UPCET / UPSEE Modulus — practice questions

Explore 2 free Modulus questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Modulus questions and exercises with answers

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$\int_{-1}^{1} |5x - 3|\,dx$ equals:Read the answer and worked solution →If $f(x) = |x - 1| + |x - 3|$, then $f'(2)$ equals:Read the answer and worked solution →

Worked practice questions

$\int_{-1}^{1} |5x - 3|\,dx$ equals:

$4/5$
$34/5$
$10$
$13$

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Correct answer: B. $34/5$

$5x - 3 < 0$ for $x < 3/5$, $> 0$ for $x > 3/5$. **Split:** $\int_{-1}^{3/5} (3 - 5x)\,dx + \int_{3/5}^1 (5x - 3)\,dx$. Evaluating each (textbook Ex. 9): the total is $\boxed{34/5}$.

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If $f(x) = |x - 1| + |x - 3|$, then $f'(2)$ equals:

$0$
$2$
$1$
$-1$

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Correct answer: A. $0$

For $1 < x < 3$: $|x - 1| = x - 1$, $|x - 3| = 3 - x$. So $f(x) = (x-1) + (3-x) = 2$ (constant!). **Hence $f'(2) = 0$.**