Statement 'A' is correct but statement 'B' is incorrect.

• Only the Narmada, the Tapti, and the Mahi rivers run from east to west and flow in a rift valley. Hence statement B is incorrect

• Himalayan rivers cross many Himalayan ranges and the Shivalik Hills and enter into the plain area. ​Hence statements A is correct.

• Shiwalik Range
  • Also known as Outer Himalayas.
  • Located in between the Great Plains and Lesser Himalayas.
  • The altitude varies from 600 to 1500 meters.
  • It has a length of about 2,400 km from the Potwar Plateau to the Brahmaputra valley.
  • The southern slopes are steep while the northern slopes are gentle.
• Peninsular river
  • The Peninsular drainage system is older than the Himalayan one.
  • This is evident from the broad, largely-graded shallow valleys, and the maturity of the rivers.
  • The Narmada and the Tapi are the peninsular rivers that flow through a rift valley.
  • Most of the major Peninsular Rivers except Narmada and Tapi flow from west to east. 
  • Hence statements B is incorrect.
  • Mahanadi, Godavari, Tungabhadra, Kaveri in the Deccan the
    gradient flows from West at the height of Western Ghats to the East into the Bay of Bengal.
• The geological faults (rifts) created between two ancient mountain ranges, ‘Vindhya’ & ‘Satpura’, when the Indian plate moved into the Eurasian plate.
  • They arise in the Chota Nagpur plateau in the east of the Deccan peninsula and from there, the gradient is down towards the Arabian Sea in the West; that is why they travel from the east to the west.  
  • These faults run parallel to the Vindhyas and the Satpuras.