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1
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is $$\int {{{dx} \over {x({x^7} + 1)}}} $$ equal to ?
A
$${1 \over 2}\ln \left| {{{{x^7} - 1} \over {{x^7} + 1}}} \right| + C$$
B
$${1 \over 7}\ln \left| {{{{x^7} + 1} \over {{x^7}}}} \right| + C$$
C
$${1 \over 2}\ln \left| {{{{x^7} - 1} \over {7x}}} \right| + C$$
D
$${1 \over 7}\ln \left| {{{{x^7}} \over {{x^7} + 1}}} \right| + C$$
2
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
$${1 \over e}\ln ({x^e} + {e^x}) + C$$
3
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
4
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
$${{{{(1 - {{\cos }^2}x)}^2}} \over 4} + C$$
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