Recently Active Mathematics Questions

\int_{0}^{\infty}{e^{-x^2}dx}=\sqrt{\frac{\pi }{2}} then find value of \int_{0}^{\infty}{e^{-ax^2}dx},a>0 ...

Find f(x) if \int_{0}^{a}{f(x)dx}=\frac{6a-sin2a}{4};a>0 ...

Ques1) Show that the extremum value of the function f(x) = 1 / (sinx+4) - 1 / (cos x -4), where x belongs to R is 2 2 / (4 2 + 1). Ques2) If a2x4 + b2y4 = c6, then show that the max value of xy is c3 / 2ab . Ques3) If x7 - x5 ...

Find the number of solutions of equation sinx+2sin2x=3+sin3x ,x ε[0,π] ...

Use the Pigeon-Hole Principle to derive Euler's totient function....[62] ...

If tan^{-1}(x+h)=tan^{-1}x+(hsiny)(siny)-(hsiny)^2.\frac{sin2y}{2}+(hsiny)^3.\frac{sin3y}{3}+..........\infty if x\epsilon (0,1),y\epsilon (\frac{\pi }{4},\frac{\pi }{2}) then y = ? ...

\int_{-1}^{1}{\frac{sinx-x^2}{3-[x]}}dx ...

For some g,let f(x)=x(x+3)eg(x) be a continuous function. If there exists only one point x=d such that f'(d)=0,then find interval in which d lies. ...

f(x)=sin(x-a)/sin(x-b) Find prove that f(x) assumes maximum or minimum values for a-b=nπ ,n ε I ...

\lim_{x\rightarrow 0}\int_{0}^{x}{\frac{t^2dt}{(x-sinx)\sqrt{a+t}}}=1 ...

Find the maximun and minimum value of : 4 sin2 x + 3 cos2 x + sin x/2 + cos x/2 ...

Doubt 1 : What is an increasing function ? Doubt 2 : If b>a then the eqn. (x-a)(x-b)-1=0 has A. both roots in [a,b] B.both roots in (-∞,a) C. both roots in (b,+∞) D. One root in (-∞,a)and the other in (b,+∞) Doubt ...

Let z1, z2, z3 be complex numbers such that 1) |z1| = |z2| = |z3| = 1, 2) z1 + z2 + z3 is not equal to zero, and 3) z12 + z22 + z32 = 0. Then, prove that for all integers n >= 2, the quantity |z1n + z2n ...

Perform the following integration: \int\dfrac{\mathrm dx}{1+x^4} ...

If 0<x<y<Ï€/2, show that : x - sin x < y - sin y ...

Ques1) Show that the sum of the series 1 / 1.3 + 2 / 1.3.5 + 3 / 1.3.5.7 + ........... upto n terms is 1/2. Ques2) Show that the sum of n terms for series 3/4 + 5/36 + 7/144 + 9/400 + 11 / 900 + ......... is 1. Ques3) If the ...

A rectangular hyperbola passes through two fixed points and its assymptotes are in given directions.prove that its vertices lie on an ellipse and hyperbola which intersect orthogonally ...

http://targetiit.com/iit-jee-forum/posts/solve-this-10617.html can anybody explain nishant byah explanation here ...

find the are area bound by a2x2=y3(2a-y)and y-axis ...

6 dices are thrown together.Find the probability of getting a sum of 15. What is the easiest and quickest way to do it? ...

in a test an examinee either guesses or copies or he knows the answer to a multiple choice question, with more than one answer, and having 4 alternatives. the probabilty that he makes guess is 1/3 and that he copies the answe ...

A bag contains a coin of value M and a number of other coins whose aggregate value is m.A person draws on at a time till he draws coin M Find value of his expectation ...

Ques1) The eqn of tangen to the curve y = cos(x+y) where -2pie ≤ x ≤ 2 pie, that are parallel to the line x+2y = 0 (a) x+2y = pie/2 and x+2y = -3 pie/2 (b) x+2y = pie/2 and x+2y = 3 pie/2 (c) x+2y = 0 and x+2y = pie (d) n ...

∫ dx / (x + √x2-1)2 = ? ( here its a whole square root) ...

The nth therm of a sequence in given by nn/n! .... Show that this sequence converges and find it's limit... ...

In right angled triangle ABC,right angled at B,s-a=3 and s-c=2. Find values of a and c ...

Let k=1 ,then find value of 2sin2k + 4sin4k + 6sin6k +... + 180sin180k ...

This question is given in arihant... Prove that the min value of the expression x2+3y2+2xy-6x-3y is -11 Any hints on how to solve this ? ...

If xi>0 for 1≤i≤n and x1+x2+....+xn=π ,then find greatest value of sinx1+sinx2+.......+sinxn ...

What is the minimum distance between circle x2+y2=9 and curve 2x2+10y2+6xy=1? ...