Select Page ## A Trigonometric Substitution, ISI Entrance 2019, Subjective Solution to Problem – 6 .

Understand the problem  For all natural numbers(n), let          (A_n=sqrt{2-sqrt{2+sqrt{2+cdots +sqrt{2}}}})           (( n) many radicals) (a) Show that for (nge 2,  A_n=2sin frac{π}{2^{n+1}}). (b) Hence, or otherwise, evaluate the limit                            ... ## Two Similar Triangles, ISI B.Math/B.Stat Entrance 2018, Subjective Solution of Problem No. 2

Understand the problem Suppose that (PQ) and (RS) are two chords of a circle intersecting at a point (O) , It is given that (PO=3) cm and ( SO=4) cm . Moreover, the area of the triangle (POR) is (7 cm^2 ) . Find the are of the triangle (QOS) .   Source of the problem... ## Pythagorean Triple, ISI B.Math/B.Stat Entrance 2018, Subjective Solution of Problem No. 7

Understand the problem  Let (a,b,c in mathbb{N}) be such that (a^2+b^2=c^2) and (c-b=1).Prove that (i) (a) is odd,(ii) (b) is divisible by 4,(iii) (a^b+b^a) is divisible by (c).   Source of the problem I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance... ## Powers of 2 – I.S.I. B.Math/B.Stat Entrance 2019 Subjective Solution Problem 1

Understand the problem  Prove that the positive integers (n) that cannot be written as a sum of (r) consecutive positive integers, with (r>1) ,are of the form (n=2^l) for some (lge 0).   Source of the problem I.S.I. (Indian Statistical Institute) B.Stat/B.Math...