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

Mathematics

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NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following statements in respect of the function f(x) = $\left\{\begin{array}{rc}|x|+1, & 0<|x| \leqslant 3 \\ 1, & x = 0\end{array}\right.$

1. The function attains maximum value only at x = 3

2. The function attains local minimum only at x = 0

Which of the statements given above is/are correct ?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

What is $\displaystyle\int_0^1 \ln \left(\frac{1}{x}−1\right)$dx equal to ?

−1

ln 2

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 ?

$\frac{e^2−1}{e}$

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

$\frac{1−e^2}{e}$

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