If f: R 2 →R 2 is a function defined as $f(x,y) = \begin{cases} \frac{x}{\sqrt{x^2+y^2}}, & x\neq0,y\neq0\\ 2, & x=0,y=0 \end{cases}$ then, which of the following is correct?

f(x,y) is not continuous at origin

If f: R 2 →R 2 is a function defined as $$f(x,y) = \begin{cases} \frac{x}{\sqrt{x^2+y^2}}, & x\neq0,y\neq0\\ 2, & x=0,y=0 \end{cases}$$ then, which of the following is correct?}

f(x,y) is not continuous at origin

f(x,y) is differentiable at origin

$\lim\limits_{(x,y)\rightarrow(0,0)}$ f(x,y) exists and is equal to 2

f(x,y) is not continuous at origin

If f: R2→R2 is a function defined as f(x,y)={x/√x2+y2, x≠0,y≠0 2,x=0,y=0then, which of the following is correct?

List-I	List-II
(A) \( f(x) = \|x\| \)	(I) Not differentiable at \( x = -2 \) only
(B) \( f(x) = \|x + 2\| \)	(II) Not differentiable at \( x = 0 \) only
(C) \( f(x) = \|x^2 - 4\| \)	(III) Not differentiable at \( x = 2 \) only
(D) \( f(x) = \|x - 2\| \)	(IV) Not differentiable at \( x = 2, -2 \) only

Match List-I with List-II\[\begin{array}{|c|c|} \hline \textbf{Provision} & \textbf{Case Law} \\ \hline \text{(A) Strict Liability} & \text{(1) Ryland v. Fletcher} \\ \hline \text{(B) Absolute Liability} & \text{(II) M.C. Mehta v. Union of India} \\ \hline \text{(C) Negligence} & \text{(III) Nicholas v. Marsland} \\ \hline \text{(D) Act of God} & \text{(IV) MCD v. Subhagwanti} \\ \hline \end{array}\]

CUET (PG) - 2025
Law of Torts

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Match Fibre with Application.\[\begin{array}{|l|l|} \hline \textbf{LIST I} & \textbf{LIST II} \\ \textbf{Fibre} & \textbf{Application} \\ \hline \hline \text{A. Silk fibre} & \text{I. Fire retardant} \\ \hline \text{B. Wool fibre} & \text{II. Directional lustre} \\ \hline \text{C. Nomex fibre} & \text{III. Bulletproof} \\ \hline \text{D. Kevlar fibre} & \text{IV. Thermal insulation} \\ \hline \end{array}\]