1
GATE ME 2024
MCQ (Single Correct Answer)
+1
-0.33
Let $f(.)$ be a twice differentiable function from $ \mathbb{R}^{2} \rightarrow \mathbb{R}$. If $P, \mathbf{x}_{0} \in \mathbb{R}^{2}$ where $\vert \vert P\vert \vert$ is sufficiently small (here $\vert \vert . \vert \vert$ is the Euclidean norm or distance function), then $f (\mathbf{x}_{0} + p) = f(\mathbf{x}_{0}) + \nabla f(\mathbf{x}_{0})^{T}p + \dfrac{1}{2} p^{T} \nabla^{2}f(\psi)p$ where $\psi \in \mathbb{R}^{2}$ is a point on the line segment joining $\mathbf{x}_{0}$ and $\mathbf{x}_{0} + p$. If $\mathbf{x}_{0}$ is a strict local minimum of $f (\mathbf{x})$, then which one of the following statements is TRUE?
2
GATE ME 2020 Set 1
MCQ (Single Correct Answer)
+1
-0.33
Define [x] as the greatest integer less than or equal to x, for each x ϵ (-∞, ∞). If y = [x], then area under y for x ϵ [1,4] is
3
GATE ME 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The value of $$\mathop {\lim }\limits_{x \to 0} \left( {{{{x^3} - \sin \left( x \right)} \over x}} \right)$$ is
4
GATE ME 2016 Set 3
MCQ (Single Correct Answer)
+1
-0.3
$$\mathop {Lt}\limits_{x \to 0} {{{{\log }_e}\left( {1 + 4x} \right)} \over {{e^{3x}} - 1}}$$ is equal to
Questions Asked from Calculus (Marks 1)
Number in Brackets after Paper Indicates No. of Questions
GATE ME 2024 (1)
GATE ME 2020 Set 1 (1)
GATE ME 2017 Set 1 (1)
GATE ME 2016 Set 3 (1)
GATE ME 2016 Set 2 (1)
GATE ME 2015 Set 3 (1)
GATE ME 2015 Set 2 (1)
GATE ME 2015 Set 1 (1)
GATE ME 2014 Set 4 (1)
GATE ME 2014 Set 2 (1)
GATE ME 2014 Set 3 (1)
GATE ME 2014 Set 1 (1)
GATE ME 2013 (1)
GATE ME 2012 (4)
GATE ME 2011 (3)
GATE ME 2010 (3)
GATE ME 2009 (2)
GATE ME 2008 (2)
GATE ME 2007 (1)
GATE ME 2005 (2)
GATE ME 2004 (1)
GATE ME 1999 (1)
GATE ME 1997 (1)
GATE ME 1996 (1)
GATE ME 1995 (1)
GATE ME 1994 (2)
GATE ME 1993 (2)
GATE ME Subjects
Engineering Mechanics
Machine Design
Strength of Materials
Heat Transfer
Production Engineering
Industrial Engineering
Turbo Machinery
Theory of Machines
Engineering Mathematics
Fluid Mechanics
Thermodynamics
General Aptitude