1
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$f(x) = \sqrt {25 - {x^2}} $$, then what is $$\mathop {\lim }\limits_{x \to 1} {{f(x) - f(1)} \over {x - 1}}$$ equal to ?
2
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the function
$$f(x) = \left\{ {\matrix{ {ax - 2,} & {for} & { - 2 < x < - 1} \cr { - 1,} & {for} & { - 1 \le x \le 1} \cr {a + 2{{(x - 1)}^2},} & {for} & {1 < x < 2} \cr } } \right.$$
What is the value of a for which f(x) is continuous at x = $$-$$1 and x = 1?
$$f(x) = \left\{ {\matrix{ {ax - 2,} & {for} & { - 2 < x < - 1} \cr { - 1,} & {for} & { - 1 \le x \le 1} \cr {a + 2{{(x - 1)}^2},} & {for} & {1 < x < 2} \cr } } \right.$$
What is the value of a for which f(x) is continuous at x = $$-$$1 and x = 1?
3
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
The function $$f(x) = {{1 - \sin x + \cos x} \over {1 + \sin x + \cos x}}$$ is not defined at x = $$\pi$$. The value of f($$\pi$$), so that f(x) is continuous at x = $$\pi$$, is
4
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following functions
1. $$f(x) = \left\{ \matrix{ {1 \over x},\,if\,x \ne 0 \hfill \cr 0,\,if\,x = 0 \hfill \cr} \right.$$
$$f(x) = \left\{ {\matrix{ {2x + 5,} & {if\,x > 0} \cr {{x^2} + 2x + 5,} & {if\,x \le 0} \cr } } \right.$$
Which of the above functions is/are derivable at x = 0 ?
1. $$f(x) = \left\{ \matrix{ {1 \over x},\,if\,x \ne 0 \hfill \cr 0,\,if\,x = 0 \hfill \cr} \right.$$
$$f(x) = \left\{ {\matrix{ {2x + 5,} & {if\,x > 0} \cr {{x^2} + 2x + 5,} & {if\,x \le 0} \cr } } \right.$$
Which of the above functions is/are derivable at x = 0 ?
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