Consider the following: I. du/dx=-v II. dv/dx=-u Which of the above is/are correct?

Correct Answer is : Neither I nor II

Correct Answer is : Neither I nor II

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UPSC NDA II 2025 Mathematics Paper

Question Numbers: 85-86

For the following two (02) items:

Let

u=∫e^{x}cosxdx

and

v=∫e^{x}sinxdx.

Question : 86 of 120

Marks: +1, -0

Consider the following:

\frac{du}{dx}=-v

\frac{dv}{dx}=-u

Which of the above is/are correct?

Solution:

Concept:

The derivatives of the given integrals u and v do not match the negative of the other function, so both statements are false.

Explanation:

Let

u = \int e^{x} \cos x \, dx

and

v = \int e^{x} \sin x \, dx

Then

\frac{du}{dx} = e^{x} \cos x

, which is not equal to

-v

Similarly,

\frac{dv}{dx} = e^{x} \sin x

, which is not equal to

-u

Thus, neither given differential relation holds.

Answer:

Option D (Neither I nor II)

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