1
GATE EE 2025
MCQ (More than One Correct Answer)
+2
-0

Let $a_R$ be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of $n$, the divergence of the radial vector field $f(R)=a_R \frac{1}{R^n}$ is independent of $R$ ?

A
-2
B
-1
C
1
D
2
2
GATE EE 2025
Numerical
+2
-0
Let $(x, y) \in \Re^2$. The rate of change of the real valued function, $V(x, y)=x^2+x+y^2+1$ at the origin in the direction of the point $(1,2)$ is _________ (round off to the nearest integer)
Your input ____
3
GATE EE 2024
MCQ (Single Correct Answer)
+2
-1.33

Consider a vector $\vec{u} = 2\hat{x} + \hat{y} + 2\hat{z}$, where $\hat{x}$, $\hat{y}$, $\hat{z}$ represent unit vectors along the coordinate axes $x$, $y$, $z$ respectively. The directional derivative of the function $f(x, y, z) = 2\ln(xy) + \ln(yz) + 3\ln(xz)$ at the point $(x, y, z) = (1, 1, 1)$ in the direction of $\vec{u}$ is

A

0

B

$\frac{7}{5\sqrt{2}}$

C

7

D

21

4
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

Let $$f(x,y,z) = 4{x^2} + 7xy + 3x{z^2}$$. The direction in which the function f(x, y, z) increases most rapidly at point P = (1, 0, 2) is

A
$$20\widehat i + 7\widehat j$$
B
$$20\widehat i + 7\widehat j + 12\widehat k$$
C
$$20\widehat i + 12\widehat k$$
D
$$20\widehat i$$
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