Ques 1Gate 2022 Set-1

Consider the following expression:
sin (y+it)+ cos(y-it)
where z, y, and t are variables, and i = √-1 is a complex number. The partial differential equation derived from the above expression is

a.

∂²z / ∂t²

+

∂²z / ∂y²

=0
b.

∂²z / ∂t²

-

∂²z / ∂y²

=0
c.

∂z / ∂t

-i

∂z / ∂y

=0
d.

∂z / ∂t

+i

∂z / ∂y

=0

Ques 2Gate 2022 Set-1

For the equation

d³y/dx³

+x(

dy/ dx

)^3/2 +x²y = 0
the correct description is

a. an ordinary differential equation of order 3 and degree 2.
b. an ordinary differential equation of order 3 and degree 3.
c. an ordinary differential equation of order 2 and degree 3.
d. an ordinary differential equation of order 3 and degree 3/2.

Ques 3Gate 2020 Set-2

A fair (unbiased) coin is tossed 15 times. The probability of getting exactly 8 Heads(round off to three decimal places), is ________.

Ques 4Gate 2018 Set-1

At the point 𝑥 = 0, the function 𝑓(𝑥) = 𝑥³ has

a. local maximum
b. local minimum
c. both local maximum and minimum
d. neither local maximum nor local minimum

Ques 5Gate 2017 Set-1

The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

a. 2 and 2
b. 1 and 2
c. 2 and 1
d. 1 and 1

Ques 6Gate 2016 Set-2

The spot speeds (expressed in km/hr) observed at a road section are 66, 62, 45, 79, 32, 51, 56, 60, 53, and 49. The median speed (expressed in km/hr) is _________
(Note: answer with one decimal accuracy)

Ques 7Gate 2016 Set-2

The optimum value of the function f(x) = x² – 4x +2 is

a. 2 (maximum)
b. 2 (minimum)
c. −2 (maximum)
d. −2 (minimum)

Ques 8Gate 2016 Set-1

Newton-Raphson method is to be used to find root of equation 3x − e^x + sin x = 0. If the initial trial value for the root is taken as 0.333, the next approximation for the root would be _________
(note: answer up to three decimal)