GATE EC Engineering Mathematics questions

Practise Engineering Mathematics questions for GATE EC. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

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SubjectTopicYearType

The Taylor series expansion of

\dfrac{\sin x}{x-\pi}

x=\pi

is given by

The eigen values of the following matrix are

\left[\begin{array}{ccc} -1 & 3 & 5 \\ -3 & -1 & 6 \\ 0 & 0 & 3 \end{array}\right]

All the four entries of the

2 \times 2

matrix

\mathbf{P}=\left[\begin{array}{ll}p_{11} & p_{12} \\ p_{21} & p_{22}\end{array}\right]

are nonzero, and one of its eigenvalues is zero. Which of the following statements is true?

The system of linear equations

\begin{array}{l} 4 x+2 y=7 \\ 2 x+y=6 \end{array}

has

For real values of

x

, the minimum value of the function

f(x)=\exp (x)+\exp (-x)

Which of the following functions would have only odd powers of

x

in its Taylor series expansion about the point

x=0?

Consider the matrix

\mathbf{P}=\left[\begin{array}{cc}0 & 1 \\ -2 & -3\end{array}\right]

. The value of

\mathbf{e}^{\mathbf{P}}

In the Taylor series expansion of

\exp (x)+\sin (x)

about the point

x=\pi

, the coefficient of

(x-\pi)^{2}

The following plot shows a function

y

which varies linearly with

x

. The value of the integral

I=\displaystyle{}\int_1^2 y d x

For

|x| \ll 1

\operatorname{coth}(x)

can be approximated as

\displaystyle{}\lim _{\theta \rightarrow 0} \frac{\sin (\theta / 2)}{\theta}

Which one of the following functions is strictly bounded?

For the function

e^{-x}

, the linear approximation around

x=2

It is given that

X_{1}, X_{2}, \cdots ,X_{M}

are

M

non-zero, orthogonal vectors. The dimension of the vector space spanned by the

2 M

vectors

X_{1}, X_{2}, \cdots, X_{M},-X_{1},-X_{2}, \cdots,-X_{M}

Consider the function

f(x)=x^{2}-x-2

. The maximum value of

f(x)

in the closed interval

[-4,4]

The rank of the matrix

\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{array}\right]

\nabla \times \nabla \times \mathrm{P},

where

\mathrm{P}

is a vector, is equal to

\displaystyle{}\iint(\nabla \times \mathrm{P}) \bullet \mathrm{ds},

where

\mathrm{P}

is a vector, is equal to

A probability density function is of the form

\qquad p(x)=\mathrm{Ke}^{-\alpha|x|}, x \in(-\infty, \infty)

The value of

\text{K}

A solution for the differential equation

\qquad \dot{x}(t)+2 x(t)=\delta(t)

with initial condition

x(0-)=0