NDA 2017 Paper 1 | Indefinite Integration Question 8 | Mathematics

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?

Both the statements are true and Statement 2 is the correct explanation of Statement 1

Both the statements are true but Statement 2 is not the correct explanation of Statement 1

Statement 1 is true but Statement 2 is false

Statement 1 is false but Statement 2 is true

NDA 2018 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

What is $$\int {{{\sin }^3}x\cos x\,dx} $$ equal to ?

$${\cos ^4}x + C$$

$${\sin ^4}x + C$$

$${{{{(1 - {{\sin }^2}x)}^2}} \over 4} + C$$

$${{{{(1 - {{\cos }^2}x)}^2}} \over 4} + C$$

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 ?

$${1 \over {ab}}{\tan ^{ - 1}}\left( {{{a\tan x} \over b}} \right) + C$$

$${1 \over {ab}}{\tan ^{ - 1}}\left( {{{b\tan x} \over b}} \right) + C$$

None of the above

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is $$\int {{{dx} \over {{2^x} - 1}}} $$ equal to ?

$$\ln ({2^x} - 1) + C$$

$${{\ln (1 - {2^x})} \over {\ln 2}} + C$$

$${{\ln ({2^{ - x}} - 1)} \over {2\ln 2}} + C$$

$${{\ln (1 + {2^{ - x}})} \over {1 - {2^{ - x}}}} + C$$

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