CSIR NET MATHEMATICS DEC 2019 ||REAL ANALYSIS || SOLUTION.

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Real analysis,
Limit, continuity, differentiability, sequence, series, Convergent, divergent, sup., inf., limit superior, limit inferior,radius of convergence,Countability, Riemann integral, Uniform convergence, uniform continuity, function of several variable, bounded variations, improper integral,graph of a function.
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Sir, In the second question if we choose f as a continuous function with f ( 1/4)>0 and f (3/4)<0 then f( alfa) = 0 right??
So option 4 also wrong right?
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