1
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+2
-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?
A
Eigenvalue $$3$$ has a multiplicity of $$2,$$ and only one independent eigenvector exists.
B
Eigenvalue $$3$$ has a multiplicity of $$2,$$ and two independent eigen vectors exist.
C
Eigenvalue $$3$$ has a multiplicity of $$2,$$ and no independent eigen vector exists
D
Eigenvalues are $$3$$ and $$-3,$$ and two independent eigenvectors exist
2
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+1
-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?
A
$$PQ = {\rm I}\,\,\,but\,\,\,QP \ne {\rm I}$$
B
$$QP = {\rm I}\,\,\,but\,\,\,PQ \ne {\rm I}$$
C
$$PQ = {\rm I}\,\,\,and\,\,\,QP = {\rm I}$$
D
$$PQ - QP = {\rm I}$$
3
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+1
-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
A
$${e^{e - x}}$$
B
$${e^{ - {e^{ - x}}}}$$
C
$${e^{ - {e^x}}}$$
D
$${e^{ - x}}$$
4
GATE CE 2017 Set 1
Numerical
+1
-0
$$\mathop {Lim}\limits_{x \to 0} \left( {{{\tan x} \over {{x^2} - x}}} \right)$$ is equal to _________.
Your input ____
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12