Consider the following functions for non-zero positive integers, p and q.…

GATE · 2022 · AE · General AptitudeGATE · 2022 · GE · General AptitudeGATE · 2022 · ME · Set 2 · General Aptitude

Consider the following functions for non-zero positive integers, p and q.

f(p,q)=p×p×p×………×p⏟q terms=pq;f(p,1)=pf(p,q)=\underbrace{p\times p\times p\times\ldots\ldots\ldots\times p}_{q\text{ terms}}=p^q;\quad f(p,1)=p

g(p,q)=ppppp⋱(up to q terms);g(p,1)=pg(p,q)=p^{p^{p^{p^{p^{\ddots\text{(up to }q\text{ terms)}}}}}};\quad g(p,1)=p

Which one of the following options is correct based on the above?

  1. A.

    f(2,2)=g(2,2)f(2,2)=g(2,2)

  2. B.

    f(g(2,2),2)<f(2,g(2,2))f(g(2,2),2)<f(2,g(2,2))

  3. C.

    g(2,1)≠f(2,1)g(2,1)\ne f(2,1)

  4. D.

    f(3,2)>g(3,2)f(3,2)>g(3,2)

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