**(d)**∵ discontinuity exists due to**(i)**Non-existence of limit i.e., Either L.H.L ≠ R.H.L or any one of these are infinite or does not exist uniquely.**(ii)**and all polynomials are continuous function whatever may be its degree.**(a)***f*(0^{-}) =*f*(0^{+}) =*f*(0) =*a*⇒

*a*= 0**(d)***f*(*x*) = [*x*]^{2}- [x^{2}] and let*k*∈ ℤ, then∴ For continuity at k;

⟹ (

*k*- 1)^{2}< (*k*+*h*)^{2}< (*k*- 1)^{2}+ 1 and*k*^{2}< (*k*+*h*)^{2}<*k*^{2}+ 1 for*h*→ 0^{+}

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