Previous Year Questions

Q1 MCQ GATE ME Medium 1 Mark 2026

ENGINEERING MATHEMATICS → CALCULUS

Domain A is bounded by curve $x^2=4y$, ordinate $x=2$, and x axis. The value of $\iint_A y dxdy$ is

Choose One:

A) 1/5

B) 1/3

C) 5/12

D) 1/2

Q2 MCQ GATE ME Easy 1 Mark 2026

ENGINEERING MATHEMATICS → CALCULUS

Let $\phi$ be a scalar function. Then, $\nabla \phi$ is

Choose One:

A) always perpendicular to the surface of constant $\phi$

B) always parallel to the surface of constant $\phi$

C) the minimum rate of change of scalar $\phi$

D) always zero

Q3 MCQ GATE ME Medium 2 Marks 2026

ENGINEERING MATHEMATICS → DIFFERENTIAL EQUATIONS

Let $f(t)$ be a function of $t$ defined for all positive values of $t$. The Laplace transform of $f(t)$ denoted by $L\{f(t)\}=\int_{0}^{\infty}e^{-st}f(t)dt$, provided that the integral exists where $s$ is a parameter which may be a real or complex number.

The Laplace transform of $f(t)=\sin 2t \sin 4t$ is

Choose One:

A) $\frac{16s}{(s^2+4)(s^2+36)}$

B) $\frac{32s}{(s^2+4)(s^2+36)}$

C) $\frac{16}{(s^2+4)(s^2+36)}$

D) $\frac{32}{(s^2+4)(s^2+36)}$

Q4 MCQ GATE ME Easy 1 Mark 2026

ENGINEERING MATHEMATICS → DIFFERENTIAL EQUATIONS

The order and degree of the following differential equation are $m$ and $n$, respectively.

$\frac{\partial^3 \phi}{\partial x^3} + \frac{\partial^2 \phi}{\partial y^2}\frac{\partial \phi}{\partial x} + (\frac{\partial^2 \phi}{\partial x^2})^2 + \frac{\partial \phi}{\partial y} = 0$

The value of $(m-n)$ is

Choose One:

A) 2

B) 3

C) 1

D) 0

Q5 MCQ GATE ME Medium 2 Marks 2026

ENGINEERING MATHEMATICS → DIFFERENTIAL EQUATIONS

Consider the following differential equation

$\frac{\partial y}{\partial x} = 3\frac{\partial y}{\partial t} + y$

If $y(x,0) = 10e^{-2x}$, then the solution of the differential equation is

Choose One:

A) $y(x,t) = 10e^{-2x-t}$

B) $y(x,t) = 10e^{-2x+t}$

C) $y(x,t) = 10e^{-2x-2t}$

D) $y(x,t) = 10e^{-2x+2t}$

PYQBOOK

Filter Questions

Domain A is bounded by curve $x^2=4y$, ordinate $x=2$, and x axis. The value of $\iint_A y dxdy$ is

Choose One:

Let $\phi$ be a scalar function. Then, $\nabla \phi$ is

Choose One:

Choose One:

Choose One:

Consider the following differential equation

$\frac{\partial y}{\partial x} = 3\frac{\partial y}{\partial t} + y$

If $y(x,0) = 10e^{-2x}$, then the solution of the differential equation is

Choose One:

PYQBOOK

Filter Questions

Domain A is bounded by curve $x^2=4y$, ordinate $x=2$, and x axis. The value of $\iint_A y dxdy$ is

Choose One:

Let $\phi$ be a scalar function. Then, $\nabla \phi$ is

Choose One:

Choose One:

Choose One:

Consider the following differential equation$\frac{\partial y}{\partial x} = 3\frac{\partial y}{\partial t} + y$If $y(x,0) = 10e^{-2x}$, then the solution of the differential equation is

Choose One:

Consider the following differential equation

$\frac{\partial y}{\partial x} = 3\frac{\partial y}{\partial t} + y$

If $y(x,0) = 10e^{-2x}$, then the solution of the differential equation is