Recently Active Mathematics Questions

If θ is the fundamental period of the function f(x) = sin99x + sin99(x + 2π/3) + sin99(x + 4π/3), then the complex number z = r(cosθ + isinθ) lies in the quadrant??? I m getting θ= 2π/3 and hence the ans should be 2... ...

lim 0 to 2Π∫ecosθcos(sinθ)dθ = ? 1) 2Π2) Π3) Π/2 4) none ...

$Determine the minimum value of the expression:\\\\ $A =x^2-10xy+27y^2-8y+8.$\\\\ For what values of $x,y$ take the minimum value of the expression A. ...

Consider these two questions- 1) find the number of non negative integral solutions of x+y+z+w = 20 2) find the number of positive integral solutions of x+y+z+w = 20 answer to 1) is 23C3 and 2) is 19C3 Is there any difference ...

log(1+x)= x - xx/2 + xxx/3 - xxxx/4 ....... x=1, log 2 = 1 - 1/2 + 1/3 -1/4 .... multiply both sides by 2, 2log2 = 2 - 2/2 +2/3 -2/4 +2/5 -2/6... = 2- 1 + 2/3 -1/2 +2/5 -1/3... =1 -1/2 + 1/3 -1/4 .... 2log2 = log 2 2=1 ...

1. If x,y and z are real numbers such that (x - 3)2 + (y - 4)2 + (z - 5)2 = 0. Then, x + y + z = (A) -12 (B) 0 (C) 8 (D) 12 Please do show the steps..! ...

find the solution set for z given that, |z+a| + |z-a| = |a| where a = real number ...

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for a sufficiently large value of n the sum of the square roots of the first n positive integers i.e. √1 + √2 + .... √n is approximately equal to?? ...

(1) \lim_{x \to \frac{\pi}{4}}\frac{\sqrt{1-\sqrt{sin2x}}}{(\pi-4x)}=$ ...

1) \ f(x)\ is\ a\ polynomial\ of\ degree\ 4\ with\ real\ coefficients\ such \that\ f(x)\ =\ 0\ is\ satisfied\ by\ x\ = \1,2,3\ only\ , \ then\ f ' (1). f'(2). f'(3)\ is\ equals\ to \ \\\\\ (a)\ 0\ (b)\ 2\ (c)\ -1\ (d)\ none\ ...

$Find value of $x$ that satisfy the equation $x^{\lfloor \ x\rfloor}=\frac{9}{2}$\\\\ Where $\lfloor x \rfloor $= G.I.F=greatest integer function. ...

Let " a " and " b " be real numbers in the interval [ 0 , Î / 2 ] . Then for how many integral valued pairs of " a " and " b " must be there who satisfy .......... sin 6 ( a ) + 3 sin 2 ( a ) cos 2 ( b ) + cos 6 ( b ) = 1 Not ...

$Determine The no. of real roots of the equation $(2^x+x-1).(x-3)=-2$ ...

Yesterday on 26|12|10, there was a question in FTRE... If x2 - y2 = 101, where x and y are natural numbers. Then x2 + y2 =? There were few options... I don't remember well but, one of them was can't be determined.... What mus ...

Prove that 1)Limx--->0 loge(1+x)/x = 1. 2)Limx-->0 ax-1/x = logea, a>0,a≠0. In the second one,its 'a' to the power 'x' minus 1 divided by 'x' to give log 'a' to the base 'e'. ...

$Calculate value of $sec^2(\frac{\pi}{9})+sec^2(\frac{2\pi}{9})+sec^2(\frac{4\pi}{9})=$ ...

lim n→∞ (an + bn)(1/n) ...

Since our exams are approaching fast , I have taken an initiative to post and solve problems that I have found to be quite intriguing . These are all from IIT - JEE syllabus , and I hope to create a field of mutual participat ...

(2) $Calculate $\int\frac{(x^2-1)}{x.\sqrt{x^2+\alpha x+1}.\sqrt{x^2+\beta x+1}}dx$ ...

1) If (1-x)n = C0 - C1x + C2x2 -..... + (-1)nCnxn, then the value of C0 - C1 + C2 - .... + C100 is, where n>102 a) 0 b) nC101 c) n-1C101 d) 2nC100 ...

Find all continuous functions f, g, h : R → R for all real values of x and y satisfying the functional equation f(x + y) = g(x)+h(y) . ...

If f be a periodic function as well as an odd function with period p and and x belongs to [ -p/2, p/2] Prove that ∫f(t)dt (lower and upper limits are a and x resp.) is periodic with period p. In the solution, there is a ste ...

1) Find the domain of f(x) = cos^{-1}\sqrt{log_{[x]}(\left|x \right|/x)} ...

1. \int \frac{dx}{tanx+secx+sinx+cosx+cotx+cosecx} 2. U_{n}=\int_{0}^{1}{x^{n}\left(2-x \right)^{n}dx}, V_{n}=\int_{0}^{1}{x^{n}\left(1-x \right)^{n}dx} ; prove\ \right| that\ \right| U_{n}=2^{2n}V_{n} ...

If x,y,z are the roots of 7x3-x-2=0, then the value of Σ(x/y+ y/z) is _____________. (ans= -3) ...

1) prove \lim_{x\rightarrow 0} sin x / x =1 by squeeze theorem. 2)prove that all roots of e^x [ d^n/d x^n(x^n/e^x)] are positive 3) prove that e is irrational. ...

1) if A(1,-1,3) B(2,1,-2) C(-5,2,-6) are the vertices of a triangle ABC , then the length of internal angular bisctor of angle A is?? 2)the median AD of triangle ABC is bisected at E and BE meets AC at F then AF:FC ??? 3)if x ...