List of top Questions asked in GATE PI

Which ONE of the following is the value of \( \frac{1}{i^n} \)?

where \( i = \sqrt{-1} \), and \( n \) is an even positive integer.

Which ONE of the following options is the closest approximation to the value of the given definite integral?
\[ \int_0^1 e^{-x^2} dx \]
Note: Use numerical integration

Which ONE of the following is FALSE with respect to filler material used in brazing?

An arc welding process is being carried out with a power source of 6 kW to weld two similar metals. The total energy loss is 50%, the area of cross-section of the weld is \( 10 \ mm^2 \), and the specific energy needed to melt the metal is \( 15 \ J/mm^3 \).
The speed of welding is ______ mm/s.

In the given figure, \(\overline{PQ}\) is the diameter of a circle with center \(O\). Two points \(R\) and \(S\) are chosen on the circle such that \(\angle ROS = 80^\circ\). When \(\overline{PR}\) and \(\overline{QS}\) are extended, they meet at \(T\).

The value of \(\angle RTS\) is ______

Which ONE of the following steps is NOT a part of product concept selection?

\(P\) and \(Q\) are two positive integers such that \(P^2 = Q^2 + 13\).
The product of the numbers \(P\) and \(Q\) is ______

Based on the relationship between each polygon and the number inside it, the value of 'X' is ______

Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF state. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules:
Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON.
Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
The state of any bulb not meeting the conditions above is left unchanged.
The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.

The number of bulbs which are ON at the end of Step 8 is ______

At how many points will the curves \( y = x^2 \) and \( y = -x^2 - 2x - 1 \) intersect in the real \( (x, y) \) plane?

The figure below is supposed to show three non-overlapping shapes, one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated by '?' and completes the oval and the two triangles?

'If Anish had scored hundred runs in today's match, he would have been made the captain of his team. He would have then become the youngest captain in his team's history. Unfortunately, he got out without scoring any runs. Hence, there won't be any change in the captaincy for now.'
Based on the paragraph above, which one of the following statements is true?

Match the words in Column I with their synonyms in Column II.

Column I	Column II
(i) Lonely	(p) Verbatim
(ii) Literal	(q) Solitary
(iii) Lousy	(r) Deadly
(iv) Lethal	(s) Terrible

Which one of the following figures P, Q, R, or S, correctly shows the \( 45^\circ \) clockwise-rotated version of figure (I)?

'The shopkeeper sells lemons.'
In this sentence, the word 'lemons' is the ________.

Three principal stresses at a point in a material are 300 MPa, 250 MPa, and 100 MPa. If the yielding just starts at that point, the yield strength (in MPa) of the material as per Tresca criterion is ............
Answer: The yield strength lies between 199 to 201 MPa.

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)

The pitch of the single-start lead screw of a lathe is 6 mm. It is used to cut double start thread of 3 mm pitch on a cylindrical work piece. During the thread cutting, the spindle rotates at 400 revolutions per minute (RPM). The speed (in RPM) of the lead screw is ............ (Answer in integer)

Two options are available to meet the annual demand of batteries in a toy company. In option 1, batteries are manufactured in the plant having fixed cost of Rupees 2,00,000 and a variable cost of Rupees 70 per unit. Option 2 consists of buying batteries from the market at a price of Rupees 90 per unit. The annual demand (in number of batteries) at which the company should switch from buying to making the batteries in the plant is .......... (Answer in integer)

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)

While inspecting final assembly of automobile-gear-boxes, 15 features were considered critical-to-quality (CTQ). During last quarter, 40000 gear boxes were produced among which 1500 defects were found of the CTQ features. The defects per million opportunities (DPMO) is .......... (Answer in integer)

The value of the integral \[ \int_1^3 \left( x^2 - 2x \right) \, dx \] obtained by using Simpson’s 1/3 rule with 4 subintervals is equal to \( \frac{n}{3} \). The value of \( n \) 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 .............