The Central Nervous System (CNS) is one of the most crucial parts of the human body. Brain tumor is one of the deadliest diseases that affect CNS and they should be detected earlier to avoid serious health implications. As it is one of the most dangerous types of cancer, its diagnosis is a crucial part of the healthcare sector. A brain tumor can be malignant or benign and its grade recognition is a tedious task for the radiologist. In the recent past, researchers have proposed various automatic detection and classification techniques that use different imaging modalities focusing on increased accuracy. In this paper, we have done an in-depth study of 19 different trained deep learning models like Alexnet, VGGnet, DarkNet, DenseNet, ResNet, InceptionNet, ShuffleNet, NasNet and their variants for the detection of brain tumors using deep transfer learning. The performance parameters show that NASNet-Large is outperforming others with an accuracy of 98.03% for detection and 97.87% for classification. The thresholding algorithm is used for segmenting out the tumor region if the detected output is other than normal.