Let f(x) be a polynomial of degree 51 such that when f(x) is divided by (x – 1), (x – 2), (x – 3),...and (x – 51), it leaves 1, 2, 3,... and 51 respectively, as the remainders. Find the value of f(52) + f(0).
In KAT exam there are three sections namely QA, VA and DI with 50, 40 and 30 questions respectively. Each correctly answered question fetches 1 mark. There is progressive negative marking in each section for incorrectly attempted questions with first 6 wrong answers carrying 1/4 negative marks each, next 6 incorrectly attempted questions carrying 1/3 negative marks each and beyond that every wrong answer carries 1/2 negative marks. The sectional cut-offs and the overall cut-off marks required to get oneself qualified for the next round of evaluation are- QA-11,VA-12,DI-9, OVERALL-35.
A student whose marks, in a particular section (or overall), is equal to the
given cut-offs is said to have ‘just managed’ to clear the cut-off in that section (or overall).
What can be the minimum number of unattempted questions in the exam such that a student just manages to clear all the three sectional cut-offs?
there are 13 teams playing in a tournament. team winning will get 3 points,draw is 2 points ,1 point for losing.the winning team scored 30 points. What is the min. points scored by last team ?
A,B and C started a business by investing 20000,28000 and 36000 respectively. after 6 months A and B withdraw an amount of 8000 each and C invested an additional amount of 8000.all of them invested for equal period of time.if at the end of the year,C got 12550 as his share of profit,what was the total profit earned?
The volume of a cuboid is 144 cm3 and the length of the largest side is ‘A”. How many possible values of A are there if the value of breadth of the given cuboid is the average of the length and the height.
In a aeroplane, the fuel burnt is directly proportional to the square root of its speed. If the aeroplane travels 800 km at a speed of 441 km/hr, the amount of fuel burnt is equal to 1250 litres. Find the distance travelled by the aeroplane, if 2000 litres of fuel was burnt while travelling at 784 km/hr.
An hourglass is formed from two identical cones, one kept on top of the other. When the upper cone is full of sand and the lower one is empty, it takes an hour for the sand to flow, at a constant rate, from the upper cone to lower cone. How long does it take for the depth of sand in the lower cone to be one third of the depth of sand in the upper cone?
A cube, one centimeter on a side, is sliced into two equal halves in such a way that the slice through the middle forms a regular hexagon. What's the area of the regular hexagon?
There are 5 identical triangular pyramids. Four of these pyramids are attached one on each face of the fifth pyramid. What is the ratio of the total surface area of the solid such formed to that of one pyramid?