1
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$f(x) = {{\sin ({e^{x - 2}} - 1)} \over {\ln (x - 1)}}$$, then $$\mathop {\lim }\limits_{x \to 2} $$ f(x) is equal to
2
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the function
$$f(x) = \left\{ {\matrix{ { - 2\sin x,} & {if} & {x \le - {\pi \over 2}} \cr {A\sin x + B,} & {if} & { - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x,} & {if} & {x \ge {\pi \over 2}} \cr } } \right.$$
which is continuous everywhere.
$$f(x) = \left\{ {\matrix{ { - 2\sin x,} & {if} & {x \le - {\pi \over 2}} \cr {A\sin x + B,} & {if} & { - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x,} & {if} & {x \ge {\pi \over 2}} \cr } } \right.$$
which is continuous everywhere.
The value of A is
3
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the function
$$f(x) = \left\{ {\matrix{ { - 2\sin x,} & {if} & {x \le - {\pi \over 2}} \cr {A\sin x + B,} & {if} & { - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x,} & {if} & {x \ge {\pi \over 2}} \cr } } \right.$$
which is continuous everywhere.
$$f(x) = \left\{ {\matrix{ { - 2\sin x,} & {if} & {x \le - {\pi \over 2}} \cr {A\sin x + B,} & {if} & { - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x,} & {if} & {x \ge {\pi \over 2}} \cr } } \right.$$
which is continuous everywhere.
The value of B is
4
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following in respect of the function
$$f(x) = \left\{ \matrix{ 2 + x,x \ge 0 \hfill \cr 2 - x,x < 0 \hfill \cr} \right.$$.
I. $$\mathop {\lim }\limits_{x \to 1} f(x)$$ does not exist.
II. f(x) is differentiable at x = 0.
III. f(x) is continuous at x = 0.
Which of the above statements is/are correct?
$$f(x) = \left\{ \matrix{ 2 + x,x \ge 0 \hfill \cr 2 - x,x < 0 \hfill \cr} \right.$$.
I. $$\mathop {\lim }\limits_{x \to 1} f(x)$$ does not exist.
II. f(x) is differentiable at x = 0.
III. f(x) is continuous at x = 0.
Which of the above statements is/are correct?
Questions Asked from Limit, Continuity and Differentiability (Marks 2.5)
Number in Brackets after Paper Indicates No. of Questions
NDA Subjects
Mathematics
Algebra
Sets, Relations and Functions Logarithms Quadratic Equations and Inequalities Sequence And Series Binomial Theorem Matrices Determinants Permutations and Combinations Probability Complex Numbers Vector Algebra Three Dimensional Geometry Statistics
Trigonometry
Trigonometric Angles and Equations Inverse Trigonometric Function Height and Distance Properties of Triangles
Coordinate Geometry
Calculus
English
General Studies