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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Identify the correct option(s):
A. A modulus function is continuous at every point in its domain.
B. A modulus function may or may not be continuous at every point in its domain.
C. Every rational function is continuous in its domain.
D. If a function $f$ is differentiable at a point then it is also continuous at that point.
E. If a function $f$ is continuous at a point then it is also differentiable at that point.
Choose the correct answer from the options given below:
Solution
A. A modulus function $|x|$ is continuous at every point in its domain.
Hence A is true.
B. Since modulus function is continuous everywhere in its domain, this statement is false.
C. A rational function $\frac{p(x)}{q(x)}$ is continuous at every point where $q(x)\neq0$.
Thus it is continuous in its domain. Hence C is true.
D. If a function is differentiable at a point, then it must be continuous at that point.
Hence D is true.
E. Continuity does not necessarily imply differentiability (example: $f(x)=|x|$ at $x=0$).
Hence E is false.
Correct statements are A, C and D.
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