Cyclic Integral 2 | Let's Crack IIT JAM | Satyendra Kumar #shorts

Let f(x) be a polynomial with integral coefficients. If f(1) and f(2) both are odd integers, prove that f(x) = 0 can' t have any integral root.

Let f(r) be the number of integral points inside a circle of radius r and centre at origin (integral point is a point both of whose coordinates are integers),then lim_(r rarr oo)(f(r))/(pi r^(2)) is equal to

1. Until the MBA arrived on the scene the IIT graduate was king A. A degree from one of the five IIT's was a passport to a well-payingjob, great prospects abroad and, for some, a decent dowry to boot. B. From the day he or she cracked the joint entrance exam, the IIT student commanded the awe of neighbours and close relatives. C. IIT students had, meanwhile, also developed their own special culture, complete with lingo and attitude, which they passed down. D. True, the success stories of IIT graduates are legion and they now constitute the cream of the Indian diaspora. 6. But not many alumni would agree that the IIT undergraduate mindset merits a serious psychological study, let alone an interactive one.

Let P (n) be the statement." 2^(3n-1) is integral multiple of 7". Then, P (1), P (2) and P (3) are true ?

Let A= {1, 2, 3, . . 20} . Let R_1 and R_2 two relation on A such that R_1 = {(a, b) : b is divisible by a} R_2 = {(a, b) : a is an integral multiple of b}. Then, number of elements in R_1 – R_2 is equal to ________.

If the equation x^(2)-3x+|3x-a|le0 is to be satisfied by atleast one xgt0 , then let Mbe the interval of values of a needed, then integral part of length of M is -----------

Let f : R to R be defined by f(x) = |2-x| - |x+1| The number of integral values of a for which f(x) =a has exactly one solution is:

Consider the quadratic equation (c-3) x^2 - 2cx + (c - 2) = 0 , c ne 3 . Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is: