ExamSIDE (Powered by ExamGOAL)
Questions
PREVIOUS NEXT
1
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is $$\int {{{({x^{e - 1}} + {e^{x - 1}})dx} \over {{x^e} + {e^x}}}} $$ equal to ?
A
$${{{x^2}} \over 2} + C$$
B
$$\ln (x + e) + C$$
C
$$\ln ({x^e} + {e^x}) + C$$
D
$${1 \over e}\ln ({x^e} + {e^x}) + C$$
2
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Let f(x) be an indefinite integral of sin2x.

Consider the following statements

Statement I The function f(x) satisfies f(x + $$\pi$$) = f(x) for real x.

Statement II sin2(x + $$\pi$$) = sin2x for all real x.

Which one of the following is correct in respect of the above statements?
A
Both the statements are true and Statement 2 is the correct explanation of Statement 1
B
Both the statements are true but Statement 2 is not the correct explanation of Statement 1
C
Statement 1 is true but Statement 2 is false
D
Statement 1 is false but Statement 2 is true
3
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
What is $$\int {{{\sin }^3}x\cos x\,dx} $$ equal to ?
A
$${\cos ^4}x + C$$
B
$${\sin ^4}x + C$$
C
$${{{{(1 - {{\sin }^2}x)}^2}} \over 4} + C$$
D
$${{{{(1 - {{\cos }^2}x)}^2}} \over 4} + C$$
4
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
What is $$\int {{{dx} \over {{a^2}{{\sin }^2}x + {b^2}{{\cos }^2}x}}} $$ equal to ?
A
$${1 \over {ab}}{\tan ^{ - 1}}\left( {{{a\tan x} \over b}} \right) + C$$
B
$${1 \over {ab}}{\tan ^{ - 1}}\left( {{{a\tan x} \over b}} \right) + C$$
C
$${1 \over {ab}}{\tan ^{ - 1}}\left( {{{b\tan x} \over b}} \right) + C$$
D
None of the above
PREVIOUS NEXT
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
Coordinate System and Straight Line Circle Parabola Ellipse Hyperbola Conic Section
Calculus
Functions Limit, Continuity and Differentiability Differentiation Application of Derivatives Indefinite Integration Definite Integration Area Under The Curves Differential Equations
English
Reading Comprehension Synonyms Antonyms Cloze Rearranging Sentences in a Paragraph Idioms and Phrases Word Classes Sentence Completion Improvement of Sentence
General Science
Physics Chemistry Biology
General Studies
History Geography Polity Economy General Knowledge
EXAM MAP
Joint Entrance Examination
JEE MainJEE AdvancedMHT CETBITSATCOMEDKWB JEEKCETVITEEEAP EAPCETTS EAMCETIAT (IISER)
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12