Recently Active Mathematics Questions

evaluate the limit: \lim_{x\rightarrow \propto } \frac{x^{2}(1+sin^{2}x)}{(x+sinx)^{2}} ...

If the line 2x - y +1=0 touches the circle at the point (2,5) and the centre of the circle lies on the line x + y -9 =0. find the equation of the circle. ...

The expressions 1 + x, 1+x+x^2, 1+ x+ x^2 +x^3, .............. 1 + x + x^2 +........+ x^n are multiplied together and the terms of the product thus obtained are arranged in increasing powers of x in the form of a0 + a1X + a2^ ...

1)prove that (2+√5)1/3 + (2-√5)1/3 is rational. 2)Let a,b,c be distinct real numbers.prove that (a-b)1/3+ (b-c)1/3+ (c-a)1/3≠0 ...

1) Prove that nn> 1.3.5.....(2n-3)(2n-1) 2) Let a, b, c be the sides of a triangle with perimeter 2. Prove that a2+b2+c2+2abc<2 3) -5<x<11. What is the greatest value of (11-x)3(x+5)5 4) x,y,z are positive real nu ...

*Image* ...

Show that nC0 nC0 - n+1C1 nC1 + n+2C2 nC2 - .......................... = (-1)n ...

$If A= $\lim_{x \to \frac{\pi}{2}}\frac{1-sin^{\lambda+\mu}x}{\sqrt{(1-sin^\lambda x).(1-sin^\mu}x)}$\\\\ where $\lambda,\mu>0$, Then find $A=$ ...

Q1. \int_{0}^{\pi /2}{ln(a^2cos^2\theta +b^2sin^2\theta )d\theta } Q2. \int_{0}^{\infty }{\frac{ln(1+a^2x^2)}{1+b^2x^2}dx } Q3. If lxl < 1 then find the sum of the series \frac{1}{1+x}+\frac{2x}{1+x^2}+\frac{4x^3}{1+x^4}+\ ...

$Let $x_{i}=2^i$ and $i=1,2,3...........16$\\\\ Then find Min. of the function $f(x) = \sum_{i=1}^{16}|x-x_{i}|$ ...

I am confused in the approach to two similar questions. So I am posting both- 1) A team of 8 couples (husband and wife) attend a lucky draw in which 4 persons are picked up for a prize. The probability that there is atleast o ...

$If $mn=1$, Then find Least value of $m^2+2mn-4n^2=$ ...

$Calculate $\int_{-\infty}^{+\infty}\frac{1}{(x^2+x+1)^3}dx=$ ...

Find the numbers of 4x4 array whose entries are from the set {0,1,2,3} and which are such that the sum of the numbers in each of the four rows and four columns is divisible by 4. ...

] On an in finite chessboard (whose squares are labeled by (x; y), where x and y range over all integers), a king is placed at (0; 0). On each turn, it has probability of 0.1 of moving to each of the four edge- neighboring sq ...

A curve is represented parametrically by the equation x= t+eat and y = -t + eat when t belongs to R and a> 0.. If the curve touches the axis of x at the point A, then the coordinates of the point A are 1. (1,0) 2 (1/e, 0) ...

[1] range of f(x)= *Image* is_______? ...

If f:[0,pi]→R is continuous and ∫(0 to pi) of f(x) cos x dx=∫(0 to pi) of f(x) sin x dx=0,then the number of roots of f(x) in (0,pi) is ___________? ...

Let alpha = e ^ i8pi / 11 , then find Re ( alpha + alpha ^2 + alpha ^3 + alpha ^4 + alpha ^5). ...

Is there any relation in a semicircle and a cone of the same radius? ...

$Determine all Polynomial $p(x)$ with real coefficients such that $p(2)=12$\\\\ and $p(x^2)=x^2(x^2+1)p(x),\forall x\in R.$ ...

$(1) Solve the equation $6^x+27^{x-1} = 8^x-1.$ $(2) Solve the equation $5.2^x+4.3^x = 3.4^x+2.5^x$ $(3) Solve the equation $3^{x+1}-9^x+3.5^x-25^x=15^x+3$ ...

*Image* Prove that AD = BD = CD if LB = 900 ...

From where can i download free a dasgupta iit maths solutions? ...

$(1) Solve the equation $x^3-x^2+9\lambda x-\lambda=0$. if It is known to have only\\\\ positive roots. and also find value of $\lambda$\\\\ (2) Determine The no. of local extreme of \\\\$f(x)=(x-1).(x-2)^2.(x-3)^3.(x-4)^4... ...

If a , b ,c r distinct +ve integers such that ab + bc + ca is greater than equal to 107 , then find the minimum value of 1/6 ( a^3 + b^3 + c^3 - 3abc ) ...

How many functions f from {−1005, . . . , 1005} to {−2010, . . . , 2010} are there such that the following two conditions are satisfied? • If a < b then f(a) < f(b). • There is no n in {−1005, . . . , 1005} su ...

Find solution/s to : (x)[x]=1. here ( ) is Least Integer Function. [ ]=Greatest Integer Function ...

many good questions are directly solved by experts......let this one be here.... and lets see if an aspirant is able to sove it well the question is quite basic and trivial : \sum_{k=1}^{n-1}{\tan^2\frac{k\pi}{2n}}=\frac{(n-1 ...

if a,b,c,d are in Harmonic progression prove ab+bc+cd=3ad ...