Yes I agree with the given statement that with out Himalayas India would be  a cold and dry desert because the Himalayas act as a barrier to prevent the entry of the cold central winds into Indian and even they see through that the monsoon winds are going towards the northern neighboring countries.  
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The formation of Himalayas influences the climate in various ways.These acts as barriers protecting the great plains of India from the cold winds of Central Asia during severe winter.The Himalayas are reason for summer rains and monsoon type of climate in regions that are beyond the Western Ghats of India.In it's absence this region would have remained drier.The Himalayan rivers have a perennial flow since these are fed by the glaciers and bring a lot of silt,making these plains very fertile.
By these we can say that without the Himalayas a large area of India would be drier.
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