Qus : 1 3

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1 f is neither continuous nor differentiable at x = 0
2 f is continuous nor differentiable at x = 0
3 f is continuous but not differentiable at x = 0
4 f is not continuous but differentiable at x = 0
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Qus : 2 3

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1 f(x) is not continuous at x=0
2 f(x) is not differentiable at x=0
3 f'(x) is not continuous at x=0
4 f'(x) is continuous at x=0
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Qus : 3 4

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1 $f(x)$ is not continuous at x = 0
2 $f(x)$ is continuous but not differentiable at x = 0
3 $f(x)$ is differentiable at x = 0 and $f'(0) = -\frac{\pi}{2}$
4 None of the above
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Qus : 4 2

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1
2
3
4
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Qus : 5 1

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1 $f(x)$ is continuous at x = 0 for all $\alpha{\lt}0\, and \beta\in\mathbb{R}$
2 $f(x)$ is continuous at x = 0, for all $\alpha and\beta\in\mathbb{R}$
3 $f(x)$ is continuous at x = 10 for only $\alpha{\gt}0\, and \beta >0$ \in R$
4 $f(x)$ is differentiable at $x=0$ for all  $\alpha{\gt}0\, and \beta >0$ \in R$
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Qus : 6 2

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1 1
2 0
3 - 1
4 None of these
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