Thyroid disease is one of the most common diseases among the female mass in Bangladesh. Hypothyroid is a common variation of thyroid disease. It is clearly visible that hypothyroid disease is mostly seen in female patients. Most people are not aware of that disease as a result of which, it is rapidly turning into a critical disease. It is very much important to detect it in the primary stage so that doctors can provide better medication to keep itself turning into a serious matter. Predicting disease in machine learning is a difficult task. Machine learning plays an important role in predicting diseases. Again distinct feature selection techniques have facilitated this process prediction and assumption of diseases. There are two types of thyroid diseases namely 1. Hyperthyroid and 2.Hypothyroid. Here, in this paper, we have attempted to predict hypothyroid in the primary stage. To do so, we have mainly used three feature selection techniques along with diverse classification techniques. Feature selection techniques used by us are Recursive Feature Selection(RFE), Univariate Feature Selection(UFS) and Principal Component Analysis(PCA) along with classification algorithms named Support Vector Machine(SVM), Decision Tree(DT), Random Forest(RF), Logistic Regression(LR) and Naive Bayes(NB). By observing the results, we could extrapolate that the RFE feature selection technique helps us to provide constant 99.35% accuracy for all four classification algorithms. Thus it's deduced from our research that RFE helps each classifier to attain better accuracy than all the other feature selection methods used.