Which of the following amines is most basic in nature?a) 2, 4 — Dichloroanilineb) 2, 4 — Dimethylanilinec) 2, 4 — Dinitroanilined) 2, 4 — Dibromoaniline
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answer :- option (b) 2, 4 - dimethylaniline
explanation :- Any group present on benzene ring that has electron withdrawing effect (– NO2, – CN, – SO3H, – COOH – Cl, C6H5, etc.) decreases basicity of aniline.
and An electron repelling effect (– NH2, – OR, R –, etc.) increases basicity of aniline.
hence, from above rule 2, 4 - dimethylaniline is most basic in nature .
explanation :- Any group present on benzene ring that has electron withdrawing effect (– NO2, – CN, – SO3H, – COOH – Cl, C6H5, etc.) decreases basicity of aniline.
and An electron repelling effect (– NH2, – OR, R –, etc.) increases basicity of aniline.
hence, from above rule 2, 4 - dimethylaniline is most basic in nature .
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We know, p(x)=[g(x)×q(x)]+r(x)
∴p(x)−r(x)=g(x)×q(x)
∴p(x)+{−r(x)}=g(x)×q(x)
It is clear that RHS is divisible by g(x). ∴LHS is also divisible by g(x)
Thus, if we add −r(x) to p(x), then the resulting polynomial is divisible by g(x).
Let us divide p(x)=x
4
+2x
3
−2x
2
+x−1 by g(x)=x
2
+2x−3 to find the remainder r(x).
∴r(x)=−x+2⇒{−r(x)}=x−2
Hence, we should add (x−2) to p(x)=x
4
+2x
3
−2x
2
+x−1 so that the resulting polynomial is exactly divisible by x
2
+2x−3.
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