1
GATE ECE 2022
MCQ (Single Correct Answer)
+2
-0.67
The function f(x) = 8loge x $$-$$ x2 + 3 attains its minimum over the interval [1, e] at x = __________.
(Here loge x is the natural logarithm of x.)
2
GATE ECE 2022
Numerical
+2
-0
The value of the integral
$$\int\!\!\!\int\limits_D {3({x^2} + {y^2})dx\,dy} $$,
where D is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest integer).
Your input ____
3
GATE ECE 2018
Numerical
+2
-0
Let r = x2 + y - z and z3 - xy + yz + y3 = 1. Assume that x and y are independent
variables. At (x, y, z) = (2, -1, 1), the value (correct to two decimal places) of $${{\partial r} \over {\partial x}}$$ is ________________.
Your input ____
4
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let $$\,\,f\left( x \right) = {e^{x + {x^2}}}\,\,$$ for real $$x.$$ From among the following. Choose the Taylor series approximation of $$f$$ $$(x)$$ around $$x=0,$$ which includes all powers of $$x$$ less than or equal to $$3.$$
Questions Asked from Calculus (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE 2024 (1)
GATE ECE 2023 (2)
GATE ECE 2022 (2)
GATE ECE 2018 (1)
GATE ECE 2017 Set 1 (2)
GATE ECE 2017 Set 2 (2)
GATE ECE 2016 Set 1 (2)
GATE ECE 2016 Set 3 (1)
GATE ECE 2015 Set 2 (1)
GATE ECE 2015 Set 1 (2)
GATE ECE 2014 Set 4 (1)
GATE ECE 2014 Set 3 (1)
GATE ECE 2014 Set 1 (2)
GATE ECE 2009 (1)
GATE ECE 2008 (2)
GATE ECE 2007 (1)
GATE ECE 2000 (1)
GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series Fourier Transform Continuous Time Signal Laplace Transform Discrete Time Signal Fourier Series Fourier Transform Discrete Fourier Transform and Fast Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Discrete Time Linear Time Invariant Systems Transmission of Signal Through Continuous Time LTI Systems Sampling Transmission of Signal Through Discrete Time Lti Systems Miscellaneous
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics