List of top Mathematics for Economy Questions on Preliminaries and functions asked in IIT JAM EN

Let 2𝑧=-3+√3 𝑖 , 𝑖 = √−1. Then 2z ⁸ is equal to

Let 𝑓, 𝑔∶ℝ → ℝ be defined by

Then

Let an = \((1+\frac{1}{n})^{\frac{n}{2}}\) be the n^𝑡ℎ term of the sequence 〈a_n 〉, n = 1, 2, 3, …. Then which one of the following is NOT CORRECT?

Which of the following is NOT CORRECT?

Among the following statements which one is CORRECT?
S1: 𝑥²+𝑦²=6 is a level curve of 𝑓(𝑥, 𝑦)=\(\sqrt{𝑥^2+𝑦^2}\)−𝑥²−𝑦²+2 
S2: 𝑥²−𝑦2=−3 is a level curve of 𝑔(𝑥, 𝑦) =\(𝑒−{^𝑥}^{2} 𝑒{^y}^{2}\)+𝑥⁴−2−2𝑥²𝑦²+y⁴

Let [𝑡] denote the greatest integer ≤ 𝑡. The number of points of discontinuity of the function 𝑓(𝑥)= [𝑥²−3𝑥+2] for 𝑥∈[0, 4] is _______ (in integer)

Let 𝑓: R² → R be the function defined by

Then

Which of the following functions is/are homogeneous?

If \(\int t\log(1+\frac{2}{t})dt=g(t)(\frac{t^2}{2}-2)+f(t)\frac{t^2}{2}+Kt+C\), where C is an arbitrary constant, then 2K is ______ (in integer).