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1
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If $I_1 =\int\frac{e^x dx}{e^x + e^{-x}}$ and $I_2 =\int\frac{dx}{e^{2x} + 1},$then what is I1 + I2 equal to?
A
$\frac{x}{2}+c$
B
x + c
C
ln (ex + e-x) + c
D
ln (ex - e-x) + c
2
NDA Mathematics 14 November 2021
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the integral of f(x) = 1 + x2 + x4 with respect to x2?
A
$\rm x + \frac{x^3}{3}+\frac{x^5}{5}+C$
B
$\rm \frac{x^3}{3}+\frac{x^5}{5}+C$
C
$\rm x^2 + \frac{x^4}{4}+\frac{x^6}{6}+C$
D
$\rm x^2 + \frac{x^4}{2}+\frac{x^6}{3}+C$
3
NDA Mathematics 14 November 2021
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If $\rm \int \sqrt{1 - sin 2x} \space dx$ = A sinx + B cosx + C, where 0 < x < $\frac{\pi}{4}$, then which one of the following is correct?
A
A + B = 0
B
A + B - 2 = 0
C
A + B + 2 = 0
D
A + B - 1 = 0
4
NDA Mathematics 14 November 2021
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is $\rm \int \frac{dx}{x(x^2 + 1)}$ equal to?
A
$\rm \frac{1}{2}ln\left(\frac{x^2}{x^2 + 1}\right) + C$
B
$\rm ln\left(\frac{x^2}{x^2 + 1}\right) + C$
C
$\rm \frac{3}{2}ln\left(\frac{x^2}{x^2 + 1}\right) + C$
D
$\rm \frac{1}{2}ln\left(\frac{x^2+1}{x^2}\right) + C$
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