1
GATE CE 2023 Set 1
Numerical
+1
-0
In the differential equation $\frac{dy}{dx}+\alpha\ x\ y =0, \alpha$ is a positive constant. If y = 1.0 at x = 0.0, and y = 0.8 at x = 1.0, the value of α is ________ (rounded off to three decimal places).
Your input ____
2
GATE CE 2023 Set 1
MCQ (Single Correct Answer)
+2
-0.66

A function f(x), that is smooth and convex-shaped between interval (xl , su) is shown in the figure. This function is observed at odd number of regularly spaced points. If the area under the function is computed numerically, then . 

GATE CE 2023 Set 1 Engineering Mathematics - Numerical Methods Question 1 English
A
the numerical value of the area obtained using the trapezoidal rule will be less than the actual
B
the numerical value of the area obtained using the trapezoidal rule will be more than the actual
C
the numerical value of the area obtained using the trapezoidal rule will be exactly equal to the actual
D
with the given details, the numerical value of area cannot be obtained using trapezoidal rule 
3
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]
4
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
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