GATE MT area:engineering-mathematics PYQs & Answers — Page 8

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Questions 71–80 of 87. Imported answers require independent review unless marked reviewed.

Topic practice 87 questionsPage 8 of 9

The probability of solving a problem by Student A is (1/3), and the probability of solving the same problem by Student B is (2/5). The probability (rounded off to two decimal places) that at least one of the students solves the problem is _____________.

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Numerical value of work done (rounded off to the nearest integer) by a position-dependent force

(where

and

are unit vectors) along the path,

, from (0,0) to (2,2) in the xy plane is _____________.

Diagram for Metallurgical Engineering question 38

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The estimated value of the cube root of 37 (rounded off to two decimal places) obtained from the Newton-Raphson method after two iterations (x₂) is _____________.

[Start with an initial guess value of x₀ = 1].

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Steady state radial heat conduction through a hollow, infinitely long zirconia cylinder is governed by the following ordinary differential equation:

Here, T is the temperature and r is the radial distance. The inner surface of the hollow cylinder is maintained at 1473 K and the outer surface at 973 K. The rate of heat loss per unit length through the outer surface of the hollow cylinder (in W.m⁻¹, rounded off to the nearest integer) is _____________.

Given: Inner radius of cylinder = 0.05 m; outer radius of cylinder = 0.07 m and thermal conductivity of zirconia (k) = 2 W.m⁻¹.K⁻¹.

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For

and

are both decreasing functions in the interval ______.

Your answerChoose one option.

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A vector field is given as follows:

The divergence of this field evaluated at

is ______________ .

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Consider the following Ordinary Differential Equation:

In a domain

, with boundary conditions

and

, pick the appropriate choice for

from the following options:

Your answerChoose one option.

Diagram for Metallurgical Engineering question 35

Diagram for Metallurgical Engineering question 35 (figure 2)

Diagram for Metallurgical Engineering question 35 (figure 3)

Diagram for Metallurgical Engineering question 35 (figure 4)

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A classroom of 20 students can be categorized on the basis of blood-types: 5 students each with “A”, “B”, “AB”, and “O” blood-types. If four students are selected at random from this class, what is the probability that each student has a different blood-type?

Your answerChoose one option.

0.250

0.128

0.0625

0.0156

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Using the trapezoidal rule with two equal intervals (n = 2, Δx = 1), the definite integral

______________ (to two decimal places).

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For the matrix,

Your answerChoose one option.

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GATE MT area:engineering-mathematics PYQs

Question 37

Question 38

Question 39

Question 41

Question 3

Question 23

Question 35

Question 38

Question 54

Question 1