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.

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Parajumble

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.

  1. 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.
  2. The Indian judiciary doesn’t seem to fully appreciate the consequences of its judgments.
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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?

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Verbal Question of the Day

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

 
A. Keen
B. Dull
C. Sharp
D. Large
E. Blunt
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Counting in Geometry


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

  1. The number of straight lines that can be formed by joining them is nC2.
  2. The number of triangles that can be formed by joining them is nC3.
  3. The number of polygons with k sides that can be formed by joining them is nCk.

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

  1. The number of straight lines that can be formed by joining them is nC2mC2 + 1.
  2. The number of triangles that can be formed by joining them is nC3mC3.
  3. The number of polygons with k sides that can be formed by joining them is nCkmCk.

(c) The number of diagonals of an n sided polygon is nC2 – n = n × (n – 3)/2

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Algebra

 

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) .

Quant Question of the Day: 17/06/2017 :

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Numbers

The number of divisors the form 4n +1, n ≥0, of the number 1010 × 1111 × 1313
__________
A. 256
B. 924
C. 1024
D. 512
E. None of these

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Geometry

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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