A plane electromagnetic wave of wavelength λ has an intensity I. It is propagating along the positive Y-direction. The allowed expressions for the electric and magnetic fields are given by:

→E=√Iε₀Ccos[2πλ(y−ct)]^i; →B=1/cE^k
→E=√Iε₀Ccos[2πλ(y−ct)]^k; →B=−1/cE^i
→E=√2Iε₀Ccos[2πλ(y−ct)]^k; →B=+1/cE^i
→E=√2Iε₀Ccos[2πλ(y+ct)]^k; →B=1/cE^i

The correct option is C →E=√2Iε₀Ccos[2πλ(y−ct)]^k; →B=+1/cE^i
E is the electric field vector, and B is the magnetic field vector of the EM wave. For electromagnetic waves E and B are always perpendicular to each other and perpendicular to the direction of propagation. The direction of propagation is the direction of E x B.
So, if the wave propagates in the +Y direction then the direction of E and B should be in +X and +Z or vice versa i.e +Z and +X respectively.
Case 1. Let us suppose →E is in ^i and →B is in ^k
Then →E x →B will be in −^j
Not Possible.
Case 2. Let us suppose →E is in ^k and →B is in ^i
Then →E x →B will be in ^j
This is satisfying option (3) as the electric and magnetic field also propagate in positive y direction with time so (y−ct) should be there in wave equation. Also
I=cε₀/2|Eo|²
|Eo|=√2Icε₀
From these, we can say that option (c) would be the best option.