1
GATE CE 2023 Set 1
MCQ (More than One Correct Answer)
+2
-0

For the matrix

$[A]= \begin{bmatrix}1&2&3\\\ 3&2&1\\\ 3&1&2 \end{bmatrix} $

which of the following statements is/are TRUE?

A
The eigenvalues of [A]T are same as the eigenvalues of [A] 
B
The eigenvalues of [A]-1 are the reciprocals of the eigenvalues of [A]
C
The eigenvectors of [A]T are same as the eigenvectors of [A] 
D
The eigenvectors of [A]-1 are same as the eigenvectors of [A]
2
GATE CE 2023 Set 1
MCQ (More than One Correct Answer)
+2
-0
For the function f(x) = ex |sin x|; x ∈ ℝ, which of the following statements is/are TRUE?
A
The function is continuous at all x
B
The function is differentiable at all x
C
The function is periodic
D
The function is bounded
3
GATE CE 2023 Set 1
Numerical
+2
-0

The differential equation,

$\rm \frac{du}{dt}+2tu^2=1,$

is solved by employing a backward difference scheme within the finite difference framework. The value of 𝑢 at the (𝑛 − 1) th time-step, for some 𝑛, is 1.75. The corresponding time (t) is 3.14 s. Each time step is 0.01 s long. Then, the value of (un - un -1) _________ is (round off to three decimal places). 

Your input ____
4
GATE CE 2023 Set 1
MCQ (Single Correct Answer)
+1
-0.33
Which one of the following statements is TRUE for Greenhouse Gas (GHG) in the atmosphere?
A
GHG absorbs the incoming short wavelength solar radiation to the earth surface, and allows the long wavelength radiation coming from the earth surface to pass through
B
GHG allows the incoming long wavelength solar radiation to pass through to the earth surface, and absorbs the short wavelength radiation coming from the earth surface 
C
GHG allows the incoming long wavelength solar radiation to pass through to the earth surface, and allows the short wavelength radiation coming from the earth surface to pass through
D
GHG allows the incoming short wavelength solar radiation to pass through to the earth surface, and absorbs the long wavelength radiation coming from the earth surface 
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