GATE ME 2022 Set 2 | GATE ME Year Wise Previous Years Questions

GATE ME 2022 Set 2

MCQ (Single Correct Answer)

-0.33

Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point (1, 2, 3). The surface integral $\int_A \vec{F}.d\vec{A}$ of a vector field $\vec{F}=3x\hat{i}+5y\hat{j}+6z\hat{k}$ over the entire surface A of the cube is ______.

GATE ME 2022 Set 2

MCQ (Single Correct Answer)

-0.33

Consider the definite integral

$\int^2_1(4x^2+2x+6)dx$

Let I_e be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is I_s. The percentage error is defined as e = 100 × (I_e - I_s)/I_e The value of e is

2.5

3.5

1.2

GATE ME 2022 Set 2

MCQ (Single Correct Answer)

-0.33

Given $\int^{\infty}_{-\infty}e^{-x^2}dx=\sqrt{\pi}$

If a and b are positive integers, the value of $\int^{\infty}_{-\infty}e^{-a(x+b)^2}dx$ is _________.

$\sqrt{\pi a}$

$\sqrt{\frac{\pi}{a}} $

$b\sqrt{\pi a}$

$b\sqrt{\frac{\pi}{a}}$

GATE ME 2022 Set 2

MCQ (Single Correct Answer)

-0.33

A polynomial ψ(s) = a_nsⁿ + a_n-1s^n-1 + ......+ a₁s + a₀ of degree n > 3 with constant real coefficients a_n, a_n-1, ... a₀ has triple roots at s = -σ. Which one of the following conditions must be satisfied?

ψ(s) = 0 at all the three values of s satisfying s³ + σ³ = 0

ψ(s) = 0, $\frac{d\psi(s)}{ds}=0$ and $\frac{d^2\psi(s)}{ds^2}=0$ at s = -σ

ψ(s) = 0, $\frac{d^2\psi(s)}{ds^2}=0$ and $\frac{d^4\psi(s)}{ds^4}=0$ at s = -σ

ψ(s) = 0, $\frac{d^3\psi(s)}{ds^3}=0$ at s = -σ

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