List of top Questions asked in GATE CE- 2021

A solid circular torsional member OPQ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is 160 MPa.
 

The absolute maximum shear stress in the member (in MPa, round off to one decimal place) is \(\underline{\hspace{1cm}}\).

The value (round off to one decimal place) of \[ \int_{-1}^1 x e^{|x|} \, dx \text{ is \(\underline{\hspace{1cm}}\).} \]
Which of the following statement(s) is/are correct?
The softening point of bitumen has the same unit as that of
The hardness of a water sample is measured directly by titration with 0.01 M solution of ethylenediamine tetraacetic acid (EDTA) using eriochrome black T (EBT) as an indicator. The EBT reacts and forms complexes with divalent metallic cations present in the water. During titration, the EDTA replaces the EBT in the complex. When the replacement of EBT is complete at the end point of the titration, the colour of the solution changes from
Relationship between traffic speed and density is described using a negatively sloped straight line. If \( v_f \) is the free-flow speed, then the speed at which the maximum flow occurs is:
The most appropriate triaxial test to assess the long-term stability of an excavated clay slope is
In case of bids in Two-Envelope System, the correct option is
Seasoning of timber for use in construction is done essentially to

A single story building model is shown in the figure. The rigid bar of mass \( m \) is supported by three massless elastic columns whose ends are fixed against rotation. For each of the columns, the applied lateral force (P) and corresponding moment (M) are also shown in the figure. The lateral deflection (\( \delta \)) of the bar is given by \( \delta = \dfrac{PL^3}{12EI} \) where \( L \) is the effective length of the column, \( E \) is the Young's modulus of elasticity and \( I \) is the area moment of inertia of the column cross-section with respect to its neutral axis. 
For the lateral deflection profile of the columns as shown in the figure, the natural frequency of the system for horizontal oscillation is 

Strain hardening of structural steel means
In general, the CORRECT sequence of surveying operations is
If A is a square matrix then orthogonality property mandates
In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer. The minimum area of the triangle PQR possible, in cm², is
1. Some football players play cricket.
2. All cricket players play hockey.
Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q. The probability that any point picked randomly within the square falls in the shaded area is 

The author said, "Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks." Based on the above passage, which one of the following is TRUE?
On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P. The distance of point Q to point O, in the same units, should be \(\underline{\hspace{2cm}}\)
Four persons P, Q, R, and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

\( \oplus \) and \( \odot \) are two operators on numbers \( p \) and \( q \) such that 
\( p \odot q = p - q\) and \(p \oplus q = p \times q. \) 
Then, \( (9 \odot (6 \oplus 7)) \odot (7 \oplus (6 \odot 5)) = ? \)

Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled on each die is:

The mirror image of the above text about the x-axis is 

Which of the following sentences are grammatically correct?
(i) Arun and Aparna are here.
(ii) Arun and Aparna is here.
(iii) Arun's families is here.
(iv) Arun's family is here.

The hyetograph in the figure corresponds to a rainfall event of 3 cm. 

If the rainfall event has produced a direct runoff of 1.6 cm, the \(\phi\)-index of the event (in mm/hour, round off to one decimal place) would be \(\underline{\hspace{1cm}}\).

An activated sludge process (ASP) is designed for secondary treatment of 7500 m\(^3\)/day of municipal wastewater. After primary clarifier, the ultimate BOD of the influent, which enters into the ASP reactor, is 200 mg/L. Treated effluent after secondary clarifier is required to have an ultimate BOD of 20 mg/L. Mix liquor volatile suspended solids (MLVSS) concentration in the reactor and the underflow is maintained as 3000 mg/L and 12000 mg/L, respectively. The hydraulic retention time and mean cell residence time are 0.2 day and 10 days, respectively. A representative flow diagram of the ASP is shown below. 

The underflow volume (in m}^3\text{/day, round off to one decimal place) of sludge wastage is \(\underline{\hspace{1cm}}\).