# A scalar function is given by $f(x, y)=x^{2}+y^{2}$. Take $\hat{\imath}$ and $\hat{\jmath}$ as unit vectors along the $x$ and $y$ axes, respectively. At $(x, y)=(3,4),$ the direction along which $f$ increases the fastest is (A) $\frac{1}{5}(4 \hat{\imath}-3 \hat{\jmath})$ (B) $\frac{1}{5}(3 \hat{\imath}-4 \hat{\jmath})$ (C) $\frac{1}{5}(3 \hat{\imath}+4 \hat{\jmath})$ (D) $\frac{1}{5}(4 \hat{\imath}+3 \hat{\jmath})$

## Question ID - 155433 :- A scalar function is given by $f(x, y)=x^{2}+y^{2}$. Take $\hat{\imath}$ and $\hat{\jmath}$ as unit vectors along the $x$ and $y$ axes, respectively. At $(x, y)=(3,4),$ the direction along which $f$ increases the fastest is (A) $\frac{1}{5}(4 \hat{\imath}-3 \hat{\jmath})$ (B) $\frac{1}{5}(3 \hat{\imath}-4 \hat{\jmath})$ (C) $\frac{1}{5}(3 \hat{\imath}+4 \hat{\jmath})$ (D) $\frac{1}{5}(4 \hat{\imath}+3 \hat{\jmath})$

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(C) $\frac{1}{5}(3 \hat{\imath}+4 \hat{\jmath})$

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The dimensions of kinematic viscosity of a fluid (where $L$ is length, $T$ is time) are
(A) $L T^{-1}$
(B) $L^{2} T^{-1}$
(C) $L T^{-2}$
(D) $L^{-2} T$