The anser is b guess and test
(1+x^2)^8
=(1+8x^2+8*7/(1*2)x^4+8*7*6/(1*2*3)x^6+8*7*6*5/(1*2*3*4)x^8+....)
=1+8x^2+28x^4+56x^6+70x^8+....)
For x<1, higher power terms diminish in value, hence we can approximate powers of numbers.
1.01=(1+0.1^2) => x=0.1 in the above expansion
(1.01)^8
=1+8(0.1^2)+28(0.1^4)+56(0.1^6) [ limited to four terms, as requested]
=1+0.08+0.0028+0.000056 (+0.00000070)
=1.082856 (approximately)
Answer: The critical value for a two-tailed t-test = 2.056
The critical value for a one-tailed t-test = 1.706
Step-by-step explanation:
Given : Degree of freedom : df= 26
Significance level : 
Using student's t distribution table , the critical value for a two-tailed t-test will be :-

The critical value for a two-tailed t-test = 2.056
Again, Using student's t distribution table , the critical value for a one-tailed t-test will be :-

The critical value for a one-tailed t-test = 1.706
I think the answer is the third one