1
GATE EE 2023
Numerical
+2
-0

A quadratic function of two variables is given as

$$f({x_1},{x_2}) = x_1^2 + 2x_2^2 + 3{x_1} + 3{x_2} + {x_1}{x_2} + 1$$

The magnitude of the maximum rate of change of the function at the point (1, 1) is ___________ (Round off to the nearest integer).

Your input ____
2
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

As shown in the figure below, to concentric conducting spherical shells, centred at r = 0 and having radii r = c and r = d are maintained at potentials such that the potential V(r) at r = c is V1 and V(r) at r = d is V2. Assume that V(r) depends only on r, where r is the radial distance. The expression for V(r) in the region between r = c and r = d is

GATE EE 2022 Electromagnetic Fields - Electrostatics Question 4 English

A
$$V(r) = {{cd({V_2} - {V_1})} \over {(d - c)r}} - {{{V_1}c + {V_2}d - 2{V_1}d} \over {d - c}}$$
B
$$V(r) = {{cd({V_1} - {V_2})} \over {(d - c)r}} + {{{V_2}d - {V_1}c} \over {d - c}}$$
C
$$V(r) = {{cd({V_1} - {V_2})} \over {(d - c)r}} - {{{V_1}c - {V_2}c} \over {d - c}}$$
D
$$V(r) = {{cd({V_2} - {V_1})} \over {(d - c)r}} - {{{V_2}c - {V_1}c} \over {d - c}}$$
3
GATE EE 2018
Numerical
+2
-0
The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _____________ (up to 2 decimal places).
Your input ____
4
GATE EE 2017 Set 2
Numerical
+2
-0
A thin soap bubble of radius R = 1 cm, and thickness a = 3.3 µm(a << R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap in the thin bubble is $$4\mathrm{πR}^2\mathrm a$$ and that of the drop is $$\frac43\mathrm{πr}^3$$. The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is __________. (Give the answer up to two decimal places.) GATE EE 2017 Set 2 Electromagnetic Fields - Electrostatics Question 30 English
Your input ____
GATE EE Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12