Cyclic Integral 1 | 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.

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 f(x)=[x] +sqrt({x}) , where [.] denotes the integral part of x and {x} denotes the fractional part of x. Then f^(-1)(x) is

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 ________.

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:

Let Q(x) be a quadratic polynomial with real coefficients such that for all real x the relation, 2(1+Q(x)) =Q(x - 1) +Q(x +1) holds good. If Q(0) = 8 and Q(2) = 32 then The number of integral values of 'x' for which Q(x) gives negative real values.