LetN=6+66+666+⋯+100 sixes666…66 ​ ​where the last term consists of 100 digits, all of which are 6.Qu

Triangles \(ABC\) and \(DEF\) are such that \(\angle A = \angle D\), \(AB = DE = 17\), \(BC = EF = 1

If \(x=\cos1^\circ\cos2^\circ\cos3^\circ\cdots\cos89^\circ\) and \(y=\cos2^\circ\cos6^\circ\cos10^

9. Suppose \(a,b\) are integers and \(a+b\) is a root of \(x^2+ax+b=0\). What is the maximum possib

A point (P) in the interior of a regular hexagon is at distances \(8, 8, 16\) units from three cons

IOQM 2018Integers a, b, c satisfya+b−c=1anda2+b2−c2=−1.What is the sum of all possible values ofa2

IOQM 2018Let ABCD be a trapezium in which AB∥CD and AD⊥AB. Suppose ABCD has an incircle which touche

IOQM 20184. The equation 166×56=8590 is valid in some base b≥10 (that is, 1,6,5,8,9, and 0 are

IOQM 2018Consider all 6-digit numbers of the form abccba, where b is odd. Determine the number of

IOQM 2018quadrilateral ABCD with AB = AD = 13, BC = CD = 20, and BD = 24.

IOQM 2018A book is published in three volumes, the pages being numbered from 1 onwards. The page nu

n→∞lim ​(n4+1 ​n ​−(n2+1)n4+1 ​2n ​+n4+16 ​n ​−(n2+4)n4+16 ​8n ​+⋯+n4+n4 ​n ​−(n2+n2)n4+n4 ​2n⋅n2 .

Let [t] denote the greatest integer less than or equal to t. Then the least value of p∈N for which

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