1
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If y = $\frac{x \sqrt{x^2−16}}{2} − 8 \ln\left|x + \sqrt{x^2−16}\right|$, then what is $\frac{\text{dy}}{\text{dx}}$ equal to ?
A
$\text{x}\sqrt{\text{x}^2−16}$
B
$\text{x}−\sqrt{\text{x}^2−16}$
C
$\sqrt{\text{x}^2−16}$
D
$4\sqrt{\text{x}^2−16}$
2
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If y = (xx)x, then which one of the following is correct ?
A
$\frac{\text{dy}}{\text{dx}}$ + xy(1 + 2 ln x) = 0
B
$\frac{\text{dy}}{\text{dx}}$ − xy(1 + 2 ln x) = 0
C
$​\frac{\text{dy}}{\text{dx}}$ − 2xy(1 + ln x) = 0
D
$​\frac{\text{dy}}{\text{dx}}$ + 2xy(1 + ln x) = 0
3
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the maximum value of 3(sin x − cos x) + 4(cos3 x − sin3 x) ?
A
1
B
$\sqrt{2}$
C
$\sqrt{3}$
D
2
4
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the area of the region (in the first quadrant) bounded by y = $\sqrt{1−\text{x}^2}$, y = x and y = 0 ?
A
$\frac{\pi}{4}$
B
$\frac{\pi}{6}$
C
$\frac{\pi}{8}$
D
$\frac{\pi}{12}$
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