Recently Active Mathematics Questions

\boxed {1} \int_{0}^{\pi}{e^{\sec x}}\sec^3x\left(\sin^2 x+\sin x+\cos x+\sin x\cos x \right)\mathrm{dx} \boxed {2} Two rational numbers m and n are selected t random . the probability that m2+n2 is a multiple of 7 is ? \boxe ...

find real roots of equation \fn_cs \sqrt{x+2\sqrt{x+2\sqrt{x+........+2\sqrt{x+2\sqrt{3x}}}}} =x \fn_cs \left ( \textbf{n radical signs} \right ) 1) tell full solution wid explanation 2) what is radical signs?? ...

If m men can do a job in d days , then the number of days in which m+r men can do the job ? 1.d+r 2. d/m (m+r) 3. d/m+r 4. md/m+r Details Should be included ! ...

what will be the function of the graph which contains onlyl the intregral values of the universe??? ...

find : \int_{0}^{\frac{\pi}{3}}{\sin{\left( x-\frac{\pi}{6}}\right)\sin{\left( 2x-\frac{\pi}{3}}\right)\sin{\left( 3x-\frac{\pi}{2}}\right)\sin{\left( 4x-\frac{2\pi}{3}}\right)\sin{\left( 5x-\frac{5\pi}{6}}\right)} ...

what is the no of diagonals in a polygon which has n sides? ...

in how many ways can the letters of the word CINEMA be arranged so that the order of vowels do not change? ...

cosα+cos2α+p , sinα+sin2α=q then eliminate α ...

\120dpi \; \; LET A ={2,3,4,5,.........17,18}.LET \simeq BE \:\; THE\; \; EQUIVALENCE\; \; RELATION\; \; ON\; \; A\times A,\; \; DEFINED\; \; BY\; (a.b)\simeq (c.d)\; \; iff\; \; ad=bc.\; \; THEN\; \; THE\; \; NO\; \; OF\; \; ...

1) Prove that an infinite number of AP's exist, such that each of the terms is a perfect square. 2) How many ways are there to place the 1st 64 nos. on the 64 squares of a std. chessboard, such that the terms in each col. and ...

\texttt{let a,b,c be positive reals} \\ \texttt{if} \ a+b+c=3 \\ \texttt{then prove that:}\\ \frac{a}{4b^{2}+1}+\frac{b}{4c^{2}+1}+\frac{c}{4a^{2}+1}\geq\frac{3}{5} ...

1) \lim_{x\rightarrow 0} (\frac{sinx}{x}) ^{1/x} 2) \lim_{x\rightarrow +0} (log cotx ) ^{tanx} ...

sinθ+cosφ=1/√2 and cosθ+sinφ=√2/3 then find the value of sin(θ+φ) and tan (θ-φ)/2 ...

sin9°=1/4(√3+√5-√5-√5) ...

eliminate θ from atanθ +bcot2θ = c acotθ - btan2θ = c ...

In an international meeting of n≥3 participants, 14 languages are spoken. We know that: - Any 3 participants speak a common language. - No language is spoken more that by the half of the participants. What is the least valu ...

\boxed{1} \int \frac{\mathrm{dx}}{1+x^4} \\ \boxed{2}\int \frac{\sin x+\sin 2x}{\sqrt{\cos x+\cos 2x}}\mathrm{dx}\\ \boxed{3}\int \frac{1+x^{\frac{2}{3}}}{1+x}\mathrm{dx} ...

If 0∫k 1/2+8x2 = Pi/16 then k= Edit: It is whole by 2+8x2 ...

1) \lim_{x\rightarrow \Pi /2} (sinx)^{tanx} 2) \lim_{x\rightarrow \propto } (\frac{x^{2}-2x+2}{x^{2}-4x+1})^{x} ...

1) \lim_{x\rightarrow 0} \left\{tan(\Pi /4 +x ) \right\}^{1/x} ...

Which one is greater 1234230/2468462 or 1234231/2468464 ? ...

f(x)= cosx/[ 2x/pi ]+1/2 N.B - 2x/pi is in greatest integer function. nd x is not interger multiple of pi. is this fn. even , odd, neither even nor odd ??? ...

1. \lim_{x\rightarrow \frac{\prod{}}{4}} \frac{\sqrt{1-\sqrt{sin 2x}}}{\prod{-4x}} where x <pi/4 2. \lim_{x\rightarrow \propto } x^{3} \left\{{\sqrt{x^{2}+\sqrt{1+x^{4}}}- x\sqrt{2}} \right\} 3. \lim_{x\rightarrow \Pi /2} ...

If the sum of n terms of a series is Sn = n (5n – 3), find the nth term and pth term. ...

$\textrm{Show that for any real numbers }$ $a_{3 } ,a_{4},........,a_{85 }, $ $\textrm{the roots of the equation }$ $a_{85}x^{85 }+ a_{84}x^{84}+ ..........+a_{3}+ 3x^2+ 2x+ 1=0$ $ \textrm{are not real}$ ...

1) What must the radius of a circle be for the sector whose perimeter is equal to the given number P to have the greatest possible area? (my ans doesn't match) 2) Which of the cylinders with the given perimeter P=100cm, of th ...

in a certain test ,ai students gave wrong answers to at least i questions where i=1,2,3,4,5,....................k. no student gave more than k wrong answers. the total number of wrong answers given is__________ (A) a1+a2+a3+. ...

long time since posted ques.............here are some for 2011 aspirants daily updates..... Day1 Q1 Express 1*3*5*...*(2n-1)/2*4*6*8....*(2n) as a/2w where a is odd and w<2n Q2 Prove that there is no prime number in sequen ...

\large \\ f=\left\{\left(1,3 \right),(2,5),(3,7) \right\} \newline g=\left\{\left(3,7 \right), (5,9), (7,10) \right\} \newline\newline \:give\: reasons\: why\: fog\: is\: not\: possible ...

Prove:::::::: If gcd(a,n)=1,then the integers c,c+a,c+2a,c+3a,...........................,c+(n-1)a form a complete set of reidues modulo n, for any c. ...