# Geometry

Let ABCD be a rectangle with sides 12 and 15 as shown. Let m be a circle centered at A of the circle passing through F, C, and E.

Let ABCD be a rectangle with sides 12 and 15 as shown. Let m be a circle centered at A of the circle passing through F, C, and E.

The sentences given in the question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Write the sequence of numbers, the sentences of which create the most coherent paragraph.

- Through such judgments, the judiciary has failed not only to protect the legitimate rights of owners, but also to provide economic justice enshrined in Article 38 of the Constitution.
- The Indian judiciary doesn’t seem to fully appreciate the consequences of its judgments.

Numbers

Among the integers 1, 2,3, 4,……, 2018, what is the maximum number of integers that can be selected such that the sum of any two selected numbers is not a multiple of 7?

Which one of the following is a synonym of ‘*obtuse’?*

A. Keen

B. Dull

C. Sharp

D. Large

E. Blunt

(a) In a plane, if there are n points of which no three are collinear, then

- The number of straight lines that can be formed by joining them is
^{n}C_{2}. - The number of triangles that can be formed by joining them is
^{n}C_{3}. - The number of polygons with k sides that can be formed by joining them is
^{n}C_{k}.

(b) In a plane, if there are n points out of which m points are collinear, then

- The number of straight lines that can be formed by joining them is
^{n}C_{2}–^{m}C_{2}+ 1. - The number of triangles that can be formed by joining them is
^{n}C_{3}–^{m}C_{3}. - The number of polygons with k sides that can be formed by joining them is
^{n}C_{k}–^{m}C_{k}.

(c) The number of diagonals of an n sided polygon is ^{n}C_{2} – n = n × (n – 3)/2

If a, b and c are positive real numbers such that ab + a + b = bc + b + c = ca + c + a = 35. Find the value of (a + 1) (b +1)(c+1) .

The number of divisors the form 4n +1, n ≥0, of the number 10^{10} × 11^{11} × 13^{13}

__________

A. 256

B. 924

C. 1024

D. 512

E. None of these

In the figure, ABCD is a rhombus. Point E is on the diagonal AC such that AE = 41, EC = 9 and measure of ∠ABE = 90º. Find the area of this rhombus.

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