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Jamia Millia Islamia Previous Year Questions (PYQs)
Jamia Millia Islamia Differentibility PYQ
Jamia Millia Islamia PYQ
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2021 PYQ
. Find the number of points where
$f(x) = |2x + 1| - 3|x + 2| + |x^2 + x - 2|$
is non-differentiable.
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2021 PYQ
Solution
**Solution:** Non-differentiable points occur where expressions inside modulus = 0. 1. $2x + 1 = 0 \Rightarrow x = -\dfrac{1}{2}$ 2. $x + 2 = 0 \Rightarrow x = -2$ 3. $x^2 + x - 2 = 0 \Rightarrow x = 1, -2$ Unique points: $x = -2, -\dfrac{1}{2}, 1$ Hence, number of non-differentiable points = 3. $\boxed{\text{Answer: (B) 3}}$
Jamia Millia Islamia PYQ
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2020 PYQ
Which of the following functions show that the statement
"If a function is continuous at $x=0$, then it is differentiable at $x=0$" is false?
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2020 PYQ
Solution
$f(x) = x^{1/3}$ is continuous at $x = 0$ but derivative $\dfrac{df}{dx} = \dfrac{1}{3}x^{-2/3}$ is not defined at $x = 0.$ Hence, function is continuous but not differentiable at 0.
Jamia Millia Islamia PYQ
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2019 PYQ
Number of points at which the function $f(x) = \min(|x|, |x+1|, |x-4|)$
is not differentiable is:
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2019 PYQ
Solution
Each $|x|$ term is non-differentiable at the point where its argument = 0. Points: $x = 0, -1, 4$.
Jamia Millia Islamia PYQ
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ
If $f(x) = \max{x,,x^3}$, number of points where $f(x)$ is not differentiable are
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ
Solution
$x=x^3$ → $x=0,\pm1$.Jamia Millia Islamia
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