1
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following for the next items that follow:
Let $f(x)=\frac{a^{x-1}+b^{x-1}}{2}$ and g(x) = x - 1.
What is $\displaystyle \lim _{x \rightarrow 1} f(x)^{\frac{1}{g(x)}}$ equal to?
2
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following for the next items that follow:
Let f(x) = |x| and g(x) = [x] - 1, where [.] is the greatest integer function.
Let $ h(x)=\frac{f(g(x))}{g(f(x))}$.
What is $\displaystyle \lim _{x \rightarrow 0+}$ h(x) equal to ?
3
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following for the next items that follow:
Let f(x) = |x| and g(x) = [x] - 1, where [.] is the greatest integer function.
Let $ h(x)=\frac{f(g(x))}{g(f(x))}$.
What is $\displaystyle \lim _{x \rightarrow 0-}$ h(x) equal to ?
4
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following for the next items that follow:
Let $f(x)= \begin{cases}\frac{x-3}{|x-3|}+a ; & x<3 \\ a-b ; & x=3 \\ \frac{x-3}{|x-3|}+b ; & x>3\end{cases}$ and f(x) be continuous at x = 3.
What is the value of a ?
Questions Asked from Limit, Continuity and Differentiability (Marks 2.5)
Number in Brackets after Paper Indicates No. of Questions
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