Recently Active Mathematics Questions

1. \int_{e^-^1}^{e^2}{|lnx / x | } dx = ? 2. \int_{sinx}^{1}{t^2 f(t)dt }= ( 1 - sinx ) , then find f (1 / √3) = ? 3. \lim_{x \rightarrow infinity}1/\pi \sum_{r=1}^{n}{tan^-^1(1/2r ^2)} = ? ...

1.the edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a cap , b cap, c cap. such that dotproduct of any of these unit vectors taken 2 at a time is 1/2. Find volume of parallelopiped. ...

In a lottery, tickets are given 9-digit nos using only the digits 1,2,3.They are also coloured red, blue or green in such a way that 2 tickets whose numbers differ in all the 9 places get different colours! Suppose the ticket ...

Find all Complex no. Z which satisfy the following expression (1)Z(bar) = i(Z2) without using Z=x+iy (2) question Z2+|Z|=0 ...

This question is not for the advanced students.. but for those who fear the name Functional equations and have not tried too many.... SOlve this one to get some hold on the topic.. Determine f(x) such that... x^2f(x)+f(1-x)=2 ...

Let f:A1→B1, g : A2→B2, p:A3→B3 , and h : A4---->B4 are real valued functions.If the range of h(x)=g(f(p(x))) is a set y then y A. y\subseteq B1 B. y\subseteq B2 C. y\subseteq B3 D.can't say p.s - RTPF stands for Ran ...

\int _{0}^{1/2}\frac {dx}{\sqrt {1-x^{2n}}} where n≥1 ...

Find the equation of the line passing through the point (4, -14, 4) and intersecting the line of intersection of the planes: 3x+2y-z = 5 and x-2y-2z = -1 at right angles. ...

If α and β are roots of z +1/z=2(cosθ +isinθ) ,0<θ<π , show that l α-i l=l β-i l ...

Why it is said that no of roots of x3=0 is 3 repeated roots... Then why sin(x)=1 has only one root in (0,pi) ...

z1,z2,z3,z4 are four complex nos. If z1 + z2 = 0 , and z1z2 + z3z4 = 0 , then prove that these are concyclic. ...

It all started with b555's classic integration siikho thread..and now nishant sir started some more threads on it.... I ma starting one small on inequalities..A lot of inequlaities thread are already there on site..I know tha ...

Find the distance of the point P(-2, 3, -4) from the line x+2/3 = 2y+3/4 = 3z+4/5 measured parallel to the plane 4x+12y - 3z +1 = 0. ...

For positive x and y, establish the following inequality x^y + y^x>1 . ...

*Image* ...

0∫1 x (1-x)/(1+x) = ?? one method was to write f(1-x) n put x=2 sin2θ n solve.. ne other method ?? ...

Reduce to simplest form tan^{-1}(\frac {xcos\theta}{1-xsin\theta})-cot^{-1}(\frac {cos\theta}{x-sin\theta}) ...

Prove that the interval [0,1] can be split into black and white intervals for any quadratic polynomial P(x) , such that the sum of weights of the black intervals is equal to the sum of weights of the white intervals. (Define ...

If a,b ≥ 0 and p,q are rational numbers such that p > 1, and 1/p + 1/q =1, then show that ab ≤ ap/p + bq/q ...

log27 is: a)integer b)rational c)irrational d)complex roots give proof as well ...

21 people take a test with 15 true or false questions. It is known that every 2 people have at least 1 correct answer in common. What is the minimum number of people that could have correctly answered the question which the m ...

16 students took part in a competition. All problems were multiple choice style. Each problem had four choices. It was said that any two students had at most one answer in common, find the maximum number of problems. ...

In a wagon, every m≥3 people have exactly one common friend. (When A is B's friend, B is also A's friend. No one was considered as his own friend.) Find the number of friends of the person who has the most friends. ...

I look at askiitians.com only when I am VERY VERY BORED. But one post took me quite by surprise, when the student asked, if f:N→N is a strictly increasing function satisfying f(f(n)) = 3n for all n, find f(11). ...

Let f(x) = 4x/4x+2 . What is the value of \sum_{1}^{1000}{f\frac{i}{1000}} Source: Chinese: 1986 ...

limit n-n2{(n+1)(n+1/2)(n+1/22)...(n+1/2n)} n→∞ ...

if Sn be the sum of n consecutive terms of an A.P.show that (Sn+3)-(3Sn+2)+(3Sn+1)-Sn=0 ...

We say x,y,z can be symmetric in an expression..........pls explain wht do we mean by saying so ? To illustrate my doubt, I'm posting one example : Case I : Let x,y,z be real variables which satisfy xy+yz+zx=7 and x+y+z=6 We ...

f(x)=cos(tan x + cot x)cos(tan x - cot x) ...

‘O’ is a fixed point and ‘P’ , any point on a given circle ; OP is joined and on it a point ‘Q’ is taken so that OP . OQ = a constant quantity k ; prove that the locus of Q is a circle which becomes a straight lin ...