Khuda was born in Margram village, Birbhum District, Bengal Presidency, British India (now India). He passed Matriculation examination from Calcutta Madrasa in 1918 with First Division. In 1924, he received his MSc degree in Chemistry from Presidency College, Kolkata. Later, he studied in London University. In 1929, he received D. Sc. in physics from this institute.