List of top Questions asked in GATE PI

The solidification of a casting starts at 10 AM. However, the solidification of the molten metal at the center-line of the mold starts at 10:03 AM and ends at 10:10 AM. The casting is considered solidified completely when the solidification is completed at the center-line of the mold. The center-line feeding resistance (CFR) in percentage is .............
If \( i \), \( j \), and \( k \) are the orthogonal unit vectors in Cartesian x-y-z coordinate system, the rate of change of the function \( f(x, y, z) = x^2 + 2y^2 + z \) at point \( (1, 1, 1) \) in the direction of \( 3i + 4k \) is .............
In a wire drawing of a perfectly-plastic material with flow stress of 300 MPa, the back tension is zero and front tension is 200 MPa. Assuming ideal deformation with zero friction, the percentage reduction of the cross-sectional area of the wire is .............
In a cold rolling process without front and back tensions, the required minimum coefficient of friction is 0.04. Assume large rolls. If the draft is doubled and roll diameters are halved, then the required minimum coefficient of friction is .............
A company estimates the demand of 2000 bulbs for the next year. The ordering cost is Rupees 300 per order and the annual carrying cost per bulb is Rupees 30. The economic order quantity (number of bulbs) is .......... (Answer in integer)
The solution of the linear differential equation \[ \frac{dy}{dx} + y = e^x, \] when \( y(0) = 0 \), is:
Which one of the following functions is analytic, given \( i = \sqrt{-1} \)?
In an orthogonal straight turning process, the feed is 0.1 mm/rev and the depth of cut is 0.5 mm. In ASA system, the side cutting edge angle of the cutting tool is 0°. The width (in mm) of the chip is ............ (Rounded off to one decimal place)
Which one of the following statements is FALSE with respect to the injection molding of polymer composite?
A through hole of 8 mm diameter is to be drilled in a 30 mm thick mild steel plate. Which one of the following processes is the most appropriate to achieve high dimensional accuracy with less processing time?
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.

A CNC milling operation is carried out by moving the tool from the point A to point B in anti-clockwise direction to cut a slot of quarter circle with center at C, as shown. The coordinates of the points A and B are (0,0) and (10,10), respectively. All dimensions are in mm. If the feed rate at point P along x-axis is 6 mm/min, then the feed rate (in mm/min) at point P along y-axis is ______ . (Rounded off to 1 decimal place)
A CNC milling operation is carried out by moving the tool from the point A to point B