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In a book, the proof for demorgan's law, (A∩B)* = A*unionB* [*=complement] starts with,saying that for all x belongs to (A∩B)* , x is not a member of AunionB. But how can we say that, for example, if A = {1,2,3} and B = ( ...

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1) If f( x+y/2 ) = f(x) + f(y)/2 for x,y belongs to R anf f'(0) exists and equal to -1 and f(0) = 1 then the value of f(2) is 1) 0 2) 1 3)-1 4) 2 answer 3 ---------------------------------------------------------------------- ...

I m new here & dis is my 1st post So help me out.Some of these probs mite b vry easy fr u guys & nt of IIT level bt stl pls solve them.Give suitable xplanations. 1) If f is an odd function and limx→0f(x) exists then limx→ ...

Anyone having the download link for the e-book "C and C++ Datastructures by Tanenbaum".........pls post it. I'm in dire need of it. Thanks in advance. ...

Can anyone explain me this step please- coefficient of xn in [C0(1+x)2n - C1(1+x)2n-2 + C2(1+x)2n-4............... ] = coefficient of xn in [-1 + (1+x)2]n Thanks alot ...

CBSE gives Rs 1000/- per month scholarship for securing 90% in Xii(gen. cat.) and then pursuing graduate studies. Other cat. gets relaxation. For more details..visit cbse website. I am regretting because i payed more attentio ...

Find the value of: tan81° - tan63° - tan27° + tan9° ...

If A+B+C=pi FInd the least value of 2tanA + 3 tan B + tanc. ...

1. (sin-1x+sin-1w) (sin-1y+sin-1z) = π2 then, \begin{vmatrix} X^{N_{1}} & Y^{N_{2}}\\ Z^{N_{3}} & W^{N_{4}} \end{vmatrix} where N1,N2,N3,N4 ε N : a) has a max. value of 2 b) has a min value of -2 c) is independent of Ni d) ...

if x= y cos 2pie/3 = z cos 4pie/3 then xy+yz+xz=? ...

1.If sin-1x + tan-1x =/2 then 2x2 + 1 = a) 5 b)[sqrt(]5-1)/2 c)2 d)none 2.If cos-1x/2 + cos-1y/3 =0, 9x2 - axycosθ + by2=csin2θ prove that a-b+c=44. ...

Draw the graph of [y] = [sinx] and y =cosx. Hence find the no. of solutions. [.] is GIF. In interval -π to π) Problem: I could draw it approximately but it's getting tougher to find solns. Well, my graph becomes dirty. ...

Evaluate \huge \frac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2-.....\frac{1}{2-1/2}}}}}} We have 100 2's ...

Find all pairs (a,b) of real numbers such that whenever α is a root of x2 + ax + b = 0, α2 - 2 is also a root of the equation. I am confused with the solution of this question... case1 : When α = β So there is only one po ...

Show that \sum_{k=0}^{n}{C(n,k)sinkx cos(n-k)x} = 2^{n-1}sinnx ...

1) A line drawn from P(p,q) intersects the curve x^2+2hxy+by^2-1=0 at points Q and R(P not lying on th curve).If the product PQ . PR is always equal to 2,then: a)p=1, q=-1 b)p^2 + q^2 = 2 c)p=0, q=2 d)p=-1, q=1 ...

which has greater b.p acetone or butanone.... plz give me the reason.... ...

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A is the point (4,0) and M is the foot of the perpendicular drawn from a point to the y-axis.If P moves such that the distances PA and PM are equal find the locus of P. I get the answer as 8x=16+y2. Am I right? If not,plz sho ...

The line joining A = ( b cosα,b sinα ) and B = ( acosβ,asinβ ) is produced to a point M(x,y) so that AM:BM = b:a. Prove that x+y tan( α+β/2 ) = 0. ...

Find the last term of the A.P formed by the common terms of both the A.P's 15,17,19....... 135 and, 21,27,33........ 561 ...

Q-1 A point charge q is located a distance d from an infinite plane. Determine the electric flux through the plane due to the point charge. Q-2 A point charge q is located a very small distance from the center of a very large ...

in triangle ABC the coordinates of the vertex A are (4, -1) and the lines x-y-1=0 and 2x-y-3=0 are internal bisectors of angles B and C then , radius of incircle of triangle ABC is ...

\lim_{x\rightarrow a}\frac{1}{(x-a)}\int_{\sqrt{a}}^{\sqrt{x}}(te^t sin t)dt a>0 ...

When a mass of water at 100°C changes to steam at the same temperature, does the internal energy remain unchanged?? If not; why??? ...

Now that we have solved the probability of product of 2 integers being a multiple of 2n can we generalize this to probability that the product of n integers is divisible by 2m? ...

Find the square root of... \sqrt{a-b}+\sqrt{b-c}+\sqrt{c-a} ...

What is the number of pairs of 2 consecutve 4 digit integers which can be added without any carry? ...

3SINX - 4 SIN3X - K=0 ANGLE A AND ANGLE B SATISFY THE ABOVE EQUATION. A>B (GIVEN) FIND ANGLE C? WHERE A,B AND C ARE THE ANGLES OF A TRIANGLE ABC....... ...