Recently Active Mathematics Questions

Q1. Every one of the 10 available lamps can be switched on to illuminate a certain hall. The total number of ways in which the hall can be illuminated is -: a) 55 b) 1023 c) 210 d) 10! My Working : Each lamp can or cannot ill ...

1) Let S=1+\frac{1}{2}+\frac{1}{3}+...\frac{1}{2^n-1} . S lies between a) 0 & n/2 b) n/2 & n c) n and 2n d) none. 2) IIT-1996. Let f(x) be evn. Given f(x) satisfies f(x)=f\left(\frac{x+1}{x+2} \right) find all possible values ...

\lim_{x\rightarrow0}\frac{e^\frac{-1}{x}}{x} I Cannot Solve it ! I Even Dont Know The Answer ! ...

*Image* ...

1) Every living person has shaken hands with a certain number of other persons . prove that the count of the number of the people who have shaken hands an odd number of time must yield an even number. 2) In a chess is it poss ...

3a=(b+c+d)^3 3b=(e+c+d)^3 3c=(e+a+d)^3 3d=(e+a+b)^3 3e=(c+a+b)^3 . find all reals (a,b,c,d,e). Source - INMO. ...

Prove if gcd(a,b)=1,then gcd(a^2,b^2)=1. ...

Q1 Statement 1: \int e^x(log_{e}x + \frac{1}{x^2}) dx = e^x (log_{e}x - \frac{1}{x}) + C Statement 2: \int e^x (f(x) + f^{ '}(x)) dx = e^x f(x)+ C Answer: Both are true and 1 is correct explanation for 2 But shouldn't Stateme ...

The values of α for which the system of equations x+y+z=1 x+4y+10z=α2. x+2y+4z=α....is consistent are given by.. Ans.(1.2) ...

FIND ALL THE INTEGRAL TRIANGLES WHOSE PERIMETER EQUALS THERE AREA . ...

1>how many odered pairs of (m,n) of positive integer are solution to 4/m + 2/n = 1 ? 2>prove that if a +b + c =0 then a3+b3+c3 = 3abc ...

1.Let f(x) be a function satisfying 2f(x)-3f(1/x)=x2 for any x≠0.then the value of f(2) is.... Ans.-7/4 ...

today i encountered a problem in which we have three redunant constraints[x>0 ,y> 0 and one more] but in answer they gave only the last one......so does it mean tht x>0 n y>0 are UNIVERSALLY NON_REDUNANT CONSTRAIN ...

sorry! ...

1.Prove that 24 divides 2.7^n+3.5^n-5.(n>=1) 2.Prove that the sum of the squares of two odd integers cannot be a perfect square. 3.If there exists x and y for which ax+by=gcd(a,b),then gcd(x,y)=1.(a,b are integers) 4.Prove ...

Let the sides of a triangle ABC are all integers with A as the origin. If (2,-1) and (3,6) are points on the line AB and AC respectively(lines AB andAC may be extended to contain these points),and lengths of any two sides are ...

The equation to the pairs of opposite sides of a parallelogram are x2 – 5x + 6 = 0 and y2 – 6y + 5. Find the equations of its diagonals. ...

Find the angle subtended by the double ordinate of length 2a of the parabola y2 = ax at its vertex ...

The point (–4, 5) is the vertex of a square and one of its diagonals is 7x – y + 8 = 0. The equation of the other diagonal is (A) 7x – y + 23 = 0 (B) 7y + x = 30 (C) 7y + x = 31 (D) x – 7y = 30 ...

In limit we often come across terms like 0∞,∞0etc etc. Now i give some terms .please tell whether they are determinant or determinant and their values if determinant. 1.0∞=(my ans 0) 2.∞0=(my ans 1) 3.∞∞=(my ans â ...

Suppose positive integers m, n, K satisfy mn = K2 + K + 3. Prove that at least one of the following Diophantine equations x2+11y2=4m and x2+11y2=4n has a solution (x, y) with x, y being odd numbers EDITED sorry for the incorr ...

lim 2.x1/2 +3.x1/3 +4.x1/4+..........+n.x1/n x→∞ (3x-4)1/2+(3x-4)1/3+..........+(3x-4)1/n (WITHOUT USING L-HOSPITAL) plzzzzzzzzzz HELPPPP!!!! ...

Prove that from a point (a,b) of the circle x(x-a) + y(y-b) = 0, two chords, each bisected by the axis of x, can be drawn if a2>8b2 ...

The number of solutions of the equation in the interval [-2Ï€,2Ï€] 2Cosx=/Sinx/ is _____ the answer is 8 bt i am getting 4.....can sumbody plzz give a graphical solution??? { /. / refers to modulus} ...

what is the highest power of 30! that divides 3000! ? ...

Find all natural numbers n > 1 such that n2 does not divide (n − 2)!. ...

how to identify different types of differential equation ...

f(x) = x - l x - x2 l x ε [ -1 , 1] Then the no of points at which f(x) is discontinuos (A) 2 (B) 1 (C) 0 (D) None ...

*Image* @Q1 its only tan x,not tan2x ...

*Image* ...