NDA Mathematics 16 April 2023 | NDA Year Wise Previous Years Questions

Mathematics

NDA Mathematics 16 April 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next two (02) items that follow :

Let f(x) = sin[π²]x + cos[-π²]x where [.] is a greatest ‘integer function

What is $f\left(\frac{\pi}{4}\right)$ equal to ?

$- \frac{1}{\sqrt 2}$

-1

$ \frac{1}{\sqrt 2}$

NDA Mathematics 16 April 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next three (03) items that follow :

Let $I_1=\int_0^\pi \frac{x}{1+\cos ^2 x} d x$ and

$I_2=\int_0^\pi \frac{1}{1+\sin ^2 x} d x $

What is the value of $\frac{I_1+I_2}{I_1-I_2} $ ?

π²

$\frac{\pi+2}{\pi-2}$

NDA Mathematics 16 April 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next three (03) items that follow :

Let $I_1=\int_0^\pi \frac{x}{1+\cos ^2 x} d x$ and

$I_2=\int_0^\pi \frac{1}{1+\sin ^2 x} d x $

What is the value of $8 I_1^2$

π²

π³

π⁴

NDA Mathematics 16 April 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next three (03) items that follow :

Let $I_1=\int_0^\pi \frac{x}{1+\cos ^2 x} d x$ and

$I_2=\int_0^\pi \frac{1}{1+\sin ^2 x} d x $

What is the value of I₂ ?

$\frac{\pi}{ \sqrt{2}}$

$\frac{ \pi}{2 \sqrt{2}}$

$\frac{3 \pi}{2 \sqrt{2}}$

$\frac{ \pi}{4 \sqrt{2}}$