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Algebra
The equation 11x + 67y = 133 has
1. two integral solutions for 0 < x < 50
2. no integral solutions for 10 < y < 20
3. an integral solution for 100 < x < 200
4. no integral solutions for y < 0
Author: TG.Raman
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Arithmetic
A shopkeeper offers 30% off on MRP of his articles. In addition, he gives one article free for every four articles purchased. Even after all these offers, the shopkeeper manages to get a profit of 12%. By what percent has he marked up his articles?
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Geometry
Let ABCD be a rectangle with sides 15 and 20 as shown. Let m be a circle centered at A of the circle passing through F, C, and E.
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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?
Counting in Geometry
(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 nC2.
- The number of triangles that can be formed by joining them is nC3.
- 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
- The number of straight lines that can be formed by joining them is nC2 – mC2 + 1.
- The number of triangles that can be formed by joining them is nC3 – mC3.
- The number of polygons with k sides that can be formed by joining them is nCk – mCk.
(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: 1
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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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