NDA Mathematics 1st September 2024 | NDA Year Wise Previous Years Questions

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

Direction : Consider the following for the items that follow :

Let $\rm I=\int_0^{\pi/2}\frac{f(x)}{g(x)}dx$, where f(x) = sin x and g(x) = sin x + cos x + 1

What is $\rm \int_0^{\pi/2}\frac{d(x)}{g(x)}$ equal to

$\frac{\ln2}{2}$

$\frac{\ln2}{4}$

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

Direction : Consider the following for the items that follow :

Let $\rm I=\int_0^{\pi/2}\frac{f(x)}{g(x)}dx$, where f(x) = sin x and g(x) = sin x + cos x + 1

What is I equal to?

$\rm \frac{\pi}{4}+\ln2$

$\rm \frac{\pi}{4}-\ln2$

$\rm \frac{\pi}{4}-\frac{\ln2}{2}$

$\rm \frac{\pi}{4}+\frac{\ln2}{2}$

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

Direction : Consider the following for the items that follow :

Let $\rm 2\int\frac{x^2-1}{\sqrt{x^2+1}}dx=U(x) V(x)-3\ln \{U(x)+V(x)\}+c$

What is |U²(x) - V²(x)| equal to?

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

Direction : Consider the following for the items that follow :

Let $\rm 2\int\frac{x^2-1}{\sqrt{x^2+1}}dx=U(x) V(x)-3\ln \{U(x)+V(x)\}+c$

What is U(x) V(x) equal to?

$\rm\sqrt{x^2+x^4}$

$\rm\sqrt{x+x^3}$

$\rm \frac{\sqrt{x^2+x^4}}{2}$

$\rm 2\sqrt{x^2+x^4}$