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GATE Mathematics 2014 Paper

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Question : 23

Total: 55

Let a,b,c,d be real numbers with a < c < d < b . Consider the ring C [a,b ] with point wise addition and multiplication. If S={f∈C [a,b]:f(x)=0 for all x∈[c,d]} then

S is NOT an ideal of C [a,b]
S is an ideal of C [a,b] but NOT a prime ideal of C [a,b]
S is a prime ideal of C [a,b] but NOT a maximal ideal of C [a,b]
S is a maximal ideal of C [a,b]

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