Recently Active Mathematics Questions

1) If k sin2x + (1/k) cosec 2 x = 2, for all x belonging to (0, pie/2) then cos2x + 5 sinx cosx + 6 sin 2x is equals to (a) (k2+5k+6) / k2 (b) (k2-5k+6) / k2 (c)6 (d) none of these choose the correct alternative 2) If lim x↠...

(y+ y3/3 + x2/2 ) dx + ( x+xy2/4 )dy = 0 solve the above differential equation ...

Prove that there are no perfect squares in the array below: 11 111 1111 ... 22 222 2222 ... 33 333 3333 ... 44 444 4444 ... .. .. .. 99 999 9999 ... ...

Let f:R→R such that for all x,y belongs R *Image* where n belongs N.Prove that f(x) is a constant function. ...

Let a and b be two primes having at least two digits, such that a > b. Show that 240 divides a4-b4. ...

Plz sketch the graph of (x2-x+1)/(x2-3x+2) ...

1. If a,b,c be +ve real nos,prove that: a/(b+c) +b/(c+a) + c/(a+b) >= 3/2 ...

1) The eqn (cos p -1) x2 + (cosp)x + sinp =0, in the variable x ,has real roots. Then p can have any value in the interval (a) (0 , 2 pie) (b) (- pie, 0 ) (c) (- pie/2 , pie/2 ) (d) ( 0 ,pie) ...

Evaluate the integral: \int_0^1\dfrac{x-1}{\ln x}\ \mathrm dx ...

Four couples play chess together. For the match, they're paired as follows: ("man Clara" indicates the husband of Clara, etc.) Bea ≡ Eddy An≡ man Clara Freddy ≡woman Guy Debby ≡ man An Guy ≡ woman Eddy Who is Hubert ...

Given a cube in which you can put two massive spheres of radius 1. What's the smallest possible value of the side - length of the cube? Prove that your answer is the best possible. ...

Q1 If a≠b,then equation zz+az+bz+c=0 represents ? Q2 If a=b,c εR and lbl2>c ,then equation zz+az+bz+c=0 represents ? Q3 If a=b,c εR and lbl2<c ,then equation zz+az+bz+c=0 represents ? ...

give the necessary condition for a line y=mx + c to be normal to : 1)ellipse 2)parabola 3)hyperbola ...

hey guyys a nice sum.... plz try it outt if there r n points on a circle....no. of triangles that can be formed by joining them.....note:no three lines intersect at a point.....[the answer iss not nC3 u have to consider the s ...

1) Show that the soln set of eqns (x+1) 2 + [x-1] 2 = (x-1)2 + [x+1] 2 , where [x] and (x) are the gratest integer and nearest integer to x , is x belonging to I. 2) If P(x) = ax 2+bx+c and Q(x) = -ax 2+dx+c, where ac≠0, th ...

*Image* I suddenly encountered this inequality (While attempting another one [78] ), which seemingly seems true....(I mean I checked with a few values....) but i've not been able to prove it, as it is I do not even know wheth ...

This will be torn apart, still it should help us recall some useful facts: Prove that: \sum_{cyc} \frac{(a+b)(a+c)}{(a-b)(a-c)} = 1 ...

Find \lim_{n\rightarrow \infty}{\frac{a^n}{n!}} I have this soln available with me.. *Image* plz provide a new shorter soln..or help me to understand this soln.. ...

Please solve these problems 1. (x-a)(x-a)(x-a) + (x-b)(x-b)(x-b) + (x-c)(x-c)(x-c) = 0 has A)All the roots real B)one real and two imaginary roots C)three real roots namely x=a,x=b,x=c D)None 2. a+b+c = 0, then the quadratic ...

Prove that the sum of the infinite series 1+1-1+1-1+... is either 1 or 0. <edited:> the sum can be 1/2 too.. in fact, the sum is formally defined to be 1/2. So...go ahead and prove it! ...

Figure out integral solutions of x3-y2=2 ...

The number of cubic polynomials p(x) with integral co-efficients such that for three distinct integers a, b and c such that p(a)=b, p(b)=c and p(c)=a is (a) 0 (b) 1 (c) dependent on a, b, c (d) infinite ...

The following is a system of quadratic equation with a,b,c being real and a≠0..... ax12+bx1+c=x2 ax22+bx2+c=x3 ax32+bx3+c=x4 ax42+bx4+c=x5 . . . . . . . . axn-12+bxn-1+c=xn axn2+bxn+c=x1 Answer the following questions.... Q ...

1)f(xy)=f(x)+f(y) implies f(x)=klnx or f(x)=0 2)f(xy)=f(x).f(y) implies f(x)=x^n 3)f(x+y)=f(x).f(y) implies f(x)=a^kx 4)f(x+y)=f(x)=(fy) implies f(x)=k where k is a constant and 5)f(x).f(1/x)=f(x)+f(1/x) implies f(x)=±x^n +1 ...

Find number of roots of 2x=(2n+1)Ï€(1-cosx) where n is positive integer ...

1) SHow that the roots of the eqn x4+4x3-8x2+k=0 are real for k belonging to [0,3]. 2) Show that the eqn log(x2+2ax) = log(8x-6a-3) have only one solution for a=1 or a belonging to [-1/2 , -3/22]. ...

This was posted in another iitian forum (by one of our members :D). Its a nice problem so I flicked it. Let f(x) = ax2+bx+c be such that the equation f(x) = x has non-real roots. Prove that this implies that the equation f(f( ...

find coordinates of point on parabola y2=8x which is at min distance from circle x2+(y+6)2=1 is differentiation the only method ?? can we get answer by observation only ?? ...

1) Show that the least natural number a for which x + ax -2 > 2 for all x belonging to (0,∞) is 2. 2) Let f(x) = sinx+ax+b, then show that f(x)=0 has (a)only one real root which is positive if a>1, b<0 (b)only one ...

if ∫ f(x) dx = i ( UL= b, LL=a) ∫ f( x - (1/x)) dx ( UL=b,LL=a) =? UL=upper limit LL=lower limit ...