List of top Questions asked in GATE Production and Industrial Engineering- 2025

Which one of the following casting defects is caused due to the supply of the molten metal through two gates?
The relationship between the hoop stress \( \sigma_1 \) and the longitudinal stress \( \sigma_2 \) of a closed cylindrical thin-walled pressure vessel is:
Exit-hole occurrence is common in:
The proper sequence of design of a product is:
In a work sampling, out of \( n \) observations, a worker was sitting idle in \( x \) observations. The standard deviation of the mean proportion of idle time is given by:
If \( i, j, k \) are the orthogonal unit vectors in Cartesian \( x \)-\( y \)-\( z \) coordinate system, the curl of the vector \( -2y\hat{i} + x\hat{j} \) is:
If \( F(s) \) denotes the Laplace transform of some function \( f(t) \), then the Laplace transform of \( e^{bt} f(t) \), where \( b \) is a real constant, is:
Which one of the following equations is a linear differential equation?
If a real variable \( x \) satisfies \( 3^{x^2} = 27 \times 9^x \), then the value of \( \frac{2^{x^2}}{(2^x)^2} \) is:

Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let \( a_1 \) and \( a_2 \) (in years) denote the ages of the brothers and \( a_1<a_2 \). Which one of the following statements is correct about their age on the day when they attain the same weight?

Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk. 


 

A rectangle has a length \(L\) and a width \(W\), where \(L>W\). If the width, \(W\), is increased by 10%, which one of the following statements is correct for all values of \(L\) and \(W\)? 
Select the most appropriate option to complete the above sentence.

A 4 × 4 digital image has pixel intensities (U) as shown in the figure. The number of pixels with \( U \leq 4 \) is:


 

We __________ tennis in the lawn when it suddenly started to rain. 
Select the most appropriate option to complete the above sentence.

Courage : Bravery :: Yearning : 
Select the most appropriate option to complete the analogy.