GATE CE 2017 Set 1 | GATE CE Year Wise Previous Years Questions

GATE CE 2017 Set 1

MCQ (Single Correct Answer)

-0.3

Let $$x$$ be a continuous variable defined over the interval $$\left( { - \infty ,\infty } \right)$$, and $$f\left( x \right) = {e^{ - x - {e^{ - x}}}}.$$
The integral $$g\left( x \right) = \int {f\left( x \right)dx\,\,} $$ is equal to

$${e^{e - x}}$$

$${e^{ - {e^{ - x}}}}$$

$${e^{ - {e^x}}}$$

$${e^{ - x}}$$

GATE CE 2017 Set 1

Numerical

-0

$$\mathop {Lim}\limits_{x \to 0} \left( {{{\tan x} \over {{x^2} - x}}} \right)$$ is equal to _________.

Your input ____

GATE CE 2017 Set 1

MCQ (Single Correct Answer)

-0.3

The matrix $$P$$ is the inverse of a matrix $$Q.$$ If $${\rm I}$$ denotes the identity matrix, which one of the following options is correct?

$$PQ = {\rm I}\,\,\,but\,\,\,QP \ne {\rm I}$$

$$QP = {\rm I}\,\,\,but\,\,\,PQ \ne {\rm I}$$

$$PQ = {\rm I}\,\,\,and\,\,\,QP = {\rm I}$$

$$PQ - QP = {\rm I}$$

GATE CE 2017 Set 1

MCQ (Single Correct Answer)

-0.6

Consider the matrix $$\left[ {\matrix{ 5 & { - 1} \cr 4 & 1 \cr } } \right].$$ Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

Eigenvalue $$3$$ has a multiplicity of $$2,$$ and only one independent eigenvector exists.

Eigenvalue $$3$$ has a multiplicity of $$2,$$ and two independent eigen vectors exist.

Eigenvalue $$3$$ has a multiplicity of $$2,$$ and no independent eigen vector exists

Eigenvalues are $$3$$ and $$-3,$$ and two independent eigenvectors exist

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