(i) In 4x² + 7x + 7, all the indices of x are whole numbers. So, it is a polynomial in one variable x.
(ii) In y² + √2, the index of y is a whole number. So, it is a polynomial in one variable y.
(iii) In 3√t + t√2 = 3t1/2 + √2 t, here the exponent of the first term is 1/2, which is not a whole number; therefore, it is not a polynomial.
(iv) In y + 2√y = y + 2y1/2, here the exponent of the second term is 1/2, which is not a whole number; therefore, it is not a polynomial.
(v) In x10 + y³ + t50 is not a polynomial in one variable as three variables x, y and t occur in it.