Hi Ashim Malik! 

NO2 group is enough electron withdrawing to make the Hydrogen attached to Carbon acidic. The conjugate base so formed is stabilised by both the Resonance effect of NO2 (major) and -I effect of NO2.

NaOH + CH3NO2 ---> NaCH2=NO2 + H2O

The acidity of this H accounts for the Nitro - Aci Tautomerism.

This aci form of nitromethane is acidic in nature due to tautamerism, hence dissolve in NaOH.

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Thank you and good luck.