1
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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 ? 
A
$- \frac{1}{\sqrt 2}$
B
-1
C
1
D
$ \frac{1}{\sqrt 2}$
2
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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} $ ?
A
1
B
π 
C
π2
D
$\frac{\pi+2}{\pi-2}$
3
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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 $8 I_1^2$
A
π
B
π2
C
π3
D
π4
4
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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 ?
A
$\frac{\pi}{ \sqrt{2}}$
B
$\frac{ \pi}{2 \sqrt{2}}$
C
$\frac{3 \pi}{2 \sqrt{2}}$
D
$\frac{ \pi}{4 \sqrt{2}}$
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