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Basic Rules - Remainder of a product = product of remainder of factors    Eg. Remainder of 49/5 = Remainder of 7/5 x Remainder of 7/5                                          = 2x2 = 4 - Remainder of a sum = sum of reminder of each term Expansion by binomial series What is the remainder when 17^23 is divided by 16? 17 23 = (16+1) 23 = 23 C 0 16 23 1 0  + 23 C 1 16 22 1 1 +...+ 23 C 22 16 1 1 22  + 23 C 23 16 0 1 23 There are 24 terms with the first 23 containing a multiple of 16 and they are divisible by 16. The last term is 1 and that is the remainder when 17 23 is divided by 16. What is the remainder when 20^20 is divided by 23? 20 20 = (23-3) 20 = 20 C 0 23 20 3 0  -  20 C 1 23 19 3 1 +...-  20 C 19 23 1 3 19  + 20 C 20 23 0 3 20 The remainder is the remainder of last term divided by 23 = remainder of 3 20 /23 = remaind...

Chapter I of the novel begins with Robert Langdon asleep in the Ritz Hotel. Our trip begins with ourselves just outside the Ritz Hotel. One of the posh hotels with a lot of high end luxury cars parked outside. Ritz Hotel, Paris Sitting up now, Langdon frowned at his bedside Guest Relations Handbook, whose cover boasted:     SLEEP LIKE A BABY IN THE CITY OF LIGHTS. SLUMBER AT THE PARIS RITZ. In the beginning on his way to Louvre - The crisp April air whipped through the open window of the Citroën ZX as it skimmed south past the Opera House and crossed Place Vendôme . As the Citroën accelerated southward across the city, the illuminated profile of the Eiffel Tower appeared, shooting skyward in the distance to the right. Symbologists often remarked that France—a country renowned for machismo, womanizing, and diminutive insecure leaders like Napoleon and Pepin the Short—could not have chosen a more apt national emblem than a thous...

ISRO 2017 May Mechanical Questions, Answers and Explanation 1. A solid rod of 12mm diameter was tested for tensile strength with the gauge length of 50mm. Final length = 80mm; Final diameter = 4mm; Yield load = 1130N. What is the nearest yield stress and % reduction in area respectively? a) 10MPa and 10% b) 90MPa and 90% c) 10MPa and 90% d) 90MPa and 10% Answer c) 10MPa and 90% Explanation Yield stress = Yield load/Area at yield = 1130/(π (4x10 -3 ) 2 /4) =  4520x10 6 /(16π) % reduction in area = Change in area*100/Original area 2. When water at 0C is heated, its specific volume under standard atmosphere a) First increases then decreases b) First decreases then increases c) Increases steadily d) Decreases steadily Answer b) First decreases then increases Explanation The density of water is highest at 4C. That is the specific volume is minimum for water at 4C. 3. A spherical joint has ....... degree (s) of freedom. a) One b) Two c) Three d) Four ...

ISRO 2017 December Mechanical Questions, Answers and Explanation Question Set E 1. The specific metal cutting energy is expressed as a)  τ cos(β - α) ⁄ sin φ cos(φ+β-α) b)  τ sin(β - α) ⁄ sin φ cos(φ-β+α) c)  τ cos(α - β) ⁄ sin φ cos(φ-β+α) d)  τ sin(α - β) ⁄ sin φ cos(φ+β-α) where  α is rake angle,   β is friction angle,  φ is shear angle and    τ is the shear stress. Answer a)    τ cos(β - α) ⁄ sin φ cos(φ+β-α) Explanation [ Manufacturing Technology ] Specific metal cutting energy is defined as the energy expended in removing a unit volume of work-piece material.  = Energy/Volume Removed Energy = Force of cut x velocity of tool Volume Removed = Velocity of tool x Width of cut x Depth of cut Specific metal cutting energy = Force of cut/(Width of cut x Depth of cut) Shear force = shear stress x Area of shear  =  τ  x width of cut x depth of cut /sin  φ Shear force/Force of cut ...