Recently Active Mathematics Questions

Let a<b<c be reals such that a+b+c=6 and ab+bc+ca=9 Then prove that 0<a<1<b<3<c<4 ...

let x,y and z be complex nos such that x+y+z=2 x^{2}+y^{2}+z^{2}=3 xyz=4 evaluate \frac{1}{xy+z-1}+\frac{1}{yz+x-1}+\frac{1}{zx+y-1} not my doubt[1] ...

let N has total 105 factors including 1 and N.....if N is divisible by 1000 then total number of odd factors of N lying between 1 and N can be..can be..can be (ans batao)[3] btw this is a q of bmat open test of last year ...

Find a and b given that (x^6+1) = (x^2+1)(x^2+ax+1)(x^2+bx+1) is an identity ...

Ques) If x/ p + y/q = 1 touches the circle x2 + y2 = a2 , then the point (1 / p , 1/q) lies on a /an (a) Straight line (b) Circle (c) Parabola (d)Ellipse ...

Ques) A circle circumscribing an equilateral triangle with centroid (0,0) of a side a is drawn and a square is drawn touching its four sides to circle. Then find the eqn of circle circumscribing the square. ...

Find the range of x: √(x^2 -x) /1-|x| ...

Find the equation of the circle of minimum radius which contains the 3 circles. x2 + y2 - 4y - 5 = 0, x2 + y2 + 12x + 4y + 31 = 0, x2 + y2 + 6x + 12y + 36 = 0, ...

if the function 0∫x f(t) dt->5 as |x|->1,then the value of (a) so that the equation 2x + 0∫x f(t) dt =a has atleast 2 roots of opposite sign in (-1,1) is (a) a ε (0,1) (b) a ε (0,3) (c) a ε (-1,∞) (d) a ε (3,â ...

Without using binomial or any -nomial theorem and with logical reasoning find out the co-efficient of the following in the expansion of (x+1)(x+2)(x+3)...............(x+n) : 1) xn-1 2) x Ans : 1) 1+2+3+......+n 2) n!(1+ 1/2 + ...

If 5 AM's are inserted between 4 & 15 & the value of 3rd arithmetic mean be β then find value of \beta (\sum_{1\leq i}{\sum_{<j<k}{\sum_{ \leq 8}{a}}}+\sum_{i=1}^{8}{\sum_{j=1}^{8}{a}}) here a=4 ...

If x and y are integers such that (x+2y)2 + (x+4y) = 710 The value of x is (A) 13 (B) 15 (C) 18 (D) 26 ...

if a+b+c=1.................find max value of a^{a}b^{b}c^{c} + a^{b}b^{c}c^{a} + a^{c}b^{a}c^{b} / ...

Prophet sir had recently taught a method to deal with recursive functional relations i have doubt regarding that : this thread was solved long back using substitution technique http://targetiit.com/iit-jee-forum/posts/full-th ...

(1) Let ABC be a triangle with AB =3, BC =4 and CA =5. A Line L,which is perpendicular to AC,Intersects AC in Q and AB in P.Suppose there is a Circle inside the Quadrilateral PBCQ touching all its four sides (i.e, PBCQ has an ...

These are some easy ones on limit... Please explain them and help me finish limits. Q1) \lim_{x\rightarrow 0} \frac{e-(1+x)^{1/x}}{tan x} Q2) \lim_{x\rightarrow 0} \left(\frac{(1+x)^{1/x}}{e} \right)^{1/x} Q3) {P{n}}= \frac{2 ...

Q.1) \lim_{x\rightarrow 0}(\left[f(x) \right]+x^2)^1^/^\left\{f(x) \right\} , where f(x) = (tanx/x) and \left\{f(x) \right\} denotes fractional part of f(x) and [f(x)] denotes the greatest integer function of f(x). is equal t ...

if arg (z^{3/8})=\frac{1}{2}arg(z^{2}+\bar{z}\sqrt{z}) find \left|z \right| btw its my doubt ...

This one appeared in one of the Russian Olympiads. Find the final five digits of the number N = 999...9 that contains 1001 nines positioned as above. ...

find the no of +ve integral solns (x,y,z) such that x+y+z=24 x2+y2+z2=210 xyz=440 ...

Few quaries , trying to do them myself ---- would be glad to get help ---- 1 > The cubic equation , x3 + px2 + qx + r = 0 has two roots “ a “ and “ b “ such that ab + 1 = 0 . Prove that r ( r + a+ b + p ) = 0 . ...

Here is a good enough test for all maths lovers , and I really liked the question patterns , so I am uploading some of them ---- A few are very confusing , so please help in solving those ---- 1 > Find the sum of the follo ...

there is a set A of n elements. now a subset B is formed from A the set A is then reconstructed by replacing elements of B now a subset C is formed from A find the number of ways of selecting B and C so that B and C are non i ...

Find the total number of positive integral solutions of the following 1. x1x2 x3..... xn = n 2. x1 x2 x3..... xn = -n 3. x1 +x2 +x3+....+ xn = n 4. x1 +x2 +x3+....+ xn = -n ...

Evaluate Σp=132 (3p+2)[Σq=110{sin(2qΠ/11)- icos(2qΠ/11)]p ...

If α, β are the roots of the equation x2 + bx + c = 0 then find lim (1 - cos(x2 + bx + c))/(β - x)2 x->β ...

PT. 22n*3nis divsible by (6n)!.can anyone do dis by using logic . i mean to say dat can we do dis widout using pen and paper.Nishant bhaiya i thnk u got wat i wantd to say.... ...

1.is (n!)! possible?? 2.we say dat -8! is't possible...bt y is'nt it possible?? 3.the tens digit of 1!+2!+3!+....30! is?? ...

2) Given a subset X = {x1 , x2 , x3, ..............., x n } a subset P of X is formed and set is reconstructed by replacing the elements of P into X and then another subset Q of X is formed. Find the total no. of pair of subs ...

\lim_{n\rightarrow \infty }(\left(n^{2}-n^{3})^{1/3}+n \right) not my doubt......found it gud ...