1
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language
For the following two (02) items:
Consider the function $f(x)=1-\sqrt[3]{(x-1)^{2}}$
The function has
1
 a minimum at x = 1
2
a maximum at x = 1
3
 neither maximum nor minimum at x = 1
4
no extremum
2
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct?

I. The rectangle of the largest area is the square.

II. It is possible to form a rectangle of an area of$ 27c m ^ 2$

Select the answer using the code given below.

1
 I only
2
II only
3
Both I and II
4
 Neither I nor II
3
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Consider the following statements regarding the function f(x) = 1/(x - 5)

Statement-I: f(x) is decreasing on the intervals x < 5 and x > 5

Statement-II: f''(x) > 0 for all x ≠ 5.

Which one of the following is correct in respect of the above statements?

1
Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
2
 Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
3
Statement-I is correct but Statement-II is not correct
4
Statement-I is not correct but Statement-ll is correct
4
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Consider the following statements:

Statement-I: The function  $f(x)=\frac{x^{3}+128}{x}$ has a minimum value 48 at x = 4

Statement-II: As x increases through 4, f'(x) changes sign from positive to negative.

Which one of the following is correct in respect of the above statements?

1
Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
2
 Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
3
 Statement-I is correct but Statement-II is not correct
4
Statement-I is not correct but Statement-II is correct