1
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :

Let f(t) = $\rm \ln(t+\sqrt{1+t^2})$ and g(t) = tan(f(t)).  

Consider the following statements :

I. f(t) is an odd function.

Il. g(t) is an odd function.

Which of the statements given above is/are correct?  

1
I only 
2
II only
3
Both I and II
4
Neither I nor II
2
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :

Let f(t) = $\rm \ln(t+\sqrt{1+t^2})$ and g(t) = tan(f(t)).  

What is $\rm \int_{-\pi}^\pi g(t)dt$ equal to
1
-1
2
0
3
1/2
4
1
3
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :

Let f : (-1, 1) → R be a differentiable function with f(0) = -1 and f’(0) = 1 Let h(x) = f(2f(x) +2) and g(x) = (h(x))2

What is h’(0) equal to? 
1
-2
2
-1
3
0
4
2
4
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :

Let f : (-1, 1) → R be a differentiable function with f(0) = -1 and f’(0) = 1 Let h(x) = f(2f(x) +2) and g(x) = (h(x))2

What is g’(0) equal to? 
1
-4
2
-2
3
0
4
4
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