1
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the equation $$f(x) = {{{a^{[x] + x}} - 1} \over {[x] + x}}$$ where [ . ] denotes the greatest integer function.
What is $$\mathop {\lim }\limits_{x \to {0^ + }} f(x)$$ equal to
2
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the equation $$f(x) = {{{a^{[x] + x}} - 1} \over {[x] + x}}$$ where [ . ] denotes the greatest integer function.
What is $$\mathop {\lim }\limits_{x \to {0^ - }} f(x)$$ equal to?
3
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
A function f(x) is defined as follows
$$f(x) = \left\{ {\matrix{ {x + \pi ,} & {for\,x \in [ - \pi ,0)} \cr {\pi \cos x,} & {for\,x \in \left[ {0,{\pi \over 2}} \right]} \cr {{{\left( {x - {\pi \over 2}} \right)}^2},} & {for\,x \in \left( {{\pi \over 2},\pi } \right]} \cr } } \right.$$
$$f(x) = \left\{ {\matrix{ {x + \pi ,} & {for\,x \in [ - \pi ,0)} \cr {\pi \cos x,} & {for\,x \in \left[ {0,{\pi \over 2}} \right]} \cr {{{\left( {x - {\pi \over 2}} \right)}^2},} & {for\,x \in \left( {{\pi \over 2},\pi } \right]} \cr } } \right.$$
Consider the following statements
1. The function f(x) is continuous at x = 0.
2. The function f(x) is continuous at $$x = {\pi \over 2}$$
Which of the above statements is/are correct?
1. The function f(x) is continuous at x = 0.
2. The function f(x) is continuous at $$x = {\pi \over 2}$$
Which of the above statements is/are correct?
4
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
A function f(x) is defined as follows
$$f(x) = \left\{ {\matrix{ {x + \pi ,} & {for\,x \in [ - \pi ,0)} \cr {\pi \cos x,} & {for\,x \in \left[ {0,{\pi \over 2}} \right]} \cr {{{\left( {x - {\pi \over 2}} \right)}^2},} & {for\,x \in \left( {{\pi \over 2},\pi } \right]} \cr } } \right.$$
$$f(x) = \left\{ {\matrix{ {x + \pi ,} & {for\,x \in [ - \pi ,0)} \cr {\pi \cos x,} & {for\,x \in \left[ {0,{\pi \over 2}} \right]} \cr {{{\left( {x - {\pi \over 2}} \right)}^2},} & {for\,x \in \left( {{\pi \over 2},\pi } \right]} \cr } } \right.$$
Consider the following statements
1. The function f(x) is differentiable at x = 0.
2. The function f(x) is differentiable at x = $${\pi \over 2}$$.
Which of the above statements is/are correct?
1. The function f(x) is differentiable at x = 0.
2. The function f(x) is differentiable at x = $${\pi \over 2}$$.
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