Step 1: Understanding the carbylamine test.
The carbylamine test is used to detect primary amines. In this test, the amine reacts with chloroform (CHCl\(_3\)) and sodium hydroxide (NaOH) to form an isocyanide (carbylamine), which typically gives a strong odor. Secondary and tertiary amines do not give this test.
Step 2: Analyzing the options.
(A) Ethylamine: Ethylamine is a primary amine and will give a positive carbylamine test.
(B) Sec. butylamine: Sec. butylamine is a secondary amine and will not give the carbylamine test.
(C) Isopropylamine: Isopropylamine is a secondary amine and will not give the carbylamine test.
(D) Dimethylamine: Dimethylamine is a secondary amine and will not give the carbylamine test.
Step 3: Conclusion.
The correct answer is (D) Dimethylamine.