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1
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
$$\int {{{dx} \over {1 + {e^{ - x}}}}} $$ is equal to ?

where, C is the constant of integration.
A
1 + ex + C
B
ln (1 + e$$-$$x) + C
C
ln (1 + ex) + C
D
2ln (1 + e$$-$$x) + C
2
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
What is $$\int {{{{x^4} - 1} \over {{x^2}\sqrt {{x^4} + {x^2} + 1} }}dx} $$ equal to ?
A
$$\sqrt {{{{x^4} + {x^2} + 1} \over x}} + C$$
B
$$\sqrt {{x^4} + 2 - {1 \over {{x^2}}}} + C$$
C
$$\sqrt {{x^2} + {1 \over {{x^2}}} + 1} + C$$
D
$$\sqrt {{{{x^4} - {x^2} + 1} \over x}} + C$$
3
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
What is $$\int {{e^{\sin x}}} {{x{{\cos }^3}x - \sin x} \over {{{\cos }^2}x}}dx$$ equal to ?
A
$$(x + \sec x){e^{\sin x}} + C$$
B
$$(x - \sec x){e^{\sin x}} + C$$
C
$$(x + \tan x){e^{\sin x}} + C$$
D
$$(x - \tan x){e^{\sin x}} + C$$
4
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
What is $$\int {{{\tan }^{ - 1}}(\sec x + \tan x)dx} $$ equal to ?
A
$${{\pi x} \over 4} + {{{x^2}} \over 4} + C$$
B
$${{\pi x} \over 2} + {{{x^2}} \over 4} + C$$
C
$${{\pi x} \over 4} + {{\pi {x^2}} \over 4} + C$$
D
$${{\pi x} \over 4} - {{{x^2}} \over 4} + C$$
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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
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