Proving mathematical theorems by computer programs is the hot and latest buzz in automated reasoning (AR). The legality factor of a theorem ranges from the trivial to impossible state, based upon the logic used for its conceptualisation...............etc

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Abstract—Given a data point set , a query point set , and an integer , the Group Nearest Group (GNG) query finds a subset ( ) of points from such that the total distance from all points in to the nearest point in is not greater than any other subset ( ) of points in . GNG query is a partition-based clustering problem which can be found in many real applications and is NP-hard. In this paper, Exhaustive Hierarchical Combination (EHC) algorithm and Subset Hierarchial Refinement (SHR) algorithm are developed for GNG query pr..............etc

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This article is presented by:RAJAT BAKSHI
X-A
43Basic Proportionality Theorem



If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Aim- AD AE
DB EC
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Basic Rules and Tips in Group Discussions GD TIPS AND SCORING POINTS



1. Always be the initiator and concluder of the GD then being a participant.

2. But if you are particaipant always try to be the most vianl/key participant.

3. put points firmly and always try to get others support too.

4. if you find that the discussion os going offttrack then never loose an oppurtunity to bring it back to straem this is the best point to score max.

5. try to keep l..............etc

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Procedure: -
1. Select a frequency of ‘f’ Hz
2. To generate a sine wave of F Hz, define a closely spaced time vector(to represent analog signal, at least 1000 samples pr cycle)t=0:1/1000:1;
3. Generate the sinusoid, and plot the signal x_analog=sin(2*pi*F*t)
4. Select a sampling frequency Fs=10Fsamples/sec,generate a suitable time scale for this sampling signal n=0:1/Fs:1;%vector to define the sampling instants
5. Sample the analog signal at the instants specified by ’n ’
x_discreate =sin (2*pi*F*n) plot this using separa..............etc

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ABC is a triangle.From C a line segment CD is drawn on AB and from B a line segment BE is drawn on CA. The lines CD and BE intersect at a point O.
Here it is given that area of triangles 1)BOD=15 sq. unit 2)COE=10 sq. unit
and 3)BOC=25 sq. unit. Find area of ADOE..............etc

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A proof of the Heine-Borel Theorem
Theorem (Heine-Borel Theorem). A subset S of Ris compact if and only if S is closed and bounded.
Proof. First we suppose that S is compact. To see that S is bounded is fairly simple: Let In = (−n, n).
Then
1
[
n=1
In = R.
Therefore S is covered by the collection of {In}. Hence, since S is compact, finitely many will suffice.
S  (In1 [ · · · [ Ink ) = Im,
where m = max{n1, . . . , nk}. Therefore |x|  m for all x 2 S, and S is bounded.
Now we will show that S is closed. Suppose not. The..............etc

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i want to make a project on basic proportionality theorem in 3 days . please help me for that. i will be highly thankful to you for this
a needy one...............etc

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can you please help me with my project on the topic to verify the basic proportionality theorem using parallel line board and triangle cut-outs..............etc

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