0.2nCr + nC1.2n-2Cr-2 +nC2.2n-4Cr-4+..................... ...

183 + 73 + 3.18.7.25/36 + 6.243.2 + 15.81.4 + 20.27.8 + 15.9.16 + 6.3.32 + 64 Find the value of the expression. ...

prove that e^{x}+\sqrt{1+e^{2x}}>(1+x)+\sqrt{2+2x+x^{2}} for x belongs to R(note its ≥ not >) ...

Q1 A_x=\begin{bmatrix} a_{11}+x & a_{12}+x & a_{13}+x\\ a_{21}+x & a_{22}+x &a_{23}+x \\ a_{31}+x & a_{32}+x & a_{33}+x \end{bmatrix} Prove A_x=A(0)+x\sum_{k=1}^{3}{\sum_{l=1}^{3}{A_{lk}}} Q2 If a,b>0 and a3+b3=a-b,then pr ...

1)LET C1 and C2be two parabola x2=y-1 and y2=x-1.let p be any point on c1 and Q be any pont on C2. P' and Q' are the reflection of P and Q respectively w.r.t y=x line then proove: !)Prove PQ>min(PP',QQ') 2)hence determine ...