NDA Mathematics 4 September 2022 | NDA Year Wise Previous Years Questions

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NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

If $\displaystyle\int_0^{\pi/2}$(sin⁴ x + cos⁴ x)dx = k, then what is the value of $\displaystyle\int_0^{20 \pi}$(sin⁴ x + cos⁴ x)dx ?

10 k

20 k

40 k

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

What is $\displaystyle\int_{−\pi/2}^{\pi/2}$(ecos x sin x + esin x cos x)dx equal to ?

$\frac{e^2−1}{e}$

$\frac{e^2+1}{e}$

$\frac{1−e^2}{e}$

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

What is the area of the region enclosed in the first quadrant by x² + y² = π², y = sin x and x = 0 ?

$\frac{\pi^3}{4}$ − 1

$\frac{\pi^3}{4}$ − 2

$\frac{\pi^3}{2}$ − 1

$\frac{\pi^2}{4}$ − 2

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following statements:

1. The degree of the differential equation $\frac{\text{dy}}{\text{dx}} + \cos \left(\frac{\text{dy}}{\text{dx}}\right)$ = 0 is 1.

2. The order of the differential equation $\left(\frac{\text{d}^2\text{y}}{\text{dx}^2}\right)^3 + \cos \left(\frac{\text{dy}}{\text{dx}}\right) $ = 0 is 2.

Which of the statements above is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

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