Recently Active Mathematics Questions

Find the number of 4-digit numbers(in base 10) having non-zero digits and which are divisible by 4 but not by 8. ...

$\textbf{If $\mathbf{x_{1},x_{2},x_{3},.......,x_{n}}$ are the roots of the equation $\mathbf{x^n+2x^{n-1}+3x^{n-2}+.........+nx+n+1=0}$.\\\\ Then Calcuate value of $\mathbf{\sum_{k=1}^{n}\frac{x_{k}^{n+1}-1}{x_{k}-1}=}$ } ...

Find the largest interval in which x lies satisfying x^{12}-x^{9}+x^{4}-x+1>0 ...

What is the largest integer n such that 33! divisible by 2n? ...

$Prove That $\mathbf{tan\left(\frac{\pi}{11}\right)\times tan\left(\frac{2\pi}{11}\right)\times tan\left(\frac{3 \pi}{11}\right)\times tan\left(\frac{4\pi}{11}\right)\times tan\left(\frac{5\pi}{11}\right)=\sqrt{11}} ...

$\textbf{Find the Ellipse with the largest area such that $\mathbf{x+2y=2}$ is a\\\\ tangent and his foci is at $\mathbf{(-c,0)}$ and $\mathbf{(c,0)}$ for some $\mathbf{0<c<2}$}\\ ...

\mathbf{\lim_{n\to\infty}\left\{\left(\sqrt{3}+1\right)^{2n}\right\}}=$\\\\ \textbf{Where $\mathbf{\left\{.\right\} = }$Fractional part of $\mathbf{x}$} ...

(1 + tan5°) (1 + tan10°) (1 + tan15°).........( 1 + tan45°) = 2k , then k equals ___ then answer is an integer (0 - 9) ...

The order and degree of the D.E. (y+c)2=cx is? I got the answer as 2,1 resp. but the answer given is opposite. What do you say? ...

If log5k+log35+log1x= 1 then, find the value of x... ...

$\textbf{If} $\mathbf{f(x)=sin\left(\frac{2x}{1+x^2}\right)+cos\left(\frac{4x}{1+x^2}\right)+1}$\\\\\\ \textbf{Then find Max. and Min. value of f(x)}. ...

1. if a1 , a2 , a3 ... a7 are seven not necessarily distinct real numbers such that 1<ai<13 , prove that we can construct a triangle with its sides with length ai 2 If Nn denote the nth son square integer so that N1=2 , ...

(i)(x^2+x-2)^4+(2x+1)^4=(x^2+x-1)^4\\\\ (ii)(x^2+3x+2)(x^2+7x+12)+(x^2+5x-6)=0 ...

let A denotes the value of expression X4 + 4X3 + 2X2 - 4X + 7 when X= cot11pi/8 and B denotes the value of expression ( 1- cos8y)/ tan24y + (1+cos8y)/ cot24y when y=9° the value of (A-B) is ____ the question is integer type ...

\mathbf{\int_{0}^{1}\frac{dx}{x.(x+1).\left\{ln\left(1+\frac{1}{x}\right)\right\}^{2011}}}=$ ...

\mathbf{\int_{0}^{\pi}|sin(2x)-sin(3x)|dx=}\\\\ \textbf{Ans::}=\frac{5\sqrt{5}+4}{6} ...

$Solve The Equation $\mathbf{\sqrt{sinx}+sinx+sin^2x+cosx=1}$\\\\ \mathbf{Ans:=}::$\mathbf{x=2k\pi,\pi-sin^{-1}\left(\frac{\sqrt{5}-1}{2}\right)+2k\pi}$ Where $\mathbf{k\in \mathbb{Z}}$ ...

\mathbf{\int\frac{dx}{(x+2)^5(x+3)^3}=}$ ...

Is it possible to divide a given square into n squares for any n≥6? ...

If S1,S2.....Sn be the sum of first nterms of n G.Ps whose 1st terms of each unity and C.R are 1,2,3.....n respectively prove S1+S2+2S3+3S4+.....(n-1)Sn= 1n+2n+3n+.....+nn. ...

please tell me about any olympiads which undergraduates may appear for. ...

Solve: (e^4x)*(p-1) + (e^2y)*(p^2) = 0 ...

Calculate the value of " L " as depicted below - *Image* Hint : - It is not as big as looks . ...

plzz explain how to do this comprehension( JEE 2010) quesn no. 42 , 43 and 44... http://jee.iitd.ac.in/QP_M1_ANS.pdf ...

$To solve the equation:\\\\ $\mathbf{2^{2x+2}-\frac{1}{2}.2^{x^2}+2x=x^2-3}$\\\\ Ans::\Leftrightarrow$\mathbf{x=3,x=-1}$ ...

*Image* *Image* ...

1.N is a 50 digit no.All the digits except the 26th from the right are 1.If N is divisible by 13 then the unknown digit is? ...

$If $\mathbf{f:\mathbb{R}\rightarrow \mathbb{R}}$ and $\mathbf{\frac{\sqrt{5}+1}{2}f(x)=f(x+1)+f(x-1)\forall x\in \mathbb{R}}$.\\\\ Then find Period of $\mathbf{f(x)}$\\\\ Ans:=$\mathbf{10}$ ...

if one root of (l-m)x2+lx+1=0 be double of the other and if l be real, show that m≤9/8 ...

Ye kaunse chapter ka question hai?? <<Assertion-Reason type>> STATEMENT-1: ~(p \leftrightarrow ~q) is equivalent to p \leftrightarrow q. STATEMENT-2: ~(p \leftrightarrow ~q) is a tautology. ...