1
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is $\displaystyle\int_{−\pi/2}^{\pi/2}$(ecos x sin x + esin x cos x)dx equal to ?
A
$\frac{e^2−1}{e}$
B
$\frac{e^2+1}{e}$
C
$\frac{1−e^2}{e}$
D
0
2
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the area of the region enclosed in the first quadrant by x2 + y2 = π2, y = sin x and x = 0 ?
A
$​\frac{\pi^3}{4}$ − 1
B
$​\frac{\pi^3}{4}$ − 2
C
$​\frac{\pi^3}{2}$ − 1
D
$​\frac{\pi^2}{4}$ − 2
3
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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?

A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
4
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the differential equation of the family of parabolas having a vertex at origin and axis along positive y-axis?
A
x$\frac{\text{dy}}{\text{dx}}$ + 2y = 0
B
x$\frac{\text{dy}}{\text{dx}}$ − 2y = 0
C
y$\frac{\text{dx}}{\text{dy}}$ + 2x = 0
D
y$\frac{\text{dx}}{\text{dy}}$ − 2x = 0
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